diff --git a/GraspPlanning/CMakeLists.txt b/GraspPlanning/CMakeLists.txt
index e8f285bb09e5d80264289c8f8a9dec9c51886d3c..da29449b2882adee175276d6bc515609f56f6de2 100644
--- a/GraspPlanning/CMakeLists.txt
+++ b/GraspPlanning/CMakeLists.txt
@@ -17,21 +17,7 @@ ENDMACRO(ADD_GRASPSTUDIO_TEST)
########### QHULL #################
-IF(NOT BUILD_qhull)
- find_package(QHULL QUIET)
- IF (NOT QHULL_FOUND)
- MESSAGE (STATUS "Could not find QHULL, building internal version simox-qhull")
- SET (BUILD_qhull ON)
- SET (BUILD_qhull ON PARENT_SCOPE)
- ENDIF()
-ENDIF()
-
-IF(BUILD_qhull)
- ADD_SUBDIRECTORY(ExternalDependencies/qhull-2003.1)
- set(QHULL_LIBRARIES simox-qhull)
-else()
- find_package(QHULL REQUIRED)
-endif()
+find_package(QHULL REQUIRED)
########### END QHULL #################
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/Announce.txt b/GraspPlanning/ExternalDependencies/qhull-2003.1/Announce.txt
deleted file mode 100644
index 5813e25f9b6f9cb9edee1a84a7f08a420653b15f..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/Announce.txt
+++ /dev/null
@@ -1,50 +0,0 @@
-
- Qhull 2003.1 2003/12/30
-
- http://www.qhull.org
- http://savannah.gnu.org/projects/qhull/
- http://www6.uniovi.es/ftp/pub/mirrors/geom.umn.edu/software/ghindex.html
- http://www.geomview.org
- http://www.geom.uiuc.edu
-
-Qhull computes convex hulls, Delaunay triangulations, Voronoi diagrams,
-furthest-site Voronoi diagrams, and halfspace intersections about a point.
-It runs in 2-d, 3-d, 4-d, or higher. It implements the Quickhull algorithm
-for computing convex hulls. Qhull handles round-off errors from floating
-point arithmetic. It can approximate a convex hull.
-
-The program includes options for hull volume, facet area, partial hulls,
-input transformations, randomization, tracing, multiple output formats, and
-execution statistics. The program can be called from within your application.
-You can view the results in 2-d, 3-d and 4-d with Geomview.
-
-To download Qhull:
- http://www.qhull.org/download
- http://savannah.nongnu.org/files/?group=qhull
-
-Download qhull-96.ps for:
-
- Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa,
- "The Quickhull Algorithm for Convex Hulls," ACM
- Trans. on Mathematical Software, Dec. 1996.
- http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p469-barber/
- http://citeseer.nj.nec.com/83502.html
-
-Abstract:
-
-The convex hull of a set of points is the smallest convex set that contains
-the points. This article presents a practical convex hull algorithm that
-combines the two-dimensional Quickhull Algorithm with the general dimension
-Beneath-Beyond Algorithm. It is similar to the randomized, incremental
-algorithms for convex hull and Delaunay triangulation. We provide empirical
-evidence that the algorithm runs faster when the input contains non-extreme
-points, and that it uses less memory.
-
-Computational geometry algorithms have traditionally assumed that input sets
-are well behaved. When an algorithm is implemented with floating point
-arithmetic, this assumption can lead to serious errors. We briefly describe
-a solution to this problem when computing the convex hull in two, three, or
-four dimensions. The output is a set of "thick" facets that contain all
-possible exact convex hulls of the input. A variation is effective in five
-or more dimensions.
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/CMakeLists.txt b/GraspPlanning/ExternalDependencies/qhull-2003.1/CMakeLists.txt
deleted file mode 100644
index 97d07defd103a04613241a24248cf7fa7ecd00d1..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/CMakeLists.txt
+++ /dev/null
@@ -1,33 +0,0 @@
-PROJECT(simox-qhull)
-
-MESSAGE (STATUS " **** Configuring qhull")
-
-# Specify sources and headers
-FILE(GLOB SRCS ${PROJECT_SOURCE_DIR}/src/*.c)
-FILE(GLOB INCS ${PROJECT_SOURCE_DIR}/src/*.h)
-
-ADD_LIBRARY(${PROJECT_NAME} STATIC ${SRCS} ${INCS})
-
-TARGET_INCLUDE_DIRECTORIES(${PROJECT_NAME} PUBLIC ${PROJECT_SOURCE_DIR} ${PROJECT_SOURCE_DIR}/include ${PROJECT_SOURCE_DIR}/src)
-SET_TARGET_PROPERTIES(${PROJECT_NAME} PROPERTIES FOLDER "3rd_Party")
-
-# .DLL path
-SET_TARGET_PROPERTIES(${PROJECT_NAME} PROPERTIES RUNTIME_OUTPUT_DIRECTORY ${Simox_BIN_DIR})
-# .so path
-SET_TARGET_PROPERTIES(${PROJECT_NAME} PROPERTIES LIBRARY_OUTPUT_DIRECTORY ${Simox_LIB_DIR})
-# .lib path (this is needed for setting the DLL-import library path on windows)
-SET_TARGET_PROPERTIES(${PROJECT_NAME} PROPERTIES ARCHIVE_OUTPUT_DIRECTORY ${Simox_LIB_DIR})
-
-
-#######################################################################################
-############################ Setup for installation ###################################
-#######################################################################################
-
-install(TARGETS ${PROJECT_NAME}
- # IMPORTANT: Add the library to the "export-set"
- EXPORT SimoxTargets
- RUNTIME DESTINATION "${INSTALL_BIN_DIR}" COMPONENT bin
- LIBRARY DESTINATION "${INSTALL_LIB_DIR}" COMPONENT shlib
- ARCHIVE DESTINATION "${INSTALL_LIB_DIR}" COMPONENT library
- COMPONENT dev)
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/COPYING.txt b/GraspPlanning/ExternalDependencies/qhull-2003.1/COPYING.txt
deleted file mode 100644
index 7230a27a3269ee9455acf04de4793e5ab5e33d30..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/COPYING.txt
+++ /dev/null
@@ -1,34 +0,0 @@
- Qhull, Copyright (c) 1993-2003
-
- The National Science and Technology Research Center for
- Computation and Visualization of Geometric Structures
- (The Geometry Center)
- University of Minnesota
-
- email: qhull@qhull.org
-
-This software includes Qhull from The Geometry Center. Qhull is
-copyrighted as noted above. Qhull is free software and may be obtained
-via http from www.qhull.org. It may be freely copied, modified,
-and redistributed under the following conditions:
-
-1. All copyright notices must remain intact in all files.
-
-2. A copy of this text file must be distributed along with any copies
- of Qhull that you redistribute; this includes copies that you have
- modified, or copies of programs or other software products that
- include Qhull.
-
-3. If you modify Qhull, you must include a notice giving the
- name of the person performing the modification, the date of
- modification, and the reason for such modification.
-
-4. When distributing modified versions of Qhull, or other software
- products that include Qhull, you must provide notice that the original
- source code may be obtained as noted above.
-
-5. There is no warranty or other guarantee of fitness for Qhull, it is
- provided solely "as is". Bug reports or fixes may be sent to
- qhull_bug@qhull.org; the authors may or may not act on them as
- they desire.
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/File_id.diz b/GraspPlanning/ExternalDependencies/qhull-2003.1/File_id.diz
deleted file mode 100644
index 765b146c6568a927132db0c75f28af79fb7ba0b4..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/File_id.diz
+++ /dev/null
@@ -1,12 +0,0 @@
-Qhull 2003.1 - Qhull computes convex hulls,
-Delaunay triangulations, halfspace inter-
-sections about a point, Voronoi diagrams,
-furthest-site Delaunay triangulations, and
-furthest-site Voronoi diagrams. Qhull
-works with 2-d, 3-d, 4-d, 5-d, and higher
-dimensions. It computes volumes, surface
-areas, and approximations. It runs in a
-DOS window under Windows 95/NT/XP.
-www.qhull.org, freeware.
-
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/QHULL-GO.pif b/GraspPlanning/ExternalDependencies/qhull-2003.1/QHULL-GO.pif
deleted file mode 100644
index a5414428207cfe796fb9a7fff6ae0790af968500..0000000000000000000000000000000000000000
Binary files a/GraspPlanning/ExternalDependencies/qhull-2003.1/QHULL-GO.pif and /dev/null differ
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/README.txt b/GraspPlanning/ExternalDependencies/qhull-2003.1/README.txt
deleted file mode 100644
index 4cbbdde6123dbf79dba3b3bd66b13ae149c9639d..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/README.txt
+++ /dev/null
@@ -1,322 +0,0 @@
-Name
-
- qhull, rbox 2003.1 2003/12/30
-
-Convex hull, Delaunay triangulation, Voronoi diagrams, Halfspace intersection
-
- Documentation:
- html/index.htm
-
- Available from:
- <http://www.qhull.org>
- <http://savannah.gnu.org/projects/qhull>
-
- Version 1 (simplicial only):
- <http://www.qhull.org/download/qhull-1.0.tar.gz>
- <http://www.qhull.org/download/qhull.sit.hqx>
-
- News and a paper:
- <http://www.qhull.org/news>
- <http://citeseer.nj.nec.com/83502.html>
-
-Purpose
-
- Qhull is a general dimension convex hull program that reads a set
- of points from stdin, and outputs the smallest convex set that contains
- the points to stdout. It also generates Delaunay triangulations, Voronoi
- diagrams, furthest-site Voronoi diagrams, and halfspace intersections
- about a point.
-
- Rbox is a useful tool in generating input for Qhull; it generates
- hypercubes, diamonds, cones, circles, simplices, spirals,
- lattices, and random points.
-
- Qhull produces graphical output for Geomview. This helps with
- understanding the output. <http://www.geomview.org>
-
-
-Environment requirements
-
- Qhull and rbox should run on all 32-bit and 64-bit computers. Use
- an ANSI C or C++ compiler to compile the program. The software is
- self-contained.
-
- Qhull is copyrighted software. Please read COPYING.txt and REGISTER.txt
- before using or distributing Qhull.
-
-To contribute to Qhull
-
- Qhull is on Savannah at http://savannah.gnu.org/projects/qhull/
-
-Qhull on Windows 95, 98, ME, NT, 2000, XP
-
- The zip file contains rbox.exe, qhull.exe, qconvex.exe, qdelaunay.exe,
- qhalf.exe, qvoronoi.exe, documentation files, and source files.
-
- To install Qhull:
- - Unzip the files into a directory. You may use WinZip32 <www.hotfiles.com>
- - Click on QHULL-GO
-
- - In Windows 95, the DOS window needs improvement.
- - Increase the size of the screen font to 8x12.
- - If the text is too dim, fix the screen colors with shareware (e.g., crt.exe)
- - If you use qhull a lot, consider using the Cygwin Unix shell (www.cygwin.com),
-
- To learn about Qhull:
- - Execute 'qconvex' for a synopsis and examples.
- - Execute 'rbox 10 | qconvex' to compute the convex hull of 10 random points.
- - Execute 'rbox 10 | qconvex i TO file' to write results to 'file'.
- - If an error occurs, Windows 95 sends the error to stdout instead of stderr
- - use 'TO xxx' to send normal output to xxx and error output to stdout
- - Browse the documentation: qhull\html\index.htm
-
-Compiling with cygwin on Windows NT, 2000, XP
- - install cygwin [www.cygwin.com] with gcc, make, ar, and ln
- - cd qhull/src
- - make -f Makefile.txt
-
-Qhull on Unix (Debian)
-
- The gzip file, qhull.tar.gz, contains documentation and source files for
- qhull and rbox. It should compile on all Unix systems, including Debian.
- You may also use the source instructions below.
-
- To unpack the gzip file
- - tar zxf qhull.tar.gz
- - cd qhull
-
- Compile with the configure Makefile [R. Laboissiere]:
- - ./configure
- - make
-
-Compiling the source distribution
-
- The gzip file, qhull-src.tgz, contains documentation and source files for
- qhull and rbox.
-
- To unpack the gzip file
- - tar zxf qhull-src.tgz
- - cd qhull
-
- Compiling with Makefile (i.e., Makefile.txt)
- - cd src
- - in Makefile, check the CC, CCOPTS1, PRINTMAN, and PRINTC defines
- - the defaults are gcc and enscript
- - CCOPTS1 should include the ANSI flag. It defines __STDC__
- - in user.h, check the definitions of qh_SECticks and qh_CPUclock.
- - use '#define qh_CLOCKtype 2' for timing runs longer than 1 hour
- - type: make
- - this builds: qhull qconvex qdelaunay qhalf qvoronoi rbox libqhull.a
- - type: make doc
- - this prints the man page
- - See also qhull/html/index.htm
- - if your compiler reports many errors, it is probably not a ANSI C compiler
- - you will need to set the -ansi switch or find another compiler
- - if your compiler warns about missing prototypes for fprintf() etc.
- - this is ok, your compiler should have these in stdio.h
- - if your compiler warns about missing prototypes for memset() etc.
- - include memory.h in qhull_a.h
- - if your compiler is gcc-2.95.1, you need to set flag -fno-strict-aliasing.
- - This flag is set by default for other versions [Karas, Krishnaswami]
- - if your compiler reports "global.c: storage size of 'qh_qh' isn't known"
- - delete the initializer "={0}" in global.c, stat.c and mem.c
- - if your compiler warns about "stat.c: improper initializer"
- - this is ok, the initializer is not used
- - if you have trouble building libqhull.a with 'ar'
- - try 'make -f Makefile.txt qhullx'
- - if the code compiles, the qhull test case will automatically execute
- - if an error occurs, there's an incompatibility between machines
- - For gcc-2.95.1, you need to set flag -fno-strict-aliasing.
- It is set by default for other versions of gcc [Karas, Krishnaswami]
- - If you can, try a different compiler
- - You can turn off the Qhull memory manager with qh_NOmem in mem.h
- - You can turn off compiler optimization (-O2 in Makefile)
- - If you find the source of the problem, please let us know
- - if you have Geomview (www.geomview.org)
- - try 'rbox 100 | qconvex G >a' and load 'a' into Geomview
- - run 'q_eg' for Geomview examples of Qhull output (see qh-eg.htm)
- - to install the programs and their man pages:
- - define MANDIR and BINDIR
- - type 'make install'
-
-Compiling on Windows 95, 98, NT, 2000, XP
-
- Qhull compiles as a console application in Visual C++ 5.0 at warning
- level 3.
-
- Visual C++ quickstart for qhull.exe only:
- - create a "Win32 console application" called "qhull"
- - add the following files:
- geom.c geom2.c global.c io.c mem.c merge.c poly.c poly2.c qhull.c
- qset.c stat.c unix.c user.c
- - create a "Win32 console application" called "rbox"
- - add rbox.c
-
- Visual C++ quickstart for qhull library, qhull.exe, qconvex.exe, etc.
- - To simplify setting up lots of projects,
- - create a temporary "Win32 console application" called "source"
- - add all .c files from .../src/...
- - In Tools::Options::Tab
- Set tab size to 8 and indent size to 2
-
- - create a "Win32 console application" called "rbox"
- - move rbox.c from "qhull source"
- - for Project:Settings..., Link
- you only need the default libraries
- - build the project
-
- - create a "Win32 static library" called "library"
- - move these files from "qhull source"
- geom.c geom2.c global.c io.c mem.c merge.c poly.c poly2.c qhull.c
- qset.c stat.c user.c
- - set the library file (use the same for debug and release)
- - build the project
-
- - create a "Win32 console application" called "qhull"
- - Move unix.c from "qhull source"
- - Add the library file created by "library"
- - Qhull does not use other libraries
-
- - create a "Win32 console application" called "qconvex"
- - Move qconvex.c from "qhull source"
- - Copy the library file from "qhull"
-
- - do the same for qdelaun.c, qhalf, qvoronoi.c, user_eg.c, user_eg2.c
- - delete "qhull sources" since it is no longer needed
- - use Project:Settings to make any changes
- - use batch build to rebuild everything
-
- Qhull compiles with Borland C++ 5.0 bcc32. A Makefile is included.
- Execute 'make -f Mborland'. If you use the Borland IDE, set the ANSI
- option in Options:Project:Compiler:Source:Language-compliance.
-
- Qhull compiles with Borland C++ 4.02 for Win32 and DOS Power Pack.
- Use 'make -f Mborland -D_DPMI'. Qhull 1.0 compiles with Borland
- C++ 4.02. For rbox 1.0, use "bcc32 -WX -w- -O2-e -erbox -lc rbox.c".
- Use the same options for Qhull 1.0. [D. Zwick]
-
- Qhull compiles with Metrowerks C++ 1.7 with the ANSI option.
-
- If you turn on full warnings, the compiler will report a number of
- unused variables, variables set but not used, and dead code. These are
- intentional. For example, variables may be initialized (unnecessarily)
- to prevent warnings about possible use of uninitialized variables.
-
-Compiling on the Power Macintosh
-
- Qhull compiles on the Power Macintosh with Metrowerk's C compiler.
- It uses the SIOUX interface to read point coordinates and return output.
- There is no graphical output. For project files, see 'Compiling for
- Windows 95'. Instead of using SIOUX, Qhull may be embedded within an
- application.
-
- Version 1 is available for Macintosh computers by download of qhull.sit.hqx
- It reads point coordinates from a standard file and returns output
- to a standard file. There is no graphical output.
-
-
-Compiling on other machines
-
- Some users have reported problems with compiling Qhull under Irix 5.1. It
- compiles under other versions of Irix.
-
- If you have troubles with the memory manager, you can turn it off by
- defining qh_NOmem in mem.h.
-
- You may compile Qhull with a C++ compiler.
-
-
-Distributed files
-
- README.txt // instructions for installing Qhull
- REGISTER.txt // Qhull registration
- COPYING.txt // copyright notice
- QHULL-GO.pif // Windows icon for qhull-go.bat
- Announce.txt // announcement
- Changes.txt // change history for Qhull and rbox
- File_id.diz // package descriptor
- index.htm // Home page
- html/qh-faq.htm // Frequently asked questions
- html/qh-get.htm // Download page
- html/index.htm // Manual
- src/Makefile.txt // Makefile for Unix or cygwin 'make'
- src/Mborland // Makefile for Borland C++/Win32
- src/Make-config.sh // Create Debian configure and automake
-
-src/
- rbox consists of:
- rbox.exe // Win32 executable (.zip only)
- rbox.htm // html manual
- rbox.man // Unix man page
- rbox.txt
- rbox.c // source program
-
- qhull consists of:
- qhull.exe // Win32 executables (.zip only)
- qconvex.exe
- qdelaunay.exe
- qhalf.exe
- qvoronoi.exe
- qhull-go.bat // DOS window
- qconvex.htm // html manuals
- qdelaun.htm
- qdelau_f.htm
- qhalf.htm
- qvoronoi.htm
- qvoron_f.htm
- qh-eg.htm
- qh-impre.htm
- qh-in.htm
- index.htm
- qh-opt*.htm
- qh-quick.htm
- qh--4d.gif,etc. // images for manual
- qhull.man // Unix man page
- qhull.txt
- q_eg // shell script for Geomview examples
- q_egtest // shell script for Geomview test examples
- q_test // shell script to test qhull
-
- top-level source files:
- src/index.htm // index to source files
- qh-...htm // specific files
- user.h // header file of user definable constants
- qhull.h // header file for qhull
- unix.c // Unix front end to qhull
- qhull.c // Quickhull algorithm with partitioning
- user.c // user re-definable functions
- user_eg.c // example of incorporating qhull into a user program
- user_eg2.c // more complex example
- qhull_interface.cpp // call Qhull from C++
-
- other source files:
- qhull_a.h // include file for *.c
- geom.c // geometric routines
- geom2.c
- geom.h
- global.c // global variables
- io.c // input-output routines
- io.h
- mem.c // memory routines, this is stand-alone code
- mem.h
- merge.c // merging of non-convex facets
- merge.h
- poly.c // polyhedron routines
- poly2.c
- poly.h
- qset.c // set routines, this only depends on mem.c
- qset.h
- stat.c // statistics
- stat.h
-
-Authors:
-
- C. Bradford Barber Hannu Huhdanpaa
- bradb@qhull.org hannu@qhull.org
-
- The Geometry Center
- University of Minnesota
-
- Qhull 1.0 was developed under NSF grants NSF/DMS-8920161 and
- NSF-CCR-91-15793 750-7504 at the Geometry Center and Harvard
- University. If you find Qhull useful, please let us know.
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/REGISTER.txt b/GraspPlanning/ExternalDependencies/qhull-2003.1/REGISTER.txt
deleted file mode 100644
index 4682e02669f1da0583867cdc91f2c82f1a07c676..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/REGISTER.txt
+++ /dev/null
@@ -1,37 +0,0 @@
-Dear User of Geometry Center Software:
-
-We would like to find out how you are using our software. Think of
-Geometry Center software as a new kind of shareware: you share your
-science and successes with us, and we share our software and support
-with you.
-
-If you use Geometry Center software, please send us a note telling
-us what you are doing with it.
-
-We need to know:
-
- (1) What you are working on - an abstract of your work would be
- fine.
-
- (2) What Geometry Center software you use.
-
- (3) How that software has helped you, for example, by increasing
- your productivity or allowing you to do things you could not do
- before. In particular, if you feel that Geometry Center
- software has had a direct bearing on your work, please tell us
- about this.
-
-We encourage you to cite the use of any Geometry Center software you
-have used in your publications.
-
-To cite Qhull, use
-
- Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., "The Quickhull
- algorithm for convex hulls," ACM Trans. on Mathematical Software,
- Dec 1996. http://www.qhull.org
-
-Please send e-mail to
-
- qhull@qhull.org
-
-Thank you!
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/Qhull-go.bat b/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/Qhull-go.bat
deleted file mode 100644
index 22792bde3209e7eb674ddac44ada9c6fe1ce256d..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/Qhull-go.bat
+++ /dev/null
@@ -1,20 +0,0 @@
-@echo off
-echo.
-echo ========= Qhull-go.bat, DOS window for Qhull and Rbox ===========
-echo.
-echo Use arrow keys to repeat and edit commands
-echo.
-echo Use properties button to increase size to 50 lines
-echo.
-echo Change font to 8x12
-echo.
-echo Change screen colors with ansi.sys or crt.exe v4.0 (shareware)
-echo.
-echo For scrolling back, try peruse (PC Magazine utility)
-echo.
-echo If full-screen, use alt-enter to return to Windows
-echo.
-echo Type 'qconvex' for synopsis and examples.
-echo.
-doskey /insert
-%comspec%
\ No newline at end of file
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/q_eg b/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/q_eg
deleted file mode 100644
index e9d0cfb289a3a65b9173612222741c1ff5bb08d0..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/q_eg
+++ /dev/null
@@ -1,58 +0,0 @@
-#! /bin/sh
-# writes examples to eg/
-# see html/qh_eg.htm
-set -v
-rbox c D3 | qconvex s G >eg/eg.01.cube
-rbox c d G2.0 | qconvex s G >eg/eg.02.diamond.cube
-rbox s 100 D3 | qconvex s G >eg/eg.03.sphere
-rbox s 100 D2 | qconvex s G >eg/eg.04.circle
-rbox 10 l | qconvex s G >eg/eg.05.spiral
-rbox 1000 D2 | qconvex s C-0.03 Qc Gapcv >eg/eg.06.merge.square
-rbox 1000 D3 | qconvex s G >eg/eg.07.box
-rbox c G0.4 s 500 | qconvex s G >eg/eg.08a.cube.sphere
-rbox d G0.6 s 500 | qconvex s G >eg/eg.08b.diamond.sphere
-rbox 100 L3 G0.5 s | qconvex s G >eg/eg.09.lens
-rbox 100 s P0.5,0.5,0.5 | qconvex s Ga QG0 >eg/eg.10a.sphere.visible
-rbox 100 s P0.5,0.5,0.5 | qconvex s Ga QG-0 >eg/eg.10b.sphere.beyond
-rbox 100 s P0.5,0.5,0.5 | qconvex s Ga QG0 PG >eg/eg.10c.sphere.horizon
-rbox 100 s P0.5,0.5,0.5 | qconvex s Ga QV0 PgG >eg/eg.10d.sphere.cone
-rbox 100 s P0.5,0.5,0.5 | qconvex s Ga >eg/eg.10e.sphere.new
-rbox 100 s P0.5,0.5,0.5 | qhull s Ga QV0g Q0 >eg/eg.14.sphere.corner
-rbox 500 W0 | qconvex s QR0 Qc Gvp >eg/eg.15a.surface
-rbox 500 W0 | qconvex s QR0 Qt Qc Gvp >eg/eg.15b.triangle
-rbox 500 W0 | qconvex s QR0 QJ5e-2 Qc Gvp >eg/eg.15c.joggle
-echo 2 = rbox 6 r s D2, rbox 15 B0.3 W0.25, c G0.5 >eg/eg.data.17
-echo 25 >>eg/eg.data.17
-rbox 15 D2 B0.3 W0.25 c G0.5 | tail +3 >>eg/eg.data.17
-rbox 6 r s D2 B0.2 | tail +3 >>eg/eg.data.17
-qdelaunay s Qt <eg/eg.data.17 GnraD2 >eg/eg.17a.delaunay.2
-qdelaunay s <eg/eg.data.17 GnraD2 >eg/eg.17b.delaunay.2i
-qdelaunay s <eg/eg.data.17 C-0 Ga >eg/eg.17c.delaunay.2-3
-qvoronoi s QJ <eg/eg.data.17 Gna >eg/eg.17d.voronoi.2
-qvoronoi s <eg/eg.data.17 Gna >eg/eg.17e.voronoi.2i
-rbox c G0.1 d | qdelaunay Gt Qz >eg/eg.17f.delaunay.3
-rbox 10 D2 d | qdelaunay s Qu G >eg/eg.18a.furthest.2-3
-rbox 10 D2 d | qdelaunay s Qu Pd2 G >eg/eg.18b.furthest-up.2-3
-rbox 10 D2 d | qvoronoi s Qu Gv >eg/eg.18c.furthest.2
-rbox 10 D3 | qvoronoi s FQ QV5 p | qconvex s G >eg/eg.19.voronoi.region.3
-rbox r s 20 Z1 G0.2 | qconvex s QR1 G >eg/eg.20.cone
-rbox 200 s | qconvex s Qc R0.014 Gpav >eg/eg.21b.roundoff.fixed
-rbox 1000 s| qconvex s C0.01 Qc Gcrp >eg/eg.22a.merge.sphere.01
-rbox 1000 s| qconvex s C-0.01 Qc Gcrp >eg/eg.22b.merge.sphere.-01
-rbox 1000 s| qconvex s C0.05 Qc Gcrpv >eg/eg.22c.merge.sphere.05
-rbox 1000 s| qconvex s C-0.05 Qc Gcrpv >eg/eg.22d.merge.sphere.-05
-rbox 1000 | qconvex s Gcprvah C0.1 Qc >eg/eg.23.merge.cube
-rbox 5000 D4 | qconvex s GD0v Pd0:0.5 C-0.02 C0.1 >eg/eg.24.merge.cube.4d-in-3d
-rbox 5000 D4 | qconvex s s C-0.02 C0.1 Gh >eg/eg.30.4d.merge.cube
-rbox 20 D3 | qdelaunay s G >eg/eg.31.4d.delaunay
-rbox 30 s D4 | qconvex s G Pd0d1d2D3 >eg/eg.32.4d.octant
-rbox 10 r s Z1 G0.3 | qconvex G >eg/eg.33a.cone
-rbox 10 r s Z1 G0.3 | qconvex FQ FV n | qhalf G >eg/eg.33b.cone.dual
-rbox 10 r s Z1 G0.3 | qconvex FQ FV n | qhalf FQ s Fp | qconvex G >eg/eg.33c.cone.halfspace
-
-echo ==the following should generate flipped and concave facets== >/dev/null
-rbox 200 s | qhull Q0 s R0.014 Gav Po >eg/eg.21a.roundoff.errors
-echo ==the preceeding should report flipped and concave facets== >/dev/null
-
-
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/q_egtest b/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/q_egtest
deleted file mode 100644
index 8948dcb1d6c426bcdfcfe727278e2f22b0a9ce00..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/q_egtest
+++ /dev/null
@@ -1,33 +0,0 @@
-#! /bin/sh
-# writes examples to eg/
-set -v
-rbox d D3 | qconvex s Gnrv Tc Tv >eg/eg.t01.spheres.3
-rbox d D2 | qconvex s Gnv Tc Tv >eg/eg.t02.spheres.2
-rbox d D3 | qconvex s Gnrp Tc Tv >eg/eg.t03.points.3
-rbox d D2 | qconvex s Gnp Tc Tv >eg/eg.t04.points.2
-rbox c D4 | qconvex s C0.05 GnpcD3 Pd3:0.5 Tc Tv >eg/eg.t05.centrum.points.4-3
-rbox d D3 | qconvex s Gnrc Tc Tv >eg/eg.t06.centrums.3.precise
-rbox d D3 | qconvex s C0.05 Gnrc Tc Tv >eg/eg.t07.centrums.3
-rbox d D2 | qconvex s C0.05 Gc Tc Tv >eg/eg.t08.centrums.2
-rbox d D3 | qconvex s Gnha Tc Tv >eg/eg.t09.intersect.3
-rbox d D3 | qconvex s GaD0 Pd0 Tc Tv >eg/eg.t10.faces.3-2
-rbox d D3 | qconvex s GnrpD0 Pd0 Tc Tv >eg/eg.t11.points.3-2
-rbox d D3 | qconvex s C0.05 GnrcD0 Pd0 Tc Tv >eg/eg.t12.centrums.3-2
-rbox d D3 | qconvex s GnhaD0 Pd0 Tc Tv >eg/eg.t13.intersect.3-2
-rbox d D3 | qconvex s GnrvD0 Pd0 Tc Tv >eg/eg.t14.spheres.3-2
-rbox c D4 | qconvex s GvD0 Pd0:0.5 Tc Tv >eg/eg.t15.spheres.4-3
-rbox c D4 | qhull s Q0 C0 GpD0 Pd0:0.5 Tc Tv >eg/eg.t16.points.4-3
-rbox c D4 | qconvex s GahD0 Pd0:0.5 Tc Tv >eg/eg.t17.intersect.4-3
-rbox 100 s | qconvex s C-0.05 Qc Gicvprh Tc Tv >eg/eg.t18.imprecise.3
-rbox 30 s D4 | qconvex s GhD0 Pd0d1d2D3 Tc >eg/eg.t19.intersect.precise.4-3
-rbox 100 s P1,1,1 | qconvex s QG-0 Pgp Tc G >eg/eg.t20.notvisible
-rbox 100 s | qconvex s QV-10 Pgp Tc G >eg/eg.t21.notvertex
-rbox 100 r D2 P1,1 | qhull s Pd0:0.7 PD0:0.8 QgG0 G Tv >eg/eg.t22.split
-rbox 100 D2 c G1.0 | qvoronoi s A-0.95 Gna Tv >eg/eg.t23.voronoi.imprecise
-rbox 30 s D4 | qconvex s Gh Pd0d1d2D3 Tc >eg/eg.t24.intersect.precise.4d
-
-echo ==the following generates an error== >/dev/null
-rbox 1000 D4 | qhull Q0 s Po R0.005 Ga Tc Tv >eg/eg.t25.neighbors.4d
-echo ==the previous should generate an error== >/dev/null
-
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/q_test b/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/q_test
deleted file mode 100644
index bc1b3c280e74d2afc51e6578df4a09a22b922e52..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/q_test
+++ /dev/null
@@ -1,385 +0,0 @@
-#!/bin/sh
-#
-# NOTE: all tests duplicated in q_test.bat
-set -v
-echo === errors if 'user_eg' and 'user_eg2' not found ===
-echo === check user_eg ${d:-`date`} =====================
-user_eg "QR1 p n Qt" "v p" Fp
-user_eg2 "QR1 p" "v p" Fp
-echo === check front ends ${d:-`date`} ==================
-qconvex -
-qconvex .
-qconvex
-rbox c D3 | qconvex s n Qt
-rbox c D2 | qconvex s i
-rbox c D2 | qconvex o
-rbox 1000 s | qconvex s Tv FA
-rbox c d D2 | qconvex s Qc Fx
-rbox y 1000 W0 | qconvex s n
-rbox y 1000 W0 | qconvex s QJ
-rbox d G1 D12 | qconvex QR0 FA
-rbox c D6 | qconvex FA TF500
-rbox c P0 d D2 | qconvex p Fa Fc FP FI Fn FN FS Fv Fx
-rbox c d D2 | qconvex s i QV0
-rbox c | qconvex Q0
-qvoronoi -
-qvoronoi .
-qvoronoi
-rbox c P0 D2 | qvoronoi s o
-rbox c P0 D2 | qvoronoi Fi Tv
-rbox c P0 D2 | qvoronoi Fo
-rbox c P0 D2 | qvoronoi Fv
-rbox c P0 D2 | qvoronoi s Qu Qt Fv
-rbox c P0 D2 | qvoronoi Qu Fo
-rbox c G1 d D2 | qvoronoi s p
-rbox c G1 d D2 | qvoronoi QJ p
-rbox c P-0.1 P+0.1 P+0.1 D2 | qvoronoi s Fc FP FQ Fn FN
-rbox P0 c D2 | qvoronoi s Fv QV0
-qdelaunay -
-qdelaunay .
-qdelaunay
-rbox c P0 D2 | qdelaunay s o
-rbox c P0 D2 | qdelaunay i
-rbox c P0 D2 | qdelaunay Fv
-rbox c P0 D2 | qdelaunay s Qu Qt Fv
-rbox c G1 d D2 | qdelaunay s i
-rbox c G1 d D2 | qhull d Qbb Ft
-rbox c G1 d D2 | qhull d Qbb QJ s Ft
-rbox M3,4 z 100 D2 | qdelaunay s
-rbox c P-0.1 P+0.1 P+0.1 D2 | qdelaunay s Fx Fa Fc FP FQ Fn FN
-rbox P0 P0 c D2 | qdelaunay s FP QV0
-qhalf -
-qhalf .
-qhalf
-rbox d | qhull FQ n | qhalf s Qt H0,0,0 Fp
-rbox c | qhull FQ FV n | qhalf s i
-rbox c | qhull FQ FV n | qhalf o
-rbox d D2 | qhull FQ n | qhalf s H0 Fc FP Fn FN FQ Fv Fx
-echo === check quality of Qhull for ${d:-`hostname`} ${d:-`date`}
-rbox 1000 W0 | qhull QR2 QJ s Fs Tv
-rbox 1000 W0 | qhull QR2 s Fs Tv
-rbox 1000 s | qhull C0.02 Qc Tv
-rbox 500 s D4 | qhull C0.01 Qc Tv
-rbox 1000 s | qhull C-0.02 Qc Tv
-rbox 1000 s | qhull C-0.02 Qc Tv
-rbox 1000 s D4 | qhull C-0.01 Qc Tv
-rbox 200 s D5 | qhull C-0.01 Qx Qc Tv
-rbox 100 s D6 | qhull C-0.001 Qx Qc Tv
-rbox 1000 W1e-4 | qhull C-1e-6 Qc Tv
-rbox 1000 W5e-4 D4 | qhull C-1e-5 Qc Tv
-rbox 400 W1e-3 D5 | qhull C-1e-5 Qx Qc Tv
-echo === check input format etc. ${d:-`date`}
-qhull <<EOF
-2 4 #;laskdjf
-1 0 1 1 1 2 0 0
-EOF
-qhull <<EOF
-2 4 #;laskdjf
-1 0 1 1 1 2 0 0 0
-EOF
-qhull <<EOF
-2 4 #;laskdjf
-1 0 1 1 1 2 0
-EOF
-qhull <<EOF
-2
-4 #;laskdjf
-1 #kjdfasdf
-0 1 1 1 2 0
-EOF
-qhull <<EOF
-2 4 1 0 1 1 1 2 0 0
-EOF
-qhull d Qz <<EOF
-2 5 1 0 1 1 0 1 0 0 0
-EOF
-qhull d Q8 Qz <<EOF
-2 5 1 0 1 1 0 1 0 0 0
-EOF
-rbox d h | qhull Fd FV n FD Tcv | qhull Fd H Fp Tcv
-rbox 10 h | qhull Fd FD p Tcv | qhull Fd d Tcv
-echo === check rbox ${d:-`date`}
-rbox 3 n D2
-rbox 3 D2
-rbox 3 h D2
-rbox 3 z D2
-rbox 3 z h D2
-rbox 3 B10 D2
-rbox 3 z B10 D2
-rbox 4 L2 r D2
-rbox 8 L2 D2
-rbox 4 L4 r D3
-rbox 4 L4 s D5 W1e-3
-rbox y
-rbox 10 M3,4
-rbox 10 L2 s D3 | qhull Tcv
-rbox 10 L4 s W1e-3 D3 | qhull Tcv
-rbox 10 L6 D3 | qhull Tcv
-rbox 10 L1.1 s D4 | qhull Tcv
-rbox y r 100 W0 O0.5 | qhull s p Tcv
-rbox x r 100 W0 O0.5 | qhull s Tcv
-rbox 12 D8 | qhull Tcv
-rbox 12 D9 | qhull Tcv
-rbox 1000 D4 | qhull s i A-0.97 C0.2 A0.7 Tcv
-rbox 3 D2 | qhull Qb0B1:-2 p
-rbox 100 r D2 | qhull Pd0:0.7 PD0:0.8 n Tcv
-rbox 1000 s | qhull C0.05 Tcv
-rbox 1000 s t | qhull Qm C0.05 Tcv
-rbox 500 D2 | qhull n A-0.95 C0.1 Tcv
-rbox 500 s P1,1,1 | qhull QgG0 Pp Tcv
-
-rbox d | qhull m
-rbox d | qhull FM
-rbox c D2 | qhull Tcv Q0
-rbox d D2 | qhull Tcv
-rbox c D3 | qhull Tcv Q0
-rbox d D3 | qhull Tcv
-rbox c D4 | qhull Tcv Q0
-rbox d D4 | qhull Tcv
-rbox c D5 | qhull Tcv Q0
-rbox d D5 | qhull Tcv
-rbox c D6 | qhull Tcv Q0
-rbox d D6 | qhull Tcv
-rbox d D7 | qhull Tcv
-rbox c D2 | qhull Tcv C-0
-rbox c D3 | qhull Tcv C-0
-rbox c D4 | qhull Tcv C-0
-rbox c D5 | qhull Tcv C-0
-rbox c D6 | qhull Tcv C-0
-rbox c D7 | qhull Tv C-0
-rbox 20 l D3 | qhull Tcv
-rbox 100 s D2 | qhull Tcv
-rbox 100 s D3 | qhull Tcv
-rbox 100 s D4 | qhull Tcv
-rbox 100 s c D4 | qhull Tcv
-rbox 100 s d G1.5 D4 | qhull Tcv
-rbox 100 s W1e-2 | qhull Tcv
-rbox 100 | qhull Tcv
-rbox 100 W1e-3 | qhull Tcv
-rbox 100 r D2 | qhull Tcv
-rbox 100 r s Z1 | qhull Tcv
-rbox 100 r s Z1 G0.1 | qhull Tcv C-0
-rbox 100 s Z1 G0.1 | qhull Tcv
-rbox 100 s Z1e-5 G0.1 | qhull Tc Pp
-
-echo === check qhull output formats ${d:-`date`}
-rbox 5 r s D2 | qhull Tcv
-rbox 5 r s D2 | qhull s
-rbox 5 r s D2 | qhull s o
-rbox 5 r s D2 | qhull f
-rbox 5 r s D2 | qhull i
-rbox 5 r s D2 | qhull m
-rbox 5 r s D2 | qhull FM
-rbox 5 r s D2 | qhull n
-rbox 5 r s D2 | qhull p
-rbox 5 r s D2 | qhull o
-rbox 5 r s D2 | qhull Ft
-rbox 5 r s D2 | qhull Fx
-rbox 5 r s D2 | qhull p n i p p
-rbox 10 D3 | qhull f Tcv
-rbox 10 D3 | qhull i
-rbox 10 D3 | qhull p
-rbox 10 D3 | qhull o
-rbox 10 D3 | qhull Fx
-rbox 27 M1,0,1 | qhull Qc
-rbox 50 D3 s | qhull C0.1 Qc Pd0d1d2 s p Tcv
-rbox 10 D2 P0 P1e-15 | qhull d Qc FP s Tcv
-rbox 100 s | qhull C-0.003 Qc FP s
-rbox 100 s D2 | qhull C0.1 i Fx Tcv
-rbox 4 s D3 | qhull Qc Ghipv Tcv
-rbox 6 D4 | qhull f Tcv
-rbox 6 D4 | qhull i
-rbox 6 D4 | qhull p
-rbox 6 D4 | qhull o
-rbox 1000 s D2 | qhull FA Tcv
-rbox 1000 s | qhull FA Tcv
-rbox c D4 | qhull FA Tcv
-rbox c D5 | qhull FA Tcv
-rbox c D5 | qhull FA Qt Tcv
-rbox 10 D2 | qhull d FA Tcv
-rbox 10 D2 | qhull d Qu FA Tcv
-rbox 10 D2 | qhull FA Tcv
-rbox 10 c D2 | qhull Fx Tcv
-rbox 1000 s | qhull FS Tcv
-rbox 10 W0 D2 | qhull p Qc FcC Tcv
-rbox 4 z h s D2 | qhull Fd s n FD Tcv
-rbox 6 s D3 | qhull C-0.1 Qc FF s FQ Fi n Fo FQ FI Fm Fn FN FO FO FQ Fs FS FV Fv Tcv
-rbox P0.5,0.5 P0.5,0.5 W0 5 D2 | qhull d FN Qc
-rbox 10 D3 | qhull Fa PA5
-rbox 10 D3 | qhull Fa PF0.4
-
-echo === test Qt ${d:-`date`}
-rbox c | qhull Qt s o Tcv
-rbox c | qhull Qt f i
-rbox c | qhull Qt m FM n
-rbox c | qhull Qt p o
-rbox c | qhull Qt Fx
-rbox c | qhull Qt FA s Fa
-rbox 6 r s c G0.1 D2 | qhull Qt d FA Tcv
-rbox 6 r s c G0.1 D2 | qhull d FA Tcv
-rbox 6 r s c G0.1 D2 | qhull Qt v p Tcv
-rbox c | qhull Qt C-0.1 Qc FF s FQ Fi n Fo FQ FI Fm Fn FN FO FO FQ Fs FS FV Fv Tcv
-rbox 6 r s c G0.1 D2 P0.1,0.1 | qhull s FP d FO Qt
-rbox 100 W0 | qhull Tv Q11
-
-echo === test unbounded intersection ${d:-`date`}
-rbox c | qhull PD0:0.5 n | qhull H0 Fp Tcv
-rbox 1000 W1e-3 D3 | qhull PA8 Fa FS s n Tcv
-rbox 1000 W1e-3 D3 | qhull C-0.01 PM10 Fm n Tcv Qc
-rbox 1000 W1e-3 D3 | qhull C-0.01 PA8 PG n Tcv Qc
-rbox 10 | qhull FO Tz TO q_test.log.1
-cat q_test.log.1
-
-echo === check Delaunay/Voronoi ${d:-`date`}
-rbox 10 D2 | qhull d Tcv
-rbox 10 D2 | qhull d Tcv Qz
-rbox 10 D3 | qhull d Tcv
-rbox c | qhull d Qz Ft Tcv
-rbox 10 s D2 c | qhull d Tcv
-rbox 10 s D2 | qhull d Tcv Q8 Qz
-rbox 10 D2 | qhull d Tcv p
-rbox 10 D2 | qhull d Tcv i
-rbox 10 D2 | qhull d Tcv o
-rbox 10 D2 | qhull v Tcv o
-rbox 10 D2 | qhull v Tcv p
-rbox 10 D2 | qhull v Tcv G
-rbox 10 D2 | qhull v Tcv Fv
-rbox 10 D2 | qhull v Tcv Fi
-rbox 10 D2 | qhull v Tcv Fo
-rbox 10 D2 | qhull v Qu o Fv Fi Fo Tcv
-rbox 10 D3 | qhull v Fv Tcv
-rbox 10 D3 | qhull v Fi Tcv
-rbox 10 D3 | qhull v Fo Tcv
-rbox 10 D3 | qhull v Qu o Fv Fi Fo Tcv
-rbox 5 D2 | qhull v f FnN o
-
-echo === check Halfspace ${d:-`date`}
-rbox 100 s D4 | qhull FA FV n s Tcv | qhull H Fp Tcv | qhull FA Tcv
-rbox d D3 | qhull FQ n s FD Tcv | qhull Fd H0.1,0.1 Fp FQ Tcv
-rbox 5 r D2 | qhull s n Tcv | qhull H0 Fp Tcv
-
-echo === check qhull ${d:-`date`}
-rbox 10 s D3 | qhull Tcv
-rbox 10 s D3 | qhull f Pd0:0.5 Pd2 Tcv
-rbox 10 s D3 | qhull f Tcv PD2:-0.5
-rbox 10 s D3 | qhull QR-1
-rbox 10 s D3 | qhull QR-40
-rbox 1000 D3 | qhull Tcvs
-rbox 100 D3 | qhull T8 Tz TO q_test.log.1
-tail -10 q_test.log.1
-rm q_test.log.1
-rbox 100 s D3 | qhull TcvV-2
-rbox 100 s D3 | qhull TcvC2
-rbox 100 s D3 | qhull TcvV2
-rbox 100 s D3 | qhull T1cvV2P2
-rbox 100 s D3 | qhull TcvF100
-rbox 100 s D3 | qhull Qf Tcv
-rbox 100 D3 | qhull Tcv
-rbox 100 D3 | qhull Qs Tcv
-rbox 100 D5 | qhull Qs Tcv
-rbox 100 D3 | qhull Qr Tcv
-rbox 100 D3 | qhull Qxv Tcv
-rbox 100 D3 | qhull Qi f Pd0 Pd1 Pd2 Tcv
-rbox c d | qhull Qc f Tcv
-rbox c d | qhull Qc p Tcv
-rbox 100 D3 | qhull QbB FO Tcv
-rbox 1000 D2 B1e6 | qhull d Qbb FO Tcv
-rbox 10 D3 | qhull QbB p Tcv
-rbox 10 D3 | qhull Qbb p Tcv
-rbox 10 D3 | qhull Qb0:-10B2:20 p Tcv
-rbox 10 D3 | qhull Qb0:-10B2:20 p Tcv | qhull QbB p Tcv
-rbox 10 D3 | qhull Qb1:0B1:0 d Tcv Q8
-rbox 10 D3 | qhull Qb1:0B1:0B2:0 d Tcv Q8
-rbox 10 D3 | qhull Qb1:0 d Tcv
-rbox 10 D3 | qhull Qb1:0B1:0 Tcv
-echo "== next command will error ${d:-`date`} =="
-rbox 10 D2 | qhull Qb1:1B1:1 Tcv
-rbox 200 L20 D2 t | qhull FO Tcv C-0
-rbox 1000 L20 t | qhull FO Tcv C-0
-rbox 200 L20 D4 t | qhull FO Tcv C-0
-rbox 200 L20 D5 t | qhull FO Tcv Qx
-rbox 1000 W1e-3 s D2 t | qhull d FO Tcv Qu Q0
-rbox 1000 W1e-3 s D2 t | qhull d FO Tcv Qu C-0
-
-echo === check joggle and TRn ${d:-`date`}
-rbox 100 W0 | qhull QJ1e-14 Qc TR100 Tv
-rbox 100 W0 | qhull QJ1e-13 Qc TR100 Tv
-rbox 100 W0 | qhull QJ1e-12 Qc TR100 Tv
-rbox 100 W0 | qhull QJ1e-11 Qc TR100 Tv
-rbox 100 W0 | qhull QJ1e-10 Qc TR100 Tv
-rbox 100 | qhull d QJ Qb0:1e4 QB0:1e5 Qb1:1e4 QB1:1e6 Qb2:1e5 QB2:1e7 FO Tv
-
-echo === check precision options ${d:-`date`}
-rbox 100 D3 s | qhull E0.01 Qx Tcv FO
-rbox 100 D3 W1e-1 | qhull W1e-3 Tcv
-rbox 100 D3 W1e-1 | qhull W1e-2 Tcv Q0
-rbox 100 D3 W1e-1 | qhull W1e-2 Tcv
-rbox 100 D3 W1e-1 | qhull W1e-1 Tcv
-rbox 15 D2 P0 P1e-14,1e-14 | qhull d Quc Tcv
-rbox 15 D3 P0 P1e-12,1e-14,1e-14 | qhull d Qcu Tcv
-rbox 1000 s D3 | qhull C-0.01 Tcv Qc
-rbox 1000 s D3 | qhull C-0.01 V0 Qc Tcv
-rbox 1000 s D3 | qhull C-0.01 U0 Qc Tcv
-rbox 1000 s D3 | qhull C-0.01 V0 Qcm Tcv
-rbox 1000 s D3 | qhull C-0.01 Qcm Tcv
-rbox 1000 s D3 | qhull C-0.01 Q1 FO Tcv Qc
-rbox 1000 s D3 | qhull C-0.01 Q2 FO Tcv Qc
-rbox 1000 s D3 | qhull C-0.01 Q3 FO Tcv Qc
-rbox 1000 s D3 | qhull C-0.01 Q4 FO Tcv Qc
-echo === this may generate an error ${d:-`date`}
-rbox 1000 s D3 | qhull C-0.01 Q5 FO Tcv
-echo === this should generate an error ${d:-`date`}
-rbox 1000 s D3 | qhull C-0.01 Q6 FO Po Tcv Qc
-rbox 1000 s D3 | qhull C-0.01 Q7 FO Tcv Qc
-rbox 1000 s D3 | qhull C-0.01 Qx Tcv Qc
-rbox 100 s D3 t | qhull R1e-3 Tcv Qc
-rbox 100 s D3 t | qhull R1e-2 Tcv Qc
-rbox 500 s D3 t | qhull R0.05 A-1 Tcv Qc
-rbox 100 W0 D3 t | qhull R1e-3 Tcv Qc
-rbox 100 W0 D3 t | qhull R1e-3 Qx Tcv Qc
-rbox 100 W0 D3 t | qhull R1e-2 Tcv Qc
-rbox 100 W0 D3 t | qhull R1e-2 Qx Tcv Qc
-rbox 500 W0 D3 t | qhull R0.05 A-1 Tcv Qc
-rbox 500 W0 D3 t | qhull R0.05 Qx Tcv Qc
-rbox 1000 W1e-20 t | qhull Tcv Qc
-rbox 1000 W1e-20 D4 t | qhull Tcv Qc
-rbox 500 W1e-20 D5 t | qhull Tv Qc
-rbox 100 W1e-20 D6 t | qhull Tv Qc
-rbox 50 W1e-20 D6 t | qhull Qv Tv Qc
-rbox 10000 D4 t | qhull QR0 Qc C-0.01 A0.3 Tv
-rbox 1000 D2 t | qhull d QR0 Qc C-1e-8 Qu Tv
-rbox 300 D5 t |qhull A-0.999 Qx Qc Tcv
-rbox 100 D6 t |qhull A-0.9999 Qx Qc Tcv
-rbox 50 D7 t |qhull A-0.99999 Qx Qc Tcv W0.1
-
-echo === check bad cases for Qhull. May cause errors ${d:-`date`}
-rbox 1000 L100000 s G1e-6 t | qhull Tv
-rbox 1000 L100000 s G1e-6 t | qhull Tv Q10
-rbox 1000 s Z1 G1e-13 t | qhull Tv
-rbox 1000 s W1e-13 P0 t | qhull d Qbb Qc Tv
-rbox 1000 s W1e-13 t | qhull d Tv
-rbox 1000 s W1e-13 t D2 | qhull d Tv
-
-echo =======================================================
-echo =======================================================
-echo === The following commands may cause errors ${d:-`date`}
-echo =======================================================
-echo =======================================================
-rbox c D7 | qhull Q0 Tcv
-rbox 100 s D3 | qhull Q0 E1e-3 Tc Po
-rbox 100 s D3 | qhull Q0 E1e-2 Tc Po
-rbox 100 s D3 | qhull Q0 E1e-1 Tc Po
-rbox 100 s D3 | qhull Q0 R1e-3 Tc Po
-rbox 100 s D3 | qhull Q0 R1e-2 Tc Po
-rbox 100 s D3 | qhull Q0 R0.05 Tc
-rbox 100 s D3 | qhull Q0 R0.05 Tc Po
-rbox 1000 W1e-7 | qhull Q0 Tc Po
-rbox 50 s | qhull Q0 V0.05 W0.01 Tc Po
-rbox 100 s D5 | qhull Q0 R1e-2 Tc Po
-qhull
-qhull .
-qhull -
-rbox
-cat html/qhull.txt html/rbox.txt
-
-# end of q_test
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/q_test.bat b/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/q_test.bat
deleted file mode 100644
index 81b679cfda0f7ebbe7e1da8b427c07b6d95d5a54..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/q_test.bat
+++ /dev/null
@@ -1,666 +0,0 @@
-echo q_test for Windows DOS box 2002/6/1 >q_test.x
-echo === errors if 'user_eg' and 'user_eg2' not found ===
-echo === check user_eg === >>q_test.x
-echo "user_eg 'QR1 p n Qt' 'v p' Fp" >>q_test.x
-user_eg "QR1 p n Qt" "v p" Fp >>q_test.x
-echo "user_eg2 'QR1 p' 'v p' Fp" >>q_test.x
-user_eg2 "QR1 p" "v p" Fp >>q_test.x
-echo === check front ends ========================================================== >>q_test.x
-echo "qconvex -" >>q_test.x
-qconvex - >>q_test.x
-echo "qconvex ." >>q_test.x
-qconvex . >>q_test.x
-echo "qconvex" >>q_test.x
-qconvex >>q_test.x
-echo "rbox c D3 | qconvex s n Qt" >>q_test.x
-rbox c D3 | qconvex s n Qt >>q_test.x
-echo "rbox c D2 | qconvex i Qt " >>q_test.x
-rbox c D2 | qconvex i Qt >>q_test.x
-echo "rbox c D2 | qconvex o" >>q_test.x
-rbox c D2 | qconvex o >>q_test.x
-echo "rbox 1000 s | qconvex s Tv FA" >>q_test.x
-rbox 1000 s | qconvex s Tv FA >>q_test.x
-echo "rbox c d D2 | qconvex s Qc Fx" >>q_test.x
-rbox c d D2 | qconvex s Qc Fx >>q_test.x
-echo "rbox y 1000 W0 | qconvex s n " >>q_test.x
-rbox y 1000 W0 | qconvex s n >>q_test.x
-echo "rbox y 1000 W0 | qconvex s QJ" >>q_test.x
-rbox y 1000 W0 | qconvex s QJ >>q_test.x
-echo "rbox d G1 D12 | qconvex QR0 FA" >>q_test.x
-rbox d G1 D12 | qconvex QR0 FA >>q_test.x
-echo "rbox c D6 | qconvex FA TF500" >>q_test.x
-rbox c D6 | qconvex FA TF500 >>q_test.x
-echo "rbox c P0 d D2 | qconvex p Fa Fc FP FI Fn FN FS Fv Fx" >>q_test.x
-rbox c P0 d D2 | qconvex p Fa Fc FP FI Fn FN FS Fv Fx >>q_test.x
-echo "rbox c d D2 | qconvex s i QV0" >>q_test.x
-rbox c d D2 | qconvex s i QV0 >>q_test.x
-echo "rbox c | qconvex Q0" >>q_test.x
-rbox c | qconvex Q0 >>q_test.x
-echo "qvoronoi -" >>q_test.x
-qvoronoi - >>q_test.x
-echo "qvoronoi ." >>q_test.x
-qvoronoi . >>q_test.x
-echo "qvoronoi" >>q_test.x
-qvoronoi >>q_test.x
-echo "rbox c P0 D2 | qvoronoi s o" >>q_test.x
-rbox c P0 D2 | qvoronoi s o >>q_test.x
-echo "rbox c P0 D2 | qvoronoi Fi" >>q_test.x
-rbox c P0 D2 | qvoronoi Fi >>q_test.x
-echo "rbox c P0 D2 | qvoronoi Fo" >>q_test.x
-rbox c P0 D2 | qvoronoi Fo >>q_test.x
-echo "rbox c P0 D2 | qvoronoi Fv" >>q_test.x
-rbox c P0 D2 | qvoronoi Fv >>q_test.x
-echo "rbox c P0 D2 | qvoronoi s Qu Qt Fv" >>q_test.x
-rbox c P0 D2 | qvoronoi s Qu Qt Fv >>q_test.x
-echo "rbox c P0 D2 | qvoronoi Qu Fo" >>q_test.x
-rbox c P0 D2 | qvoronoi Qu Fo >>q_test.x
-echo "rbox c G1 d D2 | qvoronoi s p " >>q_test.x
-rbox c G1 d D2 | qvoronoi s p >>q_test.x
-echo "rbox c G1 d D2 | qvoronoi QJ p " >>q_test.x
-rbox c G1 d D2 | qvoronoi QJ p >>q_test.x
-echo "rbox c P-0.1 P+0.1 P+0.1 D2 | qvoronoi s Fc FP FQ Fn FN " >>q_test.x
-rbox c P-0.1 P+0.1 P+0.1 D2 | qvoronoi s Fc FP FQ Fn FN >>q_test.x
-echo "rbox P0 c D2 | qvoronoi s Fv QV0" >>q_test.x
-rbox P0 c D2 | qvoronoi s Fv QV0 >>q_test.x
-echo "qdelaunay -" >>q_test.x
-qdelaunay - >>q_test.x
-echo "qdelaunay ." >>q_test.x
-qdelaunay . >>q_test.x
-echo "qdelaunay" >>q_test.x
-qdelaunay >>q_test.x
-echo "rbox c P0 D2 | qdelaunay s o" >>q_test.x
-rbox c P0 D2 | qdelaunay s o >>q_test.x
-echo "rbox c P0 D2 | qdelaunay i" >>q_test.x
-rbox c P0 D2 | qdelaunay i >>q_test.x
-echo "rbox c P0 D2 | qdelaunay Fv" >>q_test.x
-rbox c P0 D2 | qdelaunay Fv >>q_test.x
-echo "rbox c P0 D2 | qdelaunay s Qu Qt Fv" >>q_test.x
-rbox c P0 D2 | qdelaunay s Qu Qt Fv >>q_test.x
-echo "rbox c G1 d D2 | qdelaunay s i" >>q_test.x
-rbox c G1 d D2 | qdelaunay s i >>q_test.x
-echo "rbox c G1 d D2 | qdelaunay Ft" >>q_test.x
-rbox c G1 d D2 | qdelaunay Ft >>q_test.x
-echo "rbox c G1 d D2 | qdelaunay QJ s Ft" >>q_test.x
-rbox c G1 d D2 | qdelaunay QJ s Ft >>q_test.x
-echo "rbox M3,4 z 100 D2 | qdelaunay s" >>q_test.x
-rbox M3,4 z 100 D2 | qdelaunay s >>q_test.x
-echo "rbox c P-0.1 P+0.1 P+0.1 D2 | qdelaunay s Fx Fa Fc FP FQ Fn FN" >>q_test.x
-rbox c P-0.1 P+0.1 P+0.1 D2 | qdelaunay s Fx Fa Fc FP FQ Fn FN >>q_test.x
-echo "rbox P0 P0 c D2 | qdelaunay s FP QV0" >>q_test.x
-rbox P0 P0 c D2 | qdelaunay s FP QV0 >>q_test.x
-echo "qhalf -" >>q_test.x
-qhalf - >>q_test.x
-echo "qhalf ." >>q_test.x
-qhalf . >>q_test.x
-echo "qhalf" >>q_test.x
-qhalf >>q_test.x
-echo "rbox d | qhull FQ n | qhalf s Qt H0,0,0 Fp" >>q_test.x
-rbox d | qhull FQ n | qhalf s H0,0,0 Fp >>q_test.x
-echo "rbox c | qhull FQ FV n | qhalf s i" >>q_test.x
-rbox c | qhull FQ FV n | qhalf s i >>q_test.x
-echo "rbox c | qhull FQ FV n | qhalf o" >>q_test.x
-rbox c | qhull FQ FV n | qhalf o >>q_test.x
-echo "rbox d D2 | qhull FQ n | qhalf s H0 Fc FP Fn FN FQ Fv Fx" >>q_test.x
-rbox d D2 | qhull FQ n | qhalf s H0 Fc FP Fn FN FQ Fv Fx >>q_test.x
-
-echo === check quality of merges for ${d:-`hostname`} ${d:-`date`} >>q_test.x
-echo "rbox 1000 W0 t | qhull QR2 QJ s Fs Tv" >>q_test.x
-rbox 1000 W0 t | qhull QR2 QJ s Fs Tv >>q_test.x
-echo "rbox 1000 W0 t | qhull QR2 s Fs Tv" >>q_test.x
-rbox 1000 W0 t | qhull QR2 s Fs Tv >>q_test.x
-echo "rbox 1000 s t | qhull C0.02 Qc Tv" >>q_test.x
-rbox 1000 s t | qhull C0.02 Qc Tv >>q_test.x
-echo "rbox 500 s D4 t | qhull C0.01 Qc Tv" >>q_test.x
-rbox 500 s D4 t | qhull C0.01 Qc Tv >>q_test.x
-echo "rbox 1000 s t | qhull C-0.02 Qc Tv" >>q_test.x
-rbox 1000 s t | qhull C-0.02 Qc Tv >>q_test.x
-echo "rbox 1000 s t | qhull C-0.02 Qc Tv" >>q_test.x
-rbox 1000 s t | qhull C-0.02 Qc Tv >>q_test.x
-echo "rbox 1000 s D4 t | qhull C-0.01 Qc Tv" >>q_test.x
-rbox 1000 s D4 t | qhull C-0.01 Qc Tv >>q_test.x
-echo "rbox 200 s D5 t | qhull C-0.01 Qx Qc Tv" >>q_test.x
-rbox 200 s D5 t | qhull C-0.01 Qx Qc Tv >>q_test.x
-echo "rbox 100 s D6 t | qhull C-0.001 Qx Qc Tv" >>q_test.x
-rbox 100 s D6 t | qhull C-0.001 Qx Qc Tv >>q_test.x
-echo "rbox 1000 W1e-4 t | qhull C-1e-6 Qc Tv" >>q_test.x
-rbox 1000 W1e-4 t | qhull C-1e-6 Qc Tv >>q_test.x
-echo "rbox 1000 W5e-4 D4 t | qhull C-1e-5 Qc Tv" >>q_test.x
-rbox 1000 W5e-4 D4 t | qhull C-1e-5 Qc Tv >>q_test.x
-echo "rbox 400 W1e-3 D5 t | qhull C-1e-5 Qx Qc Tv" >>q_test.x
-rbox 400 W1e-3 D5 t | qhull C-1e-5 Qx Qc Tv >>q_test.x
-
-echo === check input format etc. ${d:-`date`} >>q_test.x
-echo "rbox d h | qhull Fd FV n FD Tcv | qhull Fd H Fp Tcv" >>q_test.x
-rbox d h | qhull Fd FV n FD Tcv | qhull Fd H Fp Tcv >>q_test.x
-echo "rbox 10 h | qhull Fd FD p Tcv | qhull Fd d Tcv " >>q_test.x
-rbox 10 h | qhull Fd FD p Tcv | qhull Fd d Tcv >>q_test.x
-
-echo === check rbox ${d:-`date`} >>q_test.x
-echo "rbox 3 n D2" >>q_test.x
-rbox 3 n D2 >>q_test.x
-echo "rbox 3 D2" >>q_test.x
-rbox 3 D2 >>q_test.x
-echo "rbox 3 h D2" >>q_test.x
-rbox 3 h D2 >>q_test.x
-echo "rbox 3 z D2" >>q_test.x
-rbox 3 z D2 >>q_test.x
-echo "rbox 3 z h D2" >>q_test.x
-rbox 3 z h D2 >>q_test.x
-echo "rbox 3 B10 D2" >>q_test.x
-rbox 3 B10 D2 >>q_test.x
-echo "rbox 3 z B10 D2" >>q_test.x
-rbox 3 z B10 D2 >>q_test.x
-echo "rbox 4 L2 r D2" >>q_test.x
-rbox 4 L2 r D2 >>q_test.x
-echo "rbox 8 L2 D2" >>q_test.x
-rbox 8 L2 D2 >>q_test.x
-echo "rbox 4 L4 r D3" >>q_test.x
-rbox 4 L4 r D3 >>q_test.x
-echo "rbox y" >>q_test.x
-rbox y >>q_test.x
-echo "rbox 10 M3,4" >>q_test.x
-rbox 10 M3,4 >>q_test.x
-echo "rbox 4 L4 s D5 W1e-3 " >>q_test.x
-rbox 4 L4 s D5 W1e-3 >>q_test.x
-echo "rbox 10 L2 s D3 | qhull Tcv" >>q_test.x
-rbox 10 L2 s D3 | qhull Tcv >>q_test.x
-echo "rbox 10 L4 s W1e-3 D3 | qhull Tcv" >>q_test.x
-rbox 10 L4 s W1e-3 D3 | qhull Tcv >>q_test.x
-echo "rbox 10 L6 D3 | qhull Tcv" >>q_test.x
-rbox 10 L6 D3 | qhull Tcv >>q_test.x
-echo "rbox 10 L1.1 s D4 | qhull Tcv" >>q_test.x
-rbox 10 L1.1 s D4 | qhull Tcv >>q_test.x
-echo "rbox y r 100 W0 O0.5 | qhull s p Tcv" >>q_test.x
-rbox y r 100 W0 O0.5 | qhull s p Tcv >>q_test.x
-echo "rbox x r 100 W0 O0.5 | qhull s p Tcv" >>q_test.x
-rbox x r 100 W0 O0.5 | qhull s p Tcv >>q_test.x
-echo "rbox 12 D8 | qhull Tcv" >>q_test.x
-rbox 12 D8 | qhull Tcv >>q_test.x
-echo "rbox 12 D9 | qhull Tcv" >>q_test.x
-rbox 12 D9 | qhull Tcv >>q_test.x
-echo "rbox 1000 D4 | qhull s i A-0.97 C0.2 A0.7 Tcv" >>q_test.x
-rbox 1000 D4 | qhull s i A-0.97 C0.2 A0.7 Tcv >>q_test.x
-echo "rbox 3 D2 | qhull Qb0B1:-2 p " >>q_test.x
-rbox 3 D2 | qhull Qb0B1:-2 p >>q_test.x
-echo "rbox 100 r D2 | qhull Pd0:0.7 PD0:0.8 n Tcv" >>q_test.x
-rbox 100 r D2 | qhull Pd0:0.7 PD0:0.8 n Tcv >>q_test.x
-echo "rbox 1000 s | qhull C0.05 Tcv" >>q_test.x
-rbox 1000 s | qhull C0.05 Tcv >>q_test.x
-echo "rbox 1000 s t | qhull Qm C0.05 Tcv" >>q_test.x
-rbox 1000 s t | qhull Qm C0.05 Tcv >>q_test.x
-echo "rbox 500 D2 | qhull n A-0.95 C0.1 Tcv" >>q_test.x
-rbox 500 D2 | qhull n A-0.95 C0.1 Tcv >>q_test.x
-echo "rbox 500 s P1,1,1 | qhull QgG0 Pp Tcv" >>q_test.x
-rbox 500 s P1,1,1 | qhull QgG0 Pp Tcv >>q_test.x
-
-echo "rbox d | qhull m" >>q_test.x
-rbox d | qhull m >>q_test.x
-echo "rbox d | qhull FM" >>q_test.x
-rbox d | qhull FM >>q_test.x
-echo "rbox c D2 | qhull Q0 Tcv" >>q_test.x
-rbox c D2 | qhull Q0 Tcv >>q_test.x
-echo "rbox d D2 | qhull Tcv" >>q_test.x
-rbox d D2 | qhull Tcv >>q_test.x
-echo "rbox c D3 | qhull Q0 Tcv" >>q_test.x
-rbox c D3 | qhull Q0 Tcv >>q_test.x
-echo "rbox d D3 | qhull Tcv" >>q_test.x
-rbox d D3 | qhull Tcv >>q_test.x
-echo "rbox c D4 | qhull Q0 Tcv" >>q_test.x
-rbox c D4 | qhull Q0 Tcv >>q_test.x
-echo "rbox d D4 | qhull Tcv" >>q_test.x
-rbox d D4 | qhull Tcv >>q_test.x
-echo "rbox c D5 | qhull Q0 Tcv" >>q_test.x
-rbox c D5 | qhull Q0 Tcv >>q_test.x
-echo "rbox d D5 | qhull Tcv" >>q_test.x
-rbox d D5 | qhull Tcv >>q_test.x
-echo "rbox c D6 | qhull Q0 Tcv" >>q_test.x
-rbox c D6 | qhull Q0 Tcv >>q_test.x
-echo "rbox d D6 | qhull Tcv" >>q_test.x
-rbox d D6 | qhull Tcv >>q_test.x
-echo "rbox d D7 | qhull Tcv" >>q_test.x
-rbox d D7 | qhull Tcv >>q_test.x
-echo "rbox c D2 | qhull Tcv C-0" >>q_test.x
-rbox c D2 | qhull Tcv C-0 >>q_test.x
-echo "rbox c D3 | qhull Tcv C-0" >>q_test.x
-rbox c D3 | qhull Tcv C-0 >>q_test.x
-echo "rbox c D4 | qhull Tcv C-0" >>q_test.x
-rbox c D4 | qhull Tcv C-0 >>q_test.x
-echo "rbox c D5 | qhull Tcv C-0" >>q_test.x
-rbox c D5 | qhull Tcv C-0 >>q_test.x
-echo "rbox c D6 | qhull Tcv C-0" >>q_test.x
-rbox c D6 | qhull Tcv C-0 >>q_test.x
-echo "rbox c D7 | qhull Tv C-0" >>q_test.x
-rbox c D7 | qhull Tv C-0 >>q_test.x
-echo "rbox 20 l D3 | qhull Tcv" >>q_test.x
-rbox 20 l D3 | qhull Tcv >>q_test.x
-echo "rbox 100 s D2 | qhull Tcv" >>q_test.x
-rbox 100 s D2 | qhull Tcv >>q_test.x
-echo "rbox 100 s D3 | qhull Tcv" >>q_test.x
-rbox 100 s D3 | qhull Tcv >>q_test.x
-echo "rbox 100 s D4 | qhull Tcv" >>q_test.x
-rbox 100 s D4 | qhull Tcv >>q_test.x
-echo "rbox 100 s c D4 | qhull Tcv" >>q_test.x
-rbox 100 s c D4 | qhull Tcv >>q_test.x
-echo "rbox 100 s d G1.5 D4 | qhull Tcv" >>q_test.x
-rbox 100 s d G1.5 D4 | qhull Tcv >>q_test.x
-echo "rbox 100 s W1e-2 | qhull Tcv" >>q_test.x
-rbox 100 s W1e-2 | qhull Tcv >>q_test.x
-echo "rbox 100 | qhull Tcv" >>q_test.x
-rbox 100 | qhull Tcv >>q_test.x
-echo "rbox 100 W1e-3 | qhull Tcv" >>q_test.x
-rbox 100 W1e-3 | qhull Tcv >>q_test.x
-echo "rbox 100 r D2 | qhull Tcv" >>q_test.x
-rbox 100 r D2 | qhull Tcv >>q_test.x
-echo "rbox 100 r s Z1 | qhull Tcv" >>q_test.x
-rbox 100 r s Z1 | qhull Tcv >>q_test.x
-echo "rbox 100 r s Z1 G0.1 | qhull Tcv C-0" >>q_test.x
-rbox 100 r s Z1 G0.1 | qhull Tcv C-0 >>q_test.x
-echo "rbox 100 s Z1 G0.1 | qhull Tcv " >>q_test.x
-rbox 100 s Z1 G0.1 | qhull Tcv >>q_test.x
-echo "rbox 100 s Z1e-5 G0.1 | qhull Tc Pp" >>q_test.x
-rbox 100 s Z1e-5 G0.1 | qhull Tc Pp >>q_test.x
-
-echo === check qhull output formats ${d:-`date`} >>q_test.x
-echo "rbox 5 r s D2 | qhull Tcv" >>q_test.x
-rbox 5 r s D2 | qhull Tcv >>q_test.x
-echo "rbox 5 r s D2 | qhull s " >>q_test.x
-rbox 5 r s D2 | qhull s >>q_test.x
-echo "rbox 5 r s D2 | qhull s o " >>q_test.x
-rbox 5 r s D2 | qhull s o >>q_test.x
-echo "rbox 5 r s D2 | qhull f" >>q_test.x
-rbox 5 r s D2 | qhull f >>q_test.x
-echo "rbox 5 r s D2 | qhull i " >>q_test.x
-rbox 5 r s D2 | qhull i >>q_test.x
-echo "rbox 5 r s D2 | qhull m " >>q_test.x
-rbox 5 r s D2 | qhull m >>q_test.x
-echo "rbox 5 r s D2 | qhull FM " >>q_test.x
-rbox 5 r s D2 | qhull FM >>q_test.x
-echo "rbox 5 r s D2 | qhull n " >>q_test.x
-rbox 5 r s D2 | qhull n >>q_test.x
-echo "rbox 5 r s D2 | qhull p " >>q_test.x
-rbox 5 r s D2 | qhull p >>q_test.x
-echo "rbox 5 r s D2 | qhull o " >>q_test.x
-rbox 5 r s D2 | qhull o >>q_test.x
-echo "rbox 5 r s D2 | qhull Fx" >>q_test.x
-rbox 5 r s D2 | qhull Fx >>q_test.x
-echo "rbox 5 r s D2 | qhull p n i p p" >>q_test.x
-rbox 5 r s D2 | qhull p n i p p >>q_test.x
-echo "rbox 10 D3 | qhull f Tcv" >>q_test.x
-rbox 10 D3 | qhull f Tcv >>q_test.x
-echo "rbox 10 D3 | qhull i" >>q_test.x
-rbox 10 D3 | qhull i >>q_test.x
-echo "rbox 10 D3 | qhull p " >>q_test.x
-rbox 10 D3 | qhull p >>q_test.x
-echo "rbox 10 D3 | qhull o " >>q_test.x
-rbox 10 D3 | qhull o >>q_test.x
-echo "rbox 10 D3 | qhull Fx " >>q_test.x
-rbox 10 D3 | qhull Fx >>q_test.x
-echo "rbox 27 M1,0,1 | qhull Qc" >>q_test.x
-rbox 27 M1,0,1 | qhull Qc >>q_test.x
-echo "rbox 50 D3 s | qhull C0.1 Qc Pd0d1d2 s p Tcv" >>q_test.x
-rbox 50 D3 s | qhull C0.1 Qc Pd0d1d2 s p Tcv >>q_test.x
-echo "rbox 10 D2 P0 P1e-15 | qhull d Qc FP s Tcv" >>q_test.x
-rbox 10 D2 P0 P1e-15 | qhull d Qc FP s Tcv >>q_test.x
-echo "rbox 100 s | qhull C-0.003 Qc FP s" >>q_test.x
-rbox 100 s | qhull C-0.003 Qc FP s >>q_test.x
-echo "rbox 100 s D2 | qhull C0.1 i Fx Tcv" >>q_test.x
-rbox 100 s D2 | qhull C0.1 i Fx Tcv >>q_test.x
-echo "rbox 4 s D3 | qhull Qc Ghipv Tcv " >>q_test.x
-rbox 4 s D3 | qhull Qc Ghipv Tcv >>q_test.x
-echo "rbox 6 D4 | qhull f Tcv" >>q_test.x
-rbox 6 D4 | qhull f Tcv >>q_test.x
-echo "rbox 6 D4 | qhull i" >>q_test.x
-rbox 6 D4 | qhull i >>q_test.x
-echo "rbox 6 D4 | qhull p " >>q_test.x
-rbox 6 D4 | qhull p >>q_test.x
-echo "rbox 6 D4 | qhull o" >>q_test.x
-rbox 6 D4 | qhull o >>q_test.x
-echo "rbox 1000 s D2 | qhull FA Tcv" >>q_test.x
-rbox 1000 s D2 | qhull FA Tcv >>q_test.x
-echo "rbox 1000 s | qhull FA Tcv" >>q_test.x
-rbox 1000 s | qhull FA Tcv >>q_test.x
-echo "rbox c D4 | qhull FA Tcv" >>q_test.x
-rbox c D4 | qhull FA Tcv >>q_test.x
-echo "rbox c D5 | qhull FA Tcv" >>q_test.x
-rbox c D5 | qhull FA Tcv >>q_test.x
-echo "rbox 10 D2 | qhull d FA Tcv" >>q_test.x
-rbox 10 D2 | qhull d FA Tcv >>q_test.x
-echo "rbox 10 D2 | qhull d Qu FA Tcv" >>q_test.x
-rbox 10 D2 | qhull d Qu FA Tcv >>q_test.x
-echo "rbox 10 D2 | qhull FA Tcv" >>q_test.x
-rbox 10 D2 | qhull FA Tcv >>q_test.x
-echo "rbox 10 c D2 | qhull Fx Tcv" >>q_test.x
-rbox 10 c D2 | qhull Fx Tcv >>q_test.x
-echo "rbox 1000 s | qhull FS Tcv" >>q_test.x
-rbox 1000 s | qhull FS Tcv >>q_test.x
-echo "rbox 10 W0 D2 | qhull p Qc FcC Tcv" >>q_test.x
-rbox 10 W0 D2 | qhull p Qc FcC Tcv >>q_test.x
-echo "rbox 4 z h s D2 | qhull Fd s n FD Tcv" >>q_test.x
-rbox 4 z h s D2 | qhull Fd s n FD Tcv >>q_test.x
-echo "rbox 6 s D3 | qhull C-0.1 Qc FF s FQ Fi n Fo FQ FI Fm Fn FN FO FO FQ Fs FS FV Fv Tcv" >>q_test.x
-rbox 6 s D3 | qhull C-0.1 Qc FF s FQ Fi n Fo FQ FI Fm Fn FN FO FO FQ Fs FS FV Fv Tcv >>q_test.x
-echo "rbox P0.5,0.5 P0.5,0.5 W0 5 D2 | qhull d FN Qc" >>q_test.x
-rbox P0.5,0.5 P0.5,0.5 W0 5 D2 | qhull d FN Qc >>q_test.x
-echo "rbox 10 D3 | qhull Fa PA5" >>q_test.x
-rbox 10 D3 | qhull Fa PA5 >>q_test.x
-echo "rbox 10 D3 | qhull Fa PF0.4" >>q_test.x
-rbox 10 D3 | qhull Fa PF0.4 >>q_test.x
-
-echo === test Qt >>q_test.x
-echo "rbox c | qhull Qt s o Tcv" >>q_test.x
-rbox c | qhull Qt s o Tcv >>q_test.x
-echo "rbox c | qhull Qt f i" >>q_test.x
-rbox c | qhull Qt f i >>q_test.x
-echo "rbox c | qhull Qt m FM n" >>q_test.x
-rbox c | qhull Qt m FM n >>q_test.x
-echo "rbox c | qhull Qt p o" >>q_test.x
-rbox c | qhull Qt p o >>q_test.x
-echo "rbox c | qhull Qt Fx" >>q_test.x
-rbox c | qhull Qt Fx >>q_test.x
-echo "rbox c | qhull Qt FA s Fa" >>q_test.x
-rbox c | qhull Qt FA s Fa >>q_test.x
-echo "rbox 6 r s c G0.1 D2 | qhull Qt d FA Tcv" >>q_test.x
-rbox 6 r s c G0.1 D2 | qhull Qt d FA Tcv >>q_test.x
-echo "rbox 6 r s c G0.1 D2 | qhull d FA Tcv" >>q_test.x
-rbox 6 r s c G0.1 D2 | qhull d FA Tcv >>q_test.x
-echo "rbox 6 r s c G0.1 D2 | qhull Qt v p Tcv" >>q_test.x
-rbox 6 r s c G0.1 D2 | qhull Qt v p Tcv >>q_test.x
-echo "rbox c | qhull Qt C-0.1 Qc FF s FQ Fi n Fo FQ FI Fm Fn FN FO FO FQ Fs FS FV Fv Tcv" >>q_test.x
-rbox c | qhull Qt C-0.1 Qc FF s FQ Fi n Fo FQ FI Fm Fn FN FO FO FQ Fs FS FV Fv Tcv >>q_test.x
-echo "rbox 6 r s c G0.1 D2 P0.1,0.1 | qhull s FP d FO Qt" >>q_test.x
-rbox 6 r s c G0.1 D2 P0.1,0.1 | qhull s FP d FO Qt >>q_test.x
-echo "RBOX 100 W0 | QHULL Tv Q11 FO" >>q_test.x
-RBOX 100 W0 | QHULL Tv Q11 FO >>q_test.x
-
-echo === test unbounded intersection >>q_test.x
-echo "rbox c | qhull PD0:0.5 n | qhull H0 Fp Tcv" >>q_test.x
-rbox c | qhull PD0:0.5 n | qhull H0 Fp Tcv >>q_test.x
-echo "rbox 1000 W1e-3 D3 | qhull PA8 Fa FS s n Tcv " >>q_test.x
-rbox 1000 W1e-3 D3 | qhull PA8 Fa FS s n Tcv >>q_test.x
-echo "rbox 1000 W1e-3 D3 | qhull C-0.01 PM10 Fm n Tcv Qc" >>q_test.x
-rbox 1000 W1e-3 D3 | qhull C-0.01 PM10 Fm n Tcv Qc >>q_test.x
-echo "rbox 1000 W1e-3 D3 | qhull C-0.01 PA8 PG n Tcv Qc" >>q_test.x
-rbox 1000 W1e-3 D3 | qhull C-0.01 PA8 PG n Tcv Qc >>q_test.x
-rbox 10 | qhull FO Tz TO q_test.log.1
-echo "type q_test.log.1" >>q_test.x
-type q_test.log.1 >>q_test.x
-
-echo === check Delaunay/Voronoi ${d:-`date`} >>q_test.x
-echo "rbox 10 D2 | qhull d Tcv" >>q_test.x
-rbox 10 D2 | qhull d Tcv >>q_test.x
-echo "rbox 10 D2 | qhull d Qz Tcv" >>q_test.x
-rbox 10 D2 | qhull d Qz Tcv >>q_test.x
-echo "rbox 10 D3 | qhull d Tcv" >>q_test.x
-rbox 10 D3 | qhull d Tcv >>q_test.x
-echo "rbox c | qhull d Qz Ft Tcv" >>q_test.x
-rbox c | qhull d Qz Ft Tcv >>q_test.x
-echo "rbox 10 s D2 c | qhull d Tcv" >>q_test.x
-rbox 10 s D2 c | qhull d Tcv >>q_test.x
-echo "rbox 10 s D2 | qhull d Tcv Qz Q8" >>q_test.x
-rbox 10 s D2 | qhull d Tcv Qz Q8 >>q_test.x
-echo "rbox 10 D2 | qhull d Tcv p" >>q_test.x
-rbox 10 D2 | qhull d Tcv p >>q_test.x
-echo "rbox 10 D2 | qhull d Tcv i" >>q_test.x
-rbox 10 D2 | qhull d Tcv i >>q_test.x
-echo "rbox 10 D2 | qhull d Tcv o" >>q_test.x
-rbox 10 D2 | qhull d Tcv o >>q_test.x
-echo "rbox 10 D2 | qhull v Tcv o" >>q_test.x
-rbox 10 D2 | qhull v Tcv o >>q_test.x
-echo "rbox 10 D2 | qhull v Tcv p" >>q_test.x
-rbox 10 D2 | qhull v Tcv p >>q_test.x
-echo "rbox 10 D2 | qhull v Tcv G" >>q_test.x
-rbox 10 D2 | qhull v Tcv G >>q_test.x
-echo "rbox 10 D2 | qhull v Tcv Fv" >>q_test.x
-rbox 10 D2 | qhull v Tcv Fv >>q_test.x
-echo "rbox 10 D2 | qhull v Tcv Fi" >>q_test.x
-rbox 10 D2 | qhull v Tcv Fi >>q_test.x
-echo "rbox 10 D2 | qhull v Tcv Fo" >>q_test.x
-rbox 10 D2 | qhull v Tcv Fo >>q_test.x
-echo "rbox 10 D2 | qhull v Qu Tcv o Fv Fi Fo" >>q_test.x
-rbox 10 D2 | qhull v Qu Tcv o Fv Fi Fo >>q_test.x
-echo "rbox 10 D3 | qhull v Tcv Fv" >>q_test.x
-rbox 10 D3 | qhull v Tcv Fv >>q_test.x
-echo "rbox 10 D3 | qhull v Tcv Fi" >>q_test.x
-rbox 10 D3 | qhull v Tcv Fi >>q_test.x
-echo "rbox 10 D3 | qhull v Tcv Fo" >>q_test.x
-rbox 10 D3 | qhull v Tcv Fo >>q_test.x
-echo "rbox 10 D3 | qhull v Qu Tcv o Fv Fi Fo" >>q_test.x
-rbox 10 D3 | qhull v Qu Tcv o Fv Fi Fo >>q_test.x
-echo "rbox 5 D2 | qhull v f FnN o" >>q_test.x
-rbox 5 D2 | qhull v f FnN o >>q_test.x
-
-echo === check Halfspace ${d:-`date`} >>q_test.x
-echo "rbox 100 s D4 | qhull FA FV n s Tcv | qhull H Fp Tcv | qhull FA Tcv" >>q_test.x
-rbox 100 s D4 | qhull FA s Tcv >>q_test.x
-rbox 100 s D4 | qhull FA FV n s Tcv | qhull H Fp Tcv | qhull FA Tcv >>q_test.x
-echo "rbox d D3 | qhull FQ n s FD Tcv | qhull Fd H0.1,0.1 Fp FQ Tcv" >>q_test.x
-rbox d D3 | qhull s >>q_test.x
-rbox d D3 | qhull FQ n FD Tcv | qhull Fd H0.1,0.1 Fp FQ Tcv >>q_test.x
-echo "rbox 5 r D2 | qhull s n Tcv | qhull H0 Fp Tcv" >>q_test.x
-rbox 5 r D2 | qhull >>q_test.x
-rbox 5 r D2 | qhull n Tcv | qhull H0 Fp Tcv >>q_test.x
-
-echo === check qhull ${d:-`date`} >>q_test.x
-echo "rbox 10 s D3 | qhull Tcv" >>q_test.x
-rbox 10 s D3 | qhull Tcv >>q_test.x
-echo "rbox 10 s D3 | qhull f Pd0:0.5 Pd2 Tcv" >>q_test.x
-rbox 10 s D3 | qhull f Pd0:0.5 Pd2 Tcv >>q_test.x
-echo "rbox 10 s D3 | qhull f Tcv PD2:-0.5" >>q_test.x
-rbox 10 s D3 | qhull f Tcv PD2:-0.5 >>q_test.x
-echo "rbox 10 s D3 | qhull QR-1" >>q_test.x
-rbox 10 s D3 | qhull QR-1 >>q_test.x
-echo "rbox 10 s D3 | qhull QR-40" >>q_test.x
-rbox 10 s D3 | qhull QR-40 >>q_test.x
-echo "rbox 1000 D3 | qhull Tcvs" >>q_test.x
-rbox 1000 D3 | qhull Tcvs >>q_test.x
-echo "rbox 100 s D3 | qhull TcvV-2" >>q_test.x
-rbox 100 s D3 | qhull TcvV-2 >>q_test.x
-echo "rbox 100 s D3 | qhull TcvC2" >>q_test.x
-rbox 100 s D3 | qhull TcvC2 >>q_test.x
-echo "rbox 100 s D3 | qhull TcvV2" >>q_test.x
-rbox 100 s D3 | qhull TcvV2 >>q_test.x
-echo "rbox 100 s D3 | qhull T1cvV2P2" >>q_test.x
-rbox 100 s D3 | qhull T1cvV2P2 >>q_test.x
-echo "rbox 100 s D3 | qhull TcvF100" >>q_test.x
-rbox 100 s D3 | qhull TcvF100 >>q_test.x
-echo "rbox 100 s D3 | qhull Qf Tcv" >>q_test.x
-rbox 100 s D3 | qhull Qf Tcv >>q_test.x
-echo "rbox 100 D3 | qhull Tcv" >>q_test.x
-rbox 100 D3 | qhull Tcv >>q_test.x
-echo "rbox 100 D3 | qhull Qs Tcv" >>q_test.x
-rbox 100 D3 | qhull Qs Tcv >>q_test.x
-echo "rbox 100 D5 | qhull Qs Tcv" >>q_test.x
-rbox 100 D5 | qhull Qs Tcv >>q_test.x
-echo "rbox 100 D3 | qhull Qr Tcv" >>q_test.x
-rbox 100 D3 | qhull Qr Tcv >>q_test.x
-echo "rbox 100 D3 | qhull Qxv Tcv" >>q_test.x
-rbox 100 D3 | qhull Qxv Tcv >>q_test.x
-echo "rbox 100 D3 | qhull Qi f Pd0 Pd1 Pd2 Tcv" >>q_test.x
-rbox 100 D3 | qhull Qi f Pd0 Pd1 Pd2 Tcv >>q_test.x
-echo "rbox c d | qhull Qc f Tcv" >>q_test.x
-rbox c d | qhull Qc f Tcv >>q_test.x
-echo "rbox c d | qhull Qc p Tcv" >>q_test.x
-rbox c d | qhull Qc p Tcv >>q_test.x
-echo "rbox 100 D3 | qhull QbB FO Tcv" >>q_test.x
-rbox 100 D3 | qhull QbB FO Tcv >>q_test.x
-echo "rbox 1000 D2 B1e6 | qhull d Qbb FO Tcv" >>q_test.x
-rbox 1000 D2 B1e6 | qhull d Qbb FO Tcv >>q_test.x
-echo "rbox 10 D3 | qhull QbB p Tcv" >>q_test.x
-rbox 10 D3 | qhull QbB p Tcv >>q_test.x
-echo "rbox 10 D3 | qhull Qbb p Tcv" >>q_test.x
-rbox 10 D3 | qhull Qbb p Tcv >>q_test.x
-echo "rbox 10 D3 | qhull Qb0:-10B2:20 p Tcv" >>q_test.x
-rbox 10 D3 | qhull Qb0:-10B2:20 p Tcv >>q_test.x
-echo "rbox 10 D3 | qhull Qb0:-10B2:20 p Tcv | qhull QbB p Tcv" >>q_test.x
-rbox 10 D3 | qhull Qb0:-10B2:20 p Tcv | qhull QbB p Tcv >>q_test.x
-echo "rbox 10 D3 | qhull Qb1:0B1:0 d Tcv Q8" >>q_test.x
-rbox 10 D3 | qhull Qb1:0B1:0 d Tcv Q8 >>q_test.x
-echo "rbox 10 D3 | qhull Qb1:0B1:0B2:0 d Tcv Q8" >>q_test.x
-rbox 10 D3 | qhull Qb1:0B1:0B2:0 d Tcv Q8 >>q_test.x
-echo "rbox 10 D3 | qhull Qb1:0 d Tcv " >>q_test.x
-rbox 10 D3 | qhull Qb1:0 d Tcv >>q_test.x
-echo "rbox 10 D3 | qhull Qb1:0B1:0 Tcv" >>q_test.x
-rbox 10 D3 | qhull Qb1:0B1:0 Tcv >>q_test.x
-echo "== next command will error ==" >>q_test.x
-echo "rbox 10 D2 | qhull Qb1:1B1:1 Tcv" >>q_test.x
-rbox 10 D2 | qhull Qb1:1B1:1 Tcv >>q_test.x
-echo "rbox 200 L20 D2 t | qhull FO Tcv C-0" >>q_test.x
-rbox 200 L20 D2 t | qhull FO Tcv C-0 >>q_test.x
-echo "rbox 1000 L20 t | qhull FO Tcv C-0" >>q_test.x
-rbox 1000 L20 t | qhull FO Tcv C-0 >>q_test.x
-echo "rbox 200 L20 D4 t | qhull FO Tcv C-0" >>q_test.x
-rbox 200 L20 D4 t | qhull FO Tcv C-0 >>q_test.x
-echo "rbox 200 L20 D5 t | qhull FO Tcv Qx" >>q_test.x
-rbox 200 L20 D5 t | qhull FO Tcv Qx >>q_test.x
-echo "rbox 1000 W1e-3 s D2 t | qhull d FO Tcv Qu Q0" >>q_test.x
-rbox 1000 W1e-3 s D2 t | qhull d FO Tcv Qu Q0 >>q_test.x
-echo "rbox 1000 W1e-3 s D2 t | qhull d FO Tcv Qu C-0" >>q_test.x
-rbox 1000 W1e-3 s D2 t | qhull d FO Tcv Qu C-0 >>q_test.x
-
-echo === check joggle and TRn ${d:-`date`} >>q_test.x
-echo "rbox 100 W0 | qhull QJ1e-14 Qc TR100 Tv" >>q_test.x
-rbox 100 W0 | qhull QJ1e-14 Qc TR100 Tv >>q_test.x
-echo "rbox 100 W0 | qhull QJ1e-13 Qc TR100 Tv" >>q_test.x
-rbox 100 W0 | qhull QJ1e-13 Qc TR100 Tv >>q_test.x
-echo "rbox 100 W0 | qhull QJ1e-12 Qc TR100 Tv" >>q_test.x
-rbox 100 W0 | qhull QJ1e-12 Qc TR100 Tv >>q_test.x
-echo "rbox 100 W0 | qhull QJ1e-11 Qc TR100 Tv" >>q_test.x
-rbox 100 W0 | qhull QJ1e-11 Qc TR100 Tv >>q_test.x
-echo "rbox 100 W0 | qhull QJ1e-10 Qc TR100 Tv" >>q_test.x
-rbox 100 W0 | qhull QJ1e-10 Qc TR100 Tv >>q_test.x
-echo "rbox 100 | qhull d QJ Qb0:1e4 QB0:1e5 Qb1:1e4 QB1:1e6 Qb2:1e5 QB2:1e7 FO Tv" >>q_test.x
-rbox 100 | qhull d QJ Qb0:1e4 QB0:1e5 Qb1:1e4 QB1:1e6 Qb2:1e5 QB2:1e7 FO Tv >>q_test.x
-
-echo === check precision options ${d:-`date`} >>q_test.x
-echo "rbox 100 D3 s | qhull E0.01 Qx Tcv FO" >>q_test.x
-rbox 100 D3 s | qhull E0.01 Qx Tcv FO >>q_test.x
-echo "rbox 100 D3 W1e-1 | qhull W1e-3 Tcv" >>q_test.x
-rbox 100 D3 W1e-1 | qhull W1e-3 Tcv >>q_test.x
-echo "rbox 100 D3 W1e-1 | qhull W1e-2 Tcv Q0" >>q_test.x
-rbox 100 D3 W1e-1 | qhull W1e-2 Tcv Q0 >>q_test.x
-echo "rbox 100 D3 W1e-1 | qhull W1e-2 Tcv" >>q_test.x
-rbox 100 D3 W1e-1 | qhull W1e-2 Tcv >>q_test.x
-echo "rbox 100 D3 W1e-1 | qhull W1e-1 Tcv" >>q_test.x
-rbox 100 D3 W1e-1 | qhull W1e-1 Tcv >>q_test.x
-echo "rbox 15 D2 P0 P1e-14,1e-14 | qhull d Quc Tcv" >>q_test.x
-rbox 15 D2 P0 P1e-14,1e-14 | qhull d Quc Tcv >>q_test.x
-echo "rbox 15 D3 P0 P1e-12,1e-14,1e-14 | qhull d Qcu Tcv" >>q_test.x
-rbox 15 D3 P0 P1e-12,1e-14,1e-14 | qhull d Qcu Tcv >>q_test.x
-echo "rbox 1000 s D3 | qhull C-0.01 Tcv Qc" >>q_test.x
-rbox 1000 s D3 | qhull C-0.01 Tcv Qc >>q_test.x
-echo "rbox 1000 s D3 | qhull C-0.01 V0 Qc Tcv" >>q_test.x
-rbox 1000 s D3 | qhull C-0.01 V0 Qc Tcv >>q_test.x
-echo "rbox 1000 s D3 | qhull C-0.01 U0 Qc Tcv" >>q_test.x
-rbox 1000 s D3 | qhull C-0.01 U0 Qc Tcv >>q_test.x
-echo "rbox 1000 s D3 | qhull C-0.01 V0 Qcm Tcv" >>q_test.x
-rbox 1000 s D3 | qhull C-0.01 V0 Qcm Tcv >>q_test.x
-echo "rbox 1000 s D3 | qhull C-0.01 Qcm Tcv" >>q_test.x
-rbox 1000 s D3 | qhull C-0.01 Qcm Tcv >>q_test.x
-echo "rbox 1000 s D3 | qhull C-0.01 Q1 FO Tcv Qc" >>q_test.x
-rbox 1000 s D3 | qhull C-0.01 Q1 FO Tcv Qc >>q_test.x
-echo "rbox 1000 s D3 | qhull C-0.01 Q2 FO Tcv Qc" >>q_test.x
-rbox 1000 s D3 | qhull C-0.01 Q2 FO Tcv Qc >>q_test.x
-echo "rbox 1000 s D3 | qhull C-0.01 Q3 FO Tcv Qc" >>q_test.x
-rbox 1000 s D3 | qhull C-0.01 Q3 FO Tcv Qc >>q_test.x
-echo "rbox 1000 s D3 | qhull C-0.01 Q4 FO Tcv Qc" >>q_test.x
-rbox 1000 s D3 | qhull C-0.01 Q4 FO Tcv Qc >>q_test.x
-echo === this may generate an error ${d:-`date`} >>q_test.x
-echo "rbox 1000 s D3 | qhull C-0.01 Q5 FO Tcv " >>q_test.x
-rbox 1000 s D3 | qhull C-0.01 Q5 FO Tcv >>q_test.x
-echo === this should generate an error ${d:-`date`} >>q_test.x
-echo "rbox 1000 s D3 | qhull C-0.01 Q6 FO Po Tcv Qc" >>q_test.x
-rbox 1000 s D3 | qhull C-0.01 Q6 FO Po Tcv Qc >>q_test.x
-echo "rbox 1000 s D3 | qhull C-0.01 Q7 FO Tcv Qc" >>q_test.x
-rbox 1000 s D3 | qhull C-0.01 Q7 FO Tcv Qc >>q_test.x
-echo "rbox 1000 s D3 | qhull C-0.01 Qx Tcv Qc" >>q_test.x
-rbox 1000 s D3 | qhull C-0.01 Qx Tcv Qc >>q_test.x
-echo "rbox 100 s D3 t | qhull R1e-3 Tcv Qc" >>q_test.x
-rbox 100 s D3 t | qhull R1e-3 Tcv Qc >>q_test.x
-echo "rbox 100 s D3 t | qhull R1e-2 Tcv Qc" >>q_test.x
-rbox 100 s D3 t | qhull R1e-2 Tcv Qc >>q_test.x
-echo "rbox 500 s D3 t | qhull R0.05 A-1 Tcv Qc" >>q_test.x
-rbox 500 s D3 t | qhull R0.05 A-1 Tcv Qc >>q_test.x
-echo "rbox 100 W0 D3 t | qhull R1e-3 Tcv Qc" >>q_test.x
-rbox 100 W0 D3 t | qhull R1e-3 Tcv Qc >>q_test.x
-echo "rbox 100 W0 D3 t | qhull R1e-3 Qx Tcv Qc" >>q_test.x
-rbox 100 W0 D3 t | qhull R1e-3 Qx Tcv Qc >>q_test.x
-echo "rbox 100 W0 D3 t | qhull R1e-2 Tcv Qc" >>q_test.x
-rbox 100 W0 D3 t | qhull R1e-2 Tcv Qc >>q_test.x
-echo "rbox 100 W0 D3 t | qhull R1e-2 Qx Tcv Qc" >>q_test.x
-rbox 100 W0 D3 t | qhull R1e-2 Qx Tcv Qc >>q_test.x
-echo "rbox 500 W0 D3 t | qhull R0.05 A-1 Tcv Qc" >>q_test.x
-rbox 500 W0 D3 t | qhull R0.05 A-1 Tcv Qc >>q_test.x
-echo "rbox 500 W0 D3 t | qhull R0.05 Qx Tcv Qc" >>q_test.x
-rbox 500 W0 D3 t | qhull R0.05 Qx Tcv Qc >>q_test.x
-echo "rbox 1000 W1e-20 t | qhull Tcv Qc" >>q_test.x
-rbox 1000 W1e-20 t | qhull Tcv Qc >>q_test.x
-echo "rbox 1000 W1e-20 D4 t | qhull Tcv Qc" >>q_test.x
-rbox 1000 W1e-20 D4 t | qhull Tcv Qc >>q_test.x
-echo "rbox 500 W1e-20 D5 t | qhull Tv Qc" >>q_test.x
-rbox 500 W1e-20 D5 t | qhull Tv Qc >>q_test.x
-echo "rbox 100 W1e-20 D6 t | qhull Tv Qc" >>q_test.x
-rbox 100 W1e-20 D6 t | qhull Tv Qc >>q_test.x
-echo "rbox 50 W1e-20 D6 t | qhull Qv Tv Qc" >>q_test.x
-rbox 50 W1e-20 D6 t | qhull Qv Tv Qc >>q_test.x
-echo "rbox 10000 D4 t | qhull QR0 Qc C-0.01 A0.3 Tv" >>q_test.x
-rbox 10000 D4 t | qhull QR0 Qc C-0.01 A0.3 Tv >>q_test.x
-echo "rbox 1000 D2 t | qhull d QR0 Qc C-1e-8 Qu Tv" >>q_test.x
-rbox 1000 D2 t | qhull d QR0 Qc C-1e-8 Qu Tv >>q_test.x
-echo "rbox 300 D5 t |qhull A-0.999 Qc Tcv" >>q_test.x
-rbox 300 D5 t |qhull A-0.999 Qc Tcv >>q_test.x
-echo "rbox 100 D6 t |qhull A-0.9999 Qc Tcv" >>q_test.x
-rbox 100 D6 t |qhull A-0.9999 Qc Tcv >>q_test.x
-echo "rbox 50 D7 t |qhull A-0.99999 Qc Tcv W0.1" >>q_test.x
-rbox 50 D7 t |qhull A-0.99999 Qc Tcv W0.1 >>q_test.x
-
-echo === check bad cases for Qhull. May cause errors ${d:-`date`} >>q_test.x
-echo "RBOX 1000 L100000 s G1e-6 t | QHULL Tv" >>q_test.x
-RBOX 1000 L100000 s G1e-6 t | QHULL Tv >>q_test.x
-echo "RBOX 1000 L100000 s G1e-6 t | QHULL Tv Q10" >>q_test.x
-RBOX 1000 L100000 s G1e-6 t | QHULL Tv Q10 >>q_test.x
-echo "rbox 1000 s Z1 G1e-13 t | qhull Tv" >>q_test.x
-rbox 1000 s Z1 G1e-13 t | qhull Tv >>q_test.x
-echo "RBOX 1000 s W1e-13 P0 t | QHULL d Qbb Qc Tv" >>q_test.x
-RBOX 1000 s W1e-13 P0 t | QHULL d Qbb Qc Tv >>q_test.x
-echo "RBOX 1000 s W1e-13 t | QHULL d Tv" >>q_test.x
-RBOX 1000 s W1e-13 t | QHULL d Tv >>q_test.x
-echo "RBOX 1000 s W1e-13 t D2 | QHULL d Tv" >>q_test.x
-RBOX 1000 s W1e-13 t D2 | QHULL d Tv >>q_test.x
-
-echo ======================================================= >>q_test.x
-echo ======================================================= >>q_test.x
-echo === The following commands may cause errors =========== >>q_test.x
-echo ======================================================= >>q_test.x
-echo ======================================================= >>q_test.x
-echo "rbox c D7 | qhull Q0 Tcv" >>q_test.x
-rbox c D7 | qhull Q0 Tcv >>q_test.x
-echo "rbox 100 s D3 | qhull Q0 E1e-3 Tc Po" >>q_test.x
-rbox 100 s D3 | qhull Q0 E1e-3 Tc Po >>q_test.x
-echo "rbox 100 s D3 | qhull Q0 E1e-2 Tc Po" >>q_test.x
-rbox 100 s D3 | qhull Q0 E1e-2 Tc Po >>q_test.x
-echo "rbox 100 s D3 | qhull Q0 E1e-1 Tc Po" >>q_test.x
-rbox 100 s D3 | qhull Q0 E1e-1 Tc Po >>q_test.x
-echo "rbox 100 s D3 | qhull Q0 R1e-3 Tc Po" >>q_test.x
-rbox 100 s D3 | qhull Q0 R1e-3 Tc Po >>q_test.x
-echo "rbox 100 s D3 | qhull Q0 R1e-2 Tc Po" >>q_test.x
-rbox 100 s D3 | qhull Q0 R1e-2 Tc Po >>q_test.x
-echo "rbox 100 s D3 | qhull Q0 R0.05 Tc" >>q_test.x
-rbox 100 s D3 | qhull Q0 R0.05 Tc >>q_test.x
-echo "rbox 100 s D3 | qhull Q0 R0.05 Tc Po" >>q_test.x
-rbox 100 s D3 | qhull Q0 R0.05 Tc Po >>q_test.x
-echo "rbox 1000 W1e-7 | qhull Q0 Tc Po" >>q_test.x
-rbox 1000 W1e-7 | qhull Q0 Tc Po >>q_test.x
-echo "rbox 50 s | qhull Q0 V0.05 W0.01 Tc Po" >>q_test.x
-rbox 50 s | qhull Q0 V0.05 W0.01 Tc Po >>q_test.x
-echo "rbox 100 s D5 | qhull Q0 R1e-2 Tc Po" >>q_test.x
-rbox 100 s D5 | qhull Q0 R1e-2 Tc Po >>q_test.x
-echo "qhull" >>q_test.x
-qhull >>q_test.x
-echo "qhull ." >>q_test.x
-qhull . >>q_test.x
-echo "qhull -" >>q_test.x
-qhull - >>q_test.x
-echo "rbox" >>q_test.x
-rbox >>q_test.x
-
-echo "# end of q_test" >>q_test.x
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/qconvex.c b/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/qconvex.c
deleted file mode 100644
index dbd89339d9cbe86d931cefd6ab9ef1dc46978559..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/qconvex.c
+++ /dev/null
@@ -1,334 +0,0 @@
-/*<html><pre> -<a href="qh-qhull.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- qconvex.c
- compute convex hulls using qhull
-
- see unix.c for full interface
-
- copyright (c) 1993-2003, The Geometry Center
-*/
-
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-#include <ctype.h>
-#include <math.h>
-#include "qhull.h"
-#include "mem.h"
-#include "qset.h"
-
-#if __MWERKS__ && __POWERPC__
-#include <SIOUX.h>
-#include <Files.h>
-#include <console.h>
-#include <Desk.h>
-
-#elif __cplusplus
-extern "C" {
- int isatty (int);
-}
-
-#elif _MSC_VER
-#include <io.h>
-#define isatty _isatty
-
-#else
-int isatty (int); /* returns 1 if stdin is a tty
- if "Undefined symbol" this can be deleted along with call in main() */
-#endif
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="prompt">-</a>
-
- qh_prompt
- long prompt for qconvex
-
- notes:
- restricted version of qhull.c
-
- see:
- concise prompt below
-*/
-
-/* duplicated in qconvex.htm */
-char hidden_options[]=" d v H Qbb Qf Qg Qm Qr Qu Qv Qx Qz TR E V Fp Gt Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";
-
-char qh_prompta[]= "\n\
-qconvex- compute the convex hull\n\
- http://www.qhull.org %s\n\
-\n\
-input (stdin):\n\
- first lines: dimension and number of points (or vice-versa).\n\
- other lines: point coordinates, best if one point per line\n\
- comments: start with a non-numeric character\n\
-\n\
-options:\n\
- Qt - triangulated output\n\
- QJ - joggled input instead of merged facets\n\
- Qc - keep coplanar points with nearest facet\n\
- Qi - keep interior points with nearest facet\n\
-\n\
-Qhull control options:\n\
- Qbk:n - scale coord k so that low bound is n\n\
- QBk:n - scale coord k so that upper bound is n (QBk is %2.2g)\n\
- QbB - scale input to unit cube centered at the origin\n\
- Qbk:0Bk:0 - remove k-th coordinate from input\n\
- QJn - randomly joggle input in range [-n,n]\n\
- QRn - random rotation (n=seed, n=0 time, n=-1 time/no rotate)\n\
-%s%s%s%s"; /* split up qh_prompt for Visual C++ */
-char qh_promptb[]= "\
- Qs - search all points for the initial simplex\n\
- QGn - good facet if visible from point n, -n for not visible\n\
- QVn - good facet if it includes point n, -n if not\n\
-\n\
-";
-char qh_promptc[]= "\
-Trace options:\n\
- T4 - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
- Tc - check frequently during execution\n\
- Ts - print statistics\n\
- Tv - verify result: structure, convexity, and point inclusion\n\
- Tz - send all output to stdout\n\
- TFn - report summary when n or more facets created\n\
- TI file - input data from file, no spaces or single quotes\n\
- TO file - output results to file, may be enclosed in single quotes\n\
- TPn - turn on tracing when point n added to hull\n\
- TMn - turn on tracing at merge n\n\
- TWn - trace merge facets when width > n\n\
- TVn - stop qhull after adding point n, -n for before (see TCn)\n\
- TCn - stop qhull after building cone for point n (see TVn)\n\
-\n\
-Precision options:\n\
- Cn - radius of centrum (roundoff added). Merge facets if non-convex\n\
- An - cosine of maximum angle. Merge facets if cosine > n or non-convex\n\
- C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
- Rn - randomly perturb computations by a factor of [1-n,1+n]\n\
- Un - max distance below plane for a new, coplanar point\n\
- Wn - min facet width for outside point (before roundoff)\n\
-\n\
-Output formats (may be combined; if none, produces a summary to stdout):\n\
- f - facet dump\n\
- G - Geomview output (see below)\n\
- i - vertices incident to each facet\n\
- m - Mathematica output (2-d and 3-d)\n\
- n - normals with offsets\n\
- o - OFF file format (dim, points and facets; Voronoi regions)\n\
- p - point coordinates \n\
- s - summary (stderr)\n\
-\n\
-";
-char qh_promptd[]= "\
-More formats:\n\
- Fa - area for each facet\n\
- FA - compute total area and volume for option 's'\n\
- Fc - count plus coplanar points for each facet\n\
- use 'Qc' (default) for coplanar and 'Qi' for interior\n\
- FC - centrum for each facet\n\
- Fd - use cdd format for input (homogeneous with offset first)\n\
- FD - use cdd format for numeric output (offset first)\n\
- FF - facet dump without ridges\n\
- Fi - inner plane for each facet\n\
- FI - ID for each facet\n\
- Fm - merge count for each facet (511 max)\n\
- Fn - count plus neighboring facets for each facet\n\
- FN - count plus neighboring facets for each point\n\
- Fo - outer plane (or max_outside) for each facet\n\
- FO - options and precision constants\n\
- FP - nearest vertex for each coplanar point\n\
- FQ - command used for qconvex\n\
- Fs - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
- for output: #vertices, #facets,\n\
- #coplanar points, #non-simplicial facets\n\
- #real (2), max outer plane, min vertex\n\
- FS - sizes: #int (0) \n\
- #real(2) tot area, tot volume\n\
- Ft - triangulation with centrums for non-simplicial facets (OFF format)\n\
- Fv - count plus vertices for each facet\n\
- FV - average of vertices (a feasible point for 'H')\n\
- Fx - extreme points (in order for 2-d)\n\
-\n\
-";
-char qh_prompte[]= "\
-Geomview output (2-d, 3-d, and 4-d)\n\
- Ga - all points as dots\n\
- Gp - coplanar points and vertices as radii\n\
- Gv - vertices as spheres\n\
- Gi - inner planes only\n\
- Gn - no planes\n\
- Go - outer planes only\n\
- Gc - centrums\n\
- Gh - hyperplane intersections\n\
- Gr - ridges\n\
- GDn - drop dimension n in 3-d and 4-d output\n\
-\n\
-Print options:\n\
- PAn - keep n largest facets by area\n\
- Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
- PDk:n - drop facet if normal[k] >= n\n\
- Pg - print good facets (needs 'QGn' or 'QVn')\n\
- PFn - keep facets whose area is at least n\n\
- PG - print neighbors of good facets\n\
- PMn - keep n facets with most merges\n\
- Po - force output. If error, output neighborhood of facet\n\
- Pp - do not report precision problems\n\
-\n\
- . - list of all options\n\
- - - one line descriptions of all options\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="prompt2">-</a>
-
- qh_prompt2
- synopsis for qhull
-*/
-char qh_prompt2[]= "\n\
-qconvex- compute the convex hull. Qhull %s\n\
- input (stdin): dimension, number of points, point coordinates\n\
- comments start with a non-numeric character\n\
-\n\
-options (qconvex.htm):\n\
- Qt - triangulated output\n\
- QJ - joggled input instead of merged facets\n\
- Tv - verify result: structure, convexity, and point inclusion\n\
- . - concise list of all options\n\
- - - one-line description of all options\n\
-\n\
-output options (subset):\n\
- s - summary of results (default)\n\
- i - vertices incident to each facet\n\
- n - normals with offsets\n\
- p - vertex coordinates (includes coplanar points if 'Qc')\n\
- Fx - extreme points (convex hull vertices)\n\
- FA - compute total area and volume\n\
- o - OFF format (dim, n, points, facets)\n\
- G - Geomview output (2-d, 3-d, and 4-d)\n\
- m - Mathematica output (2-d and 3-d)\n\
- QVn - print facets that include point n, -n if not\n\
- TO file- output results to file, may be enclosed in single quotes\n\
-\n\
-examples:\n\
- rbox c D2 | qconvex s n rbox c D2 | qconvex i\n\
- rbox c D2 | qconvex o rbox 1000 s | qconvex s Tv FA\n\
- rbox c d D2 | qconvex s Qc Fx rbox y 1000 W0 | qconvex s n\n\
- rbox y 1000 W0 | qconvex s QJ rbox d G1 D12 | qconvex QR0 FA Pp\n\
- rbox c D7 | qconvex FA TF1000\n\
-\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="prompt3">-</a>
-
- qh_prompt3
- concise prompt for qhull
-*/
-char qh_prompt3[]= "\n\
-Qhull %s.\n\
-Except for 'F.' and 'PG', upper-case options take an argument.\n\
-\n\
- incidences mathematica normals OFF_format points\n\
- summary facet_dump\n\
-\n\
- Farea FArea_total Fcoplanars FCentrums Fd_cdd_in\n\
- FD_cdd_out FFacet_xridge Finner FIDs Fmerges\n\
- Fneighbors FNeigh_vertex Fouter FOptions FPoint_near\n\
- FQhull Fsummary FSize Fvertices FVertex_ave\n\
- Fxtremes FMaple\n\
-\n\
- Gvertices Gpoints Gall_points Gno_planes Ginner\n\
- Gcentrums Ghyperplanes Gridges Gouter GDrop_dim\n\
-\n\
- PArea_keep Pdrop d0:0D0 PFacet_area_keep Pgood PGood_neighbors\n\
- PMerge_keep Poutput_forced Pprecision_not\n\
-\n\
- QbBound 0:0.5 QbB_scale_box Qcoplanar QGood_point Qinterior\n\
- QJoggle Qrandom QRotate Qsearch_1st Qtriangulate\n\
- QVertex_good\n\
-\n\
- T4_trace Tcheck_often Tstatistics Tverify Tz_stdout\n\
- TFacet_log TInput_file TPoint_trace TMerge_trace TOutput_file\n\
- TWide_trace TVertex_stop TCone_stop\n\
-\n\
- Angle_max Centrum_size Random_dist Ucoplanar_max Wide_outside\n\
-";
-
-/*-<a href="qh-qhull.htm"
- >-------------------------------</a><a name="main">-</a>
-
- main( argc, argv )
- processes the command line, calls qhull() to do the work, and exits
-
- design:
- initializes data structures
- reads points
- finishes initialization
- computes convex hull and other structures
- checks the result
- writes the output
- frees memory
-*/
-int main(int argc, char *argv[]) {
- int curlong, totlong; /* used !qh_NOmem */
- int exitcode, numpoints, dim;
- coordT *points;
- boolT ismalloc;
-
-#if __MWERKS__ && __POWERPC__
- char inBuf[BUFSIZ], outBuf[BUFSIZ], errBuf[BUFSIZ];
- SIOUXSettings.showstatusline= false;
- SIOUXSettings.tabspaces= 1;
- SIOUXSettings.rows= 40;
- if (setvbuf (stdin, inBuf, _IOFBF, sizeof(inBuf)) < 0 /* w/o, SIOUX I/O is slow*/
- || setvbuf (stdout, outBuf, _IOFBF, sizeof(outBuf)) < 0
- || (stdout != stderr && setvbuf (stderr, errBuf, _IOFBF, sizeof(errBuf)) < 0))
- fprintf (stderr, "qhull internal warning (main): could not change stdio to fully buffered.\n");
- argc= ccommand(&argv);
-#endif
-
- if ((argc == 1) && isatty( 0 /*stdin*/)) {
- fprintf(stdout, qh_prompt2, qh_version);
- exit(qh_ERRnone);
- }
- if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
- fprintf(stdout, qh_prompta, qh_version, qh_DEFAULTbox,
- qh_promptb, qh_promptc, qh_promptd, qh_prompte);
- exit(qh_ERRnone);
- }
- if (argc >1 && *argv[1] == '.' && !*(argv[1]+1)) {
- fprintf(stdout, qh_prompt3, qh_version);
- exit(qh_ERRnone);
- }
- qh_init_A (stdin, stdout, stderr, argc, argv); /* sets qh qhull_command */
- exitcode= setjmp (qh errexit); /* simple statement for CRAY J916 */
- if (!exitcode) {
- qh_checkflags (qh qhull_command, hidden_options);
- qh_initflags (qh qhull_command);
- points= qh_readpoints (&numpoints, &dim, &ismalloc);
- if (dim >= 5) {
- qh_option ("Qxact_merge", NULL, NULL);
- qh MERGEexact= True; /* 'Qx' always */
- }
- qh_init_B (points, numpoints, dim, ismalloc);
- qh_qhull();
- qh_check_output();
- qh_produce_output();
- if (qh VERIFYoutput && !qh FORCEoutput && !qh STOPpoint && !qh STOPcone)
- qh_check_points();
- exitcode= qh_ERRnone;
- }
- qh NOerrexit= True; /* no more setjmp */
-#ifdef qh_NOmem
- qh_freeqhull( True);
-#else
- qh_freeqhull( False);
- qh_memfreeshort (&curlong, &totlong);
- if (curlong || totlong)
- fprintf (stderr, "qhull internal warning (main): did not free %d bytes of long memory (%d pieces)\n",
- totlong, curlong);
-#endif
- return exitcode;
-} /* main */
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/qdelaun.c b/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/qdelaun.c
deleted file mode 100644
index 68620fa1a9704f494cb214a6e7898df822d54cd3..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/qdelaun.c
+++ /dev/null
@@ -1,324 +0,0 @@
-/*<html><pre> -<a href="qh-qhull.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- qdelaun.c
- compute Delaunay triangulations and furthest-point Delaunay
- triangulations using qhull
-
- see unix.c for full interface
-
- copyright (c) 1993-2003, The Geometry Center
-*/
-
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-#include <ctype.h>
-#include <math.h>
-#include "qhull.h"
-#include "mem.h"
-#include "qset.h"
-
-#if __MWERKS__ && __POWERPC__
-#include <SIOUX.h>
-#include <Files.h>
-#include <console.h>
-#include <Desk.h>
-
-#elif __cplusplus
-extern "C" {
- int isatty (int);
-}
-
-#elif _MSC_VER
-#include <io.h>
-#define isatty _isatty
-
-#else
-int isatty (int); /* returns 1 if stdin is a tty
- if "Undefined symbol" this can be deleted along with call in main() */
-#endif
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="prompt">-</a>
-
- qh_prompt
- long prompt for qhull
-
- notes:
- restricted version of qhull.c
-
- see:
- concise prompt below
-*/
-
-/* duplicated in qdelau_f.htm and qdelaun.htm */
-char hidden_options[]=" d n v H U Qb QB Qc Qf Qg Qi Qm Qr QR Qv Qx TR E V FC Fi Fo Ft Fp FV Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";
-
-char qh_prompta[]= "\n\
-qdelaunay- compute the Delaunay triangulation\n\
- http://www.qhull.org %s\n\
-\n\
-input (stdin):\n\
- first lines: dimension and number of points (or vice-versa).\n\
- other lines: point coordinates, best if one point per line\n\
- comments: start with a non-numeric character\n\
-\n\
-options:\n\
- Qu - compute furthest-site Delaunay triangulation\n\
- Qt - triangulated output\n\
- QJ - joggled input instead of merged facets\n\
-\n\
-Qhull control options:\n\
- QJn - randomly joggle input in range [-n,n]\n\
-%s%s%s%s"; /* split up qh_prompt for Visual C++ */
-char qh_promptb[]= "\
- Qs - search all points for the initial simplex\n\
- Qz - add point-at-infinity to Delaunay triangulation\n\
- QGn - print Delaunay region if visible from point n, -n if not\n\
- QVn - print Delaunay regions that include point n, -n if not\n\
-\n\
-";
-char qh_promptc[]= "\
-Trace options:\n\
- T4 - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
- Tc - check frequently during execution\n\
- Ts - print statistics\n\
- Tv - verify result: structure, convexity, and in-circle test\n\
- Tz - send all output to stdout\n\
- TFn - report summary when n or more facets created\n\
- TI file - input data from file, no spaces or single quotes\n\
- TO file - output results to file, may be enclosed in single quotes\n\
- TPn - turn on tracing when point n added to hull\n\
- TMn - turn on tracing at merge n\n\
- TWn - trace merge facets when width > n\n\
- TVn - stop qhull after adding point n, -n for before (see TCn)\n\
- TCn - stop qhull after building cone for point n (see TVn)\n\
-\n\
-Precision options:\n\
- Cn - radius of centrum (roundoff added). Merge facets if non-convex\n\
- An - cosine of maximum angle. Merge facets if cosine > n or non-convex\n\
- C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
- Rn - randomly perturb computations by a factor of [1-n,1+n]\n\
- Wn - min facet width for outside point (before roundoff)\n\
-\n\
-Output formats (may be combined; if none, produces a summary to stdout):\n\
- f - facet dump\n\
- G - Geomview output (see below)\n\
- i - vertices incident to each Delaunay region\n\
- m - Mathematica output (2-d only, lifted to a paraboloid)\n\
- o - OFF format (dim, points, and facets as a paraboloid)\n\
- p - point coordinates (lifted to a paraboloid)\n\
- s - summary (stderr)\n\
-\n\
-";
-char qh_promptd[]= "\
-More formats:\n\
- Fa - area for each Delaunay region\n\
- FA - compute total area for option 's'\n\
- Fc - count plus coincident points for each Delaunay region\n\
- Fd - use cdd format for input (homogeneous with offset first)\n\
- FD - use cdd format for numeric output (offset first)\n\
- FF - facet dump without ridges\n\
- FI - ID of each Delaunay region\n\
- Fm - merge count for each Delaunay region (511 max)\n\
- FM - Maple output (2-d only, lifted to a paraboloid)\n\
- Fn - count plus neighboring region for each Delaunay region\n\
- FN - count plus neighboring region for each point\n\
- FO - options and precision constants\n\
- FP - nearest point and distance for each coincident point\n\
- FQ - command used for qdelaunay\n\
- Fs - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
- for output: #vertices, #Delaunay regions,\n\
- #coincident points, #non-simplicial regions\n\
- #real (2), max outer plane, min vertex\n\
- FS - sizes: #int (0)\n\
- #real(2) tot area, 0\n\
- Fv - count plus vertices for each Delaunay region\n\
- Fx - extreme points of Delaunay triangulation (on convex hull)\n\
-\n\
-";
-char qh_prompte[]= "\
-Geomview options (2-d and 3-d)\n\
- Ga - all points as dots\n\
- Gp - coplanar points and vertices as radii\n\
- Gv - vertices as spheres\n\
- Gi - inner planes only\n\
- Gn - no planes\n\
- Go - outer planes only\n\
- Gc - centrums\n\
- Gh - hyperplane intersections\n\
- Gr - ridges\n\
- GDn - drop dimension n in 3-d and 4-d output\n\
- Gt - transparent outer ridges to view 3-d Delaunay\n\
-\n\
-Print options:\n\
- PAn - keep n largest Delaunay regions by area\n\
- Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
- PDk:n - drop facet if normal[k] >= n\n\
- Pg - print good Delaunay regions (needs 'QGn' or 'QVn')\n\
- PFn - keep Delaunay regions whose area is at least n\n\
- PG - print neighbors of good regions (needs 'QGn' or 'QVn')\n\
- PMn - keep n Delaunay regions with most merges\n\
- Po - force output. If error, output neighborhood of facet\n\
- Pp - do not report precision problems\n\
-\n\
- . - list of all options\n\
- - - one line descriptions of all options\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="prompt2">-</a>
-
- qh_prompt2
- synopsis for qhull
-*/
-char qh_prompt2[]= "\n\
-qdelaunay- compute the Delaunay triangulation. Qhull %s\n\
- input (stdin): dimension, number of points, point coordinates\n\
- comments start with a non-numeric character\n\
-\n\
-options (qdelaun.htm):\n\
- Qu - furthest-site Delaunay triangulation\n\
- Qt - triangulated output\n\
- QJ - joggled input instead of merged facets\n\
- Tv - verify result: structure, convexity, and in-circle test\n\
- . - concise list of all options\n\
- - - one-line description of all options\n\
-\n\
-output options (subset):\n\
- s - summary of results (default)\n\
- i - vertices incident to each Delaunay region\n\
- Fx - extreme points (vertices of the convex hull)\n\
- o - OFF format (shows the points lifted to a paraboloid)\n\
- G - Geomview output (2-d and 3-d points lifted to a paraboloid)\n\
- m - Mathematica output (2-d inputs lifted to a paraboloid)\n\
- QVn - print Delaunay regions that include point n, -n if not\n\
- TO file- output results to file, may be enclosed in single quotes\n\
-\n\
-examples:\n\
- rbox c P0 D2 | qdelaunay s o rbox c P0 D2 | qdelaunay i\n\
- rbox c P0 D2 | qdelaunay Fv rbox c P0 D2 | qdelaunay s Qu Fv\n\
- rbox c G1 d D2 | qdelaunay s i rbox c G1 d D2 | qdelaunay Qt\n\
- rbox M3,4 z 100 D2 | qdelaunay s rbox M3,4 z 100 D2 | qdelaunay s Qt\n\
-\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="prompt3">-</a>
-
- qh_prompt3
- concise prompt for qhull
-*/
-char qh_prompt3[]= "\n\
-Qhull %s.\n\
-Except for 'F.' and 'PG', upper-case options take an argument.\n\
-\n\
- incidences mathematica OFF_format points_lifted summary\n\
- facet_dump\n\
-\n\
- Farea FArea_total Fcoincident Fd_cdd_in FD_cdd_out\n\
- FF_dump_xridge FIDs Fmerges Fneighbors FNeigh_vertex\n\
- FOptions FPoint_near FQdelaun Fsummary FSize\n\
- Fvertices Fxtremes FMaple\n\
-\n\
- Gvertices Gpoints Gall_points Gno_planes Ginner\n\
- Gcentrums Ghyperplanes Gridges Gouter GDrop_dim\n\
- Gtransparent\n\
-\n\
- PArea_keep Pdrop d0:0D0 Pgood PFacet_area_keep\n\
- PGood_neighbors PMerge_keep Poutput_forced Pprecision_not\n\
-\n\
- QGood_point QJoggle Qsearch_1st Qtriangulate QupperDelaunay\n\
- QVertex_good Qzinfinite\n\
-\n\
- T4_trace Tcheck_often Tstatistics Tverify Tz_stdout\n\
- TFacet_log TInput_file TPoint_trace TMerge_trace TOutput_file\n\
- TWide_trace TVertex_stop TCone_stop\n\
-\n\
- Angle_max Centrum_size Random_dist Wide_outside\n\
-";
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="main">-</a>
-
- main( argc, argv )
- processes the command line, calls qhull() to do the work, and exits
-
- design:
- initializes data structures
- reads points
- finishes initialization
- computes convex hull and other structures
- checks the result
- writes the output
- frees memory
-*/
-int main(int argc, char *argv[]) {
- int curlong, totlong; /* used !qh_NOmem */
- int exitcode, numpoints, dim;
- coordT *points;
- boolT ismalloc;
-
-#if __MWERKS__ && __POWERPC__
- char inBuf[BUFSIZ], outBuf[BUFSIZ], errBuf[BUFSIZ];
- SIOUXSettings.showstatusline= false;
- SIOUXSettings.tabspaces= 1;
- SIOUXSettings.rows= 40;
- if (setvbuf (stdin, inBuf, _IOFBF, sizeof(inBuf)) < 0 /* w/o, SIOUX I/O is slow*/
- || setvbuf (stdout, outBuf, _IOFBF, sizeof(outBuf)) < 0
- || (stdout != stderr && setvbuf (stderr, errBuf, _IOFBF, sizeof(errBuf)) < 0))
- fprintf (stderr, "qhull internal warning (main): could not change stdio to fully buffered.\n");
- argc= ccommand(&argv);
-#endif
-
- if ((argc == 1) && isatty( 0 /*stdin*/)) {
- fprintf(stdout, qh_prompt2, qh_version);
- exit(qh_ERRnone);
- }
- if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
- fprintf(stdout, qh_prompta, qh_version,
- qh_promptb, qh_promptc, qh_promptd, qh_prompte);
- exit(qh_ERRnone);
- }
- if (argc >1 && *argv[1] == '.' && !*(argv[1]+1)) {
- fprintf(stdout, qh_prompt3, qh_version);
- exit(qh_ERRnone);
- }
- qh_init_A (stdin, stdout, stderr, argc, argv); /* sets qh qhull_command */
- exitcode= setjmp (qh errexit); /* simple statement for CRAY J916 */
- if (!exitcode) {
- qh_option ("delaunay Qbbound-last", NULL, NULL);
- qh DELAUNAY= True; /* 'd' */
- qh SCALElast= True; /* 'Qbb' */
- qh KEEPcoplanar= True; /* 'Qc', to keep coplanars in 'p' */
- qh_checkflags (qh qhull_command, hidden_options);
- qh_initflags (qh qhull_command);
- points= qh_readpoints (&numpoints, &dim, &ismalloc);
- if (dim >= 5) {
- qh_option ("Qxact_merge", NULL, NULL);
- qh MERGEexact= True; /* 'Qx' always */
- }
- qh_init_B (points, numpoints, dim, ismalloc);
- qh_qhull();
- qh_check_output();
- qh_produce_output();
- if (qh VERIFYoutput && !qh FORCEoutput && !qh STOPpoint && !qh STOPcone)
- qh_check_points();
- exitcode= qh_ERRnone;
- }
- qh NOerrexit= True; /* no more setjmp */
-#ifdef qh_NOmem
- qh_freeqhull( True);
-#else
- qh_freeqhull( False);
- qh_memfreeshort (&curlong, &totlong);
- if (curlong || totlong)
- fprintf (stderr, "qhull internal warning (main): did not free %d bytes of long memory (%d pieces)\n",
- totlong, curlong);
-#endif
- return exitcode;
-} /* main */
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/qhalf.c b/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/qhalf.c
deleted file mode 100644
index 0996c545e1263b4263f0b3d61c74620507383844..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/qhalf.c
+++ /dev/null
@@ -1,325 +0,0 @@
-/*<html><pre> -<a href="qh-qhull.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- qhalf.c
- compute the intersection of halfspaces about a point
-
- see unix.c for full interface
-
- copyright (c) 1993-2003, The Geometry Center
-*/
-
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-#include <ctype.h>
-#include <math.h>
-#include "qhull.h"
-#include "mem.h"
-#include "qset.h"
-
-#if __MWERKS__ && __POWERPC__
-#include <SIOUX.h>
-#include <Files.h>
-#include <console.h>
-#include <Desk.h>
-
-#elif __cplusplus
-extern "C" {
- int isatty (int);
-}
-
-#elif _MSC_VER
-#include <io.h>
-#define isatty _isatty
-
-#else
-int isatty (int); /* returns 1 if stdin is a tty
- if "Undefined symbol" this can be deleted along with call in main() */
-#endif
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="prompt">-</a>
-
- qh_prompt
- long prompt for qhull
-
- notes:
- restricted version of qhull.c
-
- see:
- concise prompt below
-*/
-
-/* duplicated in qhalf.htm */
-char hidden_options[]=" d n v Qbb QbB Qf Qg Qm Qr QR Qv Qx Qz TR E V Fa FA FC FD FS Ft FV Gt Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";
-
-char qh_prompta[]= "\n\
-qhalf- compute the intersection of halfspaces about a point\n\
- http://www.qhull.org %s\n\
-\n\
-input (stdin):\n\
- optional interior point: dimension, 1, coordinates\n\
- first lines: dimension+1 and number of halfspaces\n\
- other lines: halfspace coefficients followed by offset\n\
- comments: start with a non-numeric character\n\
-\n\
-options:\n\
- Hn,n - specify coordinates of interior point\n\
- Qt - triangulated output\n\
- QJ - joggled input instead of merged facets\n\
- Qc - keep coplanar halfspaces\n\
- Qi - keep other redundant halfspaces\n\
-\n\
-Qhull control options:\n\
- QJn - randomly joggle input in range [-n,n]\n\
-%s%s%s%s"; /* split up qh_prompt for Visual C++ */
-char qh_promptb[]= "\
- Qbk:0Bk:0 - remove k-th coordinate from input\n\
- Qs - search all halfspaces for the initial simplex\n\
- QGn - print intersection if visible to halfspace n, -n for not\n\
- QVn - print intersections for halfspace n, -n if not\n\
-\n\
-";
-char qh_promptc[]= "\
-Trace options:\n\
- T4 - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
- Tc - check frequently during execution\n\
- Ts - print statistics\n\
- Tv - verify result: structure, convexity, and redundancy\n\
- Tz - send all output to stdout\n\
- TFn - report summary when n or more facets created\n\
- TI file - input data from file, no spaces or single quotes\n\
- TO file - output results to file, may be enclosed in single quotes\n\
- TPn - turn on tracing when halfspace n added to intersection\n\
- TMn - turn on tracing at merge n\n\
- TWn - trace merge facets when width > n\n\
- TVn - stop qhull after adding halfspace n, -n for before (see TCn)\n\
- TCn - stop qhull after building cone for halfspace n (see TVn)\n\
-\n\
-Precision options:\n\
- Cn - radius of centrum (roundoff added). Merge facets if non-convex\n\
- An - cosine of maximum angle. Merge facets if cosine > n or non-convex\n\
- C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
- Rn - randomly perturb computations by a factor of [1-n,1+n]\n\
- Un - max distance below plane for a new, coplanar halfspace\n\
- Wn - min facet width for outside halfspace (before roundoff)\n\
-\n\
-Output formats (may be combined; if none, produces a summary to stdout):\n\
- f - facet dump\n\
- G - Geomview output (dual convex hull)\n\
- i - non-redundant halfspaces incident to each intersection\n\
- m - Mathematica output (dual convex hull)\n\
- o - OFF format (dual convex hull: dimension, points, and facets)\n\
- p - vertex coordinates of dual convex hull (coplanars if 'Qc' or 'Qi')\n\
- s - summary (stderr)\n\
-\n\
-";
-char qh_promptd[]= "\
-More formats:\n\
- Fc - count plus redundant halfspaces for each intersection\n\
- - Qc (default) for coplanar and Qi for other redundant\n\
- Fd - use cdd format for input (homogeneous with offset first)\n\
- FF - facet dump without ridges\n\
- FI - ID of each intersection\n\
- Fm - merge count for each intersection (511 max)\n\
- FM - Maple output (dual convex hull)\n\
- Fn - count plus neighboring intersections for each intersection\n\
- FN - count plus intersections for each non-redundant halfspace\n\
- FO - options and precision constants\n\
- Fp - dim, count, and intersection coordinates\n\
- FP - nearest halfspace and distance for each redundant halfspace\n\
- FQ - command used for qhalf\n\
- Fs - summary: #int (8), dim, #halfspaces, #non-redundant, #intersections\n\
- for output: #non-redundant, #intersections, #coplanar\n\
- halfspaces, #non-simplicial intersections\n\
- #real (2), max outer plane, min vertex\n\
- Fv - count plus non-redundant halfspaces for each intersection\n\
- Fx - non-redundant halfspaces\n\
-\n\
-";
-char qh_prompte[]= "\
-Geomview output (2-d, 3-d and 4-d; dual convex hull)\n\
- Ga - all points (i.e., transformed halfspaces) as dots\n\
- Gp - coplanar points and vertices as radii\n\
- Gv - vertices (i.e., non-redundant halfspaces) as spheres\n\
- Gi - inner planes (i.e., halfspace intersections) only\n\
- Gn - no planes\n\
- Go - outer planes only\n\
- Gc - centrums\n\
- Gh - hyperplane intersections\n\
- Gr - ridges\n\
- GDn - drop dimension n in 3-d and 4-d output\n\
-\n\
-Print options:\n\
- PAn - keep n largest facets (i.e., intersections) by area\n\
- Pdk:n- drop facet if normal[k] <= n (default 0.0)\n\
- PDk:n- drop facet if normal[k] >= n\n\
- Pg - print good facets (needs 'QGn' or 'QVn')\n\
- PFn - keep facets whose area is at least n\n\
- PG - print neighbors of good facets\n\
- PMn - keep n facets with most merges\n\
- Po - force output. If error, output neighborhood of facet\n\
- Pp - do not report precision problems\n\
-\n\
- . - list of all options\n\
- - - one line descriptions of all options\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="prompt2">-</a>
-
- qh_prompt2
- synopsis for qhull
-*/
-char qh_prompt2[]= "\n\
-qhalf- halfspace intersection about a point. Qhull %s\n\
- input (stdin): [dim, 1, interior point], dim+1, n, coefficients+offset\n\
- comments start with a non-numeric character\n\
-\n\
-options (qhalf.htm):\n\
- Hn,n - specify coordinates of interior point\n\
- Qt - triangulated output\n\
- QJ - joggled input instead of merged facets\n\
- Tv - verify result: structure, convexity, and redundancy\n\
- . - concise list of all options\n\
- - - one-line description of all options\n\
-\n\
-output options (subset):\n\
- s - summary of results (default)\n\
- Fp - intersection coordinates\n\
- Fv - non-redundant halfspaces incident to each intersection\n\
- Fx - non-redundant halfspaces\n\
- o - OFF file format (dual convex hull)\n\
- G - Geomview output (dual convex hull)\n\
- m - Mathematica output (dual convex hull)\n\
- QVn - print intersections for halfspace n, -n if not\n\
- TO file - output results to file, may be enclosed in single quotes\n\
-\n\
-examples:\n\
- rbox d | qconvex FQ n | qhalf s H0,0,0 Fp\n\
- rbox c | qconvex FQ FV n | qhalf s i\n\
- rbox c | qconvex FQ FV n | qhalf s o\n\
-\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="prompt3">-</a>
-
- qh_prompt3
- concise prompt for qhull
-*/
-char qh_prompt3[]= "\n\
-Qhull %s.\n\
-Except for 'F.' and 'PG', upper_case options take an argument.\n\
-\n\
- incidences Geomview mathematica OFF_format point_dual\n\
- summary facet_dump\n\
-\n\
- Fc_redundant Fd_cdd_in FF_dump_xridge FIDs Fmerges\n\
- Fneighbors FN_intersect FOptions Fp_coordinates FP_nearest\n\
- FQhalf Fsummary Fv_halfspace FMaple Fx_non_redundant\n\
-\n\
- Gvertices Gpoints Gall_points Gno_planes Ginner\n\
- Gcentrums Ghyperplanes Gridges Gouter GDrop_dim\n\
-\n\
- PArea_keep Pdrop d0:0D0 Pgood PFacet_area_keep\n\
- PGood_neighbors PMerge_keep Poutput_forced Pprecision_not\n\
-\n\
- Qbk:0Bk:0_drop Qcoplanar QG_half_good Qi_redundant QJoggle\n\
- Qsearch_1st Qtriangulate QVertex_good\n\
-\n\
- T4_trace Tcheck_often Tstatistics Tverify Tz_stdout\n\
- TFacet_log TInput_file TPoint_trace TMerge_trace TOutput_file\n\
- TWide_trace TVertex_stop TCone_stop\n\
-\n\
- Angle_max Centrum_size Random_dist Ucoplanar_max Wide_outside\n\
-";
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="main">-</a>
-
- main( argc, argv )
- processes the command line, calls qhull() to do the work, and exits
-
- design:
- initializes data structures
- reads points
- finishes initialization
- computes convex hull and other structures
- checks the result
- writes the output
- frees memory
-*/
-int main(int argc, char *argv[]) {
- int curlong, totlong; /* used !qh_NOmem */
- int exitcode, numpoints, dim;
- coordT *points;
- boolT ismalloc;
-
-#if __MWERKS__ && __POWERPC__
- char inBuf[BUFSIZ], outBuf[BUFSIZ], errBuf[BUFSIZ];
- SIOUXSettings.showstatusline= false;
- SIOUXSettings.tabspaces= 1;
- SIOUXSettings.rows= 40;
- if (setvbuf (stdin, inBuf, _IOFBF, sizeof(inBuf)) < 0 /* w/o, SIOUX I/O is slow*/
- || setvbuf (stdout, outBuf, _IOFBF, sizeof(outBuf)) < 0
- || (stdout != stderr && setvbuf (stderr, errBuf, _IOFBF, sizeof(errBuf)) < 0))
- fprintf (stderr, "qhull internal warning (main): could not change stdio to fully buffered.\n");
- argc= ccommand(&argv);
-#endif
-
- if ((argc == 1) && isatty( 0 /*stdin*/)) {
- fprintf(stdout, qh_prompt2, qh_version);
- exit(qh_ERRnone);
- }
- if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
- fprintf(stdout, qh_prompta, qh_version,
- qh_promptb, qh_promptc, qh_promptd, qh_prompte);
- exit(qh_ERRnone);
- }
- if (argc >1 && *argv[1] == '.' && !*(argv[1]+1)) {
- fprintf(stdout, qh_prompt3, qh_version);
- exit(qh_ERRnone);
- }
- qh_init_A (stdin, stdout, stderr, argc, argv); /* sets qh qhull_command */
- exitcode= setjmp (qh errexit); /* simple statement for CRAY J916 */
- if (!exitcode) {
- qh_option ("Halfspace", NULL, NULL);
- qh HALFspace= True; /* 'H' */
- qh_checkflags (qh qhull_command, hidden_options);
- qh_initflags (qh qhull_command);
- if (qh SCALEinput) {
- fprintf(qh ferr, "\
-qhull error: options 'Qbk:n' and 'QBk:n' are not used with qhalf.\n\
- Use 'Qbk:0Bk:0 to drop dimension k.\n");
- qh_errexit(qh_ERRinput, NULL, NULL);
- }
- points= qh_readpoints (&numpoints, &dim, &ismalloc);
- if (dim >= 5) {
- qh_option ("Qxact_merge", NULL, NULL);
- qh MERGEexact= True; /* 'Qx' always */
- }
- qh_init_B (points, numpoints, dim, ismalloc);
- qh_qhull();
- qh_check_output();
- qh_produce_output();
- if (qh VERIFYoutput && !qh FORCEoutput && !qh STOPpoint && !qh STOPcone)
- qh_check_points();
- exitcode= qh_ERRnone;
- }
- qh NOerrexit= True; /* no more setjmp */
-#ifdef qh_NOmem
- qh_freeqhull( True);
-#else
- qh_freeqhull( False);
- qh_memfreeshort (&curlong, &totlong);
- if (curlong || totlong)
- fprintf (stderr, "qhull internal warning (main): did not free %d bytes of long memory (%d pieces)\n",
- totlong, curlong);
-#endif
- return exitcode;
-} /* main */
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/qvoronoi.c b/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/qvoronoi.c
deleted file mode 100644
index 1a3aeb4cef437b6d6ff92228e063cfb5280200f1..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/qvoronoi.c
+++ /dev/null
@@ -1,318 +0,0 @@
-/*<html><pre> -<a href="qh-qhull.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- qvoronoi.c
- compute Voronoi diagrams and furthest-point Voronoi
- diagrams using qhull
-
- see unix.c for full interface
-
- copyright (c) 1993-2003, The Geometry Center
-*/
-
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-#include <ctype.h>
-#include <math.h>
-#include "qhull.h"
-#include "mem.h"
-#include "qset.h"
-
-#if __MWERKS__ && __POWERPC__
-#include <SIOUX.h>
-#include <Files.h>
-#include <console.h>
-#include <Desk.h>
-
-#elif __cplusplus
-extern "C" {
- int isatty (int);
-}
-
-#elif _MSC_VER
-#include <io.h>
-#define isatty _isatty
-
-#else
-int isatty (int); /* returns 1 if stdin is a tty
- if "Undefined symbol" this can be deleted along with call in main() */
-#endif
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="prompt">-</a>
-
- qh_prompt
- long prompt for qhull
-
- notes:
- restricted version of qhull.c
-
- see:
- concise prompt below
-*/
-
-/* duplicated in qvoron_f.htm and qvoronoi.htm */
-char hidden_options[]=" d n m v H U Qb QB Qc Qf Qg Qi Qm Qr QR Qv Qx TR E V Fa FA FC Fp FS Ft FV Pv Gt Q0 Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 ";
-
-char qh_prompta[]= "\n\
-qvoronoi- compute the Voronoi diagram\n\
- http://www.qhull.org %s\n\
-\n\
-input (stdin):\n\
- first lines: dimension and number of points (or vice-versa).\n\
- other lines: point coordinates, best if one point per line\n\
- comments: start with a non-numeric character\n\
-\n\
-options:\n\
- Qu - compute furthest-site Voronoi diagram\n\
- Qt - triangulated output\n\
- QJ - joggled input instead of merged facets\n\
-\n\
-Qhull control options:\n\
- Qz - add point-at-infinity to Voronoi diagram\n\
- QJn - randomly joggle input in range [-n,n]\n\
-%s%s%s%s"; /* split up qh_prompt for Visual C++ */
-char qh_promptb[]= "\
- Qs - search all points for the initial simplex\n\
- QGn - Voronoi vertices if visible from point n, -n if not\n\
- QVn - Voronoi vertices for input point n, -n if not\n\
-\n\
-";
-char qh_promptc[]= "\
-Trace options:\n\
- T4 - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
- Tc - check frequently during execution\n\
- Ts - statistics\n\
- Tv - verify result: structure, convexity, and in-circle test\n\
- Tz - send all output to stdout\n\
- TFn - report summary when n or more facets created\n\
- TI file - input data from file, no spaces or single quotes\n\
- TO file - output results to file, may be enclosed in single quotes\n\
- TPn - turn on tracing when point n added to hull\n\
- TMn - turn on tracing at merge n\n\
- TWn - trace merge facets when width > n\n\
- TVn - stop qhull after adding point n, -n for before (see TCn)\n\
- TCn - stop qhull after building cone for point n (see TVn)\n\
-\n\
-Precision options:\n\
- Cn - radius of centrum (roundoff added). Merge facets if non-convex\n\
- An - cosine of maximum angle. Merge facets if cosine > n or non-convex\n\
- C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
- Rn - randomly perturb computations by a factor of [1-n,1+n]\n\
- Wn - min facet width for non-coincident point (before roundoff)\n\
-\n\
-Output formats (may be combined; if none, produces a summary to stdout):\n\
- s - summary to stderr\n\
- p - Voronoi vertices\n\
- o - OFF format (dim, Voronoi vertices, and Voronoi regions)\n\
- i - Delaunay regions (use 'Pp' to avoid warning)\n\
- f - facet dump\n\
-\n\
-";
-char qh_promptd[]= "\
-More formats:\n\
- Fc - count plus coincident points (by Voronoi vertex)\n\
- Fd - use cdd format for input (homogeneous with offset first)\n\
- FD - use cdd format for output (offset first)\n\
- FF - facet dump without ridges\n\
- Fi - separating hyperplanes for bounded Voronoi regions\n\
- FI - ID for each Voronoi vertex\n\
- Fm - merge count for each Voronoi vertex (511 max)\n\
- Fn - count plus neighboring Voronoi vertices for each Voronoi vertex\n\
- FN - count and Voronoi vertices for each Voronoi region\n\
- Fo - separating hyperplanes for unbounded Voronoi regions\n\
- FO - options and precision constants\n\
- FP - nearest point and distance for each coincident point\n\
- FQ - command used for qvoronoi\n\
- Fs - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
- for output: #Voronoi regions, #Voronoi vertices,\n\
- #coincident points, #non-simplicial regions\n\
- #real (2), max outer plane and min vertex\n\
- Fv - Voronoi diagram as Voronoi vertices between adjacent input sites\n\
- Fx - extreme points of Delaunay triangulation (on convex hull)\n\
-\n\
-";
-char qh_prompte[]= "\
-Geomview options (2-d only)\n\
- Ga - all points as dots\n\
- Gp - coplanar points and vertices as radii\n\
- Gv - vertices as spheres\n\
- Gi - inner planes only\n\
- Gn - no planes\n\
- Go - outer planes only\n\
- Gc - centrums\n\
- Gh - hyperplane intersections\n\
- Gr - ridges\n\
- GDn - drop dimension n in 3-d and 4-d output\n\
-\n\
-Print options:\n\
- PAn - keep n largest Voronoi vertices by 'area'\n\
- Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
- PDk:n - drop facet if normal[k] >= n\n\
- Pg - print good Voronoi vertices (needs 'QGn' or 'QVn')\n\
- PFn - keep Voronoi vertices whose 'area' is at least n\n\
- PG - print neighbors of good Voronoi vertices\n\
- PMn - keep n Voronoi vertices with most merges\n\
- Po - force output. If error, output neighborhood of facet\n\
- Pp - do not report precision problems\n\
-\n\
- . - list of all options\n\
- - - one line descriptions of all options\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="prompt2">-</a>
-
- qh_prompt2
- synopsis for qhull
-*/
-char qh_prompt2[]= "\n\
-qvoronoi- compute the Voronoi diagram. Qhull %s\n\
- input (stdin): dimension, number of points, point coordinates\n\
- comments start with a non-numeric character\n\
-\n\
-options (qvoronoi.htm):\n\
- Qu - compute furthest-site Voronoi diagram\n\
- Qt - triangulated output\n\
- QJ - joggled input instead of merged facets\n\
- Tv - verify result: structure, convexity, and in-circle test\n\
- . - concise list of all options\n\
- - - one-line description of all options\n\
-\n\
-output options (subset):\n\
- s - summary of results (default)\n\
- p - Voronoi vertices\n\
- o - OFF file format (dim, Voronoi vertices, and Voronoi regions)\n\
- FN - count and Voronoi vertices for each Voronoi region\n\
- Fv - Voronoi diagram as Voronoi vertices between adjacent input sites\n\
- Fi - separating hyperplanes for bounded regions, 'Fo' for unbounded\n\
- G - Geomview output (2-d only)\n\
- QVn - Voronoi vertices for input point n, -n if not\n\
- TO file- output results to file, may be enclosed in single quotes\n\
-\n\
-examples:\n\
-rbox c P0 D2 | qvoronoi s o rbox c P0 D2 | qvoronoi Fi\n\
-rbox c P0 D2 | qvoronoi Fo rbox c P0 D2 | qvoronoi Fv\n\
-rbox c P0 D2 | qvoronoi s Qu Fv rbox c P0 D2 | qvoronoi Qu Fo\n\
-rbox c G1 d D2 | qvoronoi s p rbox c G1 d D2 | qvoronoi QJ s p\n\
-rbox c P0 D2 | qvoronoi s Fv QV0\n\
-\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="prompt3">-</a>
-
- qh_prompt3
- concise prompt for qhull
-*/
-char qh_prompt3[]= "\n\
-Qhull %s.\n\
-Except for 'F.' and 'PG', upper-case options take an argument.\n\
-\n\
- OFF_format p_vertices i_delaunay summary facet_dump\n\
-\n\
- Fcoincident Fd_cdd_in FD_cdd_out FF-dump-xridge Fi_bounded\n\
- Fxtremes Fmerges Fneighbors FNeigh_region FOptions\n\
- Fo_unbounded FPoint_near FQvoronoi Fsummary Fvoronoi\n\
- FIDs\n\
-\n\
- Gvertices Gpoints Gall_points Gno_planes Ginner\n\
- Gcentrums Ghyperplanes Gridges Gouter GDrop_dim\n\
-\n\
- PArea_keep Pdrop d0:0D0 Pgood PFacet_area_keep\n\
- PGood_neighbors PMerge_keep Poutput_forced Pprecision_not\n\
-\n\
- QG_vertex_good QJoggle Qsearch_1st Qtriangulate Qupper_voronoi\n\
- QV_point_good Qzinfinite\n\
-\n\
- T4_trace Tcheck_often Tstatistics Tverify Tz_stdout\n\
- TFacet_log TInput_file TPoint_trace TMerge_trace TOutput_file\n\
- TWide_trace TVertex_stop TCone_stop\n\
-\n\
- Angle_max Centrum_size Random_dist Wide_outside\n\
-";
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="main">-</a>
-
- main( argc, argv )
- processes the command line, calls qhull() to do the work, and exits
-
- design:
- initializes data structures
- reads points
- finishes initialization
- computes convex hull and other structures
- checks the result
- writes the output
- frees memory
-*/
-int main(int argc, char *argv[]) {
- int curlong, totlong; /* used !qh_NOmem */
- int exitcode, numpoints, dim;
- coordT *points;
- boolT ismalloc;
-
-#if __MWERKS__ && __POWERPC__
- char inBuf[BUFSIZ], outBuf[BUFSIZ], errBuf[BUFSIZ];
- SIOUXSettings.showstatusline= false;
- SIOUXSettings.tabspaces= 1;
- SIOUXSettings.rows= 40;
- if (setvbuf (stdin, inBuf, _IOFBF, sizeof(inBuf)) < 0 /* w/o, SIOUX I/O is slow*/
- || setvbuf (stdout, outBuf, _IOFBF, sizeof(outBuf)) < 0
- || (stdout != stderr && setvbuf (stderr, errBuf, _IOFBF, sizeof(errBuf)) < 0))
- fprintf (stderr, "qhull internal warning (main): could not change stdio to fully buffered.\n");
- argc= ccommand(&argv);
-#endif
-
- if ((argc == 1) && isatty( 0 /*stdin*/)) {
- fprintf(stdout, qh_prompt2, qh_version);
- exit(qh_ERRnone);
- }
- if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
- fprintf(stdout, qh_prompta, qh_version,
- qh_promptb, qh_promptc, qh_promptd, qh_prompte);
- exit(qh_ERRnone);
- }
- if (argc >1 && *argv[1] == '.' && !*(argv[1]+1)) {
- fprintf(stdout, qh_prompt3, qh_version);
- exit(qh_ERRnone);
- }
- qh_init_A (stdin, stdout, stderr, argc, argv); /* sets qh qhull_command */
- exitcode= setjmp (qh errexit); /* simple statement for CRAY J916 */
- if (!exitcode) {
- qh_option ("voronoi _bbound-last _coplanar-keep", NULL, NULL);
- qh DELAUNAY= True; /* 'v' */
- qh VORONOI= True;
- qh SCALElast= True; /* 'Qbb' */
- qh_checkflags (qh qhull_command, hidden_options);
- qh_initflags (qh qhull_command);
- points= qh_readpoints (&numpoints, &dim, &ismalloc);
- if (dim >= 5) {
- qh_option ("_merge-exact", NULL, NULL);
- qh MERGEexact= True; /* 'Qx' always */
- }
- qh_init_B (points, numpoints, dim, ismalloc);
- qh_qhull();
- qh_check_output();
- qh_produce_output();
- if (qh VERIFYoutput && !qh FORCEoutput && !qh STOPpoint && !qh STOPcone)
- qh_check_points();
- exitcode= qh_ERRnone;
- }
- qh NOerrexit= True; /* no more setjmp */
-#ifdef qh_NOmem
- qh_freeqhull( True);
-#else
- qh_freeqhull( False);
- qh_memfreeshort (&curlong, &totlong);
- if (curlong || totlong)
- fprintf (stderr, "qhull internal warning (main): did not free %d bytes of long memory (%d pieces)\n",
- totlong, curlong);
-#endif
- return exitcode;
-} /* main */
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/rbox.c b/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/rbox.c
deleted file mode 100644
index 1c288bddc96bb7214908ce94ca0c498169e51de1..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/rbox.c
+++ /dev/null
@@ -1,788 +0,0 @@
-/*<html><pre> -<a href="index.htm#TOC"
- >-------------------------------</a><a name="TOP">-</a>
-
- rbox.c
- Generate input points for qhull.
-
- notes:
- 50 points generated for 'rbox D4'
-
- This code needs a full rewrite. It needs separate procedures for each
- distribution with common, helper procedures.
-
- WARNING:
- incorrect range if qh_RANDOMmax is defined wrong (user.h)
-*/
-
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-#include <ctype.h>
-#include <math.h>
-#include <limits.h>
-#include <time.h>
-
-#include "user.h"
-#if __MWERKS__ && __POWERPC__
-#include <SIOUX.h>
-#include <Files.h>
-#include <console.h>
-#include <Desk.h>
-#endif
-
-#ifdef _MSC_VER /* Microsoft Visual C++ */
-#pragma warning( disable : 4244) /* conversion from double to int */
-#endif
-
-#define MINVALUE 0.8
-#define MAXdim 200
-#define PI 3.1415926535897932384
-#define DEFAULTzbox 1e6
-
-char prompt[]= "\n\
--rbox- generate various point distributions. Default is random in cube.\n\
-\n\
-args (any order, space separated): Version: 2001/06/24\n\
- 3000 number of random points in cube, lens, spiral, sphere or grid\n\
- D3 dimension 3-d\n\
- c add a unit cube to the output ('c G2.0' sets size)\n\
- d add a unit diamond to the output ('d G2.0' sets size)\n\
- l generate a regular 3-d spiral\n\
- r generate a regular polygon, ('r s Z1 G0.1' makes a cone)\n\
- s generate cospherical points\n\
- x generate random points in simplex, may use 'r' or 'Wn'\n\
- y same as 'x', plus simplex\n\
- Pn,m,r add point [n,m,r] first, pads with 0\n\
-\n\
- Ln lens distribution of radius n. Also 's', 'r', 'G', 'W'.\n\
- Mn,m,r lattice (Mesh) rotated by [n,-m,0], [m,n,0], [0,0,r], ...\n\
- '27 M1,0,1' is {0,1,2} x {0,1,2} x {0,1,2}. Try 'M3,4 z'.\n\
- W0.1 random distribution within 0.1 of the cube's or sphere's surface\n\
- Z0.5 s random points in a 0.5 disk projected to a sphere\n\
- Z0.5 s G0.6 same as Z0.5 within a 0.6 gap\n\
-\n\
- Bn bounding box coordinates, default %2.2g\n\
- h output as homogeneous coordinates for cdd\n\
- n remove command line from the first line of output\n\
- On offset coordinates by n\n\
- t use time as the random number seed (default is command line)\n\
- tn use n as the random number seed\n\
- z print integer coordinates, default 'Bn' is %2.2g\n\
-";
-
-/* ------------------------------ prototypes ----------------*/
-int roundi( double a);
-void out1( double a);
-void out2n( double a, double b);
-void out3n( double a, double b, double c);
-int qh_rand( void);
-void qh_srand( int seed);
-
-
-/* ------------------------------ globals -------------------*/
-
- FILE *fp;
- int isinteger= 0;
- double out_offset= 0.0;
-
-
-/*--------------------------------------------
--rbox- main procedure of rbox application
-*/
-int main(int argc, char **argv) {
- int i,j,k;
- int gendim;
- int cubesize, diamondsize, seed=0, count, apex;
- int dim=3 , numpoints= 0, totpoints, addpoints=0;
- int issphere=0, isaxis=0, iscdd= 0, islens= 0, isregular=0, iswidth=0, addcube=0;
- int isgap=0, isspiral=0, NOcommand= 0, adddiamond=0, istime=0;
- int isbox=0, issimplex=0, issimplex2=0, ismesh=0;
- double width=0.0, gap=0.0, radius= 0.0;
- double coord[MAXdim], offset, meshm=3.0, meshn=4.0, meshr=5.0;
- double *simplex, *simplexp;
- int nthroot, mult[MAXdim];
- double norm, factor, randr, rangap, lensangle= 0, lensbase= 1;
- double anglediff, angle, x, y, cube= 0.0, diamond= 0.0;
- double box= qh_DEFAULTbox; /* scale all numbers before output */
- double randmax= qh_RANDOMmax;
- char command[200], *s, seedbuf[200];
- time_t timedata;
-
-#if __MWERKS__ && __POWERPC__
- char inBuf[BUFSIZ], outBuf[BUFSIZ], errBuf[BUFSIZ];
- SIOUXSettings.showstatusline= False;
- SIOUXSettings.tabspaces= 1;
- SIOUXSettings.rows= 40;
- if (setvbuf (stdin, inBuf, _IOFBF, sizeof(inBuf)) < 0 /* w/o, SIOUX I/O is slow*/
- || setvbuf (stdout, outBuf, _IOFBF, sizeof(outBuf)) < 0
- || (stdout != stderr && setvbuf (stderr, errBuf, _IOFBF, sizeof(errBuf)) < 0))
- fprintf ( stderr, "qhull internal warning (main): could not change stdio to fully buffered.\n");
- argc= ccommand(&argv);
-#endif
- if (argc == 1) {
- printf (prompt, box, DEFAULTzbox);
- exit(1);
- }
- if ((s = strrchr( argv[0], '\\'))) /* Borland gives full path */
- strcpy (command, s+1);
- else
- strcpy (command, argv[0]);
- if ((s= strstr (command, ".EXE"))
- || (s= strstr (command, ".exe")))
- *s= '\0';
- /* ============= read flags =============== */
- for (i=1; i < argc; i++) {
- if (strlen (command) + strlen(argv[i]) + 1 < sizeof(command) ) {
- strcat (command, " ");
- strcat (command, argv[i]);
- }
- if (isdigit (argv[i][0])) {
- numpoints= atoi (argv[i]);
- continue;
- }
- if (argv[i][0] == '-')
- (argv[i])++;
- switch (argv[i][0]) {
- case 'c':
- addcube= 1;
- if (i+1 < argc && argv[i+1][0] == 'G')
- cube= (double) atof (&argv[++i][1]);
- break;
- case 'd':
- adddiamond= 1;
- if (i+1 < argc && argv[i+1][0] == 'G')
- diamond= (double) atof (&argv[++i][1]);
- break;
- case 'h':
- iscdd= 1;
- break;
- case 'l':
- isspiral= 1;
- break;
- case 'n':
- NOcommand= 1;
- break;
- case 'r':
- isregular= 1;
- break;
- case 's':
- issphere= 1;
- break;
- case 't':
- istime= 1;
- if (isdigit (argv[i][1]))
- seed= atoi (&argv[i][1]);
- else {
- seed= time (&timedata);
- sprintf (seedbuf, "%d", seed);
- strcat (command, seedbuf);
- }
- break;
- case 'x':
- issimplex= 1;
- break;
- case 'y':
- issimplex2= 1;
- break;
- case 'z':
- isinteger= 1;
- break;
- case 'B':
- box= (double) atof (&argv[i][1]);
- isbox= 1;
- break;
- case 'D':
- dim= atoi (&argv[i][1]);
- if (dim < 1
- || dim > MAXdim) {
- fprintf (stderr, "rbox error: dim %d too large or too small\n", dim);
- exit (1);
- }
- break;
- case 'G':
- if (argv[i][1])
- gap= (double) atof (&argv[i][1]);
- else
- gap= 0.5;
- isgap= 1;
- break;
- case 'L':
- if (argv[i][1])
- radius= (double) atof (&argv[i][1]);
- else
- radius= 10;
- islens= 1;
- break;
- case 'M':
- ismesh= 1;
- s= argv[i]+1;
- if (*s)
- meshn= strtod (s, &s);
- if (*s == ',')
- meshm= strtod (++s, &s);
- else
- meshm= 0.0;
- if (*s == ',')
- meshr= strtod (++s, &s);
- else
- meshr= sqrt (meshn*meshn + meshm*meshm);
- if (*s) {
- fprintf (stderr, "rbox warning: assuming 'M3,4,5' since mesh args are not integers or reals\n");
- meshn= 3.0, meshm=4.0, meshr=5.0;
- }
- break;
- case 'O':
- out_offset= (double) atof (&argv[i][1]);
- break;
- case 'P':
- addpoints++;
- break;
- case 'W':
- width= (double) atof (&argv[i][1]);
- iswidth= 1;
- break;
- case 'Z':
- if (argv[i][1])
- radius= (double) atof (&argv[i][1]);
- else
- radius= 1.0;
- isaxis= 1;
- break;
- default:
- fprintf (stderr, "rbox warning: unknown flag %s.\nExecute 'rbox' without arguments for documentation.\n", argv[i]);
- }
- }
- /* ============= defaults, constants, and sizes =============== */
- if (isinteger && !isbox)
- box= DEFAULTzbox;
- if (addcube) {
- cubesize= floor(ldexp(1.0,dim)+0.5);
- if (cube == 0.0)
- cube= box;
- }else
- cubesize= 0;
- if (adddiamond) {
- diamondsize= 2*dim;
- if (diamond == 0.0)
- diamond= box;
- }else
- diamondsize= 0;
- if (islens) {
- if (isaxis) {
- fprintf (stderr, "rbox error: can not combine 'Ln' with 'Zn'\n");
- exit(1);
- }
- if (radius <= 1.0) {
- fprintf (stderr, "rbox error: lens radius %.2g should be greater than 1.0\n",
- radius);
- exit(1);
- }
- lensangle= asin (1.0/radius);
- lensbase= radius * cos (lensangle);
- }
- if (!numpoints) {
- if (issimplex2)
- ; /* ok */
- else if (isregular + issimplex + islens + issphere + isaxis + isspiral + iswidth + ismesh) {
- fprintf (stderr, "rbox error: missing count\n");
- exit(1);
- }else if (adddiamond + addcube + addpoints)
- ; /* ok */
- else {
- numpoints= 50; /* ./rbox D4 is the test case */
- issphere= 1;
- }
- }
- if ((issimplex + islens + isspiral + ismesh > 1)
- || (issimplex + issphere + isspiral + ismesh > 1)) {
- fprintf (stderr, "rbox error: can only specify one of 'l', 's', 'x', 'Ln', or 'Mn,m,r' ('Ln s' is ok).\n");
- exit(1);
- }
- fp= stdout;
- /* ============= print header with total points =============== */
- if (issimplex || ismesh)
- totpoints= numpoints;
- else if (issimplex2)
- totpoints= numpoints+dim+1;
- else if (isregular) {
- totpoints= numpoints;
- if (dim == 2) {
- if (islens)
- totpoints += numpoints - 2;
- }else if (dim == 3) {
- if (islens)
- totpoints += 2 * numpoints;
- else if (isgap)
- totpoints += 1 + numpoints;
- else
- totpoints += 2;
- }
- }else
- totpoints= numpoints + isaxis;
- totpoints += cubesize + diamondsize + addpoints;
- if (iscdd)
- fprintf(fp, "%s\nbegin\n %d %d %s\n",
- NOcommand ? "" : command,
- totpoints, dim+1,
- isinteger ? "integer" : "real");
- else if (NOcommand)
- fprintf(fp, "%d\n%d\n", dim, totpoints);
- else
- fprintf(fp, "%d %s\n%d\n", dim, command, totpoints);
- /* ============= seed randoms =============== */
- if (istime == 0) {
- for (s=command; *s; s++) {
- if (issimplex2 && *s == 'y') /* make 'y' same seed as 'x' */
- i= 'x';
- else
- i= *s;
- seed= 11*seed + i;
- }
- } /* else, seed explicitly set to n or to time */
- qh_RANDOMseed_(seed);
- /* ============= explicit points =============== */
- for (i=1; i < argc; i++) {
- if (argv[i][0] == 'P') {
- s= argv[i]+1;
- count= 0;
- if (iscdd)
- out1( 1.0);
- while (*s) {
- out1( strtod (s, &s));
- count++;
- if (*s) {
- if (*s++ != ',') {
- fprintf (stderr, "rbox error: missing comma after coordinate in %s\n\n", argv[i]);
- exit (1);
- }
- }
- }
- if (count < dim) {
- for (k= dim-count; k--; )
- out1( 0.0);
- }else if (count > dim) {
- fprintf (stderr, "rbox error: %d coordinates instead of %d coordinates in %s\n\n",
- count, dim, argv[i]);
- exit (1);
- }
- fprintf (fp, "\n");
- }
- }
- /* ============= simplex distribution =============== */
- if (issimplex+issimplex2) {
- if (!(simplex= malloc( dim * (dim+1) * sizeof(double)))) {
- fprintf (stderr, "insufficient memory for simplex\n");
- exit(0);
- }
- simplexp= simplex;
- if (isregular) {
- for (i= 0; i<dim; i++) {
- for (k= 0; k<dim; k++)
- *(simplexp++)= i==k ? 1.0 : 0.0;
- }
- for (k= 0; k<dim; k++)
- *(simplexp++)= -1.0;
- }else {
- for (i= 0; i<dim+1; i++) {
- for (k= 0; k<dim; k++) {
- randr= qh_RANDOMint;
- *(simplexp++)= 2.0 * randr/randmax - 1.0;
- }
- }
- }
- if (issimplex2) {
- simplexp= simplex;
- for (i= 0; i<dim+1; i++) {
- if (iscdd)
- out1( 1.0);
- for (k= 0; k<dim; k++)
- out1( *(simplexp++) * box);
- fprintf (fp, "\n");
- }
- }
- for (j= 0; j<numpoints; j++) {
- if (iswidth)
- apex= qh_RANDOMint % (dim+1);
- else
- apex= -1;
- for (k= 0; k<dim; k++)
- coord[k]= 0.0;
- norm= 0.0;
- for (i= 0; i<dim+1; i++) {
- randr= qh_RANDOMint;
- factor= randr/randmax;
- if (i == apex)
- factor *= width;
- norm += factor;
- for (k= 0; k<dim; k++) {
- simplexp= simplex + i*dim + k;
- coord[k] += factor * (*simplexp);
- }
- }
- for (k= 0; k<dim; k++)
- coord[k] /= norm;
- if (iscdd)
- out1( 1.0);
- for (k=0; k < dim; k++)
- out1( coord[k] * box);
- fprintf (fp, "\n");
- }
- isregular= 0; /* continue with isbox */
- numpoints= 0;
- }
- /* ============= mesh distribution =============== */
- if (ismesh) {
- nthroot= pow (numpoints, 1.0/dim) + 0.99999;
- for (k= dim; k--; )
- mult[k]= 0;
- for (i= 0; i < numpoints; i++) {
- for (k= 0; k < dim; k++) {
- if (k == 0)
- out1( mult[0] * meshn + mult[1] * (-meshm));
- else if (k == 1)
- out1( mult[0] * meshm + mult[1] * meshn);
- else
- out1( mult[k] * meshr );
- }
- fprintf (fp, "\n");
- for (k= 0; k < dim; k++) {
- if (++mult[k] < nthroot)
- break;
- mult[k]= 0;
- }
- }
- }
-
- /* ============= regular points for 's' =============== */
- else if (isregular && !islens) {
- if (dim != 2 && dim != 3) {
- fprintf(stderr, "rbox error: regular points can be used only in 2-d and 3-d\n\n");
- exit(1);
- }
- if (!isaxis || radius == 0.0) {
- isaxis= 1;
- radius= 1.0;
- }
- if (dim == 3) {
- if (iscdd)
- out1( 1.0);
- out3n( 0.0, 0.0, -box);
- if (!isgap) {
- if (iscdd)
- out1( 1.0);
- out3n( 0.0, 0.0, box);
- }
- }
- angle= 0.0;
- anglediff= 2.0 * PI/numpoints;
- for (i=0; i < numpoints; i++) {
- angle += anglediff;
- x= radius * cos (angle);
- y= radius * sin (angle);
- if (dim == 2) {
- if (iscdd)
- out1( 1.0);
- out2n( x*box, y*box);
- }else {
- norm= sqrt (1.0 + x*x + y*y);
- if (iscdd)
- out1( 1.0);
- out3n( box*x/norm, box*y/norm, box/norm);
- if (isgap) {
- x *= 1-gap;
- y *= 1-gap;
- norm= sqrt (1.0 + x*x + y*y);
- if (iscdd)
- out1( 1.0);
- out3n( box*x/norm, box*y/norm, box/norm);
- }
- }
- }
- }
- /* ============= regular points for 'r Ln D2' =============== */
- else if (isregular && islens && dim == 2) {
- double cos_0;
-
- angle= lensangle;
- anglediff= 2 * lensangle/(numpoints - 1);
- cos_0= cos (lensangle);
- for (i=0; i < numpoints; i++, angle -= anglediff) {
- x= radius * sin (angle);
- y= radius * (cos (angle) - cos_0);
- if (iscdd)
- out1( 1.0);
- out2n( x*box, y*box);
- if (i != 0 && i != numpoints - 1) {
- if (iscdd)
- out1( 1.0);
- out2n( x*box, -y*box);
- }
- }
- }
- /* ============= regular points for 'r Ln D3' =============== */
- else if (isregular && islens && dim != 2) {
- if (dim != 3) {
- fprintf(stderr, "rbox error: regular points can be used only in 2-d and 3-d\n\n");
- exit(1);
- }
- angle= 0.0;
- anglediff= 2* PI/numpoints;
- if (!isgap) {
- isgap= 1;
- gap= 0.5;
- }
- offset= sqrt (radius * radius - (1-gap)*(1-gap)) - lensbase;
- for (i=0; i < numpoints; i++, angle += anglediff) {
- x= cos (angle);
- y= sin (angle);
- if (iscdd)
- out1( 1.0);
- out3n( box*x, box*y, 0);
- x *= 1-gap;
- y *= 1-gap;
- if (iscdd)
- out1( 1.0);
- out3n( box*x, box*y, box * offset);
- if (iscdd)
- out1( 1.0);
- out3n( box*x, box*y, -box * offset);
- }
- }
- /* ============= apex of 'Zn' distribution + gendim =============== */
- else {
- if (isaxis) {
- gendim= dim-1;
- if (iscdd)
- out1( 1.0);
- for (j=0; j < gendim; j++)
- out1( 0.0);
- out1( -box);
- fprintf (fp, "\n");
- }else if (islens)
- gendim= dim-1;
- else
- gendim= dim;
- /* ============= generate random point in unit cube =============== */
- for (i=0; i < numpoints; i++) {
- norm= 0.0;
- for (j=0; j < gendim; j++) {
- randr= qh_RANDOMint;
- coord[j]= 2.0 * randr/randmax - 1.0;
- norm += coord[j] * coord[j];
- }
- norm= sqrt (norm);
- /* ============= dim-1 point of 'Zn' distribution ========== */
- if (isaxis) {
- if (!isgap) {
- isgap= 1;
- gap= 1.0;
- }
- randr= qh_RANDOMint;
- rangap= 1.0 - gap * randr/randmax;
- factor= radius * rangap / norm;
- for (j=0; j<gendim; j++)
- coord[j]= factor * coord[j];
- /* ============= dim-1 point of 'Ln s' distribution =========== */
- }else if (islens && issphere) {
- if (!isgap) {
- isgap= 1;
- gap= 1.0;
- }
- randr= qh_RANDOMint;
- rangap= 1.0 - gap * randr/randmax;
- factor= rangap / norm;
- for (j=0; j<gendim; j++)
- coord[j]= factor * coord[j];
- /* ============= dim-1 point of 'Ln' distribution ========== */
- }else if (islens && !issphere) {
- if (!isgap) {
- isgap= 1;
- gap= 1.0;
- }
- j= qh_RANDOMint % gendim;
- if (coord[j] < 0)
- coord[j]= -1.0 - coord[j] * gap;
- else
- coord[j]= 1.0 - coord[j] * gap;
- /* ============= point of 'l' distribution =============== */
- }else if (isspiral) {
- if (dim != 3) {
- fprintf(stderr, "rbox error: spiral distribution is available only in 3d\n\n");
- exit(1);
- }
- coord[0]= cos(2*PI*i/(numpoints - 1));
- coord[1]= sin(2*PI*i/(numpoints - 1));
- coord[2]= 2.0*(double)i/(double)(numpoints-1) - 1.0;
- /* ============= point of 's' distribution =============== */
- }else if (issphere) {
- factor= 1.0/norm;
- if (iswidth) {
- randr= qh_RANDOMint;
- factor *= 1.0 - width * randr/randmax;
- }
- for (j=0; j<dim; j++)
- coord[j]= factor * coord[j];
- }
- /* ============= project 'Zn s' point in to sphere =============== */
- if (isaxis && issphere) {
- coord[dim-1]= 1.0;
- norm= 1.0;
- for (j=0; j<gendim; j++)
- norm += coord[j] * coord[j];
- norm= sqrt (norm);
- for (j=0; j<dim; j++)
- coord[j]= coord[j] / norm;
- if (iswidth) {
- randr= qh_RANDOMint;
- coord[dim-1] *= 1 - width * randr/randmax;
- }
- /* ============= project 'Zn' point onto cube =============== */
- }else if (isaxis && !issphere) { /* not very interesting */
- randr= qh_RANDOMint;
- coord[dim-1]= 2.0 * randr/randmax - 1.0;
- /* ============= project 'Ln' point out to sphere =============== */
- }else if (islens) {
- coord[dim-1]= lensbase;
- for (j=0, norm= 0; j<dim; j++)
- norm += coord[j] * coord[j];
- norm= sqrt (norm);
- for (j=0; j<dim; j++)
- coord[j]= coord[j] * radius/ norm;
- coord[dim-1] -= lensbase;
- if (iswidth) {
- randr= qh_RANDOMint;
- coord[dim-1] *= 1 - width * randr/randmax;
- }
- if (qh_RANDOMint > randmax/2)
- coord[dim-1]= -coord[dim-1];
- /* ============= project 'Wn' point toward boundary =============== */
- }else if (iswidth && !issphere) {
- j= qh_RANDOMint % gendim;
- if (coord[j] < 0)
- coord[j]= -1.0 - coord[j] * width;
- else
- coord[j]= 1.0 - coord[j] * width;
- }
- /* ============= write point =============== */
- if (iscdd)
- out1( 1.0);
- for (k=0; k < dim; k++)
- out1( coord[k] * box);
- fprintf (fp, "\n");
- }
- }
- /* ============= write cube vertices =============== */
- if (addcube) {
- for (j=0; j<cubesize; j++) {
- if (iscdd)
- out1( 1.0);
- for (k=dim-1; k>=0; k--) {
- if (j & ( 1 << k))
- out1( cube);
- else
- out1( -cube);
- }
- fprintf (fp, "\n");
- }
- }
- /* ============= write diamond vertices =============== */
- if (adddiamond) {
- for (j=0; j<diamondsize; j++) {
- if (iscdd)
- out1( 1.0);
- for (k=dim-1; k>=0; k--) {
- if (j/2 != k)
- out1( 0.0);
- else if (j & 0x1)
- out1( diamond);
- else
- out1( -diamond);
- }
- fprintf (fp, "\n");
- }
- }
- if (iscdd)
- fprintf (fp, "end\nhull\n");
- return 0;
- } /* rbox */
-
-/*------------------------------------------------
--outxxx - output functions
-*/
-int roundi( double a) {
- if (a < 0.0) {
- if (a - 0.5 < INT_MIN) {
- fprintf(stderr, "rbox input error: coordinate %2.2g is too large. Reduce 'Bn'\n", a);
- exit (1);
- }
- return a - 0.5;
- }else {
- if (a + 0.5 > INT_MAX) {
- fprintf(stderr, "rbox input error: coordinate %2.2g is too large. Reduce 'Bn'\n", a);
- exit (1);
- }
- return a + 0.5;
- }
-} /* roundi */
-
-void out1(double a) {
-
- if (isinteger)
- fprintf(fp, "%d ", roundi( a+out_offset));
- else
- fprintf(fp, qh_REAL_1, a+out_offset);
-} /* out1 */
-
-void out2n( double a, double b) {
-
- if (isinteger)
- fprintf(fp, "%d %d\n", roundi(a+out_offset), roundi(b+out_offset));
- else
- fprintf(fp, qh_REAL_2n, a+out_offset, b+out_offset);
-} /* out2n */
-
-void out3n( double a, double b, double c) {
-
- if (isinteger)
- fprintf(fp, "%d %d %d\n", roundi(a+out_offset), roundi(b+out_offset), roundi(c+out_offset));
- else
- fprintf(fp, qh_REAL_3n, a+out_offset, b+out_offset, c+out_offset);
-} /* out3n */
-
-/*-------------------------------------------------
--rand & srand- generate pseudo-random number between 1 and 2^31 -2
- from Park & Miller's minimimal standard random number generator
- Communications of the ACM, 31:1192-1201, 1988.
-notes:
- does not use 0 or 2^31 -1
- this is silently enforced by qh_srand()
- copied from geom2.c
-*/
-static int seed = 1; /* global static */
-
-int qh_rand( void) {
-#define qh_rand_a 16807
-#define qh_rand_m 2147483647
-#define qh_rand_q 127773 /* m div a */
-#define qh_rand_r 2836 /* m mod a */
- int lo, hi, test;
-
- hi = seed / qh_rand_q; /* seed div q */
- lo = seed % qh_rand_q; /* seed mod q */
- test = qh_rand_a * lo - qh_rand_r * hi;
- if (test > 0)
- seed= test;
- else
- seed= test + qh_rand_m;
- return seed;
-} /* rand */
-
-void qh_srand( int newseed) {
- if (newseed < 1)
- seed= 1;
- else if (newseed >= qh_rand_m)
- seed= qh_rand_m - 1;
- else
- seed= newseed;
-} /* qh_srand */
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/unix.c b/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/unix.c
deleted file mode 100644
index 9f06fcefb3ab432ac50b502ba0624ec61e2b61de..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/unix.c
+++ /dev/null
@@ -1,377 +0,0 @@
-/*<html><pre> -<a href="qh-qhull.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- unix.c
- command line interface to qhull
- includes SIOUX interface for Macintoshes
-
- see qh-qhull.htm
-
- copyright (c) 1993-2003, The Geometry Center
-*/
-
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-#include <ctype.h>
-#include <math.h>
-#include "qhull.h"
-#include "mem.h"
-#include "qset.h"
-
-#if __MWERKS__ && __POWERPC__
-#include <SIOUX.h>
-#include <Files.h>
-#include <console.h>
-#include <Desk.h>
-
-#elif __cplusplus
-extern "C" {
- int isatty (int);
-}
-
-#elif _MSC_VER
-#include <io.h>
-#define isatty _isatty
-
-#else
-int isatty (int); /* returns 1 if stdin is a tty
- if "Undefined symbol" this can be deleted along with call in main() */
-#endif
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="prompt">-</a>
-
- qh_prompt
- long prompt for qhull
-
- see:
- concise prompt below
-*/
-char qh_prompta[]= "\n\
-qhull- compute convex hulls and related structures.\n\
- http://www.qhull.org %s\n\
-\n\
-input (stdin):\n\
- first lines: dimension and number of points (or vice-versa).\n\
- other lines: point coordinates, best if one point per line\n\
- comments: start with a non-numeric character\n\
- halfspaces: use dim plus one and put offset after coefficients.\n\
- May be preceeded by a single interior point ('H').\n\
-\n\
-options:\n\
- d - Delaunay triangulation by lifting points to a paraboloid\n\
- d Qu - furthest-site Delaunay triangulation (upper convex hull)\n\
- v - Voronoi diagram (dual of the Delaunay triangulation)\n\
- v Qu - furthest-site Voronoi diagram\n\
- Hn,n,... - halfspace intersection about point [n,n,0,...]\n\
- Qt - triangulated output\n\
- QJ - joggled input instead of merged facets\n\
- Qc - keep coplanar points with nearest facet\n\
- Qi - keep interior points with nearest facet\n\
-\n\
-Qhull control options:\n\
- Qbk:n - scale coord k so that low bound is n\n\
- QBk:n - scale coord k so that upper bound is n (QBk is %2.2g)\n\
- QbB - scale input to unit cube centered at the origin\n\
- Qbb - scale last coordinate to [0,m] for Delaunay triangulations\n\
- Qbk:0Bk:0 - remove k-th coordinate from input\n\
- QJn - randomly joggle input in range [-n,n]\n\
- QRn - random rotation (n=seed, n=0 time, n=-1 time/no rotate)\n\
-%s%s%s%s"; /* split up qh_prompt for Visual C++ */
-char qh_promptb[]= "\
- Qf - partition point to furthest outside facet\n\
- Qg - only build good facets (needs 'QGn', 'QVn', or 'PdD')\n\
- Qm - only process points that would increase max_outside\n\
- Qr - process random outside points instead of furthest ones\n\
- Qs - search all points for the initial simplex\n\
- Qu - for 'd' or 'v', compute upper hull without point at-infinity\n\
- returns furthest-site Delaunay triangulation\n\
- Qv - test vertex neighbors for convexity\n\
- Qx - exact pre-merges (skips coplanar and angle-coplanar facets)\n\
- Qz - add point-at-infinity to Delaunay triangulation\n\
- QGn - good facet if visible from point n, -n for not visible\n\
- QVn - good facet if it includes point n, -n if not\n\
- Q0 - turn off default premerge with 'C-0'/'Qx'\n\
- Q1 - sort merges by type instead of angle\n\
- Q2 - merge all non-convex at once instead of independent sets\n\
- Q3 - do not merge redundant vertices\n\
- Q4 - avoid old->new merges\n\
- Q5 - do not correct outer planes at end of qhull\n\
- Q6 - do not pre-merge concave or coplanar facets\n\
- Q7 - depth-first processing instead of breadth-first\n\
- Q8 - do not process near-inside points\n\
- Q9 - process furthest of furthest points\n\
- Q10 - no special processing for narrow distributions\n\
- Q11 - copy normals and recompute centrums for tricoplanar facets\n\
-\n\
-";
-char qh_promptc[]= "\
-Topts- Trace options:\n\
- T4 - trace at level n, 4=all, 5=mem/gauss, -1= events\n\
- Tc - check frequently during execution\n\
- Ts - print statistics\n\
- Tv - verify result: structure, convexity, and point inclusion\n\
- Tz - send all output to stdout\n\
- TFn - report summary when n or more facets created\n\
- TI file - input data from file, no spaces or single quotes\n\
- TO file - output results to file, may be enclosed in single quotes\n\
- TPn - turn on tracing when point n added to hull\n\
- TMn - turn on tracing at merge n\n\
- TWn - trace merge facets when width > n\n\
- TRn - rerun qhull n times. Use with 'QJn'\n\
- TVn - stop qhull after adding point n, -n for before (see TCn)\n\
- TCn - stop qhull after building cone for point n (see TVn)\n\
-\n\
-Precision options:\n\
- Cn - radius of centrum (roundoff added). Merge facets if non-convex\n\
- An - cosine of maximum angle. Merge facets if cosine > n or non-convex\n\
- C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge\n\
- En - max roundoff error for distance computation\n\
- Rn - randomly perturb computations by a factor of [1-n,1+n]\n\
- Vn - min distance above plane for a visible facet (default 3C-n or En)\n\
- Un - max distance below plane for a new, coplanar point (default Vn)\n\
- Wn - min facet width for outside point (before roundoff, default 2Vn)\n\
-\n\
-Output formats (may be combined; if none, produces a summary to stdout):\n\
- f - facet dump\n\
- G - Geomview output (see below)\n\
- i - vertices incident to each facet\n\
- m - Mathematica output (2-d and 3-d)\n\
- o - OFF format (dim, points and facets; Voronoi regions)\n\
- n - normals with offsets\n\
- p - vertex coordinates or Voronoi vertices (coplanar points if 'Qc')\n\
- s - summary (stderr)\n\
-\n\
-";
-char qh_promptd[]= "\
-More formats:\n\
- Fa - area for each facet\n\
- FA - compute total area and volume for option 's'\n\
- Fc - count plus coplanar points for each facet\n\
- use 'Qc' (default) for coplanar and 'Qi' for interior\n\
- FC - centrum or Voronoi center for each facet\n\
- Fd - use cdd format for input (homogeneous with offset first)\n\
- FD - use cdd format for numeric output (offset first)\n\
- FF - facet dump without ridges\n\
- Fi - inner plane for each facet\n\
- for 'v', separating hyperplanes for bounded Voronoi regions\n\
- FI - ID of each facet\n\
- Fm - merge count for each facet (511 max)\n\
- FM - Maple output (2-d and 3-d)\n\
- Fn - count plus neighboring facets for each facet\n\
- FN - count plus neighboring facets for each point\n\
- Fo - outer plane (or max_outside) for each facet\n\
- for 'v', separating hyperplanes for unbounded Voronoi regions\n\
- FO - options and precision constants\n\
- Fp - dim, count, and intersection coordinates (halfspace only)\n\
- FP - nearest vertex and distance for each coplanar point\n\
- FQ - command used for qhull\n\
- Fs - summary: #int (8), dimension, #points, tot vertices, tot facets,\n\
- output: #vertices, #facets, #coplanars, #nonsimplicial\n\
- #real (2), max outer plane, min vertex\n\
- FS - sizes: #int (0)\n\
- #real(2) tot area, tot volume\n\
- Ft - triangulation with centrums for non-simplicial facets (OFF format)\n\
- Fv - count plus vertices for each facet\n\
- for 'v', Voronoi diagram as Voronoi vertices for pairs of sites\n\
- FV - average of vertices (a feasible point for 'H')\n\
- Fx - extreme points (in order for 2-d)\n\
-\n\
-";
-char qh_prompte[]= "\
-Geomview options (2-d, 3-d, and 4-d; 2-d Voronoi)\n\
- Ga - all points as dots\n\
- Gp - coplanar points and vertices as radii\n\
- Gv - vertices as spheres\n\
- Gi - inner planes only\n\
- Gn - no planes\n\
- Go - outer planes only\n\
- Gc - centrums\n\
- Gh - hyperplane intersections\n\
- Gr - ridges\n\
- GDn - drop dimension n in 3-d and 4-d output\n\
- Gt - for 3-d 'd', transparent outer ridges\n\
-\n\
-Print options:\n\
- PAn - keep n largest facets by area\n\
- Pdk:n - drop facet if normal[k] <= n (default 0.0)\n\
- PDk:n - drop facet if normal[k] >= n\n\
- Pg - print good facets (needs 'QGn' or 'QVn')\n\
- PFn - keep facets whose area is at least n\n\
- PG - print neighbors of good facets\n\
- PMn - keep n facets with most merges\n\
- Po - force output. If error, output neighborhood of facet\n\
- Pp - do not report precision problems\n\
-\n\
- . - list of all options\n\
- - - one line descriptions of all options\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="prompt2">-</a>
-
- qh_prompt2
- synopsis for qhull
-*/
-char qh_prompt2[]= "\n\
-qhull- compute convex hulls and related structures. Qhull %s\n\
- input (stdin): dimension, n, point coordinates\n\
- comments start with a non-numeric character\n\
- halfspace: use dim+1 and put offsets after coefficients\n\
-\n\
-options (qh-quick.htm):\n\
- d - Delaunay triangulation by lifting points to a paraboloid\n\
- d Qu - furthest-site Delaunay triangulation (upper convex hull)\n\
- v - Voronoi diagram as the dual of the Delaunay triangulation\n\
- v Qu - furthest-site Voronoi diagram\n\
- H1,1 - Halfspace intersection about [1,1,0,...] via polar duality\n\
- Qt - triangulated output\n\
- QJ - joggled input instead of merged facets\n\
- Tv - verify result: structure, convexity, and point inclusion\n\
- . - concise list of all options\n\
- - - one-line description of all options\n\
-\n\
-Output options (subset):\n\
- s - summary of results (default)\n\
- i - vertices incident to each facet\n\
- n - normals with offsets\n\
- p - vertex coordinates (if 'Qc', includes coplanar points)\n\
- if 'v', Voronoi vertices\n\
- Fp - halfspace intersections\n\
- Fx - extreme points (convex hull vertices)\n\
- FA - compute total area and volume\n\
- o - OFF format (if 'v', outputs Voronoi regions)\n\
- G - Geomview output (2-d, 3-d and 4-d)\n\
- m - Mathematica output (2-d and 3-d)\n\
- QVn - print facets that include point n, -n if not\n\
- TO file- output results to file, may be enclosed in single quotes\n\
-\n\
-examples:\n\
- rbox c d D2 | qhull Qc s f Fx | more rbox 1000 s | qhull Tv s FA\n\
- rbox 10 D2 | qhull d QJ s i TO result rbox 10 D2 | qhull v Qbb Qt p\n\
- rbox 10 D2 | qhull d Qu QJ m rbox 10 D2 | qhull v Qu QJ o\n\
- rbox c | qhull n rbox c | qhull FV n | qhull H Fp\n\
- rbox d D12 | qhull QR0 FA rbox c D7 | qhull FA TF1000\n\
- rbox y 1000 W0 | qhull rbox 10 | qhull v QJ o Fv\n\
-\n\
-";
-/* for opts, don't assign 'e' or 'E' to a flag (already used for exponent) */
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="prompt3">-</a>
-
- qh_prompt3
- concise prompt for qhull
-*/
-char qh_prompt3[]= "\n\
-Qhull %s.\n\
-Except for 'F.' and 'PG', upper-case options take an argument.\n\
-\n\
- delaunay voronoi Geomview Halfspace facet_dump\n\
- incidences mathematica normals OFF_format points\n\
- summary\n\
-\n\
- Farea FArea-total Fcoplanars FCentrums Fd-cdd-in\n\
- FD-cdd-out FF-dump-xridge Finner FIDs Fmerges\n\
- Fneighbors FNeigh-vertex Fouter FOptions Fpoint-intersect\n\
- FPoint_near FQhull Fsummary FSize Ftriangles\n\
- Fvertices Fvoronoi FVertex-ave Fxtremes FMaple\n\
-\n\
- Gvertices Gpoints Gall_points Gno_planes Ginner\n\
- Gcentrums Ghyperplanes Gridges Gouter GDrop_dim\n\
- Gtransparent\n\
-\n\
- PArea-keep Pdrop d0:0D0 Pgood PFacet_area_keep\n\
- PGood_neighbors PMerge-keep Poutput_forced Pprecision_not\n\
-\n\
- QbBound 0:0.5 Qbk:0Bk:0_drop QbB-scale-box Qbb-scale-last Qcoplanar\n\
- Qfurthest Qgood_only QGood_point Qinterior Qmax_out\n\
- QJoggle Qrandom QRotate Qsearch_1st Qtriangulate\n\
- QupperDelaunay QVertex_good Qvneighbors Qxact_merge Qzinfinite\n\
-\n\
- Q0_no_premerge Q1_no_angle Q2_no_independ Q3_no_redundant Q4_no_old\n\
- Q5_no_check_out Q6_no_concave Q7_depth_first Q8_no_near_in Q9_pick_furthest\n\
- Q10_no_narrow Q11_trinormals\n\
-\n\
- T4_trace Tcheck_often Tstatistics Tverify Tz_stdout\n\
- TFacet_log TInput_file TPoint_trace TMerge_trace TOutput_file\n\
- TRerun TWide_trace TVertex_stop TCone_stop\n\
-\n\
- Angle_max Centrum_size Error_round Random_dist Visible_min\n\
- Ucoplanar_max Wide_outside\n\
-";
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="main">-</a>
-
- main( argc, argv )
- processes the command line, calls qhull() to do the work, and exits
-
- design:
- initializes data structures
- reads points
- finishes initialization
- computes convex hull and other structures
- checks the result
- writes the output
- frees memory
-*/
-int main(int argc, char *argv[]) {
- int curlong, totlong; /* used !qh_NOmem */
- int exitcode, numpoints, dim;
- coordT *points;
- boolT ismalloc;
-
-#if __MWERKS__ && __POWERPC__
- char inBuf[BUFSIZ], outBuf[BUFSIZ], errBuf[BUFSIZ];
- SIOUXSettings.showstatusline= false;
- SIOUXSettings.tabspaces= 1;
- SIOUXSettings.rows= 40;
- if (setvbuf (stdin, inBuf, _IOFBF, sizeof(inBuf)) < 0 /* w/o, SIOUX I/O is slow*/
- || setvbuf (stdout, outBuf, _IOFBF, sizeof(outBuf)) < 0
- || (stdout != stderr && setvbuf (stderr, errBuf, _IOFBF, sizeof(errBuf)) < 0))
- fprintf (stderr, "qhull internal warning (main): could not change stdio to fully buffered.\n");
- argc= ccommand(&argv);
-#endif
-
- if ((argc == 1) && isatty( 0 /*stdin*/)) {
- fprintf(stdout, qh_prompt2, qh_version);
- exit(qh_ERRnone);
- }
- if (argc > 1 && *argv[1] == '-' && !*(argv[1]+1)) {
- fprintf(stdout, qh_prompta, qh_version, qh_DEFAULTbox,
- qh_promptb, qh_promptc, qh_promptd, qh_prompte);
- exit(qh_ERRnone);
- }
- if (argc >1 && *argv[1] == '.' && !*(argv[1]+1)) {
- fprintf(stdout, qh_prompt3, qh_version);
- exit(qh_ERRnone);
- }
- qh_init_A (stdin, stdout, stderr, argc, argv); /* sets qh qhull_command */
- exitcode= setjmp (qh errexit); /* simple statement for CRAY J916 */
- if (!exitcode) {
- qh_initflags (qh qhull_command);
- points= qh_readpoints (&numpoints, &dim, &ismalloc);
- qh_init_B (points, numpoints, dim, ismalloc);
- qh_qhull();
- qh_check_output();
- qh_produce_output();
- if (qh VERIFYoutput && !qh FORCEoutput && !qh STOPpoint && !qh STOPcone)
- qh_check_points();
- exitcode= qh_ERRnone;
- }
- qh NOerrexit= True; /* no more setjmp */
-#ifdef qh_NOmem
- qh_freeqhull( True);
-#else
- qh_freeqhull( False);
- qh_memfreeshort (&curlong, &totlong);
- if (curlong || totlong)
- fprintf (stderr, "qhull internal warning (main): did not free %d bytes of long memory (%d pieces)\n",
- totlong, curlong);
-#endif
- return exitcode;
-} /* main */
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/user_eg.c b/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/user_eg.c
deleted file mode 100644
index 9f2ac81d781955721a83f4762bac571e6f13d7a8..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/user_eg.c
+++ /dev/null
@@ -1,317 +0,0 @@
-/*<html><pre> -<a href="qh-user.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- user_eg.c
- sample code for calling qhull() from an application
-
- call with:
-
- user_eg "cube/diamond options" "delaunay options" "halfspace options"
-
- for example:
-
- user_eg # return summaries
-
- user_eg "n" "o" "Fp" # return normals, OFF, points
-
- user_eg "n Qt" "o" "Fp" # triangulated cube
-
- user_eg "QR0 p" "QR0 v p" "QR0 Fp" # rotate input and return points
- # 'v' returns Voronoi
- # transform is rotated for halfspaces
-
- main() makes three runs of qhull.
-
- 1) compute the convex hull of a cube
-
- 2a) compute the Delaunay triangulation of random points
-
- 2b) find the Delaunay triangle closest to a point.
-
- 3) compute the halfspace intersection of a diamond
-
- notes:
-
- For another example, see main() in unix.c and user_eg2.c.
- These examples, call qh_qhull() directly. They allow
- tighter control on the code loaded with Qhull.
-
- For a simple C++ example, see qhull_interface.cpp
-
- Summaries are sent to stderr if other output formats are used
-
- compiled by 'make user_eg'
-
- see qhull.h for data structures, macros, and user-callable functions.
-*/
-
-#include "qhull_a.h"
-
-/*-------------------------------------------------
--internal function prototypes
-*/
-void print_summary (void);
-void makecube (coordT *points, int numpoints, int dim);
-void makeDelaunay (coordT *points, int numpoints, int dim, int seed);
-void findDelaunay (int dim);
-void makehalf (coordT *points, int numpoints, int dim);
-
-/*-------------------------------------------------
--print_summary()
-*/
-void print_summary (void) {
- facetT *facet;
- int k;
-
- printf ("\n%d vertices and %d facets with normals:\n",
- qh num_vertices, qh num_facets);
- FORALLfacets {
- for (k=0; k < qh hull_dim; k++)
- printf ("%6.2g ", facet->normal[k]);
- printf ("\n");
- }
-}
-
-/*--------------------------------------------------
--makecube- set points to vertices of cube
- points is numpoints X dim
-*/
-void makecube (coordT *points, int numpoints, int dim) {
- int j,k;
- coordT *point;
-
- for (j=0; j<numpoints; j++) {
- point= points + j*dim;
- for (k=dim; k--; ) {
- if (j & ( 1 << k))
- point[k]= 1.0;
- else
- point[k]= -1.0;
- }
- }
-} /*.makecube.*/
-
-/*--------------------------------------------------
--makeDelaunay- set points for dim Delaunay triangulation of random points
- points is numpoints X dim.
-notes:
- makeDelaunay() in user_eg2.c uses qh_setdelaunay() to project points in place.
-*/
-void makeDelaunay (coordT *points, int numpoints, int dim, int seed) {
- int j,k;
- coordT *point, realr;
-
- printf ("seed: %d\n", seed);
- qh_RANDOMseed_( seed);
- for (j=0; j<numpoints; j++) {
- point= points + j*dim;
- for (k= 0; k < dim; k++) {
- realr= qh_RANDOMint;
- point[k]= 2.0 * realr/(qh_RANDOMmax+1) - 1.0;
- }
- }
-} /*.makeDelaunay.*/
-
-/*--------------------------------------------------
--findDelaunay- find Delaunay triangle for [0.5,0.5,...]
- assumes dim < 100
-notes:
- calls qh_setdelaunay() to project the point to a parabaloid
-warning:
- This is not implemented for tricoplanar facets ('Qt'),
- See <a href="../html/qh-in.htm#findfacet">locate a facet with qh_findbestfacet()</a>
-*/
-void findDelaunay (int dim) {
- int k;
- coordT point[ 100];
- boolT isoutside;
- realT bestdist;
- facetT *facet;
- vertexT *vertex, **vertexp;
-
- for (k= 0; k < dim; k++)
- point[k]= 0.5;
- qh_setdelaunay (dim+1, 1, point);
- facet= qh_findbestfacet (point, qh_ALL, &bestdist, &isoutside);
- if (facet->tricoplanar) {
- fprintf(stderr, "findDelaunay: not implemented for triangulated, non-simplicial Delaunay regions (tricoplanar facet, f%d).\n",
- facet->id);
- qh_errexit (qh_ERRqhull, facet, NULL);
- }
- FOREACHvertex_(facet->vertices) {
- for (k=0; k < dim; k++)
- printf ("%5.2f ", vertex->point[k]);
- printf ("\n");
- }
-} /*.findDelaunay.*/
-
-/*--------------------------------------------------
--makehalf- set points to halfspaces for a (dim)-dimensional diamond
- points is numpoints X dim+1
-
- each halfspace consists of dim coefficients followed by an offset
-*/
-void makehalf (coordT *points, int numpoints, int dim) {
- int j,k;
- coordT *point;
-
- for (j=0; j<numpoints; j++) {
- point= points + j*(dim+1);
- point[dim]= -1.0; /* offset */
- for (k=dim; k--; ) {
- if (j & ( 1 << k))
- point[k]= 1.0;
- else
- point[k]= -1.0;
- }
- }
-} /*.makehalf.*/
-
-#define DIM 3 /* dimension of points, must be < 31 for SIZEcube */
-#define SIZEcube (1<<DIM)
-#define SIZEdiamond (2*DIM)
-#define TOTpoints (SIZEcube + SIZEdiamond)
-
-/*--------------------------------------------------
--main- derived from call_qhull in user.c
-
- see program header
-
- this contains three runs of Qhull for convex hull, Delaunay
- triangulation or Voronoi vertices, and halfspace intersection
-
-*/
-int main (int argc, char *argv[]) {
- int dim= DIM; /* dimension of points */
- int numpoints; /* number of points */
- coordT points[(DIM+1)*TOTpoints]; /* array of coordinates for each point */
- coordT *rows[TOTpoints];
- boolT ismalloc= False; /* True if qhull should free points in qh_freeqhull() or reallocation */
- char flags[250]; /* option flags for qhull, see qh_opt.htm */
- FILE *outfile= stdout; /* output from qh_produce_output()
- use NULL to skip qh_produce_output() */
- FILE *errfile= stderr; /* error messages from qhull code */
- int exitcode; /* 0 if no error from qhull */
- facetT *facet; /* set by FORALLfacets */
- int curlong, totlong; /* memory remaining after qh_memfreeshort */
- int i;
-
- printf ("This is the output from user_eg.c\n\n\
-It shows how qhull() may be called from an application. It is not part\n\
-of qhull itself. If it appears accidently, please remove user_eg.c from\n\
-your project.\n\n");
-
- /*
- Run 1: convex hull
- */
- printf( "\ncompute convex hull of cube after rotating input\n");
- sprintf (flags, "qhull s Tcv %s", argc >= 2 ? argv[1] : "");
- numpoints= SIZEcube;
- makecube (points, numpoints, DIM);
- for (i=numpoints; i--; )
- rows[i]= points+dim*i;
- qh_printmatrix (outfile, "input", rows, numpoints, dim);
- exitcode= qh_new_qhull (dim, numpoints, points, ismalloc,
- flags, outfile, errfile);
- if (!exitcode) { /* if no error */
- /* 'qh facet_list' contains the convex hull */
- print_summary();
- FORALLfacets {
- /* ... your code ... */
- }
- }
- qh_freeqhull(!qh_ALL); /* free long memory */
- qh_memfreeshort (&curlong, &totlong); /* free short memory and memory allocator */
- if (curlong || totlong)
- fprintf (errfile, "qhull internal warning (user_eg, #1): did not free %d bytes of long memory (%d pieces)\n", totlong, curlong);
-
- /*
- Run 2: Delaunay triangulation
- */
-
- printf( "\ncompute %d-d Delaunay triangulation\n", dim);
- sprintf (flags, "qhull s d Tcv %s", argc >= 3 ? argv[2] : "");
- numpoints= SIZEcube;
- makeDelaunay (points, numpoints, dim, time(NULL));
- for (i=numpoints; i--; )
- rows[i]= points+dim*i;
- qh_printmatrix (outfile, "input", rows, numpoints, dim);
- exitcode= qh_new_qhull (dim, numpoints, points, ismalloc,
- flags, outfile, errfile);
- if (!exitcode) { /* if no error */
- /* 'qh facet_list' contains the convex hull */
- /* If you want a Voronoi diagram ('v') and do not request output (i.e., outfile=NULL),
- call qh_setvoronoi_all() after qh_new_qhull(). */
- print_summary();
- FORALLfacets {
- /* ... your code ... */
- }
- printf( "\nfind %d-d Delaunay triangle closest to [0.5, 0.5, ...]\n", dim);
- exitcode= setjmp (qh errexit);
- if (!exitcode) {
- /* Trap Qhull errors in findDelaunay(). Without the setjmp(), Qhull
- will exit() after reporting an error */
- qh NOerrexit= False;
- findDelaunay (DIM);
- }
- qh NOerrexit= True;
- }
-#if qh_QHpointer /* see user.h */
- {
- qhT *oldqhA, *oldqhB;
- coordT pointsB[DIM*TOTpoints]; /* array of coordinates for each point */
-
-
- printf( "\nsave first triangulation and compute a new triangulation\n");
- oldqhA= qh_save_qhull();
- sprintf (flags, "qhull s d Tcv %s", argc >= 3 ? argv[2] : "");
- numpoints= SIZEcube;
- makeDelaunay (pointsB, numpoints, dim, time(NULL)+1);
- for (i=numpoints; i--; )
- rows[i]= pointsB+dim*i;
- qh_printmatrix (outfile, "input", rows, numpoints, dim);
- exitcode= qh_new_qhull (dim, numpoints, pointsB, ismalloc,
- flags, outfile, errfile);
- if (!exitcode)
- print_summary();
- printf( "\nsave second triangulation and restore first one\n");
- oldqhB= qh_save_qhull();
- qh_restore_qhull (&oldqhA);
- print_summary();
- printf( "\nfree first triangulation and restore second one.\n");
- qh_freeqhull (qh_ALL); /* free short and long memory used by first call */
- /* do not use qh_memfreeshort */
- qh_restore_qhull (&oldqhB);
- print_summary();
- }
-#endif
- qh_freeqhull(!qh_ALL); /* free long memory */
- qh_memfreeshort (&curlong, &totlong); /* free short memory and memory allocator */
- if (curlong || totlong)
- fprintf (errfile, "qhull internal warning (user_eg, #2): did not free %d bytes of long memory (%d pieces)\n", totlong, curlong);
-
- /*
- Run 3: halfspace intersection about the origin
- */
- printf( "\ncompute halfspace intersection about the origin for a diamond\n");
- sprintf (flags, "qhull H0 s Tcv %s", argc >= 4 ? argv[3] : "Fp");
- numpoints= SIZEcube;
- makehalf (points, numpoints, dim);
- for (i=numpoints; i--; )
- rows[i]= points+(dim+1)*i;
- qh_printmatrix (outfile, "input as halfspace coefficients + offsets", rows, numpoints, dim+1);
- /* use qh_sethalfspace_all to transform the halfspaces yourself.
- If so, set 'qh feasible_point and do not use option 'Hn,...' [it would retransform the halfspaces]
- */
- exitcode= qh_new_qhull (dim+1, numpoints, points, ismalloc,
- flags, outfile, errfile);
- if (!exitcode)
- print_summary();
- qh_freeqhull (!qh_ALL);
- qh_memfreeshort (&curlong, &totlong);
- if (curlong || totlong) /* could also check previous runs */
- fprintf (stderr, "qhull internal warning (user_eg, #3): did not free %d bytes of long memory (%d pieces)\n",
- totlong, curlong);
- return exitcode;
-} /* main */
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/user_eg2.c b/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/user_eg2.c
deleted file mode 100644
index 28ecbce467423160cd933c0165683c1c09108e36..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/eg/user_eg2.c
+++ /dev/null
@@ -1,542 +0,0 @@
-/*<html><pre> -<a href="qh-qhull.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- user_eg2.c
-
- sample code for calling qhull() from an application.
-
- See user_eg.c for a simpler method using qh_new_qhull().
- The method used here and in unix.c gives you additional
- control over Qhull.
-
- call with:
-
- user_eg2 "triangulated cube/diamond options" "delaunay options" "halfspace options"
-
- for example:
-
- user_eg2 # return summaries
-
- user_eg2 "n" "o" "Fp" # return normals, OFF, points
-
- user_eg2 "QR0 p" "QR0 v p" "QR0 Fp" # rotate input and return points
- # 'v' returns Voronoi
- # transform is rotated for halfspaces
-
- main() makes three runs of qhull.
-
- 1) compute the convex hull of a cube, and incrementally add a diamond
-
- 2a) compute the Delaunay triangulation of random points, and add points.
-
- 2b) find the Delaunay triangle closest to a point.
-
- 3) compute the halfspace intersection of a diamond, and add a cube
-
- notes:
-
- summaries are sent to stderr if other output formats are used
-
- derived from unix.c and compiled by 'make user_eg2'
-
- see qhull.h for data structures, macros, and user-callable functions.
-
- If you want to control all output to stdio and input to stdin,
- set the #if below to "1" and delete all lines that contain "io.c".
- This prevents the loading of io.o. Qhull will
- still write to 'qh ferr' (stderr) for error reporting and tracing.
-
- Defining #if 1, also prevents user.o from being loaded.
-*/
-
-#include "qhull_a.h"
-
-/*-------------------------------------------------
--internal function prototypes
-*/
-void print_summary (void);
-void makecube (coordT *points, int numpoints, int dim);
-void adddiamond (coordT *points, int numpoints, int numnew, int dim);
-void makeDelaunay (coordT *points, int numpoints, int dim);
-void addDelaunay (coordT *points, int numpoints, int numnew, int dim);
-void findDelaunay (int dim);
-void makehalf (coordT *points, int numpoints, int dim);
-void addhalf (coordT *points, int numpoints, int numnew, int dim, coordT *feasible);
-
-/*-------------------------------------------------
--print_summary()
-*/
-void print_summary (void) {
- facetT *facet;
- int k;
-
- printf ("\n%d vertices and %d facets with normals:\n",
- qh num_vertices, qh num_facets);
- FORALLfacets {
- for (k=0; k < qh hull_dim; k++)
- printf ("%6.2g ", facet->normal[k]);
- printf ("\n");
- }
-}
-
-/*--------------------------------------------------
--makecube- set points to vertices of cube
- points is numpoints X dim
-*/
-void makecube (coordT *points, int numpoints, int dim) {
- int j,k;
- coordT *point;
-
- for (j=0; j<numpoints; j++) {
- point= points + j*dim;
- for (k=dim; k--; ) {
- if (j & ( 1 << k))
- point[k]= 1.0;
- else
- point[k]= -1.0;
- }
- }
-} /*.makecube.*/
-
-/*--------------------------------------------------
--adddiamond- add diamond to convex hull
- points is numpoints+numnew X dim.
-
-notes:
- qh_addpoint() does not make a copy of the point coordinates.
-
- For inside points and some outside points, qh_findbestfacet performs
- an exhaustive search for a visible facet. Algorithms that retain
- previously constructed hulls should be faster for on-line construction
- of the convex hull.
-*/
-void adddiamond (coordT *points, int numpoints, int numnew, int dim) {
- int j,k;
- coordT *point;
- facetT *facet;
- boolT isoutside;
- realT bestdist;
-
- for (j= 0; j < numnew ; j++) {
- point= points + (numpoints+j)*dim;
- if (points == qh first_point) /* in case of 'QRn' */
- qh num_points= numpoints+j+1;
- /* qh num_points sets the size of the points array. You may
- allocate the points elsewhere. If so, qh_addpoint records
- the point's address in qh other_points
- */
- for (k=dim; k--; ) {
- if (j/2 == k)
- point[k]= (j & 1) ? 2.0 : -2.0;
- else
- point[k]= 0.0;
- }
- facet= qh_findbestfacet (point, !qh_ALL, &bestdist, &isoutside);
- if (isoutside) {
- if (!qh_addpoint (point, facet, False))
- break; /* user requested an early exit with 'TVn' or 'TCn' */
- }
- printf ("%d vertices and %d facets\n",
- qh num_vertices, qh num_facets);
- /* qh_produce_output(); */
- }
- if (qh DOcheckmax)
- qh_check_maxout();
- else if (qh KEEPnearinside)
- qh_nearcoplanar();
-} /*.adddiamond.*/
-
-/*--------------------------------------------------
--makeDelaunay- set points for dim-1 Delaunay triangulation of random points
- points is numpoints X dim. Each point is projected to a paraboloid.
-*/
-void makeDelaunay (coordT *points, int numpoints, int dim) {
- int j,k, seed;
- coordT *point, realr;
-
- seed= time(NULL);
- printf ("seed: %d\n", seed);
- qh_RANDOMseed_( seed);
- for (j=0; j<numpoints; j++) {
- point= points + j*dim;
- for (k= 0; k < dim-1; k++) {
- realr= qh_RANDOMint;
- point[k]= 2.0 * realr/(qh_RANDOMmax+1) - 1.0;
- }
- }
- qh_setdelaunay (dim, numpoints, points);
-} /*.makeDelaunay.*/
-
-/*--------------------------------------------------
--addDelaunay- add points to dim-1 Delaunay triangulation
- points is numpoints+numnew X dim. Each point is projected to a paraboloid.
-notes:
- qh_addpoint() does not make a copy of the point coordinates.
-
- Since qh_addpoint() is not given a visible facet, it performs a directed
- search of all facets. Algorithms that retain previously
- constructed hulls may be faster.
-*/
-void addDelaunay (coordT *points, int numpoints, int numnew, int dim) {
- int j,k;
- coordT *point, realr;
- facetT *facet;
- realT bestdist;
- boolT isoutside;
-
- for (j= 0; j < numnew ; j++) {
- point= points + (numpoints+j)*dim;
- if (points == qh first_point) /* in case of 'QRn' */
- qh num_points= numpoints+j+1;
- /* qh num_points sets the size of the points array. You may
- allocate the point elsewhere. If so, qh_addpoint records
- the point's address in qh other_points
- */
- for (k= 0; k < dim-1; k++) {
- realr= qh_RANDOMint;
- point[k]= 2.0 * realr/(qh_RANDOMmax+1) - 1.0;
- }
- qh_setdelaunay (dim, 1, point);
- facet= qh_findbestfacet (point, !qh_ALL, &bestdist, &isoutside);
- if (isoutside) {
- if (!qh_addpoint (point, facet, False))
- break; /* user requested an early exit with 'TVn' or 'TCn' */
- }
- qh_printpoint (stdout, "added point", point);
- printf ("%d points, %d extra points, %d vertices, and %d facets in total\n",
- qh num_points, qh_setsize (qh other_points),
- qh num_vertices, qh num_facets);
-
- /* qh_produce_output(); */
- }
- if (qh DOcheckmax)
- qh_check_maxout();
- else if (qh KEEPnearinside)
- qh_nearcoplanar();
-} /*.addDelaunay.*/
-
-/*--------------------------------------------------
--findDelaunay- find Delaunay triangle for [0.5,0.5,...]
- assumes dim < 100
-notes:
- calls qh_setdelaunay() to project the point to a parabaloid
-warning:
- This is not implemented for tricoplanar facets ('Qt'),
- See <a href="../html/qh-in.htm#findfacet">locate a facet with qh_findbestfacet()</a>
-*/
-void findDelaunay (int dim) {
- int k;
- coordT point[ 100];
- boolT isoutside;
- realT bestdist;
- facetT *facet;
- vertexT *vertex, **vertexp;
-
- for (k= 0; k < dim-1; k++)
- point[k]= 0.5;
- qh_setdelaunay (dim, 1, point);
- facet= qh_findbestfacet (point, qh_ALL, &bestdist, &isoutside);
- if (facet->tricoplanar) {
- fprintf(stderr, "findDelaunay: not implemented for triangulated, non-simplicial Delaunay regions (tricoplanar facet, f%d).\n",
- facet->id);
- qh_errexit (qh_ERRqhull, facet, NULL);
- }
- FOREACHvertex_(facet->vertices) {
- for (k=0; k < dim-1; k++)
- printf ("%5.2f ", vertex->point[k]);
- printf ("\n");
- }
-} /*.findDelaunay.*/
-
-/*--------------------------------------------------
--makehalf- set points to halfspaces for a (dim)-d diamond
- points is numpoints X dim+1
-
- each halfspace consists of dim coefficients followed by an offset
-*/
-void makehalf (coordT *points, int numpoints, int dim) {
- int j,k;
- coordT *point;
-
- for (j=0; j<numpoints; j++) {
- point= points + j*(dim+1);
- point[dim]= -1.0; /* offset */
- for (k=dim; k--; ) {
- if (j & ( 1 << k))
- point[k]= 1.0;
- else
- point[k]= -1.0;
- }
- }
-} /*.makehalf.*/
-
-/*--------------------------------------------------
--addhalf- add halfspaces for a (dim)-d cube to the intersection
- points is numpoints+numnew X dim+1
-notes:
- assumes dim < 100.
-
- For makehalf(), points is the initial set of halfspaces with offsets.
- It is transformed by qh_sethalfspace_all into a
- (dim)-d set of newpoints. Qhull computed the convex hull of newpoints -
- this is equivalent to the halfspace intersection of the
- orginal halfspaces.
-
- For addhalf(), the remainder of points stores the transforms of
- the added halfspaces. Qhull computes the convex hull of newpoints
- and the added points. qh_addpoint() does not make a copy of these points.
-
- Since halfspace intersection is equivalent to a convex hull,
- qh_findbestfacet may perform an exhaustive search
- for a visible facet. Algorithms that retain previously constructed
- intersections should be faster for on-line construction.
-*/
-void addhalf (coordT *points, int numpoints, int numnew, int dim, coordT *feasible) {
- int j,k;
- coordT *point, normal[100], offset, *next;
- facetT *facet;
- boolT isoutside;
- realT bestdist;
-
- for (j= 0; j < numnew ; j++) {
- offset= -1.0;
- for (k=dim; k--; ) {
- if (j/2 == k) {
- normal[k]= sqrt (dim); /* to normalize as in makehalf */
- if (j & 1)
- normal[k]= -normal[k];
- }else
- normal[k]= 0.0;
- }
- point= points + (numpoints+j)* (dim+1); /* does not use point[dim] */
- qh_sethalfspace (dim, point, &next, normal, &offset, feasible);
- facet= qh_findbestfacet (point, !qh_ALL, &bestdist, &isoutside);
- if (isoutside) {
- if (!qh_addpoint (point, facet, False))
- break; /* user requested an early exit with 'TVn' or 'TCn' */
- }
- qh_printpoint (stdout, "added offset -1 and normal", normal);
- printf ("%d points, %d extra points, %d vertices, and %d facets in total\n",
- qh num_points, qh_setsize (qh other_points),
- qh num_vertices, qh num_facets);
- /* qh_produce_output(); */
- }
- if (qh DOcheckmax)
- qh_check_maxout();
- else if (qh KEEPnearinside)
- qh_nearcoplanar();
-} /*.addhalf.*/
-
-#define DIM 3 /* dimension of points, must be < 31 for SIZEcube */
-#define SIZEcube (1<<DIM)
-#define SIZEdiamond (2*DIM)
-#define TOTpoints (SIZEcube + SIZEdiamond)
-
-/*--------------------------------------------------
--main- derived from call_qhull in user.c
-
- see program header
-
- this contains three runs of Qhull for convex hull, Delaunay
- triangulation or Voronoi vertices, and halfspace intersection
-
-*/
-int main (int argc, char *argv[]) {
- boolT ismalloc;
- int curlong, totlong, exitcode;
- char options [2000];
-
- printf ("This is the output from user_eg2.c\n\n\
-It shows how qhull() may be called from an application. It is not part\n\
-of qhull itself. If it appears accidently, please remove user_eg2.c from\n\
-your project.\n\n");
- ismalloc= False; /* True if qh_freeqhull should 'free(array)' */
- /*
- Run 1: convex hull
- */
- qh_init_A (stdin, stdout, stderr, 0, NULL);
- exitcode= setjmp (qh errexit);
- if (!exitcode) {
- coordT array[TOTpoints][DIM];
-
- strcat (qh rbox_command, "user_eg cube");
- sprintf (options, "qhull s Tcv Q11 %s ", argc >= 2 ? argv[1] : "");
- qh_initflags (options);
- printf( "\ncompute triangulated convex hull of cube after rotating input\n");
- makecube (array[0], SIZEcube, DIM);
- qh_init_B (array[0], SIZEcube, DIM, ismalloc);
- qh_qhull();
- qh_check_output();
- qh_triangulate(); /* requires option 'Q11' if want to add points */
- print_summary ();
- if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
- qh_check_points ();
- printf( "\nadd points in a diamond\n");
- adddiamond (array[0], SIZEcube, SIZEdiamond, DIM);
- qh_check_output();
- print_summary ();
- qh_produce_output(); /* delete this line to help avoid io.c */
- if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
- qh_check_points ();
- }
- qh NOerrexit= True;
- qh_freeqhull (!qh_ALL);
- qh_memfreeshort (&curlong, &totlong);
- /*
- Run 2: Delaunay triangulation
- */
- qh_init_A (stdin, stdout, stderr, 0, NULL);
- exitcode= setjmp (qh errexit);
- if (!exitcode) {
- coordT array[TOTpoints][DIM];
-
- strcat (qh rbox_command, "user_eg Delaunay");
- sprintf (options, "qhull s d Tcv %s", argc >= 3 ? argv[2] : "");
- qh_initflags (options);
- printf( "\ncompute %d-d Delaunay triangulation\n", DIM-1);
- makeDelaunay (array[0], SIZEcube, DIM);
- /* Instead of makeDelaunay with qh_setdelaunay, you may
- produce a 2-d array of points, set DIM to 2, and set
- qh PROJECTdelaunay to True. qh_init_B will call
- qh_projectinput to project the points to the paraboloid
- and add a point "at-infinity".
- */
- qh_init_B (array[0], SIZEcube, DIM, ismalloc);
- qh_qhull();
- /* If you want Voronoi ('v') without qh_produce_output(), call
- qh_setvoronoi_all() after qh_qhull() */
- qh_check_output();
- print_summary ();
- qh_produce_output(); /* delete this line to help avoid io.c */
- if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
- qh_check_points ();
- printf( "\nadd points to triangulation\n");
- addDelaunay (array[0], SIZEcube, SIZEdiamond, DIM);
- qh_check_output();
- qh_produce_output(); /* delete this line to help avoid io.c */
- if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
- qh_check_points ();
- printf( "\nfind Delaunay triangle closest to [0.5, 0.5, ...]\n");
- findDelaunay (DIM);
- }
- qh NOerrexit= True;
- qh_freeqhull (!qh_ALL);
- qh_memfreeshort (&curlong, &totlong);
- /*
- Run 3: halfspace intersection
- */
- qh_init_A (stdin, stdout, stderr, 0, NULL);
- exitcode= setjmp (qh errexit);
- if (!exitcode) {
- coordT array[TOTpoints][DIM+1]; /* +1 for halfspace offset */
- pointT *points;
-
- strcat (qh rbox_command, "user_eg halfspaces");
- sprintf (options, "qhull H0 s Tcv %s", argc >= 4 ? argv[3] : "");
- qh_initflags (options);
- printf( "\ncompute halfspace intersection about the origin for a diamond\n");
- makehalf (array[0], SIZEcube, DIM);
- qh_setfeasible (DIM); /* from io.c, sets qh feasible_point from 'Hn,n' */
- /* you may malloc and set qh feasible_point directly. It is only used for
- option 'Fp' */
- points= qh_sethalfspace_all ( DIM+1, SIZEcube, array[0], qh feasible_point);
- qh_init_B (points, SIZEcube, DIM, True); /* qh_freeqhull frees points */
- qh_qhull();
- qh_check_output();
- qh_produce_output(); /* delete this line to help avoid io.c */
- if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
- qh_check_points ();
- printf( "\nadd halfspaces for cube to intersection\n");
- addhalf (array[0], SIZEcube, SIZEdiamond, DIM, qh feasible_point);
- qh_check_output();
- qh_produce_output(); /* delete this line to help avoid io.c */
- if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
- qh_check_points ();
- }
- qh NOerrexit= True;
- qh NOerrexit= True;
- qh_freeqhull (!qh_ALL);
- qh_memfreeshort (&curlong, &totlong);
- if (curlong || totlong) /* could also check previous runs */
- fprintf (stderr, "qhull internal warning (main): did not free %d bytes of long memory (%d pieces)\n",
- totlong, curlong);
- return exitcode;
-} /* main */
-
-#if 1 /* use 1 to prevent loading of io.o and user.o */
-/*-------------------------------------------
--errexit- return exitcode to system after an error
- assumes exitcode non-zero
- prints useful information
- see qh_errexit2() in qhull.c for 2 facets
-*/
-void qh_errexit(int exitcode, facetT *facet, ridgeT *ridge) {
-
- if (qh ERREXITcalled) {
- fprintf (qh ferr, "qhull error while processing previous error. Exit program\n");
- exit(1);
- }
- qh ERREXITcalled= True;
- if (!qh QHULLfinished)
- qh hulltime= (unsigned)clock() - qh hulltime;
- fprintf (qh ferr, "\nWhile executing: %s | %s\n", qh rbox_command, qh qhull_command);
- fprintf(qh ferr, "Options selected:\n%s\n", qh qhull_options);
- if (qh furthest_id >= 0) {
- fprintf(qh ferr, "\nLast point added to hull was p%d", qh furthest_id);
- if (zzval_(Ztotmerge))
- fprintf(qh ferr, " Last merge was #%d.", zzval_(Ztotmerge));
- if (qh QHULLfinished)
- fprintf(qh ferr, "\nQhull has finished constructing the hull.");
- else if (qh POSTmerging)
- fprintf(qh ferr, "\nQhull has started post-merging");
- fprintf(qh ferr, "\n\n");
- }
- if (qh NOerrexit) {
- fprintf (qh ferr, "qhull error while ending program. Exit program\n");
- exit(1);
- }
- if (!exitcode)
- exitcode= qh_ERRqhull;
- qh NOerrexit= True;
- longjmp(qh errexit, exitcode);
-} /* errexit */
-
-
-/*-------------------------------------------
--errprint- prints out the information of the erroneous object
- any parameter may be NULL, also prints neighbors and geomview output
-*/
-void qh_errprint(char *string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex) {
-
- fprintf (qh ferr, "%s facets f%d f%d ridge r%d vertex v%d\n",
- string, getid_(atfacet), getid_(otherfacet), getid_(atridge),
- getid_(atvertex));
-} /* errprint */
-
-
-void qh_printfacetlist(facetT *facetlist, setT *facets, boolT printall) {
- facetT *facet, **facetp;
-
- /* remove these calls to help avoid io.c */
- qh_printbegin (qh ferr, qh_PRINTfacets, facetlist, facets, printall);/*io.c*/
- FORALLfacet_(facetlist) /*io.c*/
- qh_printafacet(qh ferr, qh_PRINTfacets, facet, printall); /*io.c*/
- FOREACHfacet_(facets) /*io.c*/
- qh_printafacet(qh ferr, qh_PRINTfacets, facet, printall); /*io.c*/
- qh_printend (qh ferr, qh_PRINTfacets, facetlist, facets, printall); /*io.c*/
-
- FORALLfacet_(facetlist)
- fprintf( qh ferr, "facet f%d\n", facet->id);
-} /* printfacetlist */
-
-
-
-/*-----------------------------------------
--user_memsizes- allocate up to 10 additional, quick allocation sizes
-*/
-void qh_user_memsizes (void) {
-
- /* qh_memsize (size); */
-} /* user_memsizes */
-
-#endif
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/index.htm b/GraspPlanning/ExternalDependencies/qhull-2003.1/html/index.htm
deleted file mode 100644
index 354579bc0afe2ab7af4b8005ea2e90cb157508fe..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/index.htm
+++ /dev/null
@@ -1,777 +0,0 @@
-<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
-<html>
-
-<head>
-<meta http-equiv="Content-Type"
-content="text/html; charset=iso-8859-1">
-<meta name="GENERATOR" content="Microsoft FrontPage 2.0">
-<title>Qhull manual</title>
-<!-- Navigation links
-NOTE -- verify all links by 'grep href=' 'grep name=' add # 'sort /+7'
- index.htm
--->
-</head>
-
-<body>
-
-<p><a name="TOP"><b>Up:</b></a> <a
-href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b><a
-href="http://www.qhull.org/news">News</a> about Qhull<br>
-<b>Up:</b> <a href="http://www.qhull.org/html/qh-faq.htm">FAQ</a> about Qhull<br>
-<b>To:</b> <a href="#TOC">Qhull manual: Table of Contents</a>
-(please wait while loading) <br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a><br>
-
-<hr>
-<!-- Main text of document -->
-<h1><a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/fixed.html"><img
-src="qh--rand.gif" alt="[random-fixed]" align="middle"
-width="100" height="100"></a> Qhull manual </h1>
-
-<p>Qhull is a general dimension code for computing convex hulls,
-Delaunay triangulations, halfspace intersections about a point, Voronoi
-diagrams, furthest-site Delaunay triangulations, and
-furthest-site Voronoi diagrams. These structures have
-applications in science, engineering, statistics, and
-mathematics. See <a
-href="http://www.ifor.math.ethz.ch/staff/fukuda/polyfaq/polyfaq.html">Fukuda's
-introduction</a> to convex hulls, Delaunay triangulations,
-Voronoi diagrams, and linear programming. For a detailed
-introduction, see O'Rourke [<a href="#orou94">'94</a>], <i>Computational
-Geometry in C</i>.
-</p>
-
-<p>There are six programs. Except for rbox, they use
-the same code.
-<blockquote>
-<ul>
-<li><a href="qconvex.htm">qconvex</a> -- convex hulls
-<li><a href="qdelaun.htm">qdelaunay</a> -- Delaunay triangulations and
- furthest-site Delaunay triangulations
-<li><a href="qhalf.htm">qhalf</a> -- halfspace intersections about a point
-<li><a href="qhull.htm">qhull</a> -- all structures with additional options
-<li><a href="qvoronoi.htm">qvoronoi</a> -- Voronoi diagrams and
- furthest-site Voronoi diagrams
-<li><a href="rbox.htm">rbox</a> -- generate point distributions for qhull
-</ul>
-</blockquote>
-
-<p>Qhull implements the Quickhull algorithm for computing the
-convex hull. Qhull includes options
-for hull volume, facet area, multiple output formats, and
-graphical output. It can approximate a convex hull. </p>
-
-<p>Qhull handles roundoff errors from floating point
-arithmetic. It generates a convex hull with "thick" facets.
-A facet's outer plane is clearly above all of the points;
-its inner plane is clearly below the facet's vertices. Any
-exact convex hull must lie between the inner and outer plane.
-
-<p>Qhull uses merged facets, triangulated output, or joggled
-input. Triangulated output triangulates non-simplicial, merged
-facets. Joggled input also
-guarantees simplicial output, but it
-is less accurate than merged facets. For merged facets, Qhull
-reports the maximum outer and inner plane.
-
-<p><i>Brad Barber, Cambridge MA, 2003/12/30</i></p>
-
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-
-<hr>
-
-<h2><a href="#TOP">»</a><a name="TOC">Qhull manual: Table of
-Contents </a></h2>
-
-<ul>
- <li><a href="#when">When</a> to use Qhull
- <ul>
- <li><a href="http://www.qhull.org/news">News</a> for Qhull
- with new features and reported bugs.
- <li><a href="http://www.qhull.org">Home</a> for Qhull with additional URLs
- (<a href=index.htm>local copy</a>)
- <li><a href="http://www.qhull.org/html/qh-faq.htm">FAQ</a> for Qhull (<a href="qh-faq.htm">local copy</a>)
- <li><a href="http://www.qhull.org/download">Download</a> Qhull (<a href=qh-get.htm>local copy</a>)
- <li><a href="qh-quick.htm#programs">Quick</a> reference for Qhull and its <a href="qh-quick.htm#options">options</a>
- <p>
- <li><a href="../COPYING.txt">COPYING.txt</a> - copyright notice<br>
- <li><a href="../REGISTER.txt">REGISTER.txt</a> - registration<br>
- <li><a href="../README.txt">README.txt</a> - installation
- instructions<br>
- <li><a href="../src/Changes.txt">Changes.txt</a> - change history <br>
- <li><a href="qhull.txt">qhull.txt</a> - Unix manual page
- </ul>
- <p>
- <li><a href="#description">Description</a> of Qhull
- <ul>
- <li><a href="#definition">de</a>finition • <a
- href="#input">in</a>put • <a href="#output">ou</a>tput
- • <a href="#algorithm">al</a>gorithm • <a
- href="#structure">da</a>ta structure </li>
- <li><a href="qh-impre.htm">Imprecision</a> in Qhull</li>
- <LI><a href="qh-impre.htm#joggle">Merged facets</a> or joggled input
- <li><a href="#geomview">Geomview</a>, Qhull's graphical
- viewer</li>
- <li><a href="qh-eg.htm">Examples</a> of Qhull using Geomview</li>
- </ul>
- <p>
- <li><a href=qh-quick.htm#programs>Qhull programs</a>
- <ul>
- <li><a href="qconvex.htm">qconvex</a> -- convex hulls
- <li><a href="qdelaun.htm">qdelaunay</a> -- Delaunay triangulations and
- furthest-site Delaunay triangulations
- <li><a href="qhalf.htm">qhalf</a> -- halfspace intersections about a point
- <li><a href="qhull.htm">qhull</a> -- all structures with additional options
- <li><a href="qvoronoi.htm">qvoronoi</a> -- Voronoi diagrams and
- furthest-site Voronoi diagrams
- <li><a href="rbox.htm">rbox</a> -- generate point distributions for qhull
- </ul>
- <p>
- <li>Related URLs
- <ul>
-
- <li><a href="news:comp.graphics.algorithms">Newsgroup</a>:
- comp.graphics.algorithms
- <li><a
- href="http://exaflop.org/docs/cgafaq/">FAQ</a> for computer graphics algorithms and
- <a href="http://exaflop.org/docs/cgafaq/cga6.html">geometric</a> structures.
- <li>Amenta's <a href="http://www.geom.uiuc.edu/software/cglist">Directory
- of Computational Geometry Software </a></li>
- <li>Erickson's <a
- href="http://compgeom.cs.uiuc.edu/~jeffe/compgeom/code.html">Computational
- Geometry Software</a> </li>
- <li>Fukuda's <a
- href="http://www.ifor.math.ethz.ch/staff/fukuda/polyfaq/polyfaq.html">
- introduction</a> to convex hulls, Delaunay triangulations,
- Voronoi diagrams, and linear programming.
- <li>Stony Brook's <a
- href="http://www.cs.sunysb.edu/~algorith/major_section/1.6.shtml">Algorithm Repository</a> on computational geometry.
- </li>
- </ul>
- <p>
- <li><a href="qh-quick.htm#options">Qhull options</a><ul>
- <li><a href="qh-opto.htm#output">Output</a> formats</li>
- <li><a href="qh-optf.htm#format">Additional</a> I/O
- formats</li>
- <li><a href="qh-optg.htm#geomview">Geomview</a>
- output options</li>
- <li><a href="qh-optp.htm#print">Print</a> options</li>
- <li><a href="qh-optq.htm#qhull">Qhull</a> control
- options</li>
- <li><a href="qh-optc.htm#prec">Precision</a> options</li>
- <li><a href="qh-optt.htm#trace">Trace</a> options</li>
- </ul>
- </li>
- <p>
- <li><a href="qh-in.htm">Qhull internals</a><ul>
- <li><a href="qh-in.htm#performance">Performance</a>
- of Qhull</li>
- <li><a href="qh-in.htm#library">Calling</a> Qhull
- from your program</li>
- <li><a href="qh-in.htm#enhance">Enhancements</a> to
- Qhull</li>
- <li><a href="../src/index.htm">Qhull functions, macros, and
- data structures</a> </li>
- </ul>
- </li>
- <p>
- <li><a href="#bugs">What to do</a> if something goes wrong</li>
- <li><a href="#email">Email</a></li>
- <li><a href="#authors">Authors</a></li>
- <li><a href="#ref">References</a></li>
- <li><a href="#acknowledge">Acknowledgments</a></li>
-</ul>
-<h2><a href="#TOC">»</a><a name="when">When to use Qhull</a></h2>
-<blockquote>
-
-<p>Qhull constructs convex hulls, Delaunay triangulations,
-halfspace intersections about a point, Voronoi diagrams, furthest-site Delaunay
-triangulations, and furthest-site Voronoi diagrams.</p>
-
-<p>For convex hulls and halfspace intersections, Qhull may be used
-for 2-d upto 8-d. For Voronoi diagrams and Delaunay triangulations, Qhull may be
-used for 2-d upto 7-d. In higher dimensions, the size of the output
-grows rapidly and Qhull does not work well with virtual memory.
-If <i>n</i> is the size of
-the input and <i>d</i> is the dimension (d>=3), the size of the output
-and execution time
-grows by <i>n^(floor(d/2)</i>
-[see <a href=qh-in.htm#performance>Performance</a>]. For example, do
-not try to build a 16-d convex hull of 1000 points. It will
-have on the order of 1,000,000,000,000,000,000,000,000 facets.
-
-<p>On a 600 MHz Pentium 3, Qhull computes the 2-d convex hull of
-300,000 cocircular points in 11 seconds. It computes the
-2-d Delaunay triangulation and 3-d convex hull of 120,000 points
-in 12 seconds. It computes the
-3-d Delaunay triangulation and 4-d convex hull of 40,000 points
-in 18 seconds. It computes the
-4-d Delaunay triangulation and 5-d convex hull of 6,000 points
-in 12 seconds. It computes the
-5-d Delaunay triangulation and 6-d convex hull of 1,000 points
-in 12 seconds. It computes the
-6-d Delaunay triangulation and 7-d convex hull of 300 points
-in 15 seconds. It computes the
-7-d Delaunay triangulation and 8-d convex hull of 120 points
-in 15 seconds. It computes the
-8-d Delaunay triangulation and 9-d convex hull of 70 points
-in 15 seconds. It computes the
-9-d Delaunay triangulation and 10-d convex hull of 50 points
-in 17 seconds. The 10-d convex hull of 50 points has about 90,000 facets.
-
-<!-- duplicated in index.htm and html/index.htm -->
-<p>Qhull does <i>not</i> support constrained Delaunay
-triangulations, triangulation of non-convex surfaces, mesh
-generation of non-convex objects, or medium-sized inputs in 9-D
-and higher. </p>
-
-<p>This is a big package with many options. It is one of the
-fastest available. It is the only 3-d code that handles precision
-problems due to floating point arithmetic. For example, it
-implements the identity function for extreme points (see <a
-href="qh-impre.htm">Imprecision in Qhull</a>). </p>
-
-<p>If you need a short code for convex hull, Delaunay
-triangulation, or Voronoi volumes consider Clarkson's <a
-href="http://netlib.bell-labs.com/netlib/voronoi/hull.html">hull
-program</a>. If you need 2-d Delaunay triangulations consider
-Shewchuk's <a href="http://www.cs.cmu.edu/~quake/triangle.html">triangle
-program</a>. It is much faster than Qhull and it allows
-constraints. Both programs use exact arithmetic. They are in <a
-href="ftp://netlib.bell-labs.com/netlib/voronoi">ftp://netlib.bell-labs.com/netlib/voronoi</a>.
-Qhull <a
-href="http://www.qhull.org/download">version
-1.0</a> may also meet your needs. It detects precision problems,
-but does not handle them.</p>
-
-<p><a href=http://www.algorithmic-solutions.com/enleda.htm>Leda</a> is a
-library for writing computational
-geometry programs and other combinatorial algorithms. It
-includes routines for computing 3-d convex
-hulls, 2-d Delaunay triangulations, and 3-d Delaunay triangulations.
-It provides rational arithmetic and graphical output. It runs on most
-platforms.
-
-<p>If your problem is in high dimensions with a few,
-non-simplicial facets, try Fukuda's <a
-href="http://www.cs.mcgill.ca/~fukuda/soft/cdd_home/cdd.html">cdd</a>.
-It is much faster than Qhull for these distributions. </p>
-
-<p>Custom software for 2-d and 3-d convex hulls may be faster
-than Qhull. Custom software should use less memory. Qhull uses
-general-dimension data structures and code. The data structures
-support non-simplicial facets.</p>
-
-<p>Qhull is not suitable for mesh generation or triangulation of
-arbitrary surfaces. You may use Qhull if the surface is convex or
-completely visible from an interior point (e.g., a star-shaped
-polyhedron). First, project each site to a sphere that is
-centered at the interior point. Then, compute the convex hull of
-the projected sites. The facets of the convex hull correspond to
-a triangulation of the surface. For mesh generation of arbitrary
-surfaces, see <a
-href="http://www-users.informatik.rwth-aachen.de/~roberts/meshgeneration.html">Schneiders'
-Finite Element Mesh Generation</a>.</p>
-
-<p>Qhull is not suitable for constrained Delaunay triangulations.
-With a lot of work, you can write a program that uses Qhull to
-add constraints by adding additional points to the triangulation.</p>
-
-<p>Qhull is not suitable for the subdivision of arbitrary
-objects. Use <tt>qdelaunay</tt> to subdivide a convex object.</p>
-
-</blockquote>
-<h2><a href="#TOC">»</a><a name="description">Description of
-Qhull </a></h2>
-<blockquote>
-
-<h3><a href="#TOC">»</a><a name="definition">definition</a></h3>
-<blockquote>
-
-<p>The <i>convex hull</i> of a point set <i>P</i> is the smallest
-convex set that contains <i>P</i>. If <i>P</i> is finite, the
-convex hull defines a matrix <i>A</i> and a vector <i>b</i> such
-that for all <i>x</i> in <i>P</i>, <i>Ax+b <= [0,...]</i>. </p>
-
-<p>Qhull computes the convex hull in 2-d, 3-d, 4-d, and higher
-dimensions. Qhull represents a convex hull as a list of facets.
-Each facet has a set of vertices, a set of neighboring facets,
-and a halfspace. A halfspace is defined by a unit normal and an
-offset (i.e., a row of <i>A</i> and an element of <i>b</i>). </p>
-
-<p>Qhull accounts for round-off error. It returns
-"thick" facets defined by two parallel hyperplanes. The
-outer planes contain all input points. The inner planes exclude
-all output vertices. See <a href="qh-impre.htm#imprecise">Imprecise
-convex hulls</a>.</p>
-
-<p>Qhull may be used for the Delaunay triangulation or the
-Voronoi diagram of a set of points. It may be used for the
-intersection of halfspaces. </p>
-
-</blockquote>
-<h3><a href="#TOC">»</a><a name="input">input format</a></h3>
-<blockquote>
-
-<p>The input data on <tt>stdin</tt> consists of:</p>
-
-<ul>
- <li>first line contains the dimension</li>
- <li>second line contains the number of input points</li>
- <li>remaining lines contain point coordinates</li>
-</ul>
-
-<p>For example: </p>
-
-<pre>
- 3 #sample 3-d input
- 5
- 0.4 -0.5 1.0
- 1000 -1e-5 -100
- 0.3 0.2 0.1
- 1.0 1.0 1.0
- 0 0 0
-</pre>
-
-<p>Input may be entered by hand. End the input with a control-D
-(^D) character. </p>
-
-<p>To input data from a file, use I/O redirection or '<a
-href="qh-optt.htm#TI">TI file</a>'. The filename may not
-include spaces or quotes.</p>
-
-<p>A comment starts with a non-numeric character and continues to
-the end of line. The first comment is reported in summaries and
-statistics. With multiple <tt>qhull</tt> commands, use option '<a
-href="qh-optf.htm#FQ">FQ</a>' to place a comment in the output.</p>
-
-<p>The dimension and number of points can be reversed. Comments
-and line breaks are ignored. Error reporting is better if there
-is one point per line.</p>
-
-</blockquote>
-<h3><a href="#TOC">»</a><a name="option">option format</a></h3>
-<blockquote>
-
-<p>Use options to specify the output formats and control
-Qhull. The <tt>qhull</tt> program takes all options. The
-other programs use a subset of the options. They disallow
-experimental and inappropriate options.
-
-<blockquote>
-<ul>
-<li>
-qconvex == qhull
-<li>
-qdelaunay == qhull d Qbb
-<li>
-qhalf == qhull H
-<li>
-qvoronoi == qhull v Qbb
-</ul>
-</blockquote>
-
-<p>Single letters are used for output formats and precision
-constants. The other options are grouped into menus for formats
-('<a href="qh-optf.htm#format">F</a>'), Geomview ('<a
-href="qh-optg.htm#geomview">G </a>'), printing ('<a
-href="qh-optp.htm#print">P</a>'), Qhull control ('<a
-href="qh-optq.htm#qhull">Q </a>'), and tracing ('<a
-href="qh-optt.htm#trace">T</a>'). The menu options may be listed
-together (e.g., 'GrD3' for 'Gr' and 'GD3'). Options may be in any
-order. Capitalized options take a numeric argument (except for '<a
-href="qh-optp.htm#PG">PG</a>' and '<a href="qh-optf.htm#format">F</a>'
-options). Use option '<a href="qh-optf.htm#FO">FO</a>' to print
-the selected options.</p>
-
-<p>Qhull uses zero-relative indexing. If there are <i>n</i>
-points, the index of the first point is <i>0</i> and the index of
-the last point is <i>n-1</i>.</p>
-
-<p>The default options are:</p>
-
-<ul>
- <li>summary output ('<a href="qh-opto.htm#s">s</a>') </li>
- <li>merged facets ('<a href="qh-optc.htm#C0">C-0</a>' in 2-d,
- 3-d, 4-d; '<a href="qh-optq.htm#Qx">Qx</a>' in 5-d and
- up)</li>
-</ul>
-
-<p>Except for bounding box
-('<a href="qh-optq.htm#Qbk">Qbk:n</a>', etc.), drop facets
-('<a href="qh-optp.htm#Pdk">Pdk:n</a>', etc.), and
-Qhull command ('<a href="qh-optf.htm#FQ">FQ</a>'), only the last
-occurence of an option counts.
-Bounding box and drop facets may be repeated for each dimension.
-Option 'FQ' may be repeated any number of times.
-
-<p>The Unix <tt>tcsh</tt> and <tt>ksh </tt>shells make it easy to
-try out different options. In Windows 95, use a DOS window with <tt>doskey</tt>
-and a window scroller (e.g., <tt>peruse</tt>). </p>
-
-</blockquote>
-<h3><a href="#TOC">»</a><a name="output">output format</a></h3>
-<blockquote>
-
-<p>To write the results to a file, use I/O redirection or '<a
-href="qh-optt.htm#TO">TO file</a>'. Windows 95 users should use
-'TO file' or the console. If a filename is surrounded by single quotes,
-it may include spaces.
-</p>
-
-<p>The default output option is a short summary ('<a
-href="qh-opto.htm#s">s</a>') to <tt>stdout</tt>. There are many
-others (see <a href="qh-opto.htm">output</a> and <a
-href="qh-optf.htm">formats</a>). You can list vertex incidences,
-vertices and facets, vertex coordinates, or facet normals. You
-can view Qhull objects with Geomview, Mathematica, or Maple. You can
-print the internal data structures. You can call Qhull from your
-application (see <a href="qh-in.htm#library">Qhull library</a>).</p>
-
-<p>For example, 'qhull <a href="qh-opto.htm#o">o</a>' lists the
-vertices and facets of the convex hull. </p>
-
-<p>Error messages and additional summaries ('<a
-href="qh-opto.htm#s">s</a>') go to <tt>stderr</tt>. Unless
-redirected, <tt>stderr</tt> is the console.</p>
-
-</blockquote>
-<h3><a href="#TOC">»</a><a name="algorithm">algorithm</a></h3>
-<blockquote>
-
-<p>Qhull implements the Quickhull algorithm for convex hull
-[Barber et al. <a href="#bar-dob96">'96</a>]. This algorithm
-combines the 2-d Quickhull algorithm with the <em>n</em>-d
-beneath-beyond algorithm [c.f., Preparata & Shamos <a
-href="#pre-sha85">'85</a>]. It is similar to the randomized
-algorithms of Clarkson and others [Clarkson & Shor <a
-href="#cla-sho89">'89</a>; Clarkson et al. <a href="#cla-meh93">'93</a>;
-Mulmuley <a href="#mulm94">'94</a>]. For a demonstration, see <a
-href="qh-eg.htm#how">How Qhull adds a point</a>. The main
-advantages of Quickhull are output sensitive performance (in
-terms of the number of extreme points), reduced space
-requirements, and floating-point error handling. </p>
-
-</blockquote>
-<h3><a href="#TOC">»</a><a name="structure">data structures</a></h3>
-<blockquote>
-
-<p>Qhull produces the following data structures for dimension <i>d</i>:
-</p>
-
-<ul>
- <li>A <em>coordinate</em> is a real number in floating point
- format. </li>
- <li>A <em>point</em> is an array of <i>d</i> coordinates.
- With option '<a href="qh-optq.htm#QJn">QJ</a>', the
- coordinates are joggled by a small amount. </li>
- <li>A <em>vertex</em> is an input point. </li>
- <li>A <em>hyperplane</em> is <i>d</i> normal coefficients and
- an offset. The length of the normal is one. The
- hyperplane defines a halfspace. If <i>V</i> is a normal, <i>b</i>
- is an offset, and <i>x</i> is a point inside the convex
- hull, then <i>Vx+b <0</i>.</li>
- <li>An <em>outer plane</em> is a positive
- offset from a hyperplane. When Qhull is done, all points
- will be below all outer planes.</li>
- <li>An <em>inner plane</em> is a negative
- offset from a hyperplane. When Qhull is done, all
- vertices will be above the corresponding inner planes.</li>
- <li>An <em>orientation</em> is either 'top' or 'bottom'. It is the
- topological equivalent of a hyperplane's geometric
- orientation. </li>
- <li>A <em>simplicial facet</em> is a set of
- <i>d</i> neighboring facets, a set of <i>d</i> vertices, a
- hyperplane equation, an inner plane, an outer plane, and
- an orientation. For example in 3-d, a simplicial facet is
- a triangle. </li>
- <li>A <em>centrum</em> is a point on a facet's hyperplane. A
- centrum is the average of a facet's vertices. Neighboring
- facets are <em>convex</em> if each centrum is below the
- neighbor facet's hyperplane. </li>
- <li>A <em>ridge</em> is a set of <i>d-1</i> vertices, two
- neighboring facets, and an orientation. For example in
- 3-d, a ridge is a line segment. </li>
- <li>A <em>non-simplicial facet</em> is a set of ridges, a
- hyperplane equation, a centrum, an outer plane, and an
- inner plane. The ridges determine a set of neighboring
- facets, a set of vertices, and an orientation. Qhull
- produces a non-simplicial facet when it merges two facets
- together. For example, a cube has six non-simplicial
- facets. </li>
-</ul>
-
-<p>For examples, use option '<a href="qh-opto.htm#f">f</a>'. See <a
-href="../src/qh-poly.htm">polyhedron operations</a> for further
-design documentation. </p>
-
-</blockquote>
-<h3><a href="#TOC">»</a>Imprecision in Qhull</h3>
-<blockquote>
-
-<p>See <a href="qh-impre.htm">Imprecision in Qhull</a>.</p>
-
-</blockquote>
-<h3><a href="#TOC">»</a><a name="geomview">Geomview, Qhull's
-graphical viewer</a></h3>
-<blockquote>
-
-<p><a href="http://www.geomview.org">Geomview</a>
-is an interactive geometry viewing program for Linux, SGI workstations,
-Sun workstations, AIX workstations, NeXT workstations, and X-windows.
-It is an
-<a href=http://sourceforge.net/projects/geomview>open source project</a>
-under SourceForge.
-Besides a 3-d viewer, it includes a 4-d viewer, an n-d viewer and
-many features for viewing mathematical objects. You may need to
-ftp <tt>ndview</tt> from the <tt>newpieces</tt> directory. </p>
-
-</blockquote>
-<h3><a href="#TOC">»</a>Description of Qhull examples</h3>
-<blockquote>
-
-<p>See <a href="qh-eg.htm">Examples</a>. Some of the examples
-have <a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/welcome.html">pictures
-</a>.</p>
-
-</blockquote>
-</blockquote>
-<h2><a href="#TOC">»</a>Options for using Qhull </h2>
-<blockquote>
-
-<p>See <a href="qh-quick.htm#options">Options</a>.</p>
-
-</blockquote>
-<h2><a href="#TOC">»</a>Qhull internals </h2>
-<blockquote>
-
-<p>See <a href="qh-in.htm">Internals</a>.</p>
-
-</blockquote>
-<h2><a href="#TOC">»</a><a name="bugs">What to do if something
-goes wrong</a></h2>
-<blockquote>
-
-<p>Please report bugs to <a href=mailto:qhull_bug@qhull.org>qhull_bug@qhull.org</a>
-</a>. Please report if Qhull crashes. Please report if Qhull
-generates an "internal error". Please report if Qhull
-produces a poor approximate hull in 2-d, 3-d or 4-d. Please
-report documentation errors. Please report missing or incorrect
-links.</p>
-
-<p>If you do not understand something, try a small example. The <a
-href="rbox.htm">rbox</a> program is an easy way to generate
-test cases. The <a href="#geomview">Geomview</a> program helps to
-visualize the output from Qhull.</p>
-
-<p>If Qhull does not compile, it is due to an incompatibility
-between your system and ours. The first thing to check is that
-your compiler is ANSI standard. Qhull produces a compiler error
-if __STDC__ is not defined. You may need to set a flag (e.g.,
-'-A' or '-ansi').</p>
-
-<p>If Qhull compiles but crashes on the test case (rbox D4),
-there's still incompatibility between your system and ours.
-Sometimes it is due to memory management. This can be turned off
-with qh_NOmem in mem.h. Please let us know if you figure out how
-to fix these problems. </p>
-
-<p>If you doubt the output from Qhull, add option '<a
-href="qh-optt.htm#Tv">Tv</a>'. It checks that every point is
-inside the outer planes of the convex hull. It checks that every
-facet is convex with its neighbors. It checks the topology of the
-convex hull.</p>
-
-<p>Qhull should work on all inputs. It may report precision
-errors if you turn off merged facets with option '<a
-href="qh-optq.htm#Q0">Q0</a>'. This can get as bad as facets with
-flipped orientation or two facets with the same vertices. You'll
-get a long help message if you run into such a case. They are
-easy to generate with <tt>rbox</tt>.</p>
-
-<p>If you do find a problem, try to simplify it before reporting
-the error. Try different size inputs to locate the smallest one
-that causes an error. You're welcome to hunt through the code
-using the execution trace ('<a href="qh-optt.htm#Tn">T4</a>') as
-a guide. This is especially true if you're incorporating Qhull
-into your own program. </p>
-
-<p>When you report an error, please attach a data set to the end
-of your message. Include the options that you used with Qhull,
-the results of option '<a href="qh-optf.htm#FO">FO</a>', and any
-messages generated by Qhull. This allows me to see the error for
-myself. Qhull is maintained part-time. </p>
-
-</blockquote>
-<h2><a href="#TOC">»</a><a name="email">Email</a></h2>
-<blockquote>
-
-<p>Please send correspondence to Brad Barber at <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-and report bugs to <a href=mailto:qhull_bug@qhull.org>qhull_bug@qhull.org</a>
-</a>. Let me know how you use Qhull. If you mention it in a
-paper, please send a reference and abstract.</p>
-
-<p>If you would like to get Qhull announcements (e.g., a new
-version) and news (any bugs that get fixed, etc.), let us know
-and we will add you to our mailing list. If you would like to
-communicate with other Qhull users, I will add you to the
-qhull_users alias. For Internet news about geometric algorithms
-and convex hulls, look at comp.graphics.algorithms and
-sci.math.num-analysis. For Qhull news look at <a
-href="http://www.qhull.org/news">qhull-news.html</a>.</p>
-
-</blockquote>
-<h2><a href="#TOC">»</a><a name="authors">Authors</a></h2>
-<blockquote>
-
-<pre> C. Bradford Barber Hannu Huhdanpaa
- bradb@qhull.org hannu@qhull.org
-
- c/o The Geometry Center
- University of Minnesota
- 400 Lind Hall
- 207 Church Street S.E.
- Minneapolis, MN 55455
-</pre>
-
-</blockquote>
-<h2><a href="#TOC">»</a><a name="acknowledge">Acknowledgments</a></h2>
-<blockquote>
-
-<p>A special thanks to David Dobkin for his guidance. A special
-thanks to Albert Marden, Victor Milenkovic, the Geometry Center,
-and Harvard University for supporting this work.</p>
-
-<p>A special thanks to Mark Phillips, Robert Miner, and Stuart Levy for running the Geometry
- Center web site long after the Geometry Center closed.
- Stuart moved the web site to the University of Illinois at Champaign-Urbana.
-Mark and Robert are founders of <a href=http://www.geomtech.com>Geometry Technologies</a>.
-Mark, Stuart, and Tamara Munzner are the original authors of <a href=http://www.geomview.org>Geomview</a>.
-
-<p>A special thanks to <a href="http://www.endocardial.com/">Endocardial
-Solutions, Inc.</a> of St. Paul, Minnesota for their support of the
-internal documentation (<a href=../src/index.htm>src/index.htm</a>). They use Qhull to build 3-d models of
-heart chambers.</p>
-
-<p>Qhull 1.0 was developed under National Science Foundation
-grants NSF/DMS-8920161 and NSF-CCR-91-15793 750-7504. If you find
-it useful, please let us know.</p>
-
-<p>The Geometry Center was supported by grant DMS-8920161 from the
-National Science Foundation, by grant DOE/DE-FG02-92ER25137 from
-the Department of Energy, by the University of Minnesota, and by
-Minnesota Technology, Inc.</p>
-
-</blockquote>
-<h2><a href="#TOC">»</a><a name="ref">References</a></h2>
-<blockquote>
-
-<p><a name="aure91">Aurenhammer</a>, F., "Voronoi diagrams
--- A survey of a fundamental geometric data structure," <i>ACM
-Computing Surveys</i>, 1991, 23:345-405. </p>
-
-<p><a name="bar-dob96">Barber</a>, C. B., D.P. Dobkin, and H.T.
-Huhdanpaa, "The Quickhull Algorithm for Convex Hulls," <i>ACM
-Transactions on Mathematical Software</i>, Vol. 22, No. 4 (Dec.
-1996), p. 469-483 [<a
-href="http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p469-barber/">http://www.acm.org</a>;
-<a href="http://citeseer.nj.nec.com/83502.html">http://citeseer.nj.nec.com</a>].
-</p>
-
-<p><a name="cla-sho89">Clarkson</a>, K.L. and P.W. Shor,
-"Applications of random sampling in computational geometry,
-II", <i>Discrete Computational Geometry</i>, 4:387-421, 1989</p>
-
-<p><a name="cla-meh93">Clarkson</a>, K.L., K. Mehlhorn, and R.
-Seidel, "Four results on randomized incremental
-construction," <em>Computational Geometry: Theory and
-Applications</em>, vol. 3, p. 185-211, 1993.</p>
-
-<p><a name="devi01">Devillers</a>, et. al.,
-"Walking in a triangulation," <i>ACM Symposium on
-Computational Geometry</i>, June 3-5,2001, Medford MA.
-
-<p><a name="dob-kir90">Dobkin</a>, D.P. and D.G. Kirkpatrick,
-"Determining the separation of preprocessed polyhedra--a
-unified approach," in <i>Proc. 17th Inter. Colloq. Automata
-Lang. Program.</i>, in <i>Lecture Notes in Computer Science</i>,
-Springer-Verlag, 443:400-413, 1990. </p>
-
-<p><a name="edel01">Edelsbrunner</a>, H, <i>Geometry and Topology for Mesh Generation</i>,
-Cambridge University Press, 2001.
-
-<p><a name=gart99>Gartner, B.</a>, "Fast and robust smallest enclosing balls", <i>Algorithms - ESA '99</i>, LNCS 1643.
-
-<p><a name="fort93">Fortune, S.</a>, "Computational
-geometry," in R. Martin, editor, <i>Directions in Geometric
-Computation</i>, Information Geometers, 47 Stockers Avenue,
-Winchester, SO22 5LB, UK, ISBN 1-874728-02-X, 1993.</p>
-
-<p><a name="mile93">Milenkovic, V.</a>, "Robust polygon
-modeling," Computer-Aided Design, vol. 25, p. 546-566,
-September 1993. </p>
-
-<p><a name="muck96">Mucke</a>, E.P., I. Saias, B. Zhu, <i>Fast
-randomized point location without preprocessing in Two- and
-Three-dimensional Delaunay Triangulations</i>, ACM Symposium on
-Computational Geometry, p. 274-283, 1996 [<a
-href="http://www.geom.uiuc.edu/software/cglist/GeomDir/">GeomDir</a>].
-</p>
-
-<p><a name="mulm94">Mulmuley</a>, K., <i>Computational Geometry,
-An Introduction Through Randomized Algorithms</i>, Prentice-Hall,
-NJ, 1994.</p>
-
-<p><a name="orou94">O'Rourke</a>, J., <i>Computational Geometry
-in C</i>, Cambridge University Press, 1994.</p>
-
-<p><a name="pre-sha85">Preparata</a>, F. and M. Shamos, <i>Computational
-Geometry</i>, Springer-Verlag, New York, 1985.</p>
-
-</blockquote>
-<!-- Navigation links -->
-<hr>
-
-<p><b>Up:</b> <a
-href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b><a
-href="http://www.qhull.org/news">News</a> about Qhull<br>
-<b>Up:</b> <a href="http://www.qhull.org/html/qh-faq.htm">FAQ</a> about Qhull<br>
-<b>To:</b> <a href="#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a><br>
-<b>Dn:</b> <a href="qh-impre.htm">Imprecision in Qhull</a><br>
-<b>Dn:</b> <a href="qh-eg.htm">Description of Qhull examples</a><br>
-<b>Dn:</b> <a href="qh-in.htm">Qhull internals</a><br>
-<b>Dn:</b> <a href="../src/index.htm">Qhull functions, macros, and data
-structures</a>
-<!-- GC common information -->
-<hr>
-
-<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
-align="middle" width="40" height="40"></a><i>The Geometry Center
-Home Page </i></p>
-
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
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@@ -1,628 +0,0 @@
-<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
-<html>
-
-<head>
-<title>qconvex -- convex hull</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<a name="TOP"><b>Up</b></a><b>:</b>
-<a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a> -- Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a><br>
-<b>To:</b> <a href="#synopsis">sy</a>nopsis
-• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
-• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
-• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
-• <a href="#options">op</a>tions
-<hr>
-<!-- Main text of document -->
-<h1><a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html"><img
-src="qh--cone.gif" alt="[cone]" align="middle" width="100"
-height="100"></a>qconvex -- convex hull</h1>
-
-<p>The convex hull of a set of points is the smallest convex set
-containing the points. See the detailed introduction by O'Rourke
-[<a href="index.htm#orou94">'94</a>]. See <a
-href="index.htm#description">Description of Qhull</a> and <a
-href="qh-eg.htm#how">How Qhull adds a point</a>.</p>
-
-<blockquote>
-<dl>
- <dt><b>Example:</b> rbox 10 D3 | qconvex <a
- href="qh-opto.htm#s">s</a> <a href="qh-opto.htm#o">o</a> <a
- href="qh-optt.htm#TO">TO result</a></dt>
- <dd>Compute the 3-d convex hull of 10 random points. Write a
- summary to the console and the points and facets to
- 'result'.</dd>
-
- <dt> </dt>
- <dt><b>Example:</b> rbox c | qconvex <a
- href="qh-opto.htm#n">n</a></dt>
- <dd>Print the normals for each facet of a cube.</dd>
- <dt> </dt>
- <dt><b>Example:</b> rbox c | qconvex <a
- href="qh-opto.htm#i">i</a> <a href="qh-optq.htm#Qt">Qt</a></dt>
- <dd>Print the triangulated facets of a cube.</dd>
- <dt> </dt>
- <dt><b>Example:</b> rbox y 500 W0 | qconvex</dt>
- <dd>Compute the convex hull of a simplex with 500
- points on its surface.</dd>
- <dt> </dt>
- <dt><b>Example:</b> rbox x W1e-12 1000 | qconvex
- <a href="qh-optq.htm#QR">QR0</a></dt>
- <dd>Compute the convex hull of 1000 points near the
- surface of a randomly rotated simplex. Report
- the maximum thickness of a facet.</dd>
- <dt> </dt>
- <dt><b>Example:</b> rbox 1000 s | qconvex <a
- href="qh-opto.htm#s">s</a> <a
- href="qh-optf.htm#FA">FA</a> </dt>
- <dd>Compute the convex hull of 1000 cospherical
- points. Verify the results and print a summary
- with the total area and volume.</dd>
- <dt> </dt>
- <dt><b>Example:</b> rbox d D12 | qconvex <a
- href="qh-optq.htm#QRn">QR0</a> <a
- href="qh-optf.htm#FA">FA</a></dt>
- <dd>Compute the convex hull of a 12-d diamond.
- Randomly rotate the input. Note the large number
- of facets and the small volume.</dd>
- <dt> </dt>
- <dt><b>Example:</b> rbox c D7 | qconvex <a
- href="qh-optf.htm#FA">FA</a> <a
- href="qh-optt.htm#TFn">TF1000</a></dt>
- <dd>Compute the convex hull of the 7-d hypercube.
- Report on progress every 1000 facets. Computing
- the convex hull of the 9-d hypercube takes too
- much time and space. </dd>
- <dt> </dt>
- <dt><b>Example:</b> rbox c d D2 | qconvex <a
- href="qh-optq.htm#Qc">Qc</a> <a
- href="qh-opto.htm#s">s</a> <a
- href="qh-opto.htm#f">f</a> <a
- href="qh-optf.htm#Fx">Fx</a> | more</dt>
- <dd>Dump all fields of all facets for a square and a
- diamond. Also print a summary and a list of
- vertices. Note the coplanar points.</dd>
- <dt> </dt>
-</dl>
-</blockquote>
-
-<p>Except for rbox, all of the qhull programs compute a convex hull.
-
-<p>By default, Qhull merges coplanar facets. For example, the convex
-hull of a cube's vertices has six facets.
-
-<p>If you use '<a href="qh-optq.htm#Qt">Qt</a>' (triangulated output),
-all facets will be simplicial (e.g., triangles in 2-d). For the cube
-example, it will have 12 facets. Some facets may be
-degenerate and have zero area.
-
-<p>If you use '<a href="qh-optq.htm#QJn">QJ</a>' (joggled input),
-all facets will be simplicial. The corresponding vertices will be
-slightly perturbed and identical points will be joggled apart.
-Joggled input is less accurate that triangulated
-output.See <a
-href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p>
-
-<p>The output for 4-d convex hulls may be confusing if the convex
-hull contains non-simplicial facets (e.g., a hypercube). See
-<a href=qh-faq.htm#extra>Why
-are there extra points in a 4-d or higher convex hull?</a><br>
-</p>
-</p>
-
-<p>The 'qconvex' program is equivalent to
-'<a href=qhull.htm#outputs>qhull</a>' in 2-d to 4-d, and
-'<a href=qhull.htm#outputs>qhull</a> <a href=qh-optq.htm#Qx>Qx</a>'
-in 5-d and higher. It disables the following Qhull
-<a href=qh-quick.htm#options>options</a>: <i>d v H Qbb Qf Qg Qm
-Qr Qu Qv Qx Qz TR E V Fp Gt Q0,etc</i>.
-
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-
-<hr>
-
-<h3><a href="#TOP">»</a><a name="synopsis">qconvex synopsis</a></h3>
-<pre>
-qconvex- compute the convex hull.
- input (stdin): dimension, number of points, point coordinates
- comments start with a non-numeric character
-
-options (qconvex.htm):
- Qt - triangulated output
- QJ - joggle input instead of merging facets
- Tv - verify result: structure, convexity, and point inclusion
- . - concise list of all options
- - - one-line description of all options
-
-output options (subset):
- s - summary of results (default)
- i - vertices incident to each facet
- n - normals with offsets
- p - vertex coordinates (includes coplanar points if 'Qc')
- Fx - extreme points (convex hull vertices)
- FA - compute total area and volume
- o - OFF format (dim, n, points, facets)
- G - Geomview output (2-d, 3-d, and 4-d)
- m - Mathematica output (2-d and 3-d)
- QVn - print facets that include point n, -n if not
- TO file- output results to file, may be enclosed in single quotes
-
-examples:
- rbox c D2 | qconvex s n rbox c D2 | qconvex i
- rbox c D2 | qconvex o rbox 1000 s | qconvex s Tv FA
- rbox c d D2 | qconvex s Qc Fx rbox y 1000 W0 | qconvex s n
- rbox y 1000 W0 | qconvex s QJ rbox d G1 D12 | qconvex QR0 FA Pp
- rbox c D7 | qconvex FA TF1000
-</pre>
-
-<h3><a href="#TOP">»</a><a name="input">qconvex
-input</a></h3>
-<blockquote>
-
-<p>The input data on <tt>stdin</tt> consists of:</p>
-<ul>
- <li>dimension
- <li>number of points</li>
- <li>point coordinates</li>
-</ul>
-
-<p>Use I/O redirection (e.g., qconvex < data.txt), a pipe (e.g., rbox 10 | qconvex),
-or the '<a href=qh-optt.htm#TI>TI</a>' option (e.g., qconvex TI data.txt).
-
-<p>Comments start with a non-numeric character. Error reporting is
-simpler if there is one point per line. Dimension
-and number of points may be reversed.
-
-<p>Here is the input for computing the convex
-hull of the unit cube. The output is the normals, one
-per facet.</p>
-
-<blockquote>
- <p>rbox c > data </p>
- <pre>
-3 RBOX c
-8
- -0.5 -0.5 -0.5
- -0.5 -0.5 0.5
- -0.5 0.5 -0.5
- -0.5 0.5 0.5
- 0.5 -0.5 -0.5
- 0.5 -0.5 0.5
- 0.5 0.5 -0.5
- 0.5 0.5 0.5
-</pre>
- <p>qconvex s n < data</p>
- <pre>
-
-Convex hull of 8 points in 3-d:
-
- Number of vertices: 8
- Number of facets: 6
- Number of non-simplicial facets: 6
-
-Statistics for: RBOX c | QCONVEX s n
-
- Number of points processed: 8
- Number of hyperplanes created: 11
- Number of distance tests for qhull: 35
- Number of merged facets: 6
- Number of distance tests for merging: 84
- CPU seconds to compute hull (after input): 0.081
-
-4
-6
- 0 0 -1 -0.5
- 0 -1 0 -0.5
- 1 0 0 -0.5
- -1 0 0 -0.5
- 0 1 0 -0.5
- 0 0 1 -0.5
-</pre>
-</blockquote>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="outputs">qconvex outputs</a></h3>
-<blockquote>
-
-<p>These options control the output of qconvex. They may be used
-individually or together.</p>
-<blockquote>
-<dl compact>
- <dt> </dt>
- <dd><b>Vertices</b></dd>
- <dt><a href="qh-optf.htm#Fx">Fx</a></dt>
- <dd>list extreme points (i.e., vertices). The first line is the number of
- extreme points. Each point is listed, one per line. The cube example
- has eight vertices.</dd>
- <dt><a href="qh-optf.htm#Fv">Fv</a></dt>
- <dd>list vertices for each facet. The first line is the number of facets.
- Each remaining line starts with the number of vertices. For the cube example,
- each facet has four vertices.</dd>
- <dt><a href="qh-opto.htm#i">i</a></dt>
- <dd>list vertices for each facet. The first line is the number of facets. The
- remaining lines list the vertices for each facet. In 3-d and
- higher, report cospherical sites by adding extra points.</dd>
- <dt> </dt>
- <dt> </dt>
- <dd><b>Coordinates</b></dd>
- <dt><a href="qh-opto.htm#o">o</a></dt>
- <dd>print vertices and facets of the convex hull in OFF format. The
- first line is the dimension. The second line is the number of
- vertices, facets, and ridges. The vertex
- coordinates are next, followed by the facets. Each facet starts with
- the number of vertices. The cube example has four vertices per facet.</dd>
- <dt><a href="qh-optf.htm#Ft">Ft</a></dt>
- <dd>print a triangulation of the convex hull in OFF format. The first line
- is the dimension. The second line is the number of vertices and added points,
- followed by the number of facets and the number of ridges.
- The vertex coordinates are next, followed by the centrum coordinates. There is
- one centrum for each non-simplicial facet.
- The cube example has six centrums, one per square.
- Each facet starts with the number of vertices or centrums.
- In the cube example, each facet uses two vertices and one centrum.</dd>
- <dt><a href="qh-opto.htm#p">p</a></dt>
- <dd>print vertex coordinates. The first line is the dimension and the second
- line is the number of vertices. The following lines are the coordinates of each
- vertex. The cube example has eight vertices.</dd>
- <dt><a href="qh-optq.htm#Qc">Qc</a> <a href="qh-opto.htm#p">p</a></dt>
- <dd>print coordinates of vertices and coplanar points. The first line is the dimension.
- The second line is the number of vertices and coplanar points. The coordinates
- are next, one line per point. Use '<a href="qh-optq.htm#Qc">Qc</a> <a href="qh-optq.htm#Qi">Qi</a> p'
- to print the coordinates of all points.</dd>
- <dt> </dt>
- <dt> </dt>
- <dd><b>Facets</b></dd>
- <dt><a href="qh-optf.htm#Fn">Fn</a></dt>
- <dd>list neighboring facets for each facet. The first line is the
- number of facets. Each remaining line starts with the number of
- neighboring facets. The cube example has four neighbors per facet.</dd>
- <dt><a href="qh-optf.htm#FN">FN</a></dt>
- <dd>list neighboring facets for each point. The first line is the
- total number of points. Each remaining line starts with the number of
- neighboring facets. Each vertex of the cube example has three neighboring
- facets. Use '<a href="qh-optq.htm#Qc">Qc</a> <a href="qh-optq.htm#Qi">Qi</a> FN'
- to include coplanar and interior points. </dd>
- <dt><a href="qh-optf.htm#Fa">Fa</a></dt>
- <dd>print area for each facet. The first line is the number of facets.
- Facet area follows, one line per facet. For the cube example, each facet has area one.</dd>
- <dt><a href="qh-optf.htm#FI">FI</a></dt>
- <dd>list facet IDs. The first line is the number of
- facets. The IDs follow, one per line.</dd>
-
- <dt> </dt>
- <dt> </dt>
- <dd><b>Coplanar and interior points</b></dd>
- <dt><a href="qh-optf.htm#Fc">Fc</a></dt>
- <dd>list coplanar points for each facet. The first line is the number
- of facets. The remaining lines start with the number of coplanar points.
- A coplanar point is assigned to one facet.</dd>
- <dt><a href="qh-optq.htm#Qi">Qi</a> <a href="qh-optf.htm#Fc">Fc</a></dt>
- <dd>list interior points for each facet. The first line is the number
- of facets. The remaining lines start with the number of interior points.
- A coplanar point is assigned to one facet.</dd>
- <dt><a href="qh-optf.htm#FP">FP</a></dt>
- <dd>print distance to nearest vertex for coplanar points. The first line is the
- number of coplanar points. Each remaining line starts with the point ID of
- a vertex, followed by the point ID of a coplanar point, its facet, and distance.
- Use '<a href="qh-optq.htm#Qc">Qc</a> <a href="qh-optq.htm#Qi">Qi</a>
- <a href="qh-optf.htm#FP">FP</a>' for coplanar and interior points.</dd>
-
- <dt> </dt>
- <dt> </dt>
- <dd><b>Hyperplanes</b></dd>
- <dt><a href="qh-opto.htm#n">n</a></dt>
- <dd>print hyperplane for each facet. The first line is the dimension. The
- second line is the number of facets. Each remaining line is the hyperplane's
- coefficients followed by its offset.</dd>
- <dt><a href="qh-optf.htm#Fo">Fo</a></dt>
- <dd>print outer plane for each facet. The output plane is above all points.
- The first line is the dimension. The
- second line is the number of facets. Each remaining line is the outer plane's
- coefficients followed by its offset.</dd>
- <dt><a href="qh-optf.htm#Fi">Fi</a></dt>
- <dd>print inner plane for each facet. The inner plane of a facet is
- below its vertices.
- The first line is the dimension. The
- second line is the number of facets. Each remaining line is the inner plane's
- coefficients followed by its offset.</dd>
-
- <dt> </dt>
- <dt> </dt>
- <dd><b>General</b></dd>
- <dt><a href="qh-opto.htm#s">s</a></dt>
- <dd>print summary for the convex hull. Use '<a
- href="qh-optf.htm#Fs">Fs</a>' and '<a
- href="qh-optf.htm#FS">FS</a>' if you need numeric data.</dd>
- <dt><a href="qh-optf.htm#FA">FA</a></dt>
- <dd>compute total area and volume for '<a
- href="qh-opto.htm#s">s</a>' and '<a href="qh-optf.htm#FS">FS</a>'</dd>
- <dt><a href="qh-opto.htm#m">m</a></dt>
- <dd>Mathematica output for the convex hull in 2-d or 3-d.</dd>
- <dt><a href="qh-optf.htm#FM">FM</a></dt>
- <dd>Maple output for the convex hull in 2-d or 3-d.</dd>
- <dt><a href="qh-optg.htm#G">G</a></dt>
- <dd>Geomview output for the convex hull in 2-d, 3-d, or 4-d.</dd>
-
- <dt> </dt>
- <dt> </dt>
- <dd><b>Scaling and rotation</b></dd>
- <dt><a href="qh-optq.htm#Qbk">Qbk:n</a></dt>
- <dd>scale k'th coordinate to lower bound.</dd>
- <dt><a href="qh-optq.htm#QBk">QBk:n</a></dt>
- <dd>scale k'th coordinate to upper bound.</dd>
- <dt><a href="qh-optq.htm#QbB">QbB</a></dt>
- <dd>scale input to unit cube centered at the origin.</dd>
- <dt><a href="qh-optq.htm#QRn">QRn</a></dt>
- <dd>randomly rotate the input with a random seed of n. If n=0, the
- seed is the time. If n=-1, use time for the random seed, but do
- not rotate the input.</dd>
- <dt><a href="qh-optq.htm#Qb0">Qbk:0Bk:0</a></dt>
- <dd>remove k'th coordinate from input. This computes the
- convex hull in one lower dimension.</dd>
-</dl>
-</blockquote>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="controls">qconvex controls</a></h3>
-<blockquote>
-
-<p>These options provide additional control:</p>
-
-<blockquote>
-<dl compact>
- <dt><a href="qh-optq.htm#Qt">Qt</a></dt>
- <dd>triangulated output. Qhull triangulates non-simplicial facets. It may produce
- degenerate facets of zero area.</dd>
- <dt><a href="qh-optq.htm#QJn">QJ</a></dt>
- <dd>joggle the input instead of merging facets. This guarantees simplicial facets
- (e.g., triangles in 3-d). It is less accurate than triangulated output ('Qt').</dd>
- <dt><a href="qh-optq.htm#Qc">Qc</a></dt>
- <dd>keep coplanar points</dd>
- <dt><a href="qh-optq.htm#Qi">Qi</a></dt>
- <dd>keep interior points</dd>
- <dt><a href="qh-opto.htm#f">f </a></dt>
- <dd>facet dump. Print the data structure for each facet.</dd>
- <dt><a href="qh-optq.htm#QVn">QVn</a></dt>
- <dd>select facets containing point <em>n</em> as a vertex,</dd>
- <dt><a href="qh-optq.htm#QGn">QGn</a></dt>
- <dd>select facets that are visible from point <em>n</em>
- (marked 'good'). Use <em>-n</em> for the remainder.</dd>
- <dt><a href="qh-optp.htm#PDk">PDk:0</a></dt>
- <dd>select facets with a negative coordinate for dimension <i>k</i></dd>
- <dt><a href="qh-optt.htm#TFn">TFn</a></dt>
- <dd>report progress after constructing <em>n</em> facets</dd>
- <dt><a href="qh-optt.htm#Tv">Tv</a></dt>
- <dd>verify result</dd>
- <dt><a href="qh-optt.htm#TO">TI file</a></dt>
- <dd>input data from file. The filename may not use spaces or quotes.</dd>
- <dt><a href="qh-optt.htm#TO">TO file</a></dt>
- <dd>output results to file. Use single quotes if the filename
- contains spaces (e.g., <tt>TO 'file with spaces.txt'</tt></dd>
- <dt><a href="qh-optq.htm#Qs">Qs</a></dt>
- <dd>search all points for the initial simplex. If Qhull can
- not construct an initial simplex, it reports a
-descriptive message. Usually, the point set is degenerate and one
-or more dimensions should be removed ('<a href="qh-optq.htm#Qb0">Qbk:0Bk:0</a>').
-If not, use option 'Qs'. It performs an exhaustive search for the
-best initial simplex. This is expensive is high dimensions.</dd>
-</dl>
-</blockquote>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="graphics">qconvex graphics</a></h3>
-<blockquote>
-
-<p>Display 2-d, 3-d, and 4-d convex hulls with Geomview ('<a
-href="qh-optg.htm#G">G</a>').</p>
-
-<p>Display 2-d and 3-d convex hulls with Mathematica ('<a
-href="qh-opto.htm#m">m</a>').</p>
-
-<p>To view 4-d convex hulls in 3-d, use '<a
-href="qh-optp.htm#Pdk">Pd0d1d2d3</a>' to select the positive
-octant and '<a href="qh-optg.htm#GDn">GrD2</a>' to drop dimension
-2. </p>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="notes">qconvex notes</a></h3>
-<blockquote>
-
-<p>Qhull always computes a convex hull. The
-convex hull may be used for other geometric structures. The
-general technique is to transform the structure into an
-equivalent convex hull problem. For example, the Delaunay
-triangulation is equivalent to the convex hull of the input sites
-after lifting the points to a paraboloid.</p>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="conventions">qconvex
-conventions</a></h3>
-<blockquote>
-
-<p>The following terminology is used for convex hulls in Qhull.
-See <a href="index.htm#structure">Qhull's data structures</a>.</p>
-
-<ul>
- <li><em>point</em> - <em>d</em> coordinates</li>
- <li><em>vertex</em> - extreme point of the input set</li>
- <li><em>ridge</em> - <i>d-1</i> vertices between two
- neighboring facets</li>
- <li><em>hyperplane</em> - halfspace defined by a unit normal
- and offset</li>
- <li><em>coplanar point</em> - a nearly incident point to a
- hyperplane</li>
- <li><em>centrum</em> - a point on the hyperplane for testing
- convexity</li>
- <li><em>facet</em> - a facet with vertices, ridges, coplanar
- points, neighboring facets, and hyperplane</li>
- <li><em>simplicial facet</em> - a facet with <em>d</em>
- vertices, <em>d</em> ridges, and <em>d</em> neighbors</li>
- <li><em>non-simplicial facet</em> - a facet with more than <em>d</em>
- vertices</li>
- <li><em>good facet</em> - a facet selected by '<a
- href="qh-optq.htm#QVn">QVn</a>', etc.</li>
-</ul>
-</blockquote>
-<h3><a href="#TOP">»</a><a name="options">qconvex options</a></h3>
-
-<pre>
-qconvex- compute the convex hull
- http://www.qhull.org
-
-input (stdin):
- first lines: dimension and number of points (or vice-versa).
- other lines: point coordinates, best if one point per line
- comments: start with a non-numeric character
-
-options:
- Qt - triangulated output
- QJ - joggle input instead of merging facets
- Qc - keep coplanar points with nearest facet
- Qi - keep interior points with nearest facet
-
-Qhull control options:
- Qbk:n - scale coord k so that low bound is n
- QBk:n - scale coord k so that upper bound is n (QBk is 0.5)
- QbB - scale input to unit cube centered at the origin
- Qbk:0Bk:0 - remove k-th coordinate from input
- QJn - randomly joggle input in range [-n,n]
- QRn - random rotation (n=seed, n=0 time, n=-1 time/no rotate)
- Qs - search all points for the initial simplex
- QGn - good facet if visible from point n, -n for not visible
- QVn - good facet if it includes point n, -n if not
-
-Trace options:
- T4 - trace at level n, 4=all, 5=mem/gauss, -1= events
- Tc - check frequently during execution
- Ts - print statistics
- Tv - verify result: structure, convexity, and point inclusion
- Tz - send all output to stdout
- TFn - report summary when n or more facets created
- TI file - input data from file, no spaces or single quotes
- TO file - output results to file, may be enclosed in single quotes
- TPn - turn on tracing when point n added to hull
- TMn - turn on tracing at merge n
- TWn - trace merge facets when width > n
- TVn - stop qhull after adding point n, -n for before (see TCn)
- TCn - stop qhull after building cone for point n (see TVn)
-
-Precision options:
- Cn - radius of centrum (roundoff added). Merge facets if non-convex
- An - cosine of maximum angle. Merge facets if cosine > n or non-convex
- C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
- Rn - randomly perturb computations by a factor of [1-n,1+n]
- Un - max distance below plane for a new, coplanar point
- Wn - min facet width for outside point (before roundoff)
-
-Output formats (may be combined; if none, produces a summary to stdout):
- f - facet dump
- G - Geomview output (see below)
- i - vertices incident to each facet
- m - Mathematica output (2-d and 3-d)
- n - normals with offsets
- o - OFF file format (dim, points and facets; Voronoi regions)
- p - point coordinates
- s - summary (stderr)
-
-More formats:
- Fa - area for each facet
- FA - compute total area and volume for option 's'
- Fc - count plus coplanar points for each facet
- use 'Qc' (default) for coplanar and 'Qi' for interior
- FC - centrum for each facet
- Fd - use cdd format for input (homogeneous with offset first)
- FD - use cdd format for numeric output (offset first)
- FF - facet dump without ridges
- Fi - inner plane for each facet
- FI - ID for each facet
- Fm - merge count for each facet (511 max)
- FM - Maple output (2-d and 3-d)
- Fn - count plus neighboring facets for each facet
- FN - count plus neighboring facets for each point
- Fo - outer plane (or max_outside) for each facet
- FO - options and precision constants
- FP - nearest vertex for each coplanar point
- FQ - command used for qconvex
- Fs - summary: #int (8), dimension, #points, tot vertices, tot facets,
- for output: #vertices, #facets,
- #coplanar points, #non-simplicial facets
- #real (2), max outer plane, min vertex
- FS - sizes: #int (0)
- #real(2) tot area, tot volume
- Ft - triangulation with centrums for non-simplicial facets (OFF format)
- Fv - count plus vertices for each facet
- FV - average of vertices (a feasible point for 'H')
- Fx - extreme points (in order for 2-d)
-
-Geomview output (2-d, 3-d, and 4-d)
- Ga - all points as dots
- Gp - coplanar points and vertices as radii
- Gv - vertices as spheres
- Gi - inner planes only
- Gn - no planes
- Go - outer planes only
- Gc - centrums
- Gh - hyperplane intersections
- Gr - ridges
- GDn - drop dimension n in 3-d and 4-d output
-
-Print options:
- PAn - keep n largest facets by area
- Pdk:n - drop facet if normal[k] <= n (default 0.0)
- PDk:n - drop facet if normal[k] >= n
- Pg - print good facets (needs 'QGn' or 'QVn')
- PFn - keep facets whose area is at least n
- PG - print neighbors of good facets
- PMn - keep n facets with most merges
- Po - force output. If error, output neighborhood of facet
- Pp - do not report precision problems
-
- . - list of all options
- - - one line descriptions of all options
-
-</pre>
-
-<!-- Navigation links -->
-<hr>
-
-<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-•<a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a><br>
-<b>To:</b> <a href="#synopsis">sy</a>nopsis
-• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
-• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
-• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
-• <a href="#options">op</a>tions
-<!-- GC common information -->
-<hr>
-
-<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
-align="middle" width="40" height="40"></a><i>The Geometry Center
-Home Page </i></p>
-
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
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@@ -1,414 +0,0 @@
-<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
-<html>
-
-<head>
-<title>qdelaunay Qu -- furthest-site Delaunay triangulation</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<a name="TOP"><b>Up</b></a><b>:</b>
-<a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a><br>
-<b>To:</b> <a href="#synopsis">sy</a>nopsis
-• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
-• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
-• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
-• <a href="#options">op</a>tions
-
-<hr>
-<!-- Main text of document -->
-<h1><a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
-src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
-height="100"></a>qdelaunay Qu -- furthest-site Delaunay triangulation</h1>
-
-<p>The furthest-site Delaunay triangulation corresponds to the upper facets of the <a href="qdelaun.htm">Delaunay construction</a>.
-Its vertices are the
-extreme points of the input sites.
-It is the dual of the <a
-href="qvoron_f.htm">furthest-site Voronoi diagram</a>.
-
-<blockquote>
-<dl>
- <dt><b>Example:</b> rbox 10 D2 | qdelaunay <a
- href="qh-optq.htm#Qu">Qu</a> <a
- href="qh-optq.htm#Qt">Qt</a> <a href="qh-opto.htm#s">s</a>
- <a href="qh-opto.htm#i">i</a> <a href="qh-optt.htm#TO">TO
- result</a></dt>
- <dd>Compute the 2-d, furthest-site Delaunay triangulation of 10 random
- points. Triangulate the output.
- Write a summary to the console and the regions to
- 'result'.</dd>
- <dt> </dt>
- <dt><b>Example:</b> rbox 10 D2 | qdelaunay <a
- href="qh-optq.htm#Qu">Qu</a> <a
- href="qh-optq.htm#QJn">QJ</a> <a href="qh-opto.htm#s">s</a>
- <a href="qh-opto.htm#i">i</a> <a href="qh-optt.htm#TO">TO
- result</a></dt>
- <dd>Compute the 2-d, furthest-site Delaunay triangulation of 10 random
- points. Joggle the input to guarantee triangular output.
- Write a summary to the console and the regions to
- 'result'.</dd>
- <dt> </dt>
- <dt><b>Example:</b> rbox r y c G1 D2 | qdelaunay <a
- href="qh-optq.htm#Qu">Qu</a> <a href="qh-opto.htm#s">s</a>
- <a href="qh-optf.htm#Fv">Fv</a> <a href="qh-optt.htm#TO">TO
- result</a></dt>
- <dd>Compute the 2-d, furthest-site Delaunay triangulation of a triangle inside
- a square.
- Write a summary to the console and unoriented regions to 'result'.
- Merge regions for cocircular input sites (e.g., the square).
- The square is the only furthest-site
- Delaunay region.</dd>
-</dl>
-</blockquote>
-
-<p>As with the Delaunay triangulation, Qhull computes the
-furthest-site Delaunay triangulation by lifting the input sites to a
-paraboloid. The lower facets correspond to the Delaunay
-triangulation while the upper facets correspond to the
-furthest-site triangulation. Neither triangulation includes
-"vertical" facets (i.e., facets whose last hyperplane
-coefficient is nearly zero). Vertical facets correspond to input
-sites that are coplanar to the convex hull of the input. An
-example is points on the boundary of a lattice.</p>
-
-<p>By default, qdelaunay merges cocircular and cospherical regions.
-For example, the furthest-site Delaunay triangulation of a square inside a diamond
-('rbox D2 c d G4 | qdelaunay Qu') consists of one region (the diamond).
-
-<p>If you use '<a href="qh-optq.htm#Qt">Qt</a>' (triangulated output),
-all furthest-site Delaunay regions will be simplicial (e.g., triangles in 2-d).
-Some regions may be
-degenerate and have zero area.
-
-<p>If you use '<a href="qh-optq.htm#QJn">QJ</a>' (joggled input), all furthest-site
-Delaunay regions
-will be simplicial (e.g., triangles in 2-d). Joggled input
-is less accurate than triangulated output ('Qt'). See <a
-href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p>
-
-<p>The output for 3-d, furthest-site Delaunay triangulations may be confusing if the
-input contains cospherical data. See the FAQ item
-<a href=qh-faq.htm#extra>Why
-are there extra points in a 4-d or higher convex hull?</a>
-Avoid these problems with triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>') or
-joggled input ('<a href="qh-optq.htm#QJn">QJ</a>').
-</p>
-
-<p>The 'qdelaunay' program is equivalent to
-'<a href=qhull.htm#outputs>qhull d</a> <a href=qh-optq.htm#Qbb>Qbb</a>' in 2-d to 3-d, and
-'<a href=qhull.htm#outputs>qhull d</a> <a href=qh-optq.htm#Qbb>Qbb</a> <a href=qh-optq.htm#Qx>Qx</a>'
-in 4-d and higher. It disables the following Qhull
-<a href=qh-quick.htm#options>options</a>: <i>d n v H U Qb QB Qc Qf Qg Qi
-Qm Qr QR Qv Qx TR E V FC Fi Fo Fp FV Q0,etc</i>.
-
-
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-
-<hr>
-
-<h3><a href="#TOP">»</a><a name="synopsis">furthest-site qdelaunay synopsis</a></h3>
-<blockquote>
-
-See <a href="qdelaun.htm#synopsis">qdelaunay synopsis</a>. The same
-program is used for both constructions. Use option '<a href="qh-optq.htm#Qu">Qu</a>'
-for furthest-site Delaunay triangulations.
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="input">furthest-site qdelaunay
-input</a></h3>
-
-<blockquote>
-<p>The input data on <tt>stdin</tt> consists of:</p>
-<ul>
- <li>dimension
- <li>number of points</li>
- <li>point coordinates</li>
-</ul>
-
-<p>Use I/O redirection (e.g., qdelaunay Qu < data.txt), a pipe (e.g., rbox 10 | qdelaunay Qu),
-or the '<a href=qh-optt.htm#TI>TI</a>' option (e.g., qdelaunay Qu TI data.txt).
-
-<p>For example, this is a square containing four random points.
-Its furthest-site Delaunay
-triangulation contains one square.
-<p>
-<blockquote>
-<tt>rbox c 4 D2 > data</tt>
-<blockquote><pre>
-2 RBOX c 4 D2
-8
--0.4999921736307369 -0.3684622117955817
-0.2556053225468894 -0.0413498678629751
-0.0327672376602583 -0.2810408135699488
--0.452955383763607 0.17886471718444
- -0.5 -0.5
- -0.5 0.5
- 0.5 -0.5
- 0.5 0.5
-</pre></blockquote>
-
-<p><tt>qdelaunay Qu i < data</tt>
-<blockquote><pre>
-
-Furthest-site Delaunay triangulation by the convex hull of 8 points in 3-d:
-
- Number of input sites: 8
- Number of Delaunay regions: 1
- Number of non-simplicial Delaunay regions: 1
-
-Statistics for: RBOX c 4 D2 | QDELAUNAY s Qu i
-
- Number of points processed: 8
- Number of hyperplanes created: 20
- Number of facets in hull: 11
- Number of distance tests for qhull: 34
- Number of merged facets: 1
- Number of distance tests for merging: 107
- CPU seconds to compute hull (after input): 0.02
-
-1
-7 6 4 5
-</pre></blockquote>
-</blockquote>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="outputs">furthest-site qdelaunay
-outputs</a></h3>
-<blockquote>
-
-<p>These options control the output of furthest-site Delaunay triangulations:</p>
-<blockquote>
-
-<dl compact>
- <dd><b>furthest-site Delaunay regions</b></dd>
- <dt><a href="qh-opto.htm#i">i</a></dt>
- <dd>list input sites for each furthest-site Delaunay region. The first line is the number of regions. The
- remaining lines list the input sites for each region. The regions are
- oriented. In 3-d and
- higher, report cospherical sites by adding extra points. For the points-in-square example,
- the square is the only furthest-site Delaunay region.</dd>
- <dt><a href="qh-optf.htm#Fv">Fv</a></dt>
- <dd>list input sites for each furthest-site Delaunay region. The first line is the number of regions.
- Each remaining line starts with the number of input sites. The regions
- are unoriented. For the points-in-square example,
- the square is the only furthest-site Delaunay region.</dd>
- <dt><a href="qh-optf.htm#Ft">Ft</a></dt>
- <dd>print a triangulation of the furthest-site Delaunay regions in OFF format. The first line
- is the dimension. The second line is the number of input sites and added points,
- followed by the number of simplices and the number of ridges.
- The input coordinates are next, followed by the centrum coordinates. There is
- one centrum for each non-simplicial furthest-site Delaunay region. Each remaining line starts
- with dimension+1. The
- simplices are oriented.
- For the points-in-square example, the square has a centrum at the
- origin. It splits the square into four triangular regions.</dd>
- <dt><a href="qh-optf.htm#Fn">Fn</a></dt>
- <dd>list neighboring regions for each furthest-site Delaunay region. The first line is the
- number of regions. Each remaining line starts with the number of
- neighboring regions. Negative indices (e.g., <em>-1</em>) indicate regions
- outside of the furthest-site Delaunay triangulation.
- For the points-in-square example, the four neighboring regions
- are outside of the triangulation. They belong to the regular
- Delaunay triangulation.</dd>
- <dt><a href="qh-optf.htm#FN">FN</a></dt>
- <dd>list the furthest-site Delaunay regions for each input site. The first line is the
- total number of input sites. Each remaining line starts with the number of
- furthest-site Delaunay regions. Negative indices (e.g., <em>-1</em>) indicate regions
- outside of the furthest-site Delaunay triangulation.
- For the points-in-square example, the four random points belong to no region
- while the square's vertices belong to region <em>0</em> and three
- regions outside of the furthest-site Delaunay triangulation.</dd>
- <dt><a href="qh-optf.htm#Fa">Fa</a></dt>
- <dd>print area for each furthest-site Delaunay region. The first line is the number of regions.
- The areas follow, one line per region. For the points-in-square example, the
- square has unit area. </dd>
-
- <dt> </dt>
- <dt> </dt>
- <dd><b>Input sites</b></dd>
- <dt><a href="qh-optf.htm#Fx">Fx</a></dt>
- <dd>list extreme points of the input sites. These points are vertices of the furthest-point
- Delaunay triangulation. They are on the
- boundary of the convex hull. The first line is the number of
- extreme points. Each point is listed, one per line. The points-in-square example
- has four extreme points.</dd>
- <dt> </dt>
- <dt> </dt>
- <dd><b>General</b></dd>
- <dt><a href="qh-optf.htm#FA">FA</a></dt>
- <dd>compute total area for '<a href="qh-opto.htm#s">s</a>'
- and '<a href="qh-optf.htm#FS">FS</a>'. This is the
- same as the area of the convex hull.</dd>
- <dt><a href="qh-opto.htm#o">o</a></dt>
- <dd>print upper facets of the corresponding convex hull (a
- paraboloid)</dd>
- <dt><a href="qh-opto.htm#m">m</a></dt>
- <dd>Mathematica output for the upper facets of the paraboloid (2-d triangulations).</dd>
- <dt><a href="qh-optf.htm#FM">FM</a></dt>
- <dd>Maple output for the upper facets of the paraboloid (2-d triangulations).</dd>
- <dt><a href="qh-optg.htm#G">G</a></dt>
- <dd>Geomview output for the paraboloid (2-d or 3-d triangulations).</dd>
- <dt><a href="qh-opto.htm#s">s</a></dt>
- <dd>print summary for the furthest-site Delaunay triangulation. Use '<a
- href="qh-optf.htm#Fs">Fs</a>' and '<a
- href="qh-optf.htm#FS">FS</a>' for numeric data.</dd>
-</dl>
-</blockquote>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="controls">furthest-site qdelaunay
-controls</a></h3>
-<blockquote>
-
-<p>These options provide additional control:</p>
-<blockquote>
-
-<dl compact>
- <dt><a href="qh-optq.htm#Qu">Qu</a></dt>
- <dd>must be used for furthest-site Delaunay triangulation.</dd>
- <dt><a href="qh-optq.htm#Qt">Qt</a></dt>
- <dd>triangulated output. Qhull triangulates non-simplicial facets. It may produce
- degenerate facets of zero area.</dd>
- <dt><a href="qh-optq.htm#QJn">QJ</a></dt>
- <dd>joggle the input to avoid cospherical and coincident
- sites. It is less accurate than triangulated output ('Qt').</dd>
- <dt><a href="qh-optq.htm#QVn">QVn</a></dt>
- <dd>select facets adjacent to input site <em>n</em> (marked
- 'good').</dd>
- <dt><a href="qh-optt.htm#Tv">Tv</a></dt>
- <dd>verify result.</dd>
- <dt><a href="qh-optt.htm#TO">TI file</a></dt>
- <dd>input data from file. The filename may not use spaces or quotes.</dd>
- <dt><a href="qh-optt.htm#TO">TO file</a></dt>
- <dd>output results to file. Use single quotes if the filename
- contains spaces (e.g., <tt>TO 'file with spaces.txt'</tt></dd>
- <dt><a href="qh-optt.htm#TFn">TFn</a></dt>
- <dd>report progress after constructing <em>n</em> facets</dd>
- <dt><a href="qh-optp.htm#PDk">PDk:1</a></dt>
- <dd>include upper and lower facets in the output. Set <em>k</em>
- to the last dimension (e.g., 'PD2:1' for 2-d inputs). </dd>
- <dt><a href="qh-opto.htm#f">f</a></dt>
- <dd>facet dump. Print the data structure for each facet (i.e., furthest-site Delaunay region).</dd>
-</dl>
-</blockquote>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="graphics">furthest-site qdelaunay
-graphics</a></h3>
-<blockquote>
-
-See <a href="qdelaun.htm#graphics">Delaunay graphics</a>.
-They are the same except for Mathematica and Maple output.
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="notes">furthest-site
-qdelaunay notes</a></h3>
-<blockquote>
-
-<p>The furthest-site Delaunay triangulation does not
-record coincident input sites. Use <tt>qdelaunay</tt> instead.
-
-<p><tt>qdelaunay Qu</tt> does not work for purely cocircular
-or cospherical points (e.g., rbox c | qdelaunay Qu). Instead,
-use <tt>qdelaunay Qz</tt> -- when all points are vertices of the convex
-hull of the input sites, the Delaunay triangulation is the same
-as the furthest-site Delaunay triangulation.
-
-<p>A non-simplicial, furthest-site Delaunay region indicates nearly cocircular or
-cospherical input sites. To avoid non-simplicial regions triangulate
-the output ('<a href="qh-optq.htm#Qt">Qt</a>') or joggle
-the input ('<a href="qh-optq.htm#QJn">QJ</a>'). Joggled input
-is less accurate than triangulated output.
-You may also triangulate
-non-simplicial regions with option '<a
-href="qh-optf.htm#Ft">Ft</a>'. It adds
-the centrum to non-simplicial regions. Alternatively, use an <a
-href="qh-impre.htm#exact">exact arithmetic code</a>.</p>
-
-<p>Furthest-site Delaunay triangulations do not include facets that are
-coplanar with the convex hull of the input sites. A facet is
-coplanar if the last coefficient of its normal is
-nearly zero (see <a href="../src/user.h#ZEROdelaunay">qh_ZEROdelaunay</a>).
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="conventions">furthest-site qdelaunay conventions</a></h3>
-<blockquote>
-
-<p>The following terminology is used for furthest-site Delaunay
-triangulations in Qhull. The underlying structure is the upper
-facets of a convex hull in one higher dimension. See <a
-href="qconvex.htm#conventions">convex hull conventions</a>, <a
-href="qdelaun.htm#conventions">Delaunay conventions</a>,
-and <a href="index.htm#structure">Qhull's data structures</a></p>
-<blockquote>
-<ul>
- <li><em>input site</em> - a point in the input (one dimension
- lower than a point on the convex hull)</li>
- <li><em>point</em> - <i>d+1</i> coordinates. The last
- coordinate is the sum of the squares of the input site's
- coordinates</li>
- <li><em>vertex</em> - a point on the paraboloid. It
- corresponds to a unique input site. </li>
- <li><em>furthest-site Delaunay facet</em> - an upper facet of the
- paraboloid. The last coefficient of its normal is
- clearly positive.</li>
- <li><em>furthest-site Delaunay region</em> - a furthest-site Delaunay
- facet projected to the input sites</li>
- <li><em>non-simplicial facet</em> - more than <em>d</em>
- points are cocircular or cospherical</li>
- <li><em>good facet</em> - a furthest-site Delaunay facet with optional
- restrictions by '<a href="qh-optq.htm#QVn">QVn</a>', etc.</li>
-</ul>
-</blockquote>
-</blockquote>
-<h3><a href="#TOP">»</a><a name="options">furthest-site qdelaunay options</a></h3>
-<blockquote>
-
-See <a href="qdelaun.htm#options">qdelaunay options</a>. The same
-program is used for both constructions. Use option '<a href="qh-optq.htm#Qu">Qu</a>'
-for furthest-site Delaunay triangulations.
-
-</blockquote>
-<!-- Navigation links -->
-<hr>
-
-<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a><br>
-<b>To:</b> <a href="#synopsis">sy</a>nopsis
-• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
-• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
-• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
-• <a href="#options">op</a>tions
-<!-- GC common information -->
-<hr>
-
-<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
-align="middle" width="40" height="40"></a><i>The Geometry Center
-Home Page </i></p>
-
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
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-<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
-<html>
-
-<head>
-<title>qdelaunay -- Delaunay triangulation</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<a name="TOP"><b>Up</b></a><b>:</b>
-<a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a><br>
-<b>To:</b> <a href="#synopsis">sy</a>nopsis
-• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
-• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
-• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
-• <a href="#options">op</a>tions
-
-<hr>
-<!-- Main text of document -->
-<h1><a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
-src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
-height="100"></a>qdelaunay -- Delaunay triangulation</h1>
-
-<p>The Delaunay triangulation is the triangulation with empty
-circumspheres. It has many useful properties and applications.
-See the survey article by Aurenhammer [<a
-href="index.htm#aure91">'91</a>] and the detailed introduction
-by O'Rourke [<a href="index.htm#orou94">'94</a>]. </p>
-
-<blockquote>
-<dl>
- <dt><b>Example:</b> rbox r y c G0.1 D2 | qdelaunay <a href="qh-opto.htm#s">s</a>
- <a href="qh-optf.htm#Fv">Fv</a> <a href="qh-optt.htm#TO">TO
- result</a></dt>
- <dd>Compute the 2-d Delaunay triangulation of a triangle and
- a small square.
- Write a summary to the console and unoriented regions to 'result'.
- Merge regions for cocircular input sites (i.e., the
- square).</dd>
- <dt> </dt>
- <dt><b>Example:</b> rbox r y c G0.1 D2 | qdelaunay <a href="qh-opto.htm#s">s</a>
- <a href="qh-optf.htm#Fv">Fv</a> <a href="qh-optq.htm#Qt">Qt</a></dt>
- <dd>Compute the 2-d Delaunay triangulation of a triangle and
- a small square. Write a summary and unoriented
- regions to the console. Produce triangulated output.</dd>
- <dt> </dt>
- <dt><b>Example:</b> rbox 10 D2 | qdelaunay <a
- href="qh-optq.htm#QJn">QJ</a> <a href="qh-opto.htm#s">s</a>
- <a href="qh-opto.htm#i">i</a> <a href="qh-optt.htm#TO">TO
- result</a></dt>
- <dd>Compute the 2-d Delaunay triangulation of 10 random
- points. Joggle the input to guarantee triangular output.
- Write a summary to the console and the regions to
- 'result'.</dd>
-</dl>
-</blockquote>
-
-<p>Qhull computes the Delaunay triangulation by computing a
-convex hull. It lifts the input sites to a paraboloid by adding
-the sum of the squares of the coordinates. It scales the height
-of the paraboloid to improve numeric precision ('<a href=qh-optq.htm#Qbb>Qbb</a>').
-It computes the convex
-hull of the lifted sites, and projects the lower convex hull to
-the input.
-
-<p>Each region of the Delaunay triangulation
-corresponds to a facet of the lower half of the convex hull.
-Facets of the upper half of the convex hull correspond to the <a
-href="qdelau_f.htm">furthest-site Delaunay triangulation</a>.
-See the examples, <a href="qh-eg.htm#delaunay">Delaunay and
-Voronoi diagrams</a>.</p>
-
-<p>See <a href="http://www.qhull.org/html/qh-faq.htm#TOC">Qhull FAQ</a> - Delaunay and
-Voronoi diagram questions.</p>
-
-<p>By default, qdelaunay merges cocircular and cospherical regions.
-For example, the Delaunay triangulation of a square inside a diamond
-('rbox D2 c d G4 | qdelaunay') contains one region for the square.
-It identifies coincident points.
-
-<p>If you use '<a href="qh-optq.htm#Qt">Qt</a>' (triangulated output),
-all Delaunay regions will be simplicial (e.g., triangles in 2-d).
-Some regions may be
-degenerate and have zero area. Triangulated output identifies coincident
-points.
-
-<p>If you use '<a href="qh-optq.htm#QJn">QJ</a>' (joggled input), all Delaunay regions
-will be simplicial (e.g., triangles in 2-d). Coincident points will
-create small regions since the points are joggled apart. Joggled input
-is less accurate than triangulated output ('Qt'). See <a
-href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p>
-
-<p>The output for 3-d Delaunay triangulations may be confusing if the
-input contains cospherical data. See the FAQ item
-<a href=qh-faq.htm#extra>Why
-are there extra points in a 4-d or higher convex hull?</a>
-Avoid these problems with triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>') or
-joggled input ('<a href="qh-optq.htm#QJn">QJ</a>').
-</p>
-
-<p>The 'qdelaunay' program is equivalent to
-'<a href=qhull.htm#outputs>qhull d</a> <a href=qh-optq.htm#Qbb>Qbb</a>' in 2-d to 3-d, and
-'<a href=qhull.htm#outputs>qhull d</a> <a href=qh-optq.htm#Qbb>Qbb</a> <a href=qh-optq.htm#Qx>Qx</a>'
-in 4-d and higher. It disables the following Qhull
-<a href=qh-quick.htm#options>options</a>: <i>d n v H U Qb QB Qc Qf Qg Qi
-Qm Qr QR Qv Qx TR E V FC Fi Fo Fp Ft FV Q0,etc</i>.
-
-
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-
-<hr>
-
-<h3><a href="#TOP">»</a><a name="synopsis">qdelaunay synopsis</a></h3>
-
-<pre>
-qdelaunay- compute the Delaunay triangulation.
- input (stdin): dimension, number of points, point coordinates
- comments start with a non-numeric character
-
-options (qdelaun.htm):
- Qt - triangulated output
- QJ - joggle input instead of merging facets
- Qu - furthest-site Delaunay triangulation
- Tv - verify result: structure, convexity, and in-circle test
- . - concise list of all options
- - - one-line description of all options
-
-output options (subset):
- s - summary of results (default)
- i - vertices incident to each Delaunay region
- Fx - extreme points (vertices of the convex hull)
- o - OFF format (shows the points lifted to a paraboloid)
- G - Geomview output (2-d and 3-d points lifted to a paraboloid)
- m - Mathematica output (2-d inputs lifted to a paraboloid)
- QVn - print Delaunay regions that include point n, -n if not
- TO file- output results to file, may be enclosed in single quotes
-
-examples:
- rbox c P0 D2 | qdelaunay s o rbox c P0 D2 | qdelaunay i
- rbox c P0 D3 | qdelaunay Fv Qt rbox c P0 D2 | qdelaunay s Qu Fv
- rbox c G1 d D2 | qdelaunay s i rbox c G1 d D2 | qdelaunay s i Qt
- rbox M3,4 z 100 D2 | qdelaunay s rbox M3,4 z 100 D2 | qdelaunay s Qt
-</pre>
-
-
-<h3><a href="#TOP">»</a><a name="input">qdelaunay
-input</a></h3>
-
-<blockquote>
-<p>The input data on <tt>stdin</tt> consists of:</p>
-<ul>
- <li>dimension
- <li>number of points</li>
- <li>point coordinates</li>
-</ul>
-
-<p>Use I/O redirection (e.g., qdelaunay < data.txt), a pipe (e.g., rbox 10 | qdelaunay),
-or the '<a href=qh-optt.htm#TI>TI</a>' option (e.g., qdelaunay TI data.txt).
-
-<p>For example, this is four cocircular points inside a square. Its Delaunay
-triangulation contains 8 triangles and one four-sided
-figure.
-<p>
-<blockquote>
-<tt>rbox s 4 W0 c G1 D2 > data</tt>
-<blockquote><pre>
-2 RBOX s 4 W0 c D2
-8
--0.4941988586954018 -0.07594397977563715
--0.06448037284989526 0.4958248496365813
-0.4911154367094632 0.09383830681375946
--0.348353580869097 -0.3586778257652367
- -1 -1
- -1 1
- 1 -1
- 1 1
-</pre></blockquote>
-
-<p><tt>qdelaunay s i < data</tt>
-<blockquote><pre>
-
-Delaunay triangulation by the convex hull of 8 points in 3-d
-
- Number of input sites: 8
- Number of Delaunay regions: 9
- Number of non-simplicial Delaunay regions: 1
-
-Statistics for: RBOX s 4 W0 c D2 | QDELAUNAY s i
-
- Number of points processed: 8
- Number of hyperplanes created: 18
- Number of facets in hull: 10
- Number of distance tests for qhull: 33
- Number of merged facets: 2
- Number of distance tests for merging: 102
- CPU seconds to compute hull (after input): 0.028
-
-9
-1 7 5
-6 3 4
-2 3 6
-7 2 6
-2 7 1
-0 5 4
-3 0 4
-0 1 5
-1 0 3 2
-</pre></blockquote>
-</blockquote>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="outputs">qdelaunay
-outputs</a></h3>
-<blockquote>
-
-<p>These options control the output of Delaunay triangulations:</p>
-<blockquote>
-
-<dl compact>
- <dd><b>Delaunay regions</b></dd>
- <dt><a href="qh-opto.htm#i">i</a></dt>
- <dd>list input sites for each Delaunay region. The first line is the number of regions. The
- remaining lines list the input sites for each region. The regions are
- oriented. In 3-d and
- higher, report cospherical sites by adding extra points. Use triangulated
- output ('<a href="qh-optq.htm#Qt">Qt</a>') to avoid non-simpicial regions. For the circle-in-square example,
- eight Delaunay regions are triangular and the ninth has four input sites.</dd>
- <dt><a href="qh-optf.htm#Fv">Fv</a></dt>
- <dd>list input sites for each Delaunay region. The first line is the number of regions.
- Each remaining line starts with the number of input sites. The regions
- are unoriented. For the circle-in-square example,
- eight Delaunay regions are triangular and the ninth has four input sites.</dd>
- <dt><a href="qh-optf.htm#Fn">Fn</a></dt>
- <dd>list neighboring regions for each Delaunay region. The first line is the
- number of regions. Each remaining line starts with the number of
- neighboring regions. Negative indices (e.g., <em>-1</em>) indicate regions
- outside of the Delaunay triangulation.
- For the circle-in-square example, the four regions on the square are neighbors to
- the region-at-infinity.</dd>
- <dt><a href="qh-optf.htm#FN">FN</a></dt>
- <dd>list the Delaunay regions for each input site. The first line is the
- total number of input sites. Each remaining line starts with the number of
- Delaunay regions. Negative indices (e.g., <em>-1</em>) indicate regions
- outside of the Delaunay triangulation.
- For the circle-in-square example, each point on the circle belongs to four
- Delaunay regions. Use '<a href="qh-optq.htm#Qc">Qc</a> FN'
- to include coincident input sites and deleted vertices. </dd>
- <dt><a href="qh-optf.htm#Fa">Fa</a></dt>
- <dd>print area for each Delaunay region. The first line is the number of regions.
- The areas follow, one line per region. For the circle-in-square example, the
- cocircular region has area 0.4. </dd>
- <dt> </dt>
- <dt> </dt>
- <dd><b>Input sites</b></dd>
- <dt><a href="qh-optf.htm#Fc">Fc</a></dt>
- <dd>list coincident input sites for each Delaunay region.
- The first line is the number of regions. The remaining lines start with
- the number of coincident sites and deleted vertices. Deleted vertices
- indicate highly degenerate input (see'<A href="qh-optf.htm#Fs">Fs</a>').
- A coincident site is assigned to one Delaunay
- region. Do not use '<a href="qh-optq.htm#QJn">QJ</a>' with 'Fc'; the joggle will separate
- coincident sites.</dd>
- <dt><a href="qh-optf.htm#FP">FP</a></dt>
- <dd>print coincident input sites with distance to
- nearest site (i.e., vertex). The first line is the
- number of coincident sites. Each remaining line starts with the point ID of
- an input site, followed by the point ID of a coincident point, its region, and distance.
- Includes deleted vertices which
- indicate highly degenerate input (see'<A href="qh-optf.htm#Fs">Fs</a>').
- Do not use '<a href="qh-optq.htm#QJn">QJ</a>' with 'FP'; the joggle will separate
- coincident sites.</dd>
- <dt><a href="qh-optf.htm#Fx">Fx</a></dt>
- <dd>list extreme points of the input sites. These points are on the
- boundary of the convex hull. The first line is the number of
- extreme points. Each point is listed, one per line. The circle-in-square example
- has four extreme points.</dd>
- <dt> </dt>
- <dt> </dt>
- <dd><b>General</b></dd>
- <dt><a href="qh-optf.htm#FA">FA</a></dt>
- <dd>compute total area for '<a href="qh-opto.htm#s">s</a>'
- and '<a href="qh-optf.htm#FS">FS</a>'</dd>
- <dt><a href="qh-opto.htm#o">o</a></dt>
- <dd>print lower facets of the corresponding convex hull (a
- paraboloid)</dd>
- <dt><a href="qh-opto.htm#m">m</a></dt>
- <dd>Mathematica output for the lower facets of the paraboloid (2-d triangulations).</dd>
- <dt><a href="qh-optf.htm#FM">FM</a></dt>
- <dd>Maple output for the lower facets of the paraboloid (2-d triangulations).</dd>
- <dt><a href="qh-optg.htm#G">G</a></dt>
- <dd>Geomview output for the paraboloid (2-d or 3-d triangulations).</dd>
- <dt><a href="qh-opto.htm#s">s</a></dt>
- <dd>print summary for the Delaunay triangulation. Use '<a
- href="qh-optf.htm#Fs">Fs</a>' and '<a
- href="qh-optf.htm#FS">FS</a>' for numeric data.</dd>
-</dl>
-</blockquote>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="controls">qdelaunay
-controls</a></h3>
-<blockquote>
-
-<p>These options provide additional control:</p>
-<blockquote>
-
-<dl compact>
- <dt><a href="qh-optq.htm#Qt">Qt</a></dt>
- <dd>triangulated output. Qhull triangulates non-simplicial facets. It may produce
-degenerate facets of zero area.</dd>
- <dt><a href="qh-optq.htm#QJn">QJ</a></dt>
- <dd>joggle the input to avoid cospherical and coincident
- sites. It is less accurate than triangulated output ('Qt').</dd>
- <dt><a href="qh-optq.htm#Qu">Qu</a></dt>
- <dd>compute the <a href="qdelau_f.htm">furthest-site Delaunay triangulation</a>.</dd>
- <dt><a href="qh-optq.htm#Qz">Qz</a></dt>
- <dd>add a point above the paraboloid to reduce precision
- errors. Use it for nearly cocircular/cospherical input
- (e.g., 'rbox c | qdelaunay Qz'). The point is printed for
- options '<a href="qh-optf.htm#Ft">Ft</a>' and '<a
- href="qh-opto.htm#o">o</a>'.</dd>
- <dt><a href="qh-optq.htm#QVn">QVn</a></dt>
- <dd>select facets adjacent to input site <em>n</em> (marked
- 'good').</dd>
- <dt><a href="qh-optt.htm#Tv">Tv</a></dt>
- <dd>verify result.</dd>
- <dt><a href="qh-optt.htm#TO">TI file</a></dt>
- <dd>input data from file. The filename may not use spaces or quotes.</dd>
- <dt><a href="qh-optt.htm#TO">TO file</a></dt>
- <dd>output results to file. Use single quotes if the filename
- contains spaces (e.g., <tt>TO 'file with spaces.txt'</tt></dd>
- <dt><a href="qh-optt.htm#TFn">TFn</a></dt>
- <dd>report progress after constructing <em>n</em> facets</dd>
- <dt><a href="qh-optp.htm#PDk">PDk:1</a></dt>
- <dd>include upper and lower facets in the output. Set <em>k</em>
- to the last dimension (e.g., 'PD2:1' for 2-d inputs). </dd>
- <dt><a href="qh-opto.htm#f">f</a></dt>
- <dd>facet dump. Print the data structure for each facet (i.e., Delaunay region).</dd>
-</dl>
-</blockquote>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="graphics">qdelaunay
-graphics</a></h3>
-<blockquote>
-
-<p>For 2-d and 3-d Delaunay triangulations, Geomview ('qdelaunay <a
-href="qh-optg.htm#G">G</a>') displays the corresponding convex
-hull (a paraboloid). </p>
-
-<p>To view a 2-d Delaunay triangulation, use 'qdelaunay <a
-href="qh-optg.htm#GDn">GrD2</a>' to drop the last dimension. This
-is the same as viewing the hull without perspective (see
-Geomview's 'cameras' menu). </p>
-
-<p>To view a 3-d Delaunay triangulation, use 'qdelaunay <a
-href="qh-optg.htm#GDn">GrD3</a>' to drop the last dimension. You
-may see extra edges. These are interior edges that Geomview moves
-towards the viewer (see 'lines closer' in Geomview's camera
-options). Use option '<a href="qh-optg.htm#Gt">Gt</a>' to make
-the outer ridges transparent in 3-d. See <a
-href="qh-eg.htm#delaunay">Delaunay and Voronoi examples</a>.</p>
-
-<p>For 2-d Delaunay triangulations, Mathematica ('<a
-href="qh-opto.htm#m">m</a>') and Maple ('<a
-href="qh-optf.htm#FM">FM</a>') output displays the lower facets of the corresponding convex
-hull (a paraboloid). </p>
-
-<p>For 2-d, furthest-site Delaunay triangulations, Maple and Mathematica output ('<a
-href="qh-optq.htm#Qu">Qu</a> <a
-href="qh-opto.htm#m">m</a>') displays the upper facets of the corresponding convex
-hull (a paraboloid). </p>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="notes">qdelaunay
-notes</a></h3>
-<blockquote>
-
-<p>You can simplify the Delaunay triangulation by enclosing the input
-sites in a large square or cube. This is particularly recommended
-for cocircular or cospherical input data.
-
-<p>A non-simplicial Delaunay region indicates nearly cocircular or
-cospherical input sites. To avoid non-simplicial regions either triangulate
-the output ('<a href="qh-optq.htm#Qt">Qt</a>') or joggle
-the input ('<a href="qh-optq.htm#QJn">QJ</a>'). Triangulated output
-is more accurate than joggled input. Alternatively, use an <a
-href="qh-impre.htm#exact">exact arithmetic code</a>.</p>
-
-<p>Delaunay triangulations do not include facets that are
-coplanar with the convex hull of the input sites. A facet is
-coplanar if the last coefficient of its normal is
-nearly zero (see <a href="../src/user.h#ZEROdelaunay">qh_ZEROdelaunay</a>).
-
-<p>See <a href=qh-impre.htm#delaunay>Imprecision issues :: Delaunay triangulations</a>
-for a discussion of precision issues. Deleted vertices indicate
-highly degenerate input. They are listed in the summary output and
-option '<a href="qh-optf.htm#Fs">Fs</a>'.</p>
-
-<p>To compute the Delaunay triangulation of points on a sphere,
-compute their convex hull. If the sphere is the unit sphere at
-the origin, the facet normals are the Voronoi vertices of the
-input. The points may be restricted to a hemisphere. [S. Fortune]
-</p>
-
-<p>The 3-d Delaunay triangulation of regular points on a half
-spiral (e.g., 'rbox 100 l | qdelaunay') has quadratic size, while the Delaunay triangulation
-of random 3-d points is
-approximately linear for reasonably sized point sets.
-
-<p>With the <a href="qh-in.htm#library">Qhull library</a>, you
-can use <tt>qh_findbestfacet</tt> in <tt>poly2.c</tt> to locate the facet
-that contains a point. You should first lift the point to the
-paraboloid (i.e., the last coordinate is the sum of the squares
-of the point's coordinates -- <tt>qh_setdelaunay</tt>). Do not use options
-'<a href="qh-optq.htm#Qbb">Qbb</a>', '<a href="qh-optq.htm#QbB">QbB</a>',
-'<a href="qh-optq.htm#Qbk">Qbk:n</a>', or '<a
-href="qh-optq.htm#QBk">QBk:n</a>' since these scale the last
-coordinate. </p>
-
-<p>If a point is interior to the convex hull of the input set, it
-is interior to the adjacent vertices of the Delaunay
-triangulation. This is demonstrated by the following pipe for
-point 0:
-
-<pre>
- qdelaunay <data s FQ QV0 p | qconvex s Qb3:0B3:0 p
-</pre>
-
-<p>The first call to qdelaunay returns the neighboring points of
-point 0 in the Delaunay triangulation. The second call to qconvex
-returns the vertices of the convex hull of these points (after
-dropping the lifted coordinate). If point 0 is interior to the
-original point set, it is interior to the reduced point set. </p>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="conventions">qdelaunay conventions</a></h3>
-<blockquote>
-
-<p>The following terminology is used for Delaunay triangulations
-in Qhull for dimension <i>d</i>. The underlying structure is the
-lower facets of a convex hull in dimension <i>d+1</i>. For
-further information, see <a href="index.htm#structure">data
-structures</a> and <a href="qconvex.htm#conventions">convex hull
-conventions</a>.</p>
-<blockquote>
-<ul>
- <li><em>input site</em> - a point in the input (one dimension
- lower than a point on the convex hull)</li>
- <li><em>point</em> - a point has <i>d+1</i> coordinates. The
- last coordinate is the sum of the squares of the input
- site's coordinates</li>
- <li><em>coplanar point</em> - a <em>coincident</em>
- input site or a deleted vertex. Deleted vertices
- indicate highly degenerate input.</li>
- <li><em>vertex</em> - a point on the paraboloid. It
- corresponds to a unique input site. </li>
- <li><em>point-at-infinity</em> - a point added above the
- paraboloid by option '<a href="qh-optq.htm#Qz">Qz</a>'</li>
- <li><em>lower facet</em> - a facet corresponding to a
- Delaunay region. The last coefficient of its normal is
- clearly negative.</li>
- <li><em>upper facet</em> - a facet corresponding to a
- furthest-site Delaunay region. The last coefficient of
- its normal is clearly positive. </li>
- <li><em>Delaunay region</em> - a
- lower facet projected to the input sites</li>
- <li><em>upper Delaunay region</em> - an upper facet projected
- to the input sites</li>
- <li><em>non-simplicial facet</em> - more than <em>d</em>
- input sites are cocircular or cospherical</li>
- <li><em>good facet</em> - a Delaunay region with optional
- restrictions by '<a href="qh-optq.htm#QVn">QVn</a>', etc.</li>
-</ul>
-</blockquote>
-</blockquote>
-<h3><a href="#TOP">»</a><a name="options">qdelaunay options</a></h3>
-
-<pre>
-qdelaunay- compute the Delaunay triangulation
- http://www.qhull.org
-
-input (stdin):
- first lines: dimension and number of points (or vice-versa).
- other lines: point coordinates, best if one point per line
- comments: start with a non-numeric character
-
-options:
- Qt - triangulated output
- QJ - joggle input instead of merging facets
- Qu - compute furthest-site Delaunay triangulation
-
-Qhull control options:
- QJn - randomly joggle input in range [-n,n]
- Qs - search all points for the initial simplex
- Qz - add point-at-infinity to Delaunay triangulation
- QGn - print Delaunay region if visible from point n, -n if not
- QVn - print Delaunay regions that include point n, -n if not
-
-Trace options:
- T4 - trace at level n, 4=all, 5=mem/gauss, -1= events
- Tc - check frequently during execution
- Ts - print statistics
- Tv - verify result: structure, convexity, and in-circle test
- Tz - send all output to stdout
- TFn - report summary when n or more facets created
- TI file - input data from file, no spaces or single quotes
- TO file - output results to file, may be enclosed in single quotes
- TPn - turn on tracing when point n added to hull
- TMn - turn on tracing at merge n
- TWn - trace merge facets when width > n
- TVn - stop qhull after adding point n, -n for before (see TCn)
- TCn - stop qhull after building cone for point n (see TVn)
-
-Precision options:
- Cn - radius of centrum (roundoff added). Merge facets if non-convex
- An - cosine of maximum angle. Merge facets if cosine > n or non-convex
- C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
- Rn - randomly perturb computations by a factor of [1-n,1+n]
- Wn - min facet width for outside point (before roundoff)
-
-Output formats (may be combined; if none, produces a summary to stdout):
- f - facet dump
- G - Geomview output (see below)
- i - vertices incident to each Delaunay region
- m - Mathematica output (2-d only, lifted to a paraboloid)
- o - OFF format (dim, points, and facets as a paraboloid)
- p - point coordinates (lifted to a paraboloid)
- s - summary (stderr)
-
-More formats:
- Fa - area for each Delaunay region
- FA - compute total area for option 's'
- Fc - count plus coincident points for each Delaunay region
- Fd - use cdd format for input (homogeneous with offset first)
- FD - use cdd format for numeric output (offset first)
- FF - facet dump without ridges
- FI - ID of each Delaunay region
- Fm - merge count for each Delaunay region (511 max)
- FM - Maple output (2-d only, lifted to a paraboloid)
- Fn - count plus neighboring region for each Delaunay region
- FN - count plus neighboring region for each point
- FO - options and precision constants
- FP - nearest point and distance for each coincident point
- FQ - command used for qdelaunay
- Fs - summary: #int (8), dimension, #points, tot vertices, tot facets,
- for output: #vertices, #Delaunay regions,
- #coincident points, #non-simplicial regions
- #real (2), max outer plane, min vertex
- FS - sizes: #int (0)
- #real(2) tot area, 0
- Fv - count plus vertices for each Delaunay region
- Fx - extreme points of Delaunay triangulation (on convex hull)
-
-Geomview options (2-d and 3-d)
- Ga - all points as dots
- Gp - coplanar points and vertices as radii
- Gv - vertices as spheres
- Gi - inner planes only
- Gn - no planes
- Go - outer planes only
- Gc - centrums
- Gh - hyperplane intersections
- Gr - ridges
- GDn - drop dimension n in 3-d and 4-d output
- Gt - transparent outer ridges to view 3-d Delaunay
-
-Print options:
- PAn - keep n largest Delaunay regions by area
- Pdk:n - drop facet if normal[k] <= n (default 0.0)
- PDk:n - drop facet if normal[k] >= n
- Pg - print good Delaunay regions (needs 'QGn' or 'QVn')
- PFn - keep Delaunay regions whose area is at least n
- PG - print neighbors of good regions (needs 'QGn' or 'QVn')
- PMn - keep n Delaunay regions with most merges
- Po - force output. If error, output neighborhood of facet
- Pp - do not report precision problems
-
- . - list of all options
- - - one line descriptions of all options
-</pre>
-
-<!-- Navigation links -->
-<hr>
-
-<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a><br>
-<b>To:</b> <a href="#synopsis">sy</a>nopsis
-• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
-• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
-• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
-• <a href="#options">op</a>tions
-<!-- GC common information -->
-<hr>
-
-<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
-align="middle" width="40" height="40"></a><i>The Geometry Center
-Home Page </i></p>
-
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
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-<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
-<html>
-
-<head>
-<title>Examples of Qhull</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<p><a name="TOP"><b>Up:</b></a> <a href="http://www.qhull.org">Home
-page</a> for Qhull <br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a><br>
-<b>To: </b><a href="#TOC">Qhull examples: Table of Contents</a> (please wait
-while loading)<br>
-
-<hr>
-<!-- Main text of document -->
-<h1><a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/half.html"><img
-src="qh--half.gif" alt="[halfspace]" align="middle" width="100"
-height="100"></a> Examples of Qhull</h1>
-
-<p>This section of the Qhull manual will introduce you to Qhull
-and its options. Each example is a file for viewing with <a
-href="index.htm#geomview">Geomview</a>. You will need to
-use a Unix computer with a copy of Geomview.
-<p>
-If you are not running Unix, you can view <a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/welcome.html">pictures</a>
-for some of the examples. To understand Qhull without Geomview, try the
-examples in <a href="qh-quick.htm#programs">Programs</a> and
-<a href="qh-quick.htm#programs">Programs/input</a>. You can also try small
-examples that you compute by hand. Use <a href="rbox.htm">rbox</a>
-to generate examples.
-<p>
-To generate the Geomview examples, execute the shell script <tt>eg/q_eg</tt>.
-It uses <tt>rbox</tt>. The shell script <tt>eg/q_egtest</tt> generates
-test examples, and <tt>eg/q_test</tt> exercises the code. If you
-find yourself viewing the inside of a 3-d example, use Geomview's
-normalization option on the 'obscure' menu.</p>
-
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-
-<hr>
-
-<h2><a href="#TOP">»</a><a name="TOC">Qhull examples: Table of
-Contents </a></h2>
-
-<ul>
- <li><a href="#2d">2-d and 3-d examples</a></li>
- <li><a href="#how">How Qhull adds a point</a></li>
- <li><a href="#joggle">Triangulated output or joggled input</a></li>
- <li><a href="#delaunay">Delaunay and Voronoi diagrams</a></li>
- <li><a href="#merge">Facet merging for imprecision</a></li>
- <li><a href="#4d">4-d objects</a></li>
- <li><a href="#half">Halfspace intersections</a></li>
-</ul>
-
-<hr>
-<ul>
- <li><a href="#TOC">»</a><a name="2d">2-d and 3-d examples</a><ul>
- <li><a href="#01">eg.01.cube</a></li>
- <li><a href="#02">eg.02.diamond.cube</a></li>
- <li><a href="#03">eg.03.sphere</a></li>
- <li><a href="#04">eg.04.circle</a></li>
- <li><a href="#05">eg.05.spiral</a></li>
- <li><a href="#06">eg.06.merge.square</a></li>
- <li><a href="#07">eg.07.box</a></li>
- <li><a href="#08a">eg.08a.cube.sphere</a></li>
- <li><a href="#08b">eg.08b.diamond.sphere</a></li>
- <li><a href="#09">eg.09.lens</a></li>
- </ul>
- </li>
- <li><a href="#TOC">»</a><a name="how">How Qhull adds a point</a><ul>
- <li><a href="#10a">eg.10a.sphere.visible</a></li>
- <li><a href="#10b">eg.10b.sphere.beyond</a></li>
- <li><a href="#10c">eg.10c.sphere.horizon</a></li>
- <li><a href="#10d">eg.10d.sphere.cone</a></li>
- <li><a href="#10e">eg.10e.sphere.new</a></li>
- <li><a href="#14">eg.14.sphere.corner</a></li>
- </ul>
- </li>
- <li><a href="#TOC">»</a> <a name="joggle">Triangulated output or joggled input</a>
- <ul>
- <li><a href="#15a">eg.15a.surface</a></li>
- <li><a href="#15b">eg.15b.triangle</a></li>
- <li><a href="#15c">eg.15c.joggle</a></li>
- </ul>
- <li><a href="#TOC">»</a><a name="delaunay"> Delaunay and
- Voronoi diagrams</a><ul>
- <li><a href="#17a">eg.17a.delaunay.2</a></li>
- <li><a href="#17b">eg.17b.delaunay.2i</a></li>
- <li><a href="#17c">eg.17c.delaunay.2-3</a></li>
- <li><a href="#17d">eg.17d.voronoi.2</a></li>
- <li><a href="#17e">eg.17e.voronoi.2i</a></li>
- <li><a href="#17f">eg.17f.delaunay.3</a></li>
- <li><a href="#18a">eg.18a.furthest.2-3</a></li>
- <li><a href="#18b">eg.18b.furthest-up.2-3</a></li>
- <li><a href="#18c">eg.18c.furthest.2</a></li>
- <li><a href="#19">eg.19.voronoi.region.3</a></li>
- </ul>
- </li>
- <li><a href="#TOC">»</a><a name="merge">Facet merging for
- imprecision </a><ul>
- <li><a href="#20">eg.20.cone</a></li>
- <li><a href="#21a">eg.21a.roundoff.errors</a></li>
- <li><a href="#21b">eg.21b.roundoff.fixed</a></li>
- <li><a href="#22a">eg.22a.merge.sphere.01</a></li>
- <li><a href="#22b">eg.22b.merge.sphere.-01</a></li>
- <li><a href="#22c">eg.22c.merge.sphere.05</a></li>
- <li><a href="#22d">eg.22d.merge.sphere.-05</a></li>
- <li><a href="#23">eg.23.merge.cube</a></li>
- </ul>
- </li>
- <li><a href="#TOC">»</a><a name="4d">4-d objects</a><ul>
- <li><a href="#24">eg.24.merge.cube.4d-in-3d</a></li>
- <li><a href="#30">eg.30.4d.merge.cube</a></li>
- <li><a href="#31">eg.31.4d.delaunay</a></li>
- <li><a href="#32">eg.32.4d.octant</a></li>
- </ul>
- </li>
- <li><a href="#TOC">»</a><a name="half">Halfspace
- intersections</a><ul>
- <li><a href="#33a">eg.33a.cone</a></li>
- <li><a href="#33b">eg.33b.cone.dual</a></li>
- <li><a href="#33c">eg.33c.cone.halfspace</a></li>
- </ul>
- </li>
-</ul>
-
-<hr>
-
-<h2><a href="#TOC">»</a>2-d and 3-d examples</h2>
-
-<h3><a href="#2d">»</a><a name="01">rbox c D3 | qconvex G
->eg.01.cube </a></h3>
-
-<p>The first example is a cube in 3-d. The color of each facet
-indicates its normal. For example, normal [0,0,1] along the Z
-axis is (r=0.5, g=0.5, b=1.0). With the 'Dn' option in <tt>rbox</tt>,
-you can generate hypercubes in any dimension. Above 7-d the
-number of intermediate facets grows rapidly. Use '<a
-href="qh-optt.htm#TFn">TFn</a>' to track qconvex's progress. Note
-that each facet is a square that qconvex merged from coplanar
-triangles.</p>
-
-<h3><a href="#2d">»</a><a name="02">rbox c d G3.0 | qconvex G
->eg.02.diamond.cube </a></h3>
-
-<p>The second example is a cube plus a diamond ('d') scaled by <tt>rbox</tt>'s
-'G' option. In higher dimensions, diamonds are much simpler than
-hypercubes. </p>
-
-<h3><a href="#2d">»</a><a name="03">rbox s 100 D3 | qconvex G
->eg.03.sphere </a></h3>
-
-<p>The <tt>rbox s</tt> option generates random points and
-projects them to the d-sphere. All points should be on the convex
-hull. Notice that random points look more clustered than you
-might expect. You can get a smoother distribution by merging
-facets and printing the vertices, e.g.,<i> rbox 1000 s | qconvex
-A-0.95 p | qconvex G >eg.99</i>.</p>
-
-<h3><a href="#2d">»</a><a name="04">rbox s 100 D2 | qconvex G
->eg.04.circle </a></h3>
-
-<p>In 2-d, there are many ways to generate a convex hull. One of
-the earliest algorithms, and one of the fastest, is the 2-d
-Quickhull algorithm [c.f., Preparata & Shamos <a
-href="index.htm#pre-sha85">'85</a>]. It was the model for
-Qhull.</p>
-
-<h3><a href="#2d">»</a><a name="05">rbox 10 l | qconvex G
->eg.05.spiral </a></h3>
-
-<p>One rotation of a spiral.</p>
-
-<h3><a href="#2d">»</a><a name="06">rbox 1000 D2 | qconvex C-0.03
-Qc Gapcv >eg.06.merge.square</a></h3>
-
-<p>This demonstrates how Qhull handles precision errors. Option '<a
-href="qh-optc.htm#Cn">C-0.03</a>' requires a clearly convex angle
-between adjacent facets. Otherwise, Qhull merges the facets. </p>
-
-<p>This is the convex hull of random points in a square. The
-facets have thickness because they must be outside all points and
-must include their vertices. The colored lines represent the
-original points and the spheres represent the vertices. Floating
-in the middle of each facet is the centrum. Each centrum is at
-least 0.03 below the planes of its neighbors. This guarantees
-that the facets are convex.</p>
-
-<h3><a href="#2d">»</a><a name="07">rbox 1000 D3 | qconvex G
->eg.07.box </a></h3>
-
-<p>Here's the same distribution but in 3-d with Qhull handling
-machine roundoff errors. Note the large number of facets. </p>
-
-<h3><a href="#2d">»</a><a name="08a">rbox c G0.4 s 500 | qconvex G
->eg.08a.cube.sphere </a></h3>
-
-<p>The sphere is just barely poking out of the cube. Try the same
-distribution with randomization turned on ('<a
-href="qh-optq.htm#Qr">Qr</a>'). This turns Qhull into a
-randomized incremental algorithm. To compare Qhull and
-randomization, look at the number of hyperplanes created and the
-number of points partitioned. Don't compare CPU times since Qhull's
-implementation of randomization is inefficient. The number of
-hyperplanes and partitionings indicate the dominant costs for
-Qhull. With randomization, you'll notice that the number of
-facets created is larger than before. This is especially true as
-you increase the number of points. It is because the randomized
-algorithm builds most of the sphere before it adds the cube's
-vertices.</p>
-
-<h3><a href="#2d">»</a><a name="08b">rbox d G0.6 s 500 | qconvex G
->eg.08b.diamond.sphere </a></h3>
-
-<p>This is a combination of the diamond distribution and the
-sphere.</p>
-
-<h3><a href="#2d">»</a><a name="09">rbox 100 L3 G0.5 s | qconvex
-G >eg.09.lens </a></h3>
-
-<p>Each half of the lens distribution lies on a sphere of radius
-three. A directed search for the furthest facet below a point
-(e.g., qh_findbest in <tt>geom.c</tt>) may fail if started from
-an arbitrary facet. For example, if the first facet is on the
-opposite side of the lens, a directed search will report that the
-point is inside the convex hull even though it is outside. This
-problem occurs whenever the curvature of the convex hull is less
-than a sphere centered at the test point. </p>
-
-<p>To prevent this problem, Qhull does not use directed search
-all the time. When Qhull processes a point on the edge of the
-lens, it partitions the remaining points with an exhaustive
-search instead of a directed search (see qh_findbestnew in <tt>geom2.c</tt>).
-</p>
-
-<h2><a href="#TOC">»</a>How Qhull adds a point</h2>
-
-<h3><a href="#how">»</a><a name="10a">rbox 100 s P0.5,0.5,0.5 |
-qconvex Ga QG0 >eg.10a.sphere.visible</a></h3>
-
-<p>The next 4 examples show how Qhull adds a point. The point
-[0.5,0.5,0.5] is at one corner of the bounding box. Qhull adds a
-point using the beneath-beyond algorithm. First Qhull finds all
-of the facets that are visible from the point. Qhull will replace
-these facets with new facets.</p>
-
-<h3><a href="#how">»</a><a name="10b">rbox 100 s
-P0.5,0.5,0.5|qconvex Ga QG-0 >eg.10b.sphere.beyond </a></h3>
-
-<p>These are the facets that are not visible from the point.
-Qhull will keep these facets.</p>
-
-<h3><a href="#how">»</a><a name="10c">rbox 100 s P0.5,0.5,0.5 |
-qconvex PG Ga QG0 >eg.10c.sphere.horizon </a></h3>
-
-<p>These facets are the horizon facets; they border the visible
-facets. The inside edges are the horizon ridges. Each horizon
-ridge will form the base for a new facet.</p>
-
-<h3><a href="#how">»</a><a name="10d">rbox 100 s P0.5,0.5,0.5 |
-qconvex Ga QV0 PgG >eg.10d.sphere.cone </a></h3>
-
-<p>This is the cone of points from the new point to the horizon
-facets. Try combining this image with <tt>eg.10c.sphere.horizon</tt>
-and <tt>eg.10a.sphere.visible</tt>.
-</p>
-
-<h3><a href="#how">»</a><a name="10e">rbox 100 s P0.5,0.5,0.5 |
-qconvex Ga >eg.10e.sphere.new</a></h3>
-
-<p>This is the convex hull after [0.5,0.5,0.5] has been added.
-Note that in actual practice, the above sequence would never
-happen. Unlike the randomized algorithms, Qhull always processes
-a point that is furthest in an outside set. A point like
-[0.5,0.5,0.5] would be one of the first points processed.</p>
-
-<h3><a href="#how">»</a><a name="14">rbox 100 s P0.5,0.5,0.5 |
-qhull Ga QV0g Q0 >eg.14.sphere.corner</a></h3>
-
-<p>The '<a href="qh-optq.htm#QVn">QVn</a>', '<a
-href="qh-optq.htm#QGn">QGn </a>' and '<a href="qh-optp.htm#Pdk">Pdk</a>'
-options define good facets for Qhull. In this case '<a
-href="qh-optq.htm#QVn">QV0</a>' defines the 0'th point
-[0.5,0.5,0.5] as the good vertex, and '<a href="qh-optq.htm#Qg">Qg</a>'
-tells Qhull to only build facets that might be part of a good
-facet. This technique reduces output size in low dimensions. It
-does not work with facet merging.</p>
-
-<h2><a href="#TOC">»</a>Triangulated output or joggled input</h2>
-
-<h3><a href="#joggle">»</a><a name="15a">rbox 500 W0 | qconvex QR0 Qc Gvp >eg.15a.surface</a></h3>
-
-<p>This is the convex hull of 500 points on the surface of
-a cube. Note the large, non-simplicial facet for each face.
-Qhull merges non-convex facets.
-
-<p>If the facets were not merged, Qhull
-would report precision problems. For example, turn off facet merging
-with option '<a href="qh-optq.htm#Q0">Q0</a>'. Qhull may report concave
-facets, flipped facets, or other precision errors:
-<blockquote>
-rbox 500 W0 | qhull QR0 Q0
-</blockquote>
-
-<p>
-<h3><a href="#joggle">»</a><a name="15b">rbox 500 W0 | qconvex QR0 Qt Qc Gvp >eg.15b.triangle</a></h3>
-
-<p>Like the previous examples, this is the convex hull of 500 points on the
-surface of a cube. Option '<a href="qh-optq.htm#Qt">Qt</a>' triangulates the
-non-simplicial facets. Triangulated output is
-particularly helpful for Delaunay triangulations.
-
-<p>
-<h3><a href="#joggle">»</a><a name="15c">rbox 500 W0 | qconvex QR0 QJ5e-2 Qc Gvp >eg.15c.joggle</a></h3>
-
-<p>This is the convex hull of 500 joggled points on the surface of
-a cube. The option '<a href="qh-optq.htm#QJn">QJ5e-2</a>'
-sets a very large joggle to make the effect visible. Notice
-that all of the facets are triangles. If you rotate the cube,
-you'll see red-yellow lines for coplanar points.
-<p>
-With option '<a href="qh-optq.htm#QJn">QJ</a>', Qhull joggles the
-input to avoid precision problems. It adds a small random number
-to each input coordinate. If a precision
-error occurs, it increases the joggle and tries again. It repeats
-this process until no precision problems occur.
-<p>
-Joggled input is a simple solution to precision problems in
-computational geometry. Qhull can also merge facets to handle
-precision problems. See <a href="qh-impre.htm#joggle">Merged facets or joggled input</a>.
-
-<h2><a href="#TOC">»</a>Delaunay and Voronoi diagrams</h2>
-
-<h3><a href="#delaunay">»</a><a name="17a">qdelaunay Qt
-<eg.data.17 GnraD2 >eg.17a.delaunay.2</a></h3>
-
-<p>
-The input file, <tt>eg.data.17</tt>, consists of a square, 15 random
-points within the outside half of the square, and 6 co-circular
-points centered on the square.
-
-<p>The Delaunay triangulation is the triangulation with empty
-circumcircles. The input for this example is unusual because it
-includes six co-circular points. Every triangular subset of these
-points has the same circumcircle. Option '<a href="qh-optq.htm#Qt">Qt</a>'
-triangulates the co-circular facet.</p>
-
-<h3><a href="#delaunay">»</a><a name="17b">qdelaunay <eg.data.17
-GnraD2 >eg.17b.delaunay.2i</a></h3>
-
-<p>This is the same example without triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>'). qdelaunay
-merges the non-unique Delaunay triangles into a hexagon.</p>
-
-<h3><a href="#delaunay">»</a><a name="17c">qdelaunay <eg.data.17
-Ga >eg.17c.delaunay.2-3 </a></h3>
-
-<p>This is how Qhull generated both diagrams. Use Geomview's
-'obscure' menu to turn off normalization, and Geomview's
-'cameras' menu to turn off perspective. Then load this <a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html">object</a>
-with one of the previous diagrams.</p>
-
-<p>The points are lifted to a paraboloid by summing the squares
-of each coordinate. These are the light blue points. Then the
-convex hull is taken. That's what you see here. If you look up
-the Z-axis, you'll see that points and edges coincide.</p>
-
-<h3><a href="#delaunay">»</a><a name="17d">qvoronoi QJ
-<eg.data.17 Gna >eg.17d.voronoi.2</a></h3>
-
-<p>The Voronoi diagram is the dual of the Delaunay triangulation.
-Here you see the original sites and the Voronoi vertices.
-Notice the each
-vertex is equidistant from three sites. The edges indicate the
-Voronoi region for a site. Qhull does not draw the unbounded
-edges. Instead, it draws extra edges to close the unbounded
-Voronoi regions. You may find it helpful to enclose the input
-points in a square. You can compute the unbounded
-rays from option '<a href="qh-optf.htm#Fo2">Fo</a>'.
-</p>
-
-<p>Instead
-of triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>'), this
-example uses joggled input ('<a href="qh-optq.htm#QJn">QJ</a>').
-Normally, you should use neither 'QJ' nor 'Qt' for Voronoi diagrams.
-
-<h3><a href="#delaunay">»</a><a name="17e">qvoronoi <eg.data.17
-Gna >eg.17e.voronoi.2i </a></h3>
-
-<p>This looks the same as the previous diagrams, but take a look
-at the data. Run 'qvoronoi p <eg/eg.data.17'. This prints
-the Voronoi vertices.
-
-<p>With 'QJ', there are four nearly identical Voronoi vertices
-within 10^-11 of the origin. Option 'QJ' joggled the input. After the joggle,
-the cocircular
-input sites are no longer cocircular. The corresponding Voronoi vertices are
-similar but not identical.
-
-<p>This example does not use options 'Qt' or 'QJ'. The cocircular
-input sites define one Voronoi vertex near the origin. </p>
-
-<p>Option 'Qt' would triangulate the corresponding Delaunay region into
-four triangles. Each triangle is assigned the same Voronoi vertex.</p>
-
-<h3><a href="#delaunay">»</a><a name="17f"> rbox c G0.1 d |
-qdelaunay Gt Qz <eg.17f.delaunay.3 </a></h3>
-
-<p>This is the 3-d Delaunay triangulation of a small cube inside
-a prism. Since the outside ridges are transparent, it shows the
-interior of the outermost facets. If you slice open the
-triangulation with Geomview's ginsu, you will see that the innermost
-facet is a cube. Note the use of '<a href="qh-optq.htm#Qz">Qz</a>'
-to add a point "at infinity". This avoids a degenerate
-input due to cospherical points.</p>
-
-<h3><a href="#delaunay">»</a><a name="18a">rbox 10 D2 d | qdelaunay
-Qu G >eg.18a.furthest.2-3 </a></h3>
-
-<p>The furthest-site Voronoi diagram contains Voronoi regions for
-points that are <i>furthest </i>from an input site. It is the
-dual of the furthest-site Delaunay triangulation. You can
-determine the furthest-site Delaunay triangulation from the
-convex hull of the lifted points (<a href="#17c">eg.17c.delaunay.2-3</a>).
-The upper convex hull (blue) generates the furthest-site Delaunay
-triangulation. </p>
-
-<h3><a href="#delaunay">»</a><a name="18b">rbox 10 D2 d | qdelaunay
-Qu Pd2 G >eg.18b.furthest-up.2-3</a></h3>
-
-<p>This is the upper convex hull of the preceding example. The
-furthest-site Delaunay triangulation is the projection of the
-upper convex hull back to the input points. The furthest-site
-Voronoi vertices are the circumcenters of the furthest-site
-Delaunay triangles. </p>
-
-<h3><a href="#delaunay">»</a><a name="18c">rbox 10 D2 d | qvoronoi
-Qu Gv >eg.18c.furthest.2</a></h3>
-
-<p>This shows an incomplete furthest-site Voronoi diagram. It
-only shows regions with more than two vertices. The regions are
-artificially truncated. The actual regions are unbounded. You can
-print the regions' vertices with 'qvoronoi Qu <a
-href="qh-opto.htm#o">o</a>'. </p>
-
-<p>Use Geomview's 'obscure' menu to turn off normalization, and
-Geomview's 'cameras' menu to turn off perspective. Then load this
-with the upper convex hull.</p>
-
-<h3><a href="#delaunay">»</a><a name="19">rbox 10 D3 | qvoronoi QV5
-p | qconvex G >eg.19.voronoi.region.3 </a></h3>
-
-<p>This shows the Voronoi region for input site 5 of a 3-d
-Voronoi diagram.</p>
-
-<h2><a href="#TOC">»</a>Facet merging for imprecision</h2>
-
-<h3><a href="#merge">»</a><a name="20">rbox r s 20 Z1 G0.2 |
-qconvex G >eg.20.cone </a></h3>
-
-<p>There are two things unusual about this <a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html">cone</a>.
-One is the large flat disk at one end and the other is the
-rectangles about the middle. That's how the points were
-generated, and if those points were exact, this is the correct
-hull. But <tt>rbox</tt> used floating point arithmetic to
-generate the data. So the precise convex hull should have been
-triangles instead of rectangles. By requiring convexity, Qhull
-has recovered the original design.</p>
-
-<h3><a href="#merge">»</a><a name="21a">rbox 200 s | qhull Q0
-R0.01 Gav Po >eg.21a.roundoff.errors </a></h3>
-
-<p>This is the convex hull of 200 cospherical points with
-precision errors ignored ('<a href="qh-optq.htm#Q0">Q0</a>'). To
-demonstrate the effect of roundoff error, we've added a random
-perturbation ('<a href="qh-optc.htm#Rn">R0.01</a>') to every
-distance and hyperplane calculation. Qhull, like all other convex
-hull algorithms with floating point arithmetic, makes
-inconsistent decisions and generates wildly wrong results. In
-this case, one or more facets are flipped over. These facets have
-the wrong color. You can also turn on 'normals' in Geomview's
-appearances menu and turn off 'facing normals'. There should be
-some white lines pointing in the wrong direction. These
-correspond to flipped facets. </p>
-
-<p>Different machines may not produce this picture. If your
-machine generated a long error message, decrease the number of
-points or the random perturbation ('<a href="qh-optc.htm#Rn">R0.01</a>').
-If it did not report flipped facets, increase the number of
-points or perturbation.</p>
-
-<h3><a href="#merge">»</a><a name="21b">rbox 200 s | qconvex Qc
-R0.01 Gpav >eg.21b.roundoff.fixed </a></h3>
-
-<p>Qhull handles the random perturbations and returns an
-imprecise <a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/fixed.html">sphere</a>.
-In this case, the output is a weak approximation to the points.
-This is because a random perturbation of '<a
-href="qh-optc.htm#Rn">R0.01 </a>' is equivalent to losing all but
-1.8 digits of precision. The outer planes float above the points
-because Qhull needs to allow for the maximum roundoff error. </p>
-<p>
-If you start with a smaller random perturbation, you
-can use joggle ('<a href="qh-optq.htm#QJn">QJn</a>') to avoid
-precision problems. You need to set <i>n</i> significantly
-larger than the random perturbation. For example, try
-'rbox 200 s | qconvex Qc R1e-4 QJ1e-1'.
-
-<h3><a href="#merge">»</a><a name="22a">rbox 1000 s| qconvex C0.01
-Qc Gcrp >eg.22a.merge.sphere.01</a></h3>
-
-<h3><a href="#merge">»</a><a name="22b">rbox 1000 s| qconvex
-C-0.01 Qc Gcrp >eg.22b.merge.sphere.-01</a></h3>
-
-<h3><a href="#merge">»</a><a name="22c">rbox 1000 s| qconvex C0.05
-Qc Gcrpv >eg.22c.merge.sphere.05</a></h3>
-
-<h3><a href="#merge">»</a><a name="22d">rbox 1000 s| qconvex
-C-0.05 Qc Gcrpv >eg.22d.merge.sphere.-05</a></h3>
-
-<p>The next four examples compare post-merging and pre-merging ('<a
-href="qh-optc.htm#Cn2">Cn</a>' vs. '<a href="qh-optc.htm#Cn">C-n</a>').
-Qhull uses '-' as a flag to indicate pre-merging.</p>
-
-<p>Post-merging happens after the convex hull is built. During
-post-merging, Qhull repeatedly merges an independent set of
-non-convex facets. For a given set of parameters, the result is
-about as good as one can hope for.</p>
-
-<p>Pre-merging does the same thing as post-merging, except that
-it happens after adding each point to the convex hull. With
-pre-merging, Qhull guarantees a convex hull, but the facets are
-wider than those from post-merging. If a pre-merge option is not
-specified, Qhull handles machine round-off errors.</p>
-
-<p>You may see coplanar points appearing slightly outside
-the facets of the last example. This is becomes Geomview moves
-line segments forward toward the viewer. You can avoid the
-effect by setting 'lines closer' to '0' in Geomview's camera menu.
-
-<h3><a href="#merge">»</a><a name="23">rbox 1000 | qconvex s
-Gcprvah C0.1 Qc >eg.23.merge.cube</a></h3>
-
-<p>Here's the 3-d imprecise cube with all of the Geomview
-options. There's spheres for the vertices, radii for the coplanar
-points, dots for the interior points, hyperplane intersections,
-centrums, and inner and outer planes. The radii are shorter than
-the spheres because this uses post-merging ('<a href="qh-optc.htm#Cn2">C0.1</a>')
-instead of pre-merging.
-
-<h2><a href="#TOC">»</a>4-d objects</h2>
-
-<p>With Qhull and Geomview you can develop an intuitive sense of
-4-d surfaces. When you get into trouble, think of viewing the
-surface of a 3-d sphere in a 2-d plane.</p>
-
-<h3><a href="#4d">»</a><a name="24">rbox 5000 D4 | qconvex s GD0v
-Pd0:0.5 C-0.02 C0.1 >eg.24.merge.cube.4d-in-3d</a></h3>
-
-<p>Here's one facet of the imprecise cube in 4-d. It's projected
-into 3-d (the '<a href="qh-optg.htm#GDn">GDn</a>' option drops
-dimension n). Each ridge consists of two triangles between this
-facet and the neighboring facet. In this case, Geomview displays
-the topological ridges, i.e., as triangles between three
-vertices. That is why the cube looks lopsided.</p>
-
-<h3><a href="#4d">»</a><a name="30">rbox 5000 D4 | qconvex s
-C-0.02 C0.1 Gh >eg.30.4d.merge.cube </a></h3>
-
-<p><a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/4dcube.html">Here</a>
-is the equivalent in 4-d of the imprecise <a href="#06">square</a>
-and imprecise <a href="#23">cube</a>. It's the imprecise convex
-hull of 5000 random points in a hypercube. It's a full 4-d object
-so Geomview's <tt>ginsu </tt>does not work. If you view it in
-Geomview, you'll be inside the hypercube. To view 4-d objects
-directly, either load the <tt>4dview</tt> module or the <tt>ndview
-</tt>module. For <tt>4dview</tt>, you must have started Geomview
-in the same directory as the object. For <tt>ndview</tt>,
-initialize a set of windows with the prefab menu, and load the
-object through Geomview. The <tt>4dview</tt> module includes an
-option for slicing along any hyperplane. If you do this in the x,
-y, or z plane, you'll see the inside of a hypercube.</p>
-
-<p>The '<a href="qh-optg.htm#Gh">Gh</a>' option prints the
-geometric intersections between adjacent facets. Note the strong
-convexity constraint for post-merging ('<a href="qh-optc.htm#Cn2">C0.1</a>').
-It deletes the small facets.</p>
-
-<h3><a href="#4d">»</a><a name="31">rbox 20 D3 | qdelaunay G
->eg.31.4d.delaunay </a></h3>
-
-<p>The Delaunay triangulation of 3-d sites corresponds to a 4-d
-convex hull. You can't see 4-d directly but each facet is a 3-d
-object that you can project to 3-d. This is exactly the same as
-projecting a 2-d facet of a soccer ball onto a plane.</p>
-
-<p>Here we see all of the facets together. You can use Geomview's
-<tt>ndview</tt> to look at the object from several directions.
-Try turning on edges in the appearance menu. You'll notice that
-some edges seem to disappear. That's because the object is
-actually two sets of overlapping facets.</p>
-
-<p>You can slice the object apart using Geomview's <tt>4dview</tt>.
-With <tt>4dview</tt>, try slicing along the w axis to get a
-single set of facets and then slice along the x axis to look
-inside. Another interesting picture is to slice away the equator
-in the w dimension.</p>
-
-<h3><a href="#4d">»</a><a name="32">rbox 30 s D4 | qconvex s G
-Pd0d1d2D3</a></h3>
-
-<p>This is the positive octant of the convex hull of 30 4-d
-points. When looking at 4-d, it's easier to look at just a few
-facets at once. If you picked a facet that was directly above
-you, then that facet looks exactly the same in 3-d as it looks in
-4-d. If you pick several facets, then you need to imagine that
-the space of a facet is rotated relative to its neighbors. Try
-Geomview's <tt>ndview</tt> on this example.</p>
-
-<h2><a href="#TOC">»</a>Halfspace intersections</h2>
-
-<h3><a href="#half">»</a><a name="33a">rbox 10 r s Z1 G0.3 |
-qconvex G >eg.33a.cone </a></h3>
-
-<h3><a href="#half">»</a><a name="33b">rbox 10 r s Z1 G0.3 |
-qconvex FV n | qhalf G >eg.33b.cone.dual</a></h3>
-
-<h3><a href="#half">»</a><a name="33c">rbox 10 r s Z1 G0.3 |
-qconvex FV n | qhalf Fp | qconvex G >eg.33c.cone.halfspace</a></h3>
-
-<p>These examples illustrate halfspace intersection. The first
-picture is the convex hull of two 20-gons plus an apex. The
-second picture is the dual of the first. Try loading <a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/half.html">both</a>
-at once. Each vertex of the second picture corresponds to a facet
-or halfspace of the first. The vertices with four edges
-correspond to a facet with four neighbors. Similarly the facets
-correspond to vertices. A facet's normal coefficients divided by
-its negative offset is the vertice's coordinates. The coordinates
-are the intersection of the original halfspaces. </p>
-
-<p>The third picture shows how Qhull can go back and forth
-between equivalent representations. It starts with a cone,
-generates the halfspaces that define each facet of the cone, and
-then intersects these halfspaces. Except for roundoff error, the
-third picture is a duplicate of the first. </p>
-<!-- Navigation links -->
-<hr>
-
-<p><b>Up:</b> <a href="http://www.qhull.org">Home
-page for Qhull</a> <br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual: Table of Contents</a><br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
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-<b>To: </b><a href="#TOC">Qhull examples: Table of Contents</a> (please wait
-while loading)<br>
-<!-- GC common information -->
-<hr>
-
-<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
-align="middle" width="40" height="40"></a><i>The Geometry Center
-Home Page </i></p>
-
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
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-<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
-<html>
-
-<head>
-<meta http-equiv="Content-Type"
-content="text/html; charset=iso-8859-1">
-<meta name="GENERATOR" content="Microsoft FrontPage 2.0">
-<title>Qhull FAQ</title>
-<!-- Navigation links
-NOTE -- verify all links by 'grep href=' 'grep name=' add # 'sort /+7'
-<base href> does not work since #TOC is relative to base instead of doc
--->
-</head>
-
-<body>
-
-<p><a name="TOP"><b>Up:</b></a> <a
- href="http://www.qhull.org">Home page</a> for Qhull
-(http://www.qhull.org)<br>
-<b>Up:</b> <A href="index.htm#TOC">Qhull manual</A>: Table of Contents<br>
-<b>To:</b> <A href="qh-quick.htm#programs">Programs</A>
-• <A href="qh-quick.htm#options">Options</A>
-• <A href="qh-opto.htm#output">Output</A>
-• <A href="qh-optf.htm#format">Formats</A>
-• <A href="qh-optg.htm#geomview">Geomview</A>
-• <A href="qh-optp.htm#print">Print</A>
-• <A href="qh-optq.htm#qhull">Qhull</A>
-• <A href="qh-optc.htm#prec">Precision</A>
-• <A href="qh-optt.htm#trace">Trace</A> <br>
-<b>To:</b> <A href="#TOC">FAQ: Table of Contents</A> (please
-wait while loading) <br>
-
-<hr>
-<!-- Main text of document -->
-<h1><a
- href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/4dcube.html"><IMG
- align=middle alt ="[4-d cube]"
- height=100 src="qh--4d.gif" width=100 ></a> Frequently Asked Questions about Qhull</h1><!--
-<p><i>This is the most recent FAQ. It was updated Sept. 13, 1999.</i>
--->
-<p>If your question does not appear here, see: </p>
-
-<ul>
- <li><a href="http://www.qhull.org/news">News</a> about Qhull
- <li><A href="index.htm#TOC">Qhull manual:</A> table of contents
- <li><A href="../README.txt">Installation</A> instructions for Qhull and rbox
-
- <li><A href="mailto:qhull@qhull.org">Send e-mail</A> to
- qhull@qhull.org
- <li><A href="mailto:qhull_bug@qhull.org">Report bugs</A>
- to qhull_bug@qhull.org </li>
-</ul>
-
-<p>Qhull is a general dimension code for computing convex hulls,
-Delaunay triangulations, halfspace intersections about a point,
-Voronoi diagrams, furthest-site Delaunay triangulations, and
-furthest-site Voronoi diagrams. These structures have
-applications in science, engineering, statistics, and
-mathematics. For a detailed introduction, see O'Rourke [<A
- href="index.htm#orou94" >'94</A>], <i>Computational Geometry in C</i>.
-</p>
-
-<p>There are separate programs for each application of
-Qhull. These programs disable experimental and inappropriate
-options. If you prefer, you may use Qhull directly. All programs
-run the same code.
-
-<p>Version 3.1 added triangulated output ('<A href="qh-optq.htm#Qt">Qt</A>').
-It should be used for Delaunay triangulations instead of
-using joggled input ('<A href="qh-optq.htm#QJn">QJ</A>').
-
-<p><i>Brad Barber, Cambridge MA,
-2003/12/30 <!--
---> </i></p>
-
-<p><b>Copyright © 1998-2003 The Geometry Center, Minneapolis MN</b></p>
-
-<hr>
-
-<h2><A href="#TOP">»</A><a name="TOC">FAQ: Table of Contents </a></h2>
-
-<p>Within each category, the most recently asked questions are
-first.
-<ul>
- <li>Startup questions <ul>
- <li><A href="#console">How</A> do I run Qhull from Windows?
- <li><A href="#input">How</A> do I enter points for Qhull?
- <li><A href="#learn">How</A> do I learn to use Qhull?</li>
- </ul>
- <li>Convex hull questions<ul>
- <li><A href="#area">How</A> do I report just the area and volume of a
- convex hull?
- <li><A href="#extra">Why</A> are there extra points in a 4-d or higher
- convex hull?
- <li><A href="#dup">How</A> do I report duplicate
- vertices? </li>
- </ul>
- <li>Delaunay and Voronoi diagram questions<ul>
- <li><a href="#maxsphere">How</a> do I get the radii of the empty
- spheres for each Voronoi vertex?
-
- <li><A href="#flat">How</A> do I get rid of nearly flat Delaunay
- triangles?
-
- <li><A href="#square">What</A> is the Voronoi diagram of a square?
-
- <li><A href="#vclosest">How</A> do I find the Delaunay triangle or Voronoi
- region that is closest to a point?
-
- <li><A href="#mesh">How</A> do I compute the Delaunay triangulation of a
- non-convex object?
-
- <li><A href="#mesh">How</A> do I mesh a volume from a set of triangulated
- surface points?
-
- <li><A href="#constrained">Can</A> Qhull produce a triangular mesh for an
- object?
-
- <li><A href="#dridges">For</A> 3-d Delaunay triangulations, how do I
- report the triangles of each tetrahedron?
- <li><A href="#vsphere">How</A> do I construct the Voronoi diagram of
- cospherical points?
- <li><A href="#3dd">How</A> do I construct a 3-d Delaunay triangulation?
- <li><A href="#2d">How</A> do I get the triangles for a 2-d Delaunay
- triangulation and the vertices of its Voronoi diagram?
- <li><A href="#rays">Can</A> Qhull compute the unbounded rays of the
- Voronoi diagram?
- <li><A href="#big">Can </A>Qhull triangulate a
- hundred 16-d points?</li>
- </ul>
- <li>Approximation questions<ul>
- <li><A href="#simplex">How</A> do I approximate data
- with a simplex?</li>
- </ul>
- <li>Halfspace questions<ul>
- <li><A href="#halfspace">How</A> do I compute the
- intersection of halfspaces with Qhull?</li>
- </ul>
- <li><a name="library">Qhull library</a> questions<ul>
- <li><A href="#math">Is</A> Qhull available for Mathematica, Matlab, or
- Maple?
-
- <li><A href="#ridges">Why</A> are there too few ridges?
- <li><A href="#call">Can</A> Qhull use coordinates without placing them in
- a data file?
- <li><A href="#size">How</A> large are Qhull's data structures?
- <li><A href="#inc">Can</A> Qhull construct convex hulls and Delaunay
- triangulations one point at a time?
- <li><A href="#ridges2">How</A> do I visit the ridges of a Delaunay
- triangulation?
- <li><A href="#listd">How</A> do I visit the Delaunay facets?
- <LI><A
- href="#outside">When</A> is a point outside or inside a facet?
- <li><A href="#closest">How</A> do I find the facet that is closest to a
- point?
- <li><A href="#vclosest">How</A> do I find the Delaunay triangle or Voronoi
- region that is closest to a point?
- <li><A href="#vertices">How</A> do I list the vertices?
- <li><A href="#test">How</A> do I test code that uses the Qhull library?
- <li><A href="#orient">When</A> I compute a plane
- equation from a facet, I sometimes get an
- outward-pointing normal and sometimes an
- inward-pointing normal</li>
- </ul>
- </li>
-</ul>
-
-<hr>
-
-<h2><A href="#TOC">»</A><a name="startup">Startup</a> questions</h2>
-
-<h4><A href="#TOC">»</A><a name="console">How</a> do I run Qhull
-from Windows?</h4><blockquote>
-
-<p>Qhull is a console program. You will first need a DOS window
-(i.e., a "DOS prompt"). You can double click on
-'eg\Qhull-go.bat'. It loads 'doskey' to simplify rerunning qhull
-and rbox. </p>
-
-<blockquote><ul>
- <li>Type 'qconvex', 'qdelaunay', 'qhalf', 'qvoronoi,
- 'qhull', and 'rbox' for a synopsis of each program.
-
- <li>Type 'rbox c D2 | qconvex s i' to compute the
- convex hull of a square.
-
- <li>Type 'rbox c D2 | qconvex s i TO results.txt' to
- write the results to the file 'results.txt'. A summary is still printed on
- the the console.
-
- <li>Type 'rbox c D2' to see the input format for
- qconvex.
-
- <li>Type 'qconvex < data.txt s i TO results.txt' to
- read input data from 'data.txt'.
-
- <li>If you want to enter data by hand, type 'qconvex s i TO
- results.txt' to read input data from the console. Type in
- the numbers and end with a ctrl-D. </li>
-</ul></blockquote>
-
-</blockquote><h4><A href="#TOC">»</A><a name="input">How</a> do I enter
-points for Qhull?</h4><blockquote>
-
-<p>Qhull takes its data from standard input. For example, create
-a file named 'data.txt' with the following contents: </p>
-
-<blockquote>
- <pre>
-2 #sample 2-d input
-5 #number of points
-1 2 #coordinates of points
--1.1 3
-3 2.2
-4 5
--10 -10
-</pre>
-</blockquote>
-
-<p>Then call qconvex with 'qconvex < data.txt'. It will print a
-summary of the convex hull. Use 'qconvex < data.txt o' to print
-the vertices and edges. See also <A href="index.htm#input">input
-format</A>. </p>
-
-<p>You can generate sample data with rbox, e.g., 'rbox 10'
-generates 10 random points in 3-d. Use a pipe ('|') to run rbox
-and qhull together, e.g., </p>
-
-<blockquote>
- <p>rbox c | qconvex o </p>
-</blockquote>
-
-<p>computes the convex hull of a cube. </p>
-
-</blockquote><h4><A href="#TOC">»</A><a name="learn">How</a> do I learn to
-use Qhull?</h4><blockquote>
-
-<p>First read: </p>
-
-<ul>
- <li><A href="index.htm">Introduction</A> to Qhull
- <li><A href="index.htm#when">When</A> to use Qhull
- <li><A href="qconvex.htm">qconvex</A> -- convex hull
- <li><A href="qdelaun.htm">qdelaunay</A> -- Delaunay triangulation
- <li><A href="qhalf.htm">qhalf</A> -- half-space intersection about a point
-
- <li><A href="qvoronoi.htm">qvoronoi</A> -- Voronoi diagram
- <li><A href="rbox.htm">Rbox</A>, for sample inputs
- <li><A href="qh-eg.htm">Examples</A> of Qhull</li>
-</ul>
-
-<p>Look at Qhull's on-line documentation: </p>
-
-<ul>
- <li>'qconvex' gives a synopsis of qconvex and its options
-
- <li>'rbox' lists all of the options for generating point
- sets
- <li>'qconvex - | more' lists the options for qconvex
- <li>'qconvex .' gives a concise list of options
- <li>'qdelaunay', 'qhalf', 'qvoronoi', and 'qhull' also have a synopsis and option list</li>
-</ul>
-
-<p>Then try out the Qhull programs on small examples. </p>
-
-<ul>
- <li>'rbox c' lists the vertices of a cube
- <li>'rbox c | qconvex' is the convex hull of a cube
- <li>'rbox c | qconvex o' lists the vertices and facets of
- a cube
- <li>'rbox c | qconvex Qt o' triangulates the cube
- <li>'rbox c | qconvex QJ o' joggles the input and
- triangulates the cube
- <li>'rbox c D2 | qconvex' generates the convex hull of a
- square
- <li>'rbox c D4 | qconvex' generates the convex hull of a
- hypercube
- <li>'rbox 6 s D2 | qconvex p Fx' lists 6 random points in
- a circle and lists the vertices of their convex hull in order
- <li>'rbox c D2 c G2 | qdelaunay' computes the Delaunay
- triangulation of two embedded squares. It merges the cospherical facets.
- <li>'rbox c D2 c G2 | qdelaunay Qt' computes the Delaunay
- triangulation of two embedded squares. It triangulates the cospherical facets.
- <li>'rbox c D2 c G2 | qvoronoi o' computes the
- corresponding Voronoi vertices and regions.
- <li>'rbox c D2 c G2 | qvoronio Fv' shows the Voronoi diagram
- for the previous example. Each line is one edge of the
- diagram. The first number is 4, the next two numbers list
- a pair of input sites, and the last two numbers list the
- corresponding pair of Voronoi vertices. </li>
-</ul>
-
-<p>Install <a href="http://www.geomview.org">Geomview</a>
-if you are running SGI Irix, Solaris, SunOS, Linux, HP, IBM
-RS/6000, DEC Alpha, or Next. You can then visualize the output of
-Qhull. Qhull comes with Geomview <A href="qh-eg.htm">examples</A>.
-</p>
-
-<p>Then try Qhull with a small example of your application. Work
-out the results by hand. Then experiment with Qhull's options to
-find the ones that you need. </p>
-
-<p>You will need to decide how Qhull should handle precision
-problems. It can triangulate the output ('<A
- href="qh-optq.htm#Qt" >Qt</A>'), joggle the input ('<A
- href="qh-optq.htm#QJn" >QJ</A>'), or merge facets (the default). </p>
-
-<ul>
- <li>With joggle, Qhull produces simplicial (i.e.,
- triangular) output by joggling the input. After joggle,
- no points are cocircular or cospherical.
- <li>With facet merging, Qhull produces a better
- approximation and does not modify the input.
- <li>With triangulated output, Qhull merges facets and triangulates
- the result.</li>
- <li>See <A href="qh-impre.htm#joggle">Merged facets or joggled input</A>. </li>
-</ul>
-
-</blockquote>
-<h2><A href="#TOC">»</A><a name="convex">Convex hull questions</a></h2>
-
-<h4><A href="#TOC">»</A><a name="area">How</a> do I report just the area
- and volume of a convex hull?</h4><blockquote>
-
-Use option 'FS'. For example,
-
-<blockquote><pre>
-C:\qhull>rbox 10 | qconvex FS
-0
-2 2.192915621644613 0.2027867899638665
-
-C:\qhull>rbox 10 | qconvex FA
-
-Convex hull of 10 points in 3-d:
-
- Number of vertices: 10
- Number of facets: 16
-
-Statistics for: RBOX 10 | QCONVEX FA
-
- Number of points processed: 10
- Number of hyperplanes created: 28
- Number of distance tests for qhull: 44
- CPU seconds to compute hull (after input): 0
- Total facet area: 2.1929156
- Total volume: 0.20278679
-</pre></blockquote>
-
-</blockquote><h4><A href="#TOC">»</A><a name="extra">Why</a> are there extra
-points in a 4-d or higher convex hull?</h4><blockquote>
-
-<p>You may see extra points if you use options '<A
- href="qh-opto.htm#i" >i</A>' or '<A href="qh-optf.htm#Ft">Ft</A>'
- without using triangulated output ('<A href="qh-optq.htm#Qt">Qt</A>').
-The extra points occur when a facet is non-simplicial (i.e., a
-facet with more than <i>d</i> vertices). For example, Qhull
-reports the following for one facet of the convex hull of a hypercube.
-Option 'Pd0:0.5' returns the facet along the positive-x axis: </p>
-
-<blockquote>
- <pre>
-rbox c D4 | qconvex i Pd0:0.5
-12
-17 13 14 15
-17 13 12 14
-17 11 13 15
-17 14 11 15
-17 10 11 14
-17 14 12 8
-17 12 13 8
-17 10 14 8
-17 11 10 8
-17 13 9 8
-17 9 11 8
-17 11 9 13
-</pre>
-</blockquote>
-
-<p>The 4-d hypercube has 16 vertices; so point "17" was
-added by qconvex. Qhull adds the point in order to report a
-simplicial decomposition of the facet. The point corresponds to
-the "centrum" which Qhull computes to test for
-convexity. </p>
-
-<p>Triangulate the output ('<A href="qh-optq.htm#Qt">Qt</A>') to avoid the extra points.
-Since the hypercube is 4-d, each simplicial facet is a tetrahedron.
-<blockquote>
-<pre>
-C:\qhull3.1>rbox c D4 | qconvex i Pd0:0.5 Qt
-9
-9 13 14 15
-12 9 13 14
-9 11 13 15
-11 9 14 15
-9 10 11 14
-12 9 14 8
-9 12 13 8
-9 10 14 8
-10 9 11 8
-</pre>
-</blockquote>
-
-<p>Use the '<A href="qh-optf.htm#Fv">Fv</A>' option to print the
-vertices of simplicial and non-simplicial facets. For example,
-here is the same hypercube facet with option 'Fv' instead of 'i':
-</p>
-
-<blockquote>
- <pre>
-C:\qhull>rbox c D4 | qconvex Pd0:0.5 Fv
-1
-8 9 10 12 11 13 14 15 8
-</pre>
-</blockquote>
-
-<p>The coordinates of the extra point are printed with the '<A
- href="qh-optf.htm#Ft" >Ft</A>' option. </p>
-
-<blockquote>
- <pre>
-rbox c D4 | qconvex Pd0:0.5 Ft
-4
-17 12 3
- -0.5 -0.5 -0.5 -0.5
- -0.5 -0.5 -0.5 0.5
- -0.5 -0.5 0.5 -0.5
- -0.5 -0.5 0.5 0.5
- -0.5 0.5 -0.5 -0.5
- -0.5 0.5 -0.5 0.5
- -0.5 0.5 0.5 -0.5
- -0.5 0.5 0.5 0.5
- 0.5 -0.5 -0.5 -0.5
- 0.5 -0.5 -0.5 0.5
- 0.5 -0.5 0.5 -0.5
- 0.5 -0.5 0.5 0.5
- 0.5 0.5 -0.5 -0.5
- 0.5 0.5 -0.5 0.5
- 0.5 0.5 0.5 -0.5
- 0.5 0.5 0.5 0.5
- 0.5 0 0 0
-4 16 13 14 15
-4 16 13 12 14
-4 16 11 13 15
-4 16 14 11 15
-4 16 10 11 14
-4 16 14 12 8
-4 16 12 13 8
-4 16 10 14 8
-4 16 11 10 8
-4 16 13 9 8
-4 16 9 11 8
-4 16 11 9 13
-</pre>
-</blockquote>
-
-</blockquote><h4><A href="#TOC">»</A><a name="dup">How</a> do I report
-duplicate vertices?</h4><blockquote>
-
-<p>There's no direct way. You can use option
-'<A href="qh-optf.htm#FP">FP</A>' to
-report the distance to the nearest vertex for coplanar input
-points. Select the minimum distance for a duplicated vertex, and
-locate all input sites less than this distance. </p>
-
-<p>For Delaunay triangulations, all coplanar points are nearly
-incident to a vertex. If you want a report of coincident input
-sites, do not use option '<A href="qh-optq.htm#QJn">QJ</A>'. By
-adding a small random quantity to each input coordinate, it
-prevents coincident input sites. </p>
-
-</blockquote>
-<h2><A href="#TOC">»</A><a name="delaunay">Delaunay and Voronoi
-diagram questions</a></h2>
-
-<h4><A href="#TOC">»</A><a name="maxsphere">How</a> do I get the radii of the empty
- spheres for each Voronoi vertex?</h4><blockquote>
-
-Use option '<A href="qh-optf.htm#Fi">Fi</A>' to list each bisector (i.e. Delaunay ridge). Then compute the
-minimum distance for each Voronoi vertex.
-
-<p>There's other ways to get the same information. Let me know if you
-find a better method.
-
-<h4><A href="#TOC">»</A><a name="flat">How</a> do I get rid of
-nearly flat Delaunay triangles?</h4><blockquote>
-
-<p>Nearly flat triangles occur when boundary points are nearly
-collinear or coplanar. They also occur for nearly coincident
-points. Both events can easily occur when using joggle. For example
-(rbox 10 W0 D2 | qdelaunay QJ Fa) lists the areas of the Delaunay
-triangles of 10 points on the boundary of a square. Some of
-these triangles are nearly flat. This occurs when one point
-is joggled inside of two other points. In this case, nearly flat
-triangles do not occur with triangulated output (rbox 10 W0 D2 | qdelaunay Qt Fa).
-
-
-<p>Another example, (rbox c P0 P0 D2 | qdelaunay QJ Fa), computes the
-areas of the Delaunay triangles for the unit square and two
-instances of the origin. Four of the triangles have an area
-of 0.25 while two have an area of 2.0e-11. The later are due to
-the duplicated origin. With triangulated output (rbox c P0 P0 D2 | qdelaunay Qt Fa)
-there are four triangles of equal area.
-
-<p>Nearly flat triangles also occur without using joggle. For
-example, (rbox c P0 P0,0.4999999999 | qdelaunay Fa), computes
-the areas of the Delaunay triangles for the unit square,
-a nearly collinear point, and the origin. One triangle has an
-area of 3.3e-11.
-
-<p>Unfortunately, none of Qhull's merging options remove nearly
-flat Delaunay triangles due to nearly collinear or coplanar boundary
-points.
-The merging options concern the empty circumsphere
-property of Delaunay triangles. This is independent of the area of
-the Delaunay triangles. Qhull does handle nearly coincident points.
-
-<p>You can handle collinear or coplanar boundary points by
-enclosing the points in a box. For example,
-(rbox c P0 P0,0.4999999999 c G1 | qdelaunay Fa), surrounds the
-previous points with [(1,1), (1,-1), (-1,-1), (-1, 1)].
-Its Delaunay triangulation does not include a
-nearly flat triangle. The box also simplifies the graphical
-output from Qhull.
-
-<p>Without joggle, Qhull lists coincident points as "coplanar"
-points. For example, (rbox c P0 P0 D2 | qdelaunay Fa), ignores
-the duplicated origin and lists four triangles of size 0.25.
-Use 'Fc' to list the coincident points (e.g.,
-rbox c P0 P0 D2 | qdelaunay Fc).
-
-<p>There is no easy way to determine coincident points with joggle.
-Joggle removes all coincident, cocircular, and cospherical points
-before running Qhull. Instead use facet merging (the default)
-or triangulated output ('<A href="qh-optq.htm#Qt">Qt</A>').
-
-
-</blockquote>
-<h4><A href="#TOC">»</A><a name="square">What</a> is the Voronoi diagram
- of a square?</h4><blockquote>
-
-<p>
-Consider a square,
-<blockquote><pre>
-C:\qhull>rbox c D2
-2 RBOX c D2
-4
- -0.5 -0.5
- -0.5 0.5
- 0.5 -0.5
- 0.5 0.5
-</pre></blockquote>
-
-<p>There's two ways to compute the Voronoi diagram: with facet merging
-or with joggle. With facet merging, the
-result is:
-
-<blockquote><pre>
-C:\qhull>rbox c D2 | qvoronoi Qz
-
-Voronoi diagram by the convex hull of 5 points in 3-d:
-
- Number of Voronoi regions and at-infinity: 5
- Number of Voronoi vertices: 1
- Number of facets in hull: 5
-
-Statistics for: RBOX c D2 | QVORONOI Qz
-
- Number of points processed: 5
- Number of hyperplanes created: 7
- Number of distance tests for qhull: 8
- Number of merged facets: 1
- Number of distance tests for merging: 29
- CPU seconds to compute hull (after input): 0
-
-C:\qhull>rbox c D2 | qvoronoi Qz o
-2
-2 5 1
--10.101 -10.101
- 0 0
-2 0 1
-2 0 1
-2 0 1
-2 0 1
-0
-
-C:\qhull>rbox c D2 | qvoronoi Qz Fv
-4
-4 0 1 0 1
-4 0 2 0 1
-4 1 3 0 1
-4 2 3 0 1
-</pre></blockquote>
-
-<p>There is one Voronoi vertex at the origin and rays from the origin
-along each of the coordinate axes.
-The last line '4 2 3 0 1' means that there is
-a ray that bisects input points #2 and #3 from infinity (vertex 0) to
-the origin (vertex 1).
-Option 'Qz' adds an artificial point since the input is cocircular.
-Coordinates -10.101 indicate the
-vertex at infinity.
-
-<p>With triangulated output, the Voronoi vertex is
-duplicated:
-
-<blockquote><pre>
-C:\qhull3.1>rbox c D2 | qvoronoi Qt Qz
-
-Voronoi diagram by the convex hull of 5 points in 3-d:
-
- Number of Voronoi regions and at-infinity: 5
- Number of Voronoi vertices: 2
- Number of triangulated facets: 1
-
-Statistics for: RBOX c D2 | QVORONOI Qt Qz
-
- Number of points processed: 5
- Number of hyperplanes created: 7
- Number of facets in hull: 6
- Number of distance tests for qhull: 8
- Number of distance tests for merging: 33
- Number of distance tests for checking: 30
- Number of merged facets: 1
- CPU seconds to compute hull (after input): 0.05
-
-C:\qhull3.1>rbox c D2 | qvoronoi Qt Qz o
-2
-3 5 1
--10.101 -10.101
- 0 0
- 0 0
-3 2 0 1
-2 1 0
-2 2 0
-3 2 0 1
-0
-
-C:\qhull3.1>rbox c D2 | qvoronoi Qt Qz Fv
-4
-4 0 2 0 2
-4 0 1 0 1
-4 1 3 0 1
-4 2 3 0 2
-</pre></blockquote>
-
-
-<p>With joggle, the input is no longer cocircular and the Voronoi vertex is
-split into two:
-
-<blockquote><pre>
-C:\qhull>rbox c D2 | qvoronoi Qt Qz
-
-C:\qhull>rbox c D2 | qvoronoi QJ o
-2
-3 4 1
--10.101 -10.101
--4.71511718558304e-012 -1.775812830118184e-011
-9.020340030474472e-012 -4.02267108512433e-012
-2 0 1
-3 2 1 0
-3 2 0 1
-2 2 0
-
-C:\qhull>rbox c D2 | qvoronoi QJ Fv
-5
-4 0 2 0 1
-4 0 1 0 1
-4 1 2 1 2
-4 1 3 0 2
-4 2 3 0 2
-</pre></blockquote>
-
-<p>Note that the Voronoi diagram includes the same rays as
- before plus a short edge between the two vertices.</p>
-
-
-</blockquote><h4><A href="#TOC">»</A><a name="mesh">How</a> do I compute
-the Delaunay triangulation of a non-convex object?</h4><blockquote>
-
-<p>A similar question is
-"How do I mesh a volume from a set of triangulated surface points?"
-
-<p>This is an instance of the constrained Delaunay Triangulation
-problem. Qhull does not handle constraints. The boundary of the
-Delaunay triangulation is always convex. But if the input set
-contains enough points, the triangulation will include the
-boundary. The number of points needed depends on the input.
-
-<p>Shewchuk has developed a theory of constrained Delaunay triangulations.
-See his
-<a href="http://www.cs.cmu.edu/~jrs/jrspapers.html#cdt">paper</a> at the
-1998 Computational Geometry Conference. Using these ideas, constraints
-could be added to Qhull. They would have many applications.
-
-<p>There is a large literature on mesh generation and many commercial
-offerings. For pointers see
-<a href="http://www.andrew.cmu.edu/user/sowen/mesh.html">Owen's Meshing
-Research Corner</a> and
-<a href="http://www-users.informatik.rwth-aachen.de/~roberts/meshgeneration.html">Schneiders'
-Finite Element Mesh Generation page</a>.</p>
-
-</blockquote><h4><A href="#TOC">»</A><a name="constrained">Can</a> Qhull
-produce a triangular mesh for an object?</h4><blockquote>
-
-<p>Yes for convex objects, no for non-convex objects. For
-non-convex objects, it triangulates the concavities. Unless the
-object has many points on its surface, triangles may cross the
-surface. </p>
-
-</blockquote><h4><A href="#TOC">»</A><a name="dridges">For</a> 3-d Delaunay
-triangulations, how do I report the triangles of each
-tetrahedron?</h4><blockquote>
-
-<p>For points in general position, a 3-d Delaunay triangulation
-generates tetrahedron. Each face of a tetrahedron is a triangle.
-For example, the 3-d Delaunay triangulation of random points on
-the surface of a cube, is a cellular structure of tetrahedron. </p>
-
-<p>Use triangulated output ('qdelaunay Qt i') or joggled input ('qdelaunay QJ i')
-to generate the Delaunay triangulation.
-Option 'i' reports each tetrahedron. The triangles are
-every combination of 3 vertices. Each triangle is a
-"ridge" of the Delaunay triangulation. </p>
-
-<p>For example, </p>
-
-<pre>
- rbox 10 | qdelaunay Qt i
- 14
- 9 5 8 7
- 0 9 8 7
- 5 3 8 7
- 3 0 8 7
- 5 4 8 1
- 4 6 8 1
- 2 9 5 8
- 4 2 5 8
- 4 2 9 5
- 6 2 4 8
- 9 2 0 8
- 2 6 0 8
- 2 4 9 1
- 2 6 4 1
-</pre>
-
-<p>is the Delaunay triangulation of 10 random points. Ridge 9-5-8
-occurs twice. Once for tetrahedron 9 5 8 7 and the other for
-tetrahedron 2 9 5 8. </p>
-
-<p>You can also use the Qhull library to generate the triangles.
-See "<A href="#ridges2">How</A> do I visit the ridges of a
-Delaunay triangulation?"</p>
-
-</blockquote><h4><A href="#TOC">»</A><a name="vsphere">How</a> do I construct
-the Voronoi diagram of cospherical points?</h4><blockquote>
-
-<p>Three-d terrain data can be approximated with cospherical
-points. The Delaunay triangulation of cospherical points is the
-same as their convex hull. If the points lie on the unit sphere,
-the facet normals are the Voronoi vertices [via S. Fortune]. </p>
-
-<p>For example, consider the points {[1,0,0], [-1,0,0], [0,1,0],
-...}. Their convex hull is: </p>
-
-<pre>
-rbox d G1 | qconvex o
-3
-6 8 12
- 0 0 -1
- 0 0 1
- 0 -1 0
- 0 1 0
- -1 0 0
- 1 0 0
-3 3 1 4
-3 1 3 5
-3 0 3 4
-3 3 0 5
-3 2 1 5
-3 1 2 4
-3 2 0 4
-3 0 2 5
-</pre>
-
-<p>The facet normals are: </p>
-
-<pre>
-rbox d G1 | qconvex n
-4
-8
--0.5773502691896258 0.5773502691896258 0.5773502691896258 -0.5773502691896258
- 0.5773502691896258 0.5773502691896258 0.5773502691896258 -0.5773502691896258
--0.5773502691896258 0.5773502691896258 -0.5773502691896258 -0.5773502691896258
- 0.5773502691896258 0.5773502691896258 -0.5773502691896258 -0.5773502691896258
- 0.5773502691896258 -0.5773502691896258 0.5773502691896258 -0.5773502691896258
--0.5773502691896258 -0.5773502691896258 0.5773502691896258 -0.5773502691896258
--0.5773502691896258 -0.5773502691896258 -0.5773502691896258 -0.5773502691896258
- 0.5773502691896258 -0.5773502691896258 -0.5773502691896258 -0.5773502691896258
-</pre>
-
-<p>If you drop the offset from each line (the last number), each
-line is the Voronoi vertex for the corresponding facet. The
-neighboring facets for each point define the Voronoi region for
-each point. For example: </p>
-
-<pre>
-rbox d G1 | qconvex FN
-6
-4 7 3 2 6
-4 5 0 1 4
-4 7 4 5 6
-4 3 1 0 2
-4 6 2 0 5
-4 7 3 1 4
-</pre>
-
-<p>The Voronoi vertices {7, 3, 2, 6} define the Voronoi region
-for point 0. Point 0 is [0,0,-1]. Its Voronoi vertices are </p>
-
-<pre>
--0.5773502691896258 0.5773502691896258 -0.5773502691896258
- 0.5773502691896258 0.5773502691896258 -0.5773502691896258
--0.5773502691896258 -0.5773502691896258 -0.5773502691896258
- 0.5773502691896258 -0.5773502691896258 -0.5773502691896258
-</pre>
-
-<p>In this case, the Voronoi vertices are oriented, but in
-general they are unordered. </p>
-
-<p>By taking the dual of the Delaunay triangulation, you can
-construct the Voronoi diagram. For cospherical points, the convex
-hull vertices for each facet, define the input sites for each
-Voronoi vertex. In 3-d, the input sites are oriented. For
-example: </p>
-
-<pre>
-rbox d G1 | qconvex i
-8
-3 1 4
-1 3 5
-0 3 4
-3 0 5
-2 1 5
-1 2 4
-2 0 4
-0 2 5
-</pre>
-
-<p>The convex hull vertices for facet 0 are {3, 1, 4}. So Voronoi
-vertex 0 (i.e., [-0.577, 0.577, 0.577]) is the Voronoi vertex for
-input sites {3, 1, 4} (i.e., {[0,1,0], [0,0,1], [-1,0,0]}). </p>
-
-</blockquote><h4><A href="#TOC">»</A><a name="3dd">How</a> do I construct a
-3-d Delaunay triangulation?</h4><blockquote>
-
-<p>For 3-d Delaunay triangulations with cospherical input sites,
-use triangulated output ('<A href="qh-optq.htm#Qt">Qt</A>') or
-joggled input ('<A href="qh-optq.htm#QJn">QJ</A>'). Otherwise
-option 'i' will
-triangulate non-simplicial facets by adding a point to the facet.
-
-<p>If you want non-simplicial output for cospherical sites, use
-option
-'<A href="qh-optf.htm#Fv">Fv</A>' or '<A href="qh-opto.htm#o">o</A>'.
-For option 'o', ignore the last coordinate. It is the lifted
-coordinate for the corresponding convex hull in 4-d.
-
-<p>The following example is a cube
-inside a tetrahedron. The 8-vertex facet is the cube. Ignore the
-last coordinates. </p>
-
-<blockquote>
- <pre>
-C:\qhull>rbox r y c G0.1 | qdelaunay Fv
-4
-12 20 44
- 0.5 0 0 0.3055555555555555
- 0 0.5 0 0.3055555555555555
- 0 0 0.5 0.3055555555555555
- -0.5 -0.5 -0.5 0.9999999999999999
- -0.1 -0.1 -0.1 -6.938893903907228e-018
- -0.1 -0.1 0.1 -6.938893903907228e-018
- -0.1 0.1 -0.1 -6.938893903907228e-018
- -0.1 0.1 0.1 -6.938893903907228e-018
- 0.1 -0.1 -0.1 -6.938893903907228e-018
- 0.1 -0.1 0.1 -6.938893903907228e-018
- 0.1 0.1 -0.1 -6.938893903907228e-018
- 0.1 0.1 0.1 -6.938893903907228e-018
-4 2 11 1 0
-4 10 1 0 3
-4 11 10 1 0
-4 2 9 0 3
-4 9 11 2 0
-4 7 2 1 3
-4 11 7 2 1
-4 8 10 0 3
-4 9 8 0 3
-5 8 9 10 11 0
-4 10 6 1 3
-4 6 7 1 3
-5 6 8 10 4 3
-5 6 7 10 11 1
-4 5 9 2 3
-4 7 5 2 3
-5 5 8 9 4 3
-5 5 6 7 4 3
-8 5 6 8 7 9 10 11 4
-5 5 7 9 11 2
-</pre>
-</blockquote>
-
-<p>If you want simplicial output use options
-'<A href="qh-optq.htm#Qt">Qt</A> <A
- href="qh-optf.htm#Ft" >i</A>' or
-'<A href="qh-optq.htm#QJn">QJ</A> <A
- href="qh-optf.htm#Ft" >i</A>', e.g.,
-</p>
-
-<blockquote>
- <pre>
-rbox r y c G0.1 | qdelaunay Qt i
-31
-2 11 1 0
-11 10 1 0
-9 11 2 0
-11 7 2 1
-8 10 0 3
-9 8 0 3
-10 6 1 3
-6 7 1 3
-5 9 2 3
-7 5 2 3
-9 8 10 11
-8 10 11 0
-9 8 11 0
-6 8 10 4
-8 6 10 3
-6 8 4 3
-6 7 10 11
-10 6 11 1
-6 7 11 1
-8 5 4 3
-5 8 9 3
-5 6 4 3
-6 5 7 3
-5 9 10 11
-8 5 9 10
-7 5 10 11
-5 6 7 10
-8 5 10 4
-5 6 10 4
-5 9 11 2
-7 5 11 2
-</pre>
-</blockquote>
-
-</blockquote><h4><A href="#TOC">»</A><a name="2d">How</a> do I get the
-triangles for a 2-d Delaunay triangulation and the vertices of
-its Voronoi diagram?</h4><blockquote>
-
-<p>To compute the Delaunay triangles indexed by the indices of
-the input sites, use </p>
-
-<blockquote>
- <p>rbox 10 D2 | qdelaunay Qt i </p>
-</blockquote>
-
-<p>To compute the Voronoi vertices and the Voronoi region for
-each input site, use </p>
-
-<blockquote>
- <p>rbox 10 D2 | qvoronoi o </p>
-</blockquote>
-
-<p>To compute each edge ("ridge") of the Voronoi
-diagram for each pair of adjacent input sites, use</p>
-
-<blockquote>
- <p>rbox 10 D2 | qvoronoi Fv </p>
-</blockquote>
-
-<p>To compute the area and volume of the Voronoi region for input site 5,
-use </p>
-
-<blockquote>
- <p>rbox 10 D2 | qvoronoi QV5 p | qconvex s FS </p>
-</blockquote>
-
-<p>To compute the lines ("hyperplanes") that define the
-Voronoi region for input site 5, use </p>
-
-<blockquote>
- <p>rbox 10 D2 | qvoronoi QV5 p | qconvex n </p>
-</blockquote>
-or
-<blockquote>
- <p>rbox 10 D2 | qvoronoi QV5 Fi Fo</p>
-</blockquote>
-
-<p>To list the extreme points of the input sites use </p>
-
-<blockquote>
- <p>rbox 10 D2 | qdelaunay Fx </p>
-</blockquote>
-
-<p>You will get the same point ids with </p>
-
-<blockquote>
- <p>rbox 10 D2 | qconvex Fx </p>
-</blockquote>
-
-</blockquote><h4><A href="#TOC">»</A><a name="rays">Can</a> Qhull compute the
-unbounded rays of the Voronoi diagram?</h4><blockquote>
-
-<p>Use '<A href="qh-optf.htm#Fo2">Fo</A>' to compute the separating
-hyperplanes for unbounded Voronoi regions. The corresponding ray
-goes to infinity from the Voronoi vertices. If you enclose the
-input sites in a large enough box, the outermost bounded regions
-will represent the unbounded regions of the original points. </p>
-
-<p>If you do not box the input sites, you can identify the
-unbounded regions. They list '0' as a vertex. Vertex 0 represents
-"infinity". Each unbounded ray includes vertex 0 in
-option '<A href="qh-optf.htm#Fv2">Fv</A>. See <A
- href="qvoronoi.htm#graphics" >Voronoi graphics</A> and <A
- href="qvoronoi.htm#notes" >Voronoi notes</A>. </p>
-
-</blockquote><h4><A href="#TOC">»</A><a name="big">Can </a>Qhull triangulate
-a hundred 16-d points?</h4><blockquote>
-
-<p>No. This is an immense structure. A triangulation of 19, 16-d
-points has 43 simplices. If you add one point at a time, the
-triangulation increased as follows: 43, 189, 523, 1289, 2830,
-6071, 11410, 20487. The last triangulation for 26 points used 13
-megabytes of memory. When Qhull uses virtual memory, it becomes
-too slow to use. </p>
-
-</blockquote>
-<h2><A href="#TOC">»</A>Approximation questions</h2>
-
-<h4><A href="#TOC">»</A><a name="simplex">How</a> do I
-approximate data with a simplex</h4><blockquote>
-
-<p>Qhull may be used to help select a simplex that approximates a
-data set. It will take experimentation. Geomview will help to
-visualize the results. This task may be difficult to do in 5-d
-and higher. Use rbox options 'x' and 'y' to produce random
-distributions within a simplex. Your methods work if you can
-recover the simplex. </p>
-
-<p>Use Qhull's precision options to get a first approximation to
-the hull, say with 10 to 50 facets. For example, try 'C0.05' to
-remove small facets after constructing the hull. Use 'W0.05' to
-ignore points within 0.05 of a facet. Use 'PA5' to print the five
-largest facets by area. </p>
-
-<p>Then use other methods to fit a simplex to this data. Remove
-outlying vertices with few nearby points. Look for large facets
-in different quadrants. You can use option 'Pd0d1d2' to print all
-the facets in a quadrant. </p>
-
-<p>In 4-d and higher, use the outer planes (option 'Fo' or
-'facet->maxoutside') since the hyperplane of an approximate
-facet may be below many of the input points. </p>
-
-<p>For example, consider fitting a cube to 1000 uniformly random
-points in the unit cube. In this case, the first try was good: </p>
-
-<blockquote>
- <pre>
-rbox 1000 | qconvex W0.05 C0.05 PA6 Fo
-4
-6
-0.35715408374381 0.08706467018177928 -0.9299788727015564 -0.5985514741284483
-0.995841591359023 -0.02512604712761577 0.08756829720435189 -0.5258834069202866
-0.02448099521570909 -0.02685210459017302 0.9993396046151313 -0.5158104982631999
--0.9990223929415094 -0.01261133513150079 0.04236994958247349 -0.509218270408407
--0.0128069014364698 -0.9998380680115362 0.01264203427283151 -0.5002512653670584
-0.01120895057872914 0.01803671994177704 -0.9997744926535512 -0.5056824072956361
-</pre>
-</blockquote>
-
-</blockquote>
-<h2><A href="#TOC">»</A>Halfspace questions</h2>
-
-<h4><A href="#TOC">»</A><a name="halfspace">How</a> do I compute the
- intersection of halfspaces with Qhull?</h4><blockquote>
-
-<p>Qhull computes the halfspace intersection about a point. The
-point must be inside all of the halfspaces. Given a point, a
-duality turns a halfspace intersection problem into a convex
-hull problem.
-
-<p>Use linear programming if you
-do not know a point in the interior of the halfspaces.
-See the <A href="qhalf.htm#notes">manual</A>. You will need
- a linear programming code. This may require a fair amount of work to
- implement.</p>
-
-
-
-</blockquote>
-<h2><A href="#TOC">»</A><a name="library">Qhull library
-questions</a></h2>
-
-<h4><A href="#TOC">»</A><a name="math">Is</a> Qhull available for Mathematica, Matlab, or Maple?</h4><blockquote>
-
-<p>Z. You of <a href="http://www.mathworks.com">MathWorks</a> added qhull to MATLAB 6.
-See functions <a href="http://www.mathworks.com/access/helpdesk/help/techdoc/ref/convhulln.shtml"
- >convhulln</a>,
- <a href="http://www.mathworks.com/access/helpdesk/help/techdoc/ref/delaunayn.shtml"
- >delaunayn</a>,
- <a href="http://www.mathworks.com/access/helpdesk/help/techdoc/ref/griddata3.shtml"
- >griddata3</a>,
- <a href="http://www.mathworks.com/access/helpdesk/help/techdoc/ref/griddatan.shtml"
- >griddatan</a>,
- <a href="http://www.mathworks.com/access/helpdesk/help/techdoc/ref/tsearch.shtml"
- >tsearch</a>,
- <a href="http://www.mathworks.com/access/helpdesk/help/techdoc/ref/tsearchn.shtml"
- >tsearchn</a>, and
- <a href="http://www.mathworks.com/access/helpdesk/help/techdoc/ref/voronoin.shtml"
- >voronoin</a>. V. Brumberg update MATLAB R14 for Qhull 2003.1 and triangulated output.
-
-<p>See <a href="http://www.mathsource.com/Content/Enhancements/Geometry/0211-251"
- >qh-math</a>
-for a Delaunay interface to Mathematica. It includes projects for CodeWarrior
-on the Macintosh and Visual C++ on Win32 PCs.
-
-<p>See Mathematica ('<a
-href="qh-opto.htm#m">m</a>') and Maple ('<a
-href="qh-optf.htm#FM">FM</a>') output options.
-
-<p></p>
-</blockquote><h4><A href="#TOC">»</A><a name="ridges">Why</a> are there too few ridges?</h4><blockquote>
-
-The following sample code may produce fewer ridges than expected:
-
-<blockquote><pre>
- facetT *facetp;
- ridgeT *ridge, **ridgep;
-
- FORALLfacets {
- printf("facet f%d\n", facet->id);
- FOREACHridge_(facet->ridges) {
- printf(" ridge r%d between f%d and f%d\n", ridge->id, ridge->top->id, ridge->bottom->id);
- }
- }
-</pre></blockquote>
-
-<p> Qhull does not create ridges for simplicial facets.
-Instead it computes ridges from facet->neighbors. To make ridges for a
-simplicial facet, use qh_makeridges() in merge.c. Usefacet->visit_id to visit
-each ridge once (instead of twice). For example,
-
-<blockquote><pre>
- facetT *facet, *neighbor;
- ridgeT *ridge, **ridgep;
-
- qh visit_id++;
- FORALLfacets {
- printf("facet f%d\n", facet->id);
- qh_makeridges(facet);
- facet->visitId= qh visit_id;
- FOREACHridge_(facet->ridges) {
- neighbor= otherfacet_(ridge, visible);
- if (neighbor->visitid != qh visit_id)
- printf(" ridge r%d between f%d and f%d\n", ridge->id, ridge->top->id, ridge->bottom->id);
- }
- }
-</pre></blockquote>
-
-</blockquote><h4><A href="#TOC">»</A><a name="call">Can</a> Qhull use coordinates without placing
- them in a data file?</h4><blockquote>
-
-<p>Use qh_call_qhull(). See user_eg.c for an example.
-See the manual for an introduction to the Qhull library.
-
-<p>Start with a small example for which you know the
- answer.</p>
-
-
-</blockquote><h4><A href="#TOC">»</A><a name="size">How</a> large are Qhull's data structures?</h4><blockquote>
-
-<p>Qhull uses a general-dimension data structure.
-The size depends on the dimension. Use option 'Ts' to print
-out the memory statistics [e.g., 'rbox D2 10 | qconvex Ts'].
-
-
-</blockquote><h4><A href="#TOC">»</A><a name="inc">Can</a> Qhull construct
-convex hulls and Delaunay triangulations one point at a time?</h4><blockquote>
-
-<p>The Qhull library may be used to construct convex hulls and
-Delaunay triangulations one point at a time. It may not be used
-for deleting points or moving points. </p>
-
-<p>Qhull is designed for batch processing. Neither Clarkson's
-randomized incremental algorithm nor Qhull are designed for
-on-line operation. For many applications, it is better to
-reconstruct the convex hull or Delaunay triangulation from
-scratch for each new point. </p>
-
-<p>With random point sets and on-line processing, Clarkson's
-algorithm should run faster than Qhull. Clarkson uses the
-intermediate facets to reject new, interior points, while Qhull,
-when used on-line, visits every facet to reject such points. If
-used on-line for n points, Clarkson may take O(n) times as much
-memory as the average off-line case, while Qhull's space
-requirement does not change. </p>
-
-<p>If you triangulate the output before adding all the points
-(option 'Qt' and procedure qh_triangulate), you must set
-option '<A href="qh-optq.htm#Q11">Q11</A>'. It duplicates the
-normals of triangulated facets and recomputes the centrums.
-This should be avoided for regular use since triangulated facets
-are not clearly convex with their neighbors. It appears to
-work most of the time, but fails for cases that Qhull normally
-handles well [see the test call to qh_triangulate in qh_addpoint].
-
-</blockquote><h4><A href="#TOC">»</A><a name="ridges2">How</a> do I visit the
-ridges of a Delaunay triangulation?</h4><blockquote>
-
-<p>To visit the ridges of a Delaunay triangulation, visit each
-facet. Each ridge will appear twice since it belongs to two
-facets. In pseudo-code: </p>
-
-<pre>
- for each facet of the triangulation
- if the facet is Delaunay (i.e., part of the lower convex hull)
- for each ridge of the facet
- if the ridge's neighboring facet has not been visited
- ... process a ridge of the Delaunay triangulation ...
-</pre>
-
-<p>In undebugged, C code: </p>
-
-<pre>
- qh visit_id++;
- FORALLfacets_(facetlist)
- if (!facet->upperdelaunay) {
- facet->visitid= qh visit_id;
- qh_makeridges(facet);
- FOREACHridge_(facet->ridges) {
- neighbor= otherfacet_(ridge, facet);
- if (neighbor->visitid != qh visit_id) {
- /* Print ridge here with facet-id and neighbor-id */
- /*fprintf(fp, "f%d\tf%d\t",facet->id,neighbor->ID);*/
- FOREACHvertex_(ridge->vertices)
- fprintf(fp,"%d ",qh_pointid (vertex->point) );
- qh_printfacetNvertex_simplicial (fp, facet, format);
- fprintf(fp," ");
- if(neighbor->upperdelaunay)
- fprintf(fp," -1 -1 -1 -1 ");
- else
- qh_printfacetNvertex_simplicial (fp, neighbor, format);
- fprintf(fp,"\n");
- }
- }
- }
- }
-</pre>
-
-<p>Qhull should be redesigned as a class library, or at least as
-an API. It currently provides everything needed, but the
-programmer has to do a lot of work. Hopefully someone will write
-C++ wrapper classes or a Python module for Qhull. </p>
-
-</blockquote><h4><A href="#TOC">»</A><a name="listd">How</a> do I visit the
-Delaunay regions?</h4><blockquote>
-
-<p>Qhull constructs a Delaunay triangulation by lifting the
-input sites to a paraboloid. The Delaunay triangulation
-corresponds to the lower convex hull of the lifted points. To
-visit each facet of the lower convex hull, use: </p>
-
-<pre>
- facetT *facet;
-
- ...
- FORALLfacets {
- if (!facet->upperdelaunay) {
- ... only facets for Delaunay regions ...
- }
- }
-</pre>
-
-</blockquote><h4><A href="#TOC">»</A><a name="outside">When</a> is a point
-outside or inside a facet?</h4><blockquote>
-
-<p>A point is outside of a facet if it is clearly outside the
-facet's outer plane. The outer plane is defined by an offset
-(facet->maxoutside) from the facet's hyperplane. </p>
-
-<pre>
- facetT *facet;
- pointT *point;
- realT dist;
-
- ...
- qh_distplane(point, facet, &dist);
- if (dist > facet->maxoutside + 2 * qh DISTround) {
- /* point is clearly outside of facet */
- }
-</pre>
-
-<p>A point is inside of a facet if it is clearly inside the
-facet's inner plane. The inner plane is computed as the maximum
-distance of a vertex to the facet. It may be computed for an
-individual facet, or you may use the maximum over all facets. For
-example: </p>
-
-<pre>
- facetT *facet;
- pointT *point;
- realT dist;
-
- ...
- qh_distplane(point, facet, &dist);
- if (dist < qh min_vertex - 2 * qh DISTround) {
- /* point is clearly inside of facet */
- }
-</pre>
-
-<p>Both tests include two qh.DISTrounds because the computation
-of the furthest point from a facet may be off by qh.DISTround and
-the computation of the current distance to the facet may be off
-by qh.DISTround. </p>
-
-</blockquote><h4><A href="#TOC">»</A><a name="closest">How</a> do I find the
-facet that is closest to a point?</h4><blockquote>
-
-<p>Use qh_findbestfacet(). For example, </p>
-
-<pre>
- coordT point[ DIM ];
- boolT isoutside;
- realT bestdist;
- facetT *facet;
-
- ... set coordinates for point ...
-
- facet= qh_findbestfacet (point, qh_ALL, &bestdist, &isoutside);
-
- /* 'facet' is the closest facet to 'point' */
-</pre>
-
-<p>qh_findbestfacet() performs a directed search for the facet
-furthest below the point. If the point lies inside this facet,
-qh_findbestfacet() performs an exhaustive search of all facets.
-An exhaustive search may be needed because a facet on the far
-side of a lens-shaped distribution may be closer to a point than
-all of the facet's neighbors. The exhaustive search may be
-skipped for spherical distributions. </p>
-
-<p>Also see, "<A href="#vclosest">How</A> do I find the
-Delaunay triangle that is closest to a
-point?" </p>
-
-</blockquote><h4><A href="#TOC">»</A><a name="vclosest">How</a> do I find the
-Delaunay triangle or Voronoi region that is closest to a point?</h4><blockquote>
-
-<p>A Delaunay triangulation subdivides the plane, or in general
-dimension, subdivides space. Given a point, how do you determine
-the subdivision containing the point? Or, given a set of points,
-how do you determine the subdivision containing each point of the set?
-Efficiency is important -- an exhaustive search of the subdivision
-is too slow.
-
-<p>First compute the Delaunay triangle with qh_call_qhull().
-Lift the point to the paraboloid by summing the squares of the
-coordinates. Use qh_findbestfacet() [poly2.c] to find the closest Delaunay
-triangle. Determine the closest vertex to find the corresponding
-Voronoi region. Do not use options
-'<A href="qh-optq.htm#Qbb">Qbb</A>', '<A href="qh-optq.htm#QbB">QbB</A>',
-'<A href="qh-optq.htm#Qbk">Qbk:n</A>', or '<A
- href="qh-optq.htm#QBk" >QBk:n</A>' since these scale the last
-coordinate. Optimizations of qh_findbestfacet() should
-be possible for Delaunay triangulations.</p>
-
-<p>You first need to lift the point to the paraboloid (i.e., the
-last coordinate is the sum of the squares of the point's coordinates).
-The
-routine, qh_setdelaunay() [geom2.c], lifts an array of points to the
-paraboloid. The following excerpt is from findclosest() in
-user_eg.c. </p>
-
-<pre>
- coordT point[ DIM + 1]; /* one extra coordinate for lifting the point */
- boolT isoutside;
- realT bestdist;
- facetT *facet;
-
- ... set coordinates for point[] ...
-
- qh_setdelaunay (DIM+1, 1, point);
- facet= qh_findbestfacet (point, qh_ALL, &bestdist, &isoutside);
- /* 'facet' is the closest Delaunay triangle to 'point' */
-</pre>
-
-<p>The returned facet either contains the point or it is the
-closest Delaunay triangle along the convex hull of the input set.
-
-<p>Point location is an active research area in Computational
-Geometry. For a practical approach, see Mucke, et al, "Fast randomized
-point location without preprocessing in two- and
-three-dimensional Delaunay triangulations," <i>Computational
-Geometry '96</i>, p. 274-283, May 1996.
-For an introduction to planar point location see [O'Rourke '93].
-Also see, "<A
- href="#closest" >How</A> do I find the facet that is closest to a
-point?" </p>
-
-<p>To locate the closest Voronoi region, determine the closest
-vertex of the closest Delaunay triangle. </p>
-
-<pre>
- realT dist, bestdist= REALmax;
- vertexT *bestvertex= NULL, *vertex, **vertexp;
-
- /* 'facet' is the closest Delaunay triangle to 'point' */
-
- FOREACHvertex_( facet->vertices ) {
- dist= qh_pointdist( point, vertex->point, DIM );
- if (dist < bestdist) {
- bestdist= dist;
- bestvertex= vertex;
- }
- }
- /* 'bestvertex' represents the Voronoi region closest to 'point'. The corresponding
- input site is 'bestvertex->point' */
-</pre>
-
-</blockquote><h4><A href="#TOC">»</A><a name="vertices">How</a> do I list the
-vertices?</h4><blockquote>
-
-<p>To list the vertices (i.e., extreme points) of the convex hull
-use </p>
-
-<blockquote>
- <pre>
- vertexT *vertex;
-
- FORALLvertices {
- ...
- // vertex->point is the coordinates of the vertex
- // qh_pointid (vertex->point) is the point ID of the vertex
- ...
- }
- </pre>
-</blockquote>
-
-</blockquote><h4><A href="#TOC">»</A><a name="test">How</a> do I test code
-that uses the Qhull library?</h4><blockquote>
-
-<p>Compare the output from your program with the output from the
-Qhull program. Use option 'T1' or 'T4' to trace what Qhull is
-doing. Prepare a <i>small</i> example for which you know the
-output. Run the example through the Qhull program and your code.
-Compare the trace outputs. If you do everything right, the two
-trace outputs should be almost the same. The trace output will
-also guide you to the functions that you need to review. </p>
-
-</blockquote><h4><A href="#TOC">»</A><a name="orient">When</a> I compute a
-plane equation from a facet, I sometimes get an outward-pointing
-normal and sometimes an inward-pointing normal</h4><blockquote>
-
-<p>Qhull orients simplicial facets, and prints oriented output
-for 'i', 'Ft', and other options. The orientation depends on <i>both</i>
-the vertex order and the flag facet->toporient.</p>
-
-<p>Qhull does not orient
- non-simplicial facets. Instead it orients the facet's ridges. These are
- printed with the 'Qt' and 'Ft' option. The facet's hyperplane is oriented. </p>
-
-</blockquote>
-<hr><!-- Navigation links -->
-
-<p><a><b>Up:</b> </a><a
- href="http://www.qhull.org">Home page for Qhull</a><br>
-<b>Up:</b> <A href="index.htm#TOC">Qhull manual</A>: Table of Contents <br>
-<b>To:</b> <A href="qh-quick.htm#programs">Programs</A>
-• <A href="qh-quick.htm#options">Options</A>
-• <A href="qh-opto.htm#output">Output</A>
-• <A href="qh-optf.htm#format">Formats</A>
-• <A href="qh-optg.htm#geomview">Geomview</A>
-• <A href="qh-optp.htm#print">Print</A>
-• <A href="qh-optq.htm#qhull">Qhull</A>
-• <A href="qh-optc.htm#prec">Precision</A>
-• <A href="qh-optt.htm#trace">Trace</A> <br>
-<b>To:</b> <A href="#TOC">FAQ: Table of Contents</A><br><!-- GC common information -->
-
-<hr>
-
-<p><a href="http://www.geom.uiuc.edu/"><IMG align=middle
- height=40 src="qh--geom.gif" width=40 ></a><i>The Geometry Center
-Home Page </i></p>
-
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created:
-Sept. 25, 1995 --- <!-- hhmts start -->Last modified: see top
-<!-- hhmts end --> </p>
-</body>
-</html>
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qh-get.htm b/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qh-get.htm
deleted file mode 100644
index 2fd374e69272ddbaedd4234c39cdc88c2bbe87bb..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qh-get.htm
+++ /dev/null
@@ -1,125 +0,0 @@
-<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
-<html>
-
-<head>
-<title>Qhull Downloads</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<p><b>Up:</b> <a href="http://www.geom.uiuc.edu/software/download"><i>Downloadable Software from the
-Geometry Center </i></a><br>
-</p>
-
-<hr>
-
-<h1><a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html"><img
-src="../html/qh--cone.gif" alt="[CONE]" align="middle"
-width="100" height="100"></a> Qhull Downloads</h1>
-
-<ul>
- <li><a href="http://www.qhull.org">Qhull Home Page</a> <p>Qhull
- computes convex hulls, Delaunay triangulations, halfspace
- intersections about a point, Voronoi diagrams, furthest-site Delaunay
- triangulations, and furthest-site Voronoi diagrams. It
- runs in 2-d, 3-d, 4-d, and higher dimensions. It
- implements the Quickhull algorithm for computing the
- convex hull. Qhull handles roundoff errors from floating
- point arithmetic. It can approximate a convex hull. </p>
-
- <p>Visit <a href="http://www.qhull.org/news">Qhull News</a>
- for news, bug reports, change history, and users.</p>
- </li>
- <li><a
- href="http://www.qhull.org/download/qhull-2003.1.zip">Download:
- Qhull 2003.1 for Windows</a> (1.2 Mbytes) <p>Type: console programs for
- Windows 95, 98, ME, 2000, NT, XP</p>
- <p>Includes executables, documentation, sources files, and a cygwin Makefile. It runs in a
- DOS window.</p>
- </li>
- <li><a href="http://www.qhull.org/download/qhull-2003.1-src.tgz">Download:
- source for Qhull 2003.1</a> (600K) <p>Type: C source code for
- 32-bit and 64-bit architectures </p>
- <p>Includes documentation, source files, and a simple Makefile</p>
- </li>
- <li><a href=http://savannah.nongnu.org/files/?group=qhull>Download: Qhull 2002.1 for Unix</a>
- <p>Type: C source code for Unix systems (Debian configure)</b>
-
- <p>Includes documentation, source files, and a configure Makefile.
- Includes Debian configuration files. Includes downloads of Qhull's current and previous
- versions.</p>
-
- <!---
- <p>B. Pearlmutter created a
-<a href=http://packages.debian.org/stable/math/qhull-bin.html>Debian build</a> of Qhull 3.1
-and upgraded it to 2002.1.
- -->
-
- </li>
- <li><a href="http://www.qhull.org/download/qhull-2002.1-1mdk.i686.rpm">Download:
- Qhull version 2002.1 i686 rpm</a> (643K) <p>Type: rpm build for Mandrake 8.2 and RedHat 7.3</p>
-
- <p>For other Linux systems, use the <a href="http://www.qhull.org/download/qhull-2002.1-1mdk.src.rpm">src rpm</a> [L. Mazet]
- </li>
-
- <li><a href=http://savannah.gnu.org/projects/qhull/>Qhull@Savannah</a>
- <p>Type: CVS repository</b>
-
- <p>CVS repositiory of Qhull sources, documentation, and Makefiles.
- </p>
- </li>
- <li><a href=http://www6.uniovi.es/ftp/pub/mirrors/geom.umn.edu/software/ghindex.html>Spanish
- mirror site</a> <p>Download Qhull's current and
- previous versions from <a href=http://www.etsimo.uniovi.es/derechos.html>Servidor
- WWW de la Escuela de Minas</a> of the Universidad de Oviedo.</p>
- </li>
- <li><a
- href="http://citeseer.nj.nec.com/83502.html">Download:
- Article about Qhull</a> (210K) <p>Type: various formats on CiteSeer</p>
- <p>Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T.,
- "The Quickhull algorithm for convex hulls," <i>ACM
- Transactions on Mathematical Software</i>, vol. 22, pp.
- 469-483, Dec 1996 [<a
- href="http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p469-barber/">abstract</a>].</p>
- </li>
- <li><a
- href="http://www.qhull.org/download/qhull-1.0.tar.gz">Download:
- Qhull version 1.0</a> (92K) <p>Type: C source code for
- 32-bit architectures </p>
- <p>Version 1.0 is a fifth the size of version 2.4. It
- computes convex hulls and Delaunay triangulations. If a
- precision error occurs, it stops with an error message.
- It reports an initialization error for inputs made with
- 0/1 coordinates. </p>
- <p>Version 1.0 compiles on a PC with Borland C++ 4.02 for
- Win32 and DOS Power Pack. The options for rbox are
- "bcc32 -WX -w- -O2-e -erbox -lc rbox.c". The
- options for qhull are the same. [D. Zwick] </p>
- </li>
- <li><a
- href="http://www.qhull.org/download/qhull-1.0.sit.hqx">Download:
- Qhull version 1.0 (Mac)</a> (180K) <p>Type: C source
- code, packaged for Macintosh w/68881 </p>
- <p>The Macintosh implementation of Qhull 1.0 reads input
- from a file and returns the results to a file. The code
- is compiled for a 68881 floating point coprocessor. The
- package includes Think C projects for Qhull and the rbox
- input generator. </p>
- </li>
-</ul>
-<!-- Navigation links -->
-<hr>
-
-<p><b>Up:</b> <a href="http://www.geom.uiuc.edu/software/download"><i>Downloadable Software from the
-Geometry Center </i></a><br>
-<!-- GC common information --></p>
-
-<hr>
-
-<p><a href="http://www.geom.uiuc.edu/"><img src="../html/qh--geom.gif" alt="[HOME]"
-align="middle"></a> <i>The Geometry Center Home Page</i> </p>
-
-<p>Comments to: <a href="mailto:qhull@qhull.org">qhull@qhull.org</a><br>
-</body>
-</html>
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-<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
-<html>
-
-<head>
-<title>Imprecision in Qhull</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<p><a name="TOP"><b>Up:</b></a> <a href="http://www.qhull.org">Home
-page</a> for Qhull <br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of
-Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a><br>
-<b>To: </b><a href="#TOC">Qhull imprecision</a>: Table of Contents
-(please wait while loading)
-
-<hr>
-<!-- Main text of document -->
-<h1><a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/4dcube.html"><img
-src="qh--4d.gif" alt="[4-d cube]" align="middle" width="100"
-height="100"></a> Imprecision in Qhull</h1>
-
-<p>This section of the Qhull manual discusses the problems caused
-by coplanar points and why Qhull uses options '<a
-href="qh-optc.htm#C0">C-0</a>' or '<a href="qh-optq.htm#Qx">Qx</a>'
-by default. If you ignore precision issues with option '<a
-href="qh-optq.htm#Q0">Q0</a>', the output from Qhull can be
-arbitrarily bad. Qhull avoids precision problems if you merge facets (the default) or joggle
-the input ('<a
-href="qh-optq.htm#QJn">QJ</a>'). </p>
-
-<p>Use option '<a href="qh-optt.htm#Tv">Tv</a>' to verify the
-output from Qhull. It verifies that adjacent facets are clearly
-convex. It verifies that all points are on or below all facets. </p>
-
-<p>Qhull automatically tests for convexity if it detects
-precision errors while constructing the hull. </p>
-
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-
-<hr>
-
-<h2><a href="#TOP">»</a><a name="TOC">Qhull
-imprecision: Table of Contents </a></h2>
-
-<ul>
- <li><a href="#prec">Precision problems</a></li>
- <li><a href="#joggle">Merged facets or joggled input</a></li>
- <li><a href="#delaunay">Delaunay triangulations</a></li>
- <li><a href="#imprecise">Merged facets</a></li>
- <li><a href="#how">How Qhull merges facets</a></li>
- <li><a href="#limit">Limitations of merged facets</a></li>
- <li><a href="#injoggle">Joggled input</a></li>
- <li><a href="#exact">Exact arithmetic</a></li>
- <li><a href="#approximate">Approximating a convex hull</a></li>
-</ul>
-
-<hr>
-
-<h2><a href="#TOC">»</a><a name="prec">Precision problems</a></h2>
-
-<p>Since Qhull uses floating point arithmetic, roundoff error
-occurs with each calculation. This causes problems for
-geometric algorithms. Other floating point codes for convex
-hulls, Delaunay triangulations, and Voronoi diagrams also suffer
-from these problems. Qhull handles most of them.</p>
-
-<p>There are several kinds of precision errors:</p>
-
-<ul>
- <li>Representation error occurs when there are not enough
- digits to represent a number, e.g., 1/3.</li>
- <li>Measurement error occurs when the input coordinates are
- from measurements. </li>
- <li>Roundoff error occurs when a calculation is rounded to a
- fixed number of digits, e.g., a floating point
- calculation.</li>
- <li>Approximation error occurs when the user wants an
- approximate result because the exact result contains too
- much detail.</li>
-</ul>
-
-<p>Under imprecision, calculations may return erroneous results.
-For example, roundoff error can turn a small, positive number
-into a small, negative number. See Milenkovic [<a
-href="index.htm#mile93">'93</a>] for a discussion of <em>strict
-robust geometry</em>. Qhull does not meet Milenkovic's criterion
-for accuracy. Qhull's error bound is empirical instead of
-theoretical.</p>
-
-<p>Qhull 1.0 checked for precision errors but did not handle
-them. The output could contain concave facets, facets with
-inverted orientation ("flipped" facets), more than two
-facets adjacent to a ridge, and two facets with exactly the same
-set of vertices.</p>
-
-<p>Qhull 2.4 and later automatically handles errors due to
-machine round-off. Option '<a href="qh-optc.htm#C0">C-0</a>' or '<a
-href="qh-optq.htm#Qx">Qx</a>' is set by default. In 5-d and
-higher, the output is clearly convex but an input point could be
-outside of the hull. This may be corrected by using option '<a
-href="qh-optc.htm#C0">C-0</a>', but then the output may contain
-wide facets.</p>
-
-<p>Qhull 2.5 and later provides option '<a href="qh-optq.htm#QJn">QJ</a>'
-to joggled input. Each input coordinate is modified by a
-small, random quantity. If a precision error occurs, a larger
-modification is tried. When no precision errors occur, Qhull is
-done. </p>
-
-<p>Qhull 3.1 and later provides option '<a href="qh-optq.htm#Qt">Qt</a>'
-for triangulated output. This removes the need for
-joggled input ('<a href="qh-optq.htm#QJn">QJ</a>').
-Non-simplicial facets are triangulated.
-The facets may have zero area.
-Triangulated output is particularly useful for Delaunay triangulations.</p>
-
-<p>By handling round-off errors, Qhull can provide a variety of
-output formats. For example, it can return the halfspace that
-defines each facet ('<a href="qh-opto.htm#n">n</a>'). The
-halfspaces include roundoff error. If the halfspaces were exact,
-their intersection would return the original extreme points. With
-imprecise halfspaces and exact arithmetic, nearly incident points
-may be returned for an original extreme point. By handling
-roundoff error, Qhull returns one intersection point for each of
-the original extreme points. Qhull may split or merge an extreme
-point, but this appears to be unlikely.</p>
-
-<p>The following pipe implements the identity function for
-extreme points (with roundoff):
-<blockquote>
- qconvex <a href="qh-optf.htm#FV">FV</a> <a
- href="qh-opto.htm#n">n</a> | qhalf <a href="qh-optf.htm#Fp">Fp</a>
-</blockquote>
-
-<p>Bernd Gartner published his
-<a href=http://www.inf.ethz.ch/personal/gaertner/miniball.html>Miniball</a>
-algorithm ["Fast and robust smallest enclosing balls", <i>Algorithms - ESA '99</i>, LNCS 1643].
-It uses floating point arithmetic and a carefully designed primitive operation.
-It is practical to 20-D or higher, and identifies at least two points on the
-convex hull of the input set. Like Qhull, it is an incremental algorithm that
-processes points furthest from the intermediate result and ignores
-points that are close to the intermediate result.
-
-<h2><a href="#TOC">»</a><a name="joggle">Merged facets or joggled input</a></h2>
-
-<p>This section discusses the choice between merged facets and joggled input.
-By default, Qhull uses merged facets to handle
-precision problems. With option '<a href="qh-optq.htm#QJn">QJ</a>',
-the input is joggled. See <a href="qh-eg.htm#joggle">examples</a>
-of joggled input and triangulated output.
-<ul>
-<li>Use merged facets (the default)
-when you want non-simplicial output (e.g., the faces of a cube).
-<li>Use merged facets and triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>') when
-you want simplicial output and coplanar facets (e.g., triangles for a Delaunay triangulation).
-<li>Use joggled input ('<a href="qh-optq.htm#QJn">QJ</a>') when you need clearly-convex,
-simplicial output.
-</ul>
-
-<p>The choice between merged facets and joggled input depends on
-the application. Both run about the same speed. Joggled input may
-be faster if the initial joggle is sufficiently large to avoid
-precision errors.
-
-<p>Most applications should used merged facets
-with triangulated output. </p>
-
-<p>Use merged facets (the
-default, '<a href="qh-optc.htm#C0">C-0</a>')
-or triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>') if </p>
-
-<ul>
- <li>Your application supports non-simplicial facets, or
- it allows degenerate, simplicial facets (option '<a href="qh-optq.htm#Qt">Qt</a>'). </li>
- <li>You do not want the input modified. </li>
- <li>You want to set additional options for approximating the
- hull. </li>
- <li>You use single precision arithmetic (<a href="../src/user.h#realT">realT</a>).
- </li>
-</ul>
-
-<p>Use joggled input ('<a href="qh-optq.htm#QJn">QJ</a>') if </p>
-
-<ul>
- <li>Your application needs clearly convex, simplicial output</li>
- <li>Your application supports perturbed input points and narrow triangles.</li>
- <li>Seven significant digits is sufficient accuracy.</li>
-</ul>
-
-<p>You may use both techniques or combine joggle with
-post-merging ('<a href="qh-optc.htm#Cn2">Cn</a>'). </p>
-
-<p>Other researchers have used techniques similar to joggled
-input. Sullivan and Beichel [ref?] randomly perturb the input
-before computing the Delaunay triangulation. Corkum and Wyllie
-[news://comp.graphics, 1990] randomly rotate a polytope before
-testing point inclusion. Edelsbrunner and Mucke [Symp. Comp.
-Geo., 1988] and Yap [J. Comp. Sys. Sci., 1990] symbolically
-perturb the input to remove singularities. </p>
-
-<p>Merged facets ('<a href="qh-optc.htm#C0">C-0</a>') handles
-precision problems directly. If a precision problem occurs, Qhull
-merges one of the offending facets into one of its neighbors.
-Since all precision problems in Qhull are associated with one or
-more facets, Qhull will either fix the problem or attempt to merge the
-last remaining facets. </p>
-
-<h2><a href="#TOC">»</a><a name="delaunay">Delaunay
-triangulations </a></h2>
-
-<p>Programs that use Delaunay triangulations traditionally assume
-a triangulated input. By default, <a href=qdelaun.htm>qdelaunay</a>
-merges regions with cocircular or cospherical input sites.
-If you want a simplicial triangulation
-use triangulated output ('<a href="qh-optq.htm#Qt">Qt</a>') or joggled
-input ('<a href="qh-optq.htm#QJn">QJ</a>').
-
-<p>For Delaunay triangulations, triangulated
-output should produce good results. All points are within roundoff error of
-a paraboloid. If two points are nearly incident, one will be a
-coplanar point. So all points are clearly separated and convex.
-If qhull reports deleted vertices, the triangulation
-may contain serious precision faults. Deleted vertices are reported
-in the summary ('<a href="qh-opto.htm#s">s</a>', '<a href="qh-optf.htm#Fs">Fs</a>'</p>
-
-<p>You should use option '<a href="qh-optq.htm#Qbb">Qbb</a>' with Delaunay
-triangulations. It scales the last coordinate and may reduce
-roundoff error. It is automatically set for <a href=qdelaun.htm>qdelaunay</a>,
-<a href=qvoronoi.htm>qvoronoi</a>, and option '<a
-href="qh-optq.htm#QJn">QJ</a>'.</p>
-
-<p>Edelsbrunner, H, <i>Geometry and Topology for Mesh Generation</i>, Cambridge University Press, 2001.
-Good mathematical treatise on Delaunay triangulation and mesh generation for 2-d
-and 3-d surfaces. The chapter on surface simplification is
-particularly interesting. It is similar to facet merging in Qhull.
-
-<p>Veron and Leon published an algorithm for shape preserving polyhedral
-simplification with bounded error [<i>Computers and Graphics</i>, 22.5:565-585, 1998].
-It remove nodes using front propagation and multiple remeshing.
-
-<h2><a href="#TOC">»</a><a name="imprecise">Merged facets </a></h2>
-
-<p>Qhull detects precision
-problems when computing distances. A precision problem occurs if
-the distance computation is less than the maximum roundoff error.
-Qhull treats the result of a hyperplane computation as if it
-were exact.</p>
-
-<p>Qhull handles precision problems by merging non-convex facets.
-The result of merging two facets is a thick facet defined by an <i>inner
-plane</i> and an <i>outer plane</i>. The inner and outer planes
-are offsets from the facet's hyperplane. The inner plane is
-clearly below the facet's vertices. At the end of Qhull, the
-outer planes are clearly above all input points. Any exact convex
-hull must lie between the inner and outer planes.</p>
-
-<p>Qhull tests for convexity by computing a point for each facet.
-This point is called the facet's <i>centrum</i>. It is the
-arithmetic center of the facet's vertices projected to the
-facet's hyperplane. For simplicial facets with <em>d</em>
-vertices, the centrum is equivalent to the centroid or center of
-gravity. </p>
-
-<p>Two neighboring facets are convex if each centrum is clearly
-below the other hyperplane. The '<a href="qh-optc.htm#Cn2">Cn</a>'
-or '<a href="qh-optc.htm#Cn">C-n</a>' options sets the centrum's
-radius to <i>n </i>. A centrum is clearly below a hyperplane if
-the computed distance from the centrum to the hyperplane is
-greater than the centrum's radius plus two maximum roundoff
-errors. Two are required because the centrum can be the maximum
-roundoff error above its hyperplane and the distance computation
-can be high by the maximum roundoff error.</p>
-
-<p>With the '<a href="qh-optc.htm#Cn">C-n</a>' or '<a
-href="qh-optc.htm#An">A-n </a>' options, Qhull merges non-convex
-facets while constructing the hull. The remaining facets are
-clearly convex. With the '<a href="qh-optq.htm#Qx">Qx </a>'
-option, Qhull merges coplanar facets after constructing the hull.
-While constructing the hull, it merges coplanar horizon facets,
-flipped facets, concave facets and duplicated ridges. With '<a
-href="qh-optq.htm#Qx">Qx</a>', coplanar points may be missed, but
-it appears to be unlikely.</p>
-
-<p>If the user sets the '<a href="qh-optc.htm#An2">An</a>' or '<a
-href="qh-optc.htm#An">A-n</a>' option, then all neighboring
-facets are clearly convex and the maximum (exact) cosine of an
-angle is <i>n</i>.</p>
-
-<p>If '<a href="qh-optc.htm#C0">C-0</a>' or '<a
-href="qh-optq.htm#Qx">Qx</a>' is used without other precision
-options (default), Qhull tests vertices instead of centrums for
-adjacent simplices. In 3-d, if simplex <i>abc</i> is adjacent to
-simplex <i>bcd</i>, Qhull tests that vertex <i>a</i> is clearly
-below simplex <i>bcd </i>, and vertex <i>d</i> is clearly below
-simplex <i>abc</i>. When building the hull, Qhull tests vertices
-if the horizon is simplicial and no merges occur. </p>
-
-<h2><a href="#TOC">»</a><a name="how">How Qhull merges facets</a></h2>
-
-<p>If two facets are not clearly convex, then Qhull removes one
-or the other facet by merging the facet into a neighbor. It
-selects the merge which minimizes the distance from the
-neighboring hyperplane to the facet's vertices. Qhull also
-performs merges when a facet has fewer than <i>d</i> neighbors (called a
-degenerate facet), when a facet's vertices are included in a
-neighboring facet's vertices (called a redundant facet), when a
-facet's orientation is flipped, or when a ridge occurs between
-more than two facets.</p>
-
-<p>Qhull performs merges in a series of passes sorted by merge
-angle. Each pass merges those facets which haven't already been
-merged in that pass. After a pass, Qhull checks for redundant
-vertices. For example, if a vertex has only two neighbors in 3-d,
-the vertex is redundant and Qhull merges it into an adjacent
-vertex.</p>
-
-<p>Merging two simplicial facets creates a non-simplicial facet
-of <em>d+1</em> vertices. Additional merges create larger facets.
-When merging facet A into facet B, Qhull retains facet B's
-hyperplane. It merges the vertices, neighbors, and ridges of both
-facets. It recomputes the centrum if a wide merge has not
-occurred (qh_WIDEcoplanar) and the number of extra vertices is
-smaller than a constant (qh_MAXnewcentrum).</p>
-
-
-<h2><a href="#TOC">»</a><a name="limit">Limitations of merged
-facets</a></h2>
-
-<ul>
-<li><b>Uneven dimensions</b> --
-If one coordinate has a larger absolute value than other
-coordinates, it may dominate the effect of roundoff errors on
-distance computations. You may use option '<a
-href="qh-optq.htm#QbB">QbB</a>' to scale points to the unit cube.
-For Delaunay triangulations and Voronoi diagrams, <a href=qdelaun.htm>qdelaunay</a>
-and <a href=qvoronoi.htm>qvoronoi</a> always set
-option '<a href="qh-optq.htm#Qbb">Qbb</a>'. It scales the last
-coordinate to [0,m] where <i>m</i> is the maximum width of the
-other coordinates. Option '<a href="qh-optq.htm#Qbb">Qbb</a>' is
-needed for Delaunay triangulations of integer coordinates
-and nearly cocircular points.
-
-<p>For example, compare
-<pre>
- rbox 1000 W0 t | qconvex Qb2:-1e-14B2:1e-14
-</pre>
-with
-<pre>
- rbox 1000 W0 t | qconvex
-</pre>
-The distributions are the same but the first is compressed to a 2e-14 slab.
-<p>
-<li><b>Post-merging of coplanar facets</b> -- In 5-d and higher, option '<a href="qh-optq.htm#Qx">Qx</a>'
-(default) delays merging of coplanar facets until post-merging.
-This may allow "dents" to occur in the intermediate
-convex hulls. A point may be poorly partitioned and force a poor
-approximation. See option '<a href="qh-optq.htm#Qx">Qx</a>' for
-further discussion.</p>
-
-<p>This is difficult to produce in 5-d and higher. Option '<a href="qh-optq.htm#Q6">Q6</a>' turns off merging of concave
-facets. This is similar to 'Qx'. It may lead to serious precision errors,
-for example,
-<pre>
- rbox 10000 W1e-13 | qhull Q6 Tv
-</pre>
-
-<p>
-<li><b>Maximum facet width</b> --
-Qhull reports the maximum outer plane and inner planes (if
-more than roundoff error apart). There is no upper bound
-for either figure. This is an area for further research. Qhull
-does a good job of post-merging in all dimensions. Qhull does a
-good job of pre-merging in 2-d, 3-d, and 4-d. With the '<a
-href="qh-optq.htm#Qx">Qx</a>' option, it does a good job in
-higher dimensions. In 5-d and higher, Qhull does poorly at
-detecting redundant vertices. </p>
-
-<p>In the summary ('<a href="qh-opto.htm#s">s</a>'), look at the
-ratio between the maximum facet width and the maximum width of a
-single merge, e.g., "(3.4x)". Qhull usually reports a
-ratio of four or lower in 3-d and six or lower in 4-d. If it
-reports a ratio greater than 10, this may indicate an
-implementation error. Narrow distributions (see following) may
-produce wide facets.
-
-<p>For example, if special processing for narrow distributions is
-turned off ('<a href="qh-optq.htm#Q10">Q10</a>'), qhull may produce
-a wide facet:</p>
-<pre>
- RBOX 1000 L100000 s G1e-16 t1002074964 | QHULL Tv Q10
-</pre>
-
-<p>
-<li><b>Narrow distribution</b> -- In 3-d, a narrow distribution may result in a poor
-approximation. For example, if you do not use qdelaunay nor option
-'<a href="qh-optq.htm#Qbb">Qbb</a>', the furthest-site
-Delaunay triangulation of nearly cocircular points may produce a poor
-approximation:
-<pre>
- RBOX s 5000 W1e-13 D2 t1002151341 | QHULL d Qt
- RBOX 1000 s W1e-13 t1002231672 | QHULL d Tv
-</pre>
-
-<p>During
-construction of the hull, a point may be above two
-facets with opposite orientations that span the input
-set. Even though the point may be nearly coplanar with both
-facets, and can be distant from the precise convex
-hull of the input sites. Additional facets leave the point distant from
-a facet. To fix this problem, add option '<a href="qh-optq.htm#Qbb">Qbb</a>'
-(it scales the last coordinate). Option '<a href="qh-optq.htm#Qbb">Qbb</a>'
-is automatically set for <a href=qdelaun.htm>qdelaunay</a> and <a href=qvoronoi.htm>qvoronoi</a>.
-
-<p>Qhull generates a warning if the initial simplex is narrow.
-For narrow distributions, Qhull changes how it processes coplanar
-points -- it does not make a point coplanar until the hull is
-finished.
-Use option '<a href="qh-optq.htm#Q10">Q10</a>' to try Qhull without
-special processing for narrow distributions.
-For example, special processing is needed for:
-<pre>
- RBOX 1000 L100000 s G1e-16 t1002074964 | QHULL Tv Q10
-</pre>
-
-<p>You may turn off the warning message by reducing
-qh_WARNnarrow in <tt>user.h</tt> or by setting option
-'<a href="qh-optp.htm#Pp">Pp</a>'. </p>
-
-<p>Similar problems occur for distributions with a large flat facet surrounded
-with many small facet at a sharp angle to the large facet.
-Qhull 3.1 fixes most of these problems, but a poor approximation can occur.
-A point may be left outside of the convex hull ('<a href="qh-optt.htm#Tv">Tv</a>').
-Examples include
-the furthest-site Delaunay triangulation of nearly cocircular points plus the origin, and the convex hull of a cone of nearly cocircular points. The width of the band is 10^-13.
-<pre>
- rbox s 1000 W1e-13 P0 D2 t996799242 | qhull d Tv
- rbox 1000 s Z1 G1e-13 t1002152123 | qhull Tv
- RBOX 1000 s Z1 G1e-13 t1002231668 | QHULL Tv
-</pre>
-
-<p>
-<li><b>Quadratic running time</b> -- If the output contains large, non-simplicial
-facets, the running time for Qhull may be quadratic in the size of the triangulated
-output. For example, <tt>RBOX 1000 s W1e-13 c G2 | QHULL d</tt> is 4 times
-faster for 500 points. The convex hull contains two large nearly spherical facets and
-many nearly coplanar facets. Each new point retriangulates the spherical facet and repartitions the remaining points into all of the nearly coplanar facets.
-In this case, quadratic running time is avoided if you use qdelaunay,
-add option '<a href="qh-optq.htm#Qbb">Qbb</a>',
-or add the origin ('P0') to the input.
-<p>
-<li><b>Facet with zero-area</b> --
-It is possible for a zero-area facet to be convex with its
-neighbors. This can occur if the hyperplanes of neighboring
-facets are above the facet's centrum, and the facet's hyperplane
-is above the neighboring centrums. Qhull computes the facet's
-hyperplane so that it passes through the facet's vertices. The
-vertices can be collinear. </p>
-
-<p>
-<li><b>No more facets</b> -- Qhull reports an error if there are <em>d+1</em> facets left
-and two of the facets are not clearly convex. This typically
-occurs when the convexity constraints are too strong or the input
-points are degenerate. The former is more likely in 5-d and
-higher -- especially with option '<a href="qh-optc.htm#Cn">C-n</a>'.</p>
-
-<p>
-<li><b>Deleted cone</b> -- Lots of merging can end up deleting all
-of the new facets for a point. This is a rare event that has
-only been seen while debugging the code.
-
-<p>
-<li><b>Triangulated output leads to precision problems</b> -- With sufficient
-merging, the ridges of a non-simplicial facet may have serious topological
-and geometric problems. A ridge may be between more than two
-neighboring facets. If so, their triangulation ('<a href="qh-optq.htm#Qt">Qt</a>')
-will fail since two facets have the same vertex set. Furthermore,
-a triangulated facet may have flipped orientation compared to its
-neighbors.</li>
-
-<p>The triangulation process detects degenerate facets with
-only two neighbors. These are marked degenerate. They have
-zero area.
-
-<p>
-<li><b>Coplanar points</b> --
-Option '<a href="qh-optq.htm#Qc">Qc</a>' is determined by
-qh_check_maxout() after constructing the hull. Qhull needs to
-retain all possible coplanar points in the facets' coplanar sets.
-This depends on qh_RATIOnearInside in <tt>user.h.</tt>
-Furthermore, the cutoff for a coplanar point is arbitrarily set
-at the minimum vertex. If coplanar points are important to your
-application, remove the interior points by hand (set '<a
-href="qh-optq.htm#Qc">Qc</a> <a href="qh-optq.htm#Qi">Qi</a>') or
-make qh_RATIOnearInside sufficiently large.</p>
-
-<p>
-<li><b>Maximum roundoff error</b> -- Qhull computes the maximum roundoff error from the maximum
-coordinates of the point set. Usually the maximum roundoff error
-is a reasonable choice for all distance computations. The maximum
-roundoff error could be computed separately for each point or for
-each distance computation. This is expensive and it conflicts
-with option '<a href="qh-optc.htm#Cn">C-n</a>'.
-
-<p>
-<li><b>All flipped or upper Delaunay</b> -- When a lot of merging occurs for
-Delaunay triangulations, a new point may lead to no good facets. For example,
-try a strong convexity constraint:
-<pre>
- rbox 1000 s t993602376 | qdelaunay C-1e-3
-</pre>
-
-</ul>
-
-<h2><a href="#TOC">»</a><a name="injoggle">Joggled input</a></h2>
-
-<p>Joggled input is a simple work-around for precision problems
-in computational geometry ["joggle: to shake or jar
-slightly," Amer. Heritage Dictionary]. Other names are
-<i>jostled input</i> or <i>random perturbation</i>.
-Qhull joggles the
-input by modifying each coordinate by a small random quantity. If
-a precision problem occurs, Qhull joggles the input with a larger
-quantity and the algorithm is restarted. This process continues
-until no precision problems occur. Unless all inputs incur
-precision problems, Qhull will terminate. Qhull adjusts the inner
-and outer planes to account for the joggled input. </p>
-
-<p>Neither joggle nor merged facets has an upper bound for the width of the output
-facets, but both methods work well in practice. Joggled input is
-easier to justify. Precision errors occur when the points are
-nearly singular. For example, four points may be coplanar or
-three points may be collinear. Consider a line and an incident
-point. A precision error occurs if the point is within some
-epsilon of the line. Now joggle the point away from the line by a
-small, uniformly distributed, random quantity. If the point is
-changed by more than epsilon, the precision error is avoided. The
-probability of this event depends on the maximum joggle. Once the
-maximum joggle is larger than epsilon, doubling the maximum
-joggle will halve the probability of a precision error. </p>
-
-<p>With actual data, an analysis would need to account for each
-point changing independently and other computations. It is easier
-to determine the probabilities empirically ('<a href="qh-optt.htm#TRn">TRn</a>') . For example, consider
-computing the convex hull of the unit cube centered on the
-origin. The arithmetic has 16 significant decimal digits. </p>
-
-<blockquote>
- <p><b>Convex hull of unit cube</b> </p>
- <table border="1">
- <tr>
- <th align="left">joggle</th>
- <th align="right">error prob. </th>
- </tr>
- <tr>
- <td align="right">1.0e-15</td>
- <td align="center">0.983 </td>
- </tr>
- <tr>
- <td align="right">2.0e-15</td>
- <td align="center">0.830 </td>
- </tr>
- <tr>
- <td align="right">4.0e-15</td>
- <td align="center">0.561 </td>
- </tr>
- <tr>
- <td align="right">8.0e-15</td>
- <td align="center">0.325 </td>
- </tr>
- <tr>
- <td align="right">1.6e-14</td>
- <td align="center">0.185 </td>
- </tr>
- <tr>
- <td align="right">3.2e-14</td>
- <td align="center">0.099 </td>
- </tr>
- <tr>
- <td align="right">6.4e-14</td>
- <td align="center">0.051 </td>
- </tr>
- <tr>
- <td align="right">1.3e-13</td>
- <td align="center">0.025 </td>
- </tr>
- <tr>
- <td align="right">2.6e-13</td>
- <td align="center">0.010 </td>
- </tr>
- <tr>
- <td align="right">5.1e-13</td>
- <td align="center">0.004 </td>
- </tr>
- <tr>
- <td align="right">1.0e-12</td>
- <td align="center">0.002 </td>
- </tr>
- <tr>
- <td align="right">2.0e-12</td>
- <td align="center">0.001 </td>
- </tr>
- </table>
-</blockquote>
-
-<p>A larger joggle is needed for multiple points. Since the
-number of potential singularities increases, the probability of
-one or more precision errors increases. Here is an example. </p>
-
-<blockquote>
- <p><b>Convex hull of 1000 points on unit cube</b> </p>
- <table border="1">
- <tr>
- <th align="left">joggle</th>
- <th align="right">error prob. </th>
- </tr>
- <tr>
- <td align="right">1.0e-12</td>
- <td align="center">0.870 </td>
- </tr>
- <tr>
- <td align="right">2.0e-12</td>
- <td align="center">0.700 </td>
- </tr>
- <tr>
- <td align="right">4.0e-12</td>
- <td align="center">0.450 </td>
- </tr>
- <tr>
- <td align="right">8.0e-12</td>
- <td align="center">0.250 </td>
- </tr>
- <tr>
- <td align="right">1.6e-11</td>
- <td align="center">0.110 </td>
- </tr>
- <tr>
- <td align="right">3.2e-11</td>
- <td align="center">0.065 </td>
- </tr>
- <tr>
- <td align="right">6.4e-11</td>
- <td align="center">0.030 </td>
- </tr>
- <tr>
- <td align="right">1.3e-10</td>
- <td align="center">0.010 </td>
- </tr>
- <tr>
- <td align="right">2.6e-10</td>
- <td align="center">0.008 </td>
- </tr>
- <tr>
- <td align="right">5.1e-09</td>
- <td align="center">0.003 </td>
- </tr>
- </table>
-</blockquote>
-
-<p>Other distributions behave similarly. No distribution should
-behave significantly worse. In Euclidean space, the probability
-measure of all singularities is zero. With floating point
-numbers, the probability of a singularity is non-zero. With
-sufficient digits, the probability of a singularity is extremely
-small for random data. For a sufficiently large joggle, all data
-is nearly random data. </p>
-
-<p>Qhull uses an initial joggle of 30,000 times the maximum
-roundoff error for a distance computation. This avoids most
-potential singularities. If a failure occurs, Qhull retries at
-the initial joggle (in case bad luck occurred). If it occurs
-again, Qhull increases the joggle by ten-fold and tries again.
-This process repeats until the joggle is a hundredth of the width
-of the input points. Qhull reports an error after 100 attempts.
-This should never happen with double-precision arithmetic. Once
-the probability of success is non-zero, the probability of
-success increases about ten-fold at each iteration. The
-probability of repeated failures becomes extremely small. </p>
-
-<p>Merged facets produces a significantly better approximation.
-Empirically, the maximum separation between inner and outer
-facets is about 30 times the maximum roundoff error for a
-distance computation. This is about 2,000 times better than
-joggled input. Most applications though will not notice the
-difference. </p>
-
-<h2><a href="#TOC">»</a><a name="exact">Exact arithmetic</a></h2>
-
-<p>Exact arithmetic may be used instead of floating point.
-Singularities such as coplanar points can either be handled
-directly or the input can be symbolically perturbed. Using exact
-arithmetic is slower than using floating point arithmetic and the
-output may take more space. Chaining a sequence of operations
-increases the time and space required. Some operations are
-difficult to do.</p>
-
-<p>Clarkson's <a
-href="http://netlib.bell-labs.com/netlib/voronoi/hull.html">hull
-program</a> and Shewchuk's <a
-href="http://www.cs.cmu.edu/~quake/triangle.html">triangle
-program</a> are practical implementations of exact arithmetic.</p>
-
-<p>Clarkson limits the input precision to about fifteen digits.
-This reduces the number of nearly singular computations. When a
-determinant is nearly singular, he uses exact arithmetic to
-compute a precise result.</p>
-
-<h2><a href="#TOC">»</a><a name="approximate">Approximating a
-convex hull</a></h2>
-
-<p>Qhull may be used for approximating a convex hull. This is
-particularly valuable in 5-d and higher where hulls can be
-immense. You can use '<a href="qh-optq.htm#Qx">Qx</a> <a
-href="qh-optc.htm#Cn">C-n</a>' to merge facets as the hull is
-being constructed. Then use '<a href="qh-optc.htm#Cn2">Cn</a>'
-and/or '<a href="qh-optc.htm#An2">An</a>' to merge small facets
-during post-processing. You can print the <i>n</i> largest facets
-with option '<a href="qh-optp.htm#PAn">PAn</a>'. You can print
-facets whose area is at least <i>n</i> with option '<a
-href="qh-optp.htm#PFn">PFn</a>'. You can output the outer planes
-and an interior point with '<a href="qh-optf.htm#FV">FV</a> <a
-href="qh-optf.htm#Fo">Fo</a>' and then compute their intersection
-with 'qhalf'. </p>
-
-<p>To approximate a convex hull in 6-d and higher, use
-post-merging with '<a href="qh-optc.htm#Wn">Wn</a>' (e.g., qhull
-W1e-1 C1e-2 TF2000). Pre-merging with a convexity constraint
-(e.g., qhull Qx C-1e-2) often produces a poor approximation or
-terminates with a simplex. Option '<a href="qh-optq.htm#QbB">QbB</a>'
-may help to spread out the data.</p>
-
-<p>You will need to experiment to determine a satisfactory set of
-options. Use <a href="rbox.htm">rbox</a> to generate test sets
-quickly and <a href="index.htm#geomview">Geomview</a> to view
-the results. You will probably want to write your own driver for
-Qhull using the Qhull library. For example, you could select the
-largest facet in each quadrant.</p>
-
-<!-- Navigation links -->
-<hr>
-
-<p><b>Up:</b> <a href="http://www.qhull.org">Home
-page</a> for Qhull <br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of
-Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a><br>
-<b>To:</b> <a href="#TOC">Qhull imprecision: Table of Contents</a>
-
-<!-- GC common information -->
-<hr>
-
-<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
-align="middle" width="40" height="40"></a><i>The Geometry Center
-Home Page </i></p>
-
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
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@@ -1,620 +0,0 @@
-<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
-<html>
-
-<head>
-<title>Qhull internals</title>
-<!-- Navigation links -->
-</head>
-
-<body>
-
-<p><a name="TOP"><b>Up:</b></a> <a
-href="http://www.qhull.org">Home page for Qhull</a>
-<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual: Table of
-Contents</a><br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a><br>
-<b>To:</b> <a href="#TOC">Qhull internals</a>: Table of Contents
-(please wait while loading) <br>
-<b>Dn:</b> <a href="../src/index.htm">Qhull functions</a>, macros, and data
-structures
-</p>
-
-<hr>
-<!-- Main text of document -->
-<h1><a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/4dcube.html"><img
-src="qh--4d.gif" alt="[4-d cube]" align="middle" width="100"
-height="100"></a> Qhull internals</h1>
-
-<p>This section discusses the internals of Qhull. </p>
-
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-
-<hr>
-
-<h2><a href="#TOP">»</a><a name="TOC">Qhull internals: Table of
-Contents </a></h2>
-
-<ul>
- <li><a href="#performance">Performance</a> of Qhull</li>
- <li><a href="#library">Calling Qhull</a> from your program
- <ul>
- <li><a href="#constrained">Constrained Delaunay</a>
- triangulation</li>
- <li><a href="#dids">Delaunay triangulations</a> and point indices</li>
- <li><a href="#findfacet">Locate facet</a> with
- qh_findbestfacet()</li>
- <li><a href="#inc">On-line construction</a> with
- qh_addpoint()</li>
- <li><a href="#mem">Sets and quick memory</a> allocation</li>
- <li><a href="#tricoplanar">Tricoplanar facets</a> and option 'Qt'</li>
- <li><a href="#vneighbor">Vertex neighbors</a> of a vertex</li>
- <li><a href="#vertices">Voronoi vertices</a> of a region</li>
- <li><a href="#ridge">Voronoi vertices</a> of a ridge</li>
- </ul>
- </li>
- <li><a href="#enhance">Enhancements</a> to Qhull</li>
- <li><a href="../src/index.htm">Qhull functions</a>, macros, and data
- structures </li>
-</ul>
-
-<hr>
-
-<h2><a href="#TOC">»</a><a name="performance">Performance of
-Qhull </a></h2>
-
-<p>Empirically, Qhull's performance is balanced in the sense that
-the average case happens on average. This may always be true if
-the precision of the input is limited to at most <i>O(log n)</i>
-bits. Empirically, the maximum number of vertices occurs at the
-end of constructing the hull. </p>
-
-<p>Let <i>n</i> be the number of input points, <i>v</i> be the
-number of output vertices, and <i>f_v </i>be the maximum number
-of facets for a convex hull of <i>v</i> vertices. If both
-conditions hold, Qhull runs in <i>O(n log v)</i> in 2-d and 3-d
-and <i>O(n f_v/v)</i> otherwise. The function <i>f_v</i>
-increases rapidly with dimension. It is <em>O(v^floor(d/2) /
-floor(d/2)!)</em>.</p>
-
-<p>The time complexity for merging is unknown. Options '<a
-href="qh-optc.htm#C0">C-0</a>' and '<a href="qh-optq.htm#Qx">Qx</a>'
-(defaults) handle precision problems due to floating-point
-arithmetic. They are optimized for simplicial outputs. </p>
-
-<p>When running large data sets, you should monitor Qhull's
-performance with the '<a href="qh-optt.htm#TFn">TFn</a>' option.
-The time per facet is approximately constant. In high-d with many
-merged facets, the size of the ridge sets grows rapidly. For
-example the product of 8-d simplices contains 18 facets and
-500,000 ridges. This will increase the time needed per facet. </p>
-
-<p>As dimension increases, the number of facets and ridges in a
-convex hull grows rapidly for the same number of vertices. For
-example, the convex hull of 300 cospherical points in 6-d has
-30,000 facets. </p>
-
-<p>If Qhull appears to stop processing facets, check the memory
-usage of Qhull. If more than 5-10% of Qhull is in virtual memory,
-its performance will degrade rapidly. </p>
-
-<p>When building hulls in 20-d and higher, you can follow the
-progress of Qhull with option '<a href="qh-optt.htm#Tn">T1</a>'.
-It reports each major event in processing a point. </p>
-
-<p>To reduce memory requirements, recompile Qhull for
-single-precision reals (REALfloat in <tt>user.h</tt>).
-Single-precision does not work with joggle ('<a
-href="qh-optq.htm#QJn">QJ</a>'). Check qh_MEMalign in <tt>user.h</tt>
-and the match between free list sizes and data structure sizes
-(see the end of the statistics report from '<a
-href="qh-optt.htm#Ts">Ts</a>'). If free list sizes do not match,
-you may be able to use a smaller qh_MEMalign. Setting
-qh_COMPUTEfurthest saves a small amount of memory, as does
-clearing qh_MAXoutside (both in <tt>user.h</tt>).</p>
-
-<p>Shewchuk is working on a 3-d version of his triangle
-program. It is optimized for 3-d simplicial Delaunay triangulation
-and uses less memory than Qhull.</p>
-
-<p>To reduce the size of the Qhull executable, consider
-qh_NOtrace and qh_KEEPstatistics 0 in <tt>user.h</tt>. By
-changing <tt>user.c </tt>you can also remove the input/output
-code in <tt>io.c</tt>. If you don't need facet merging, then
-version 1.01 of Qhull is much smaller. It contains some bugs that
-prevent Qhull from initializing in simple test cases. It is
-slower in high dimensions.</p>
-
-<p>The precision options, '<a href="qh-optc.htm#Vn">Vn</a>', '<a
-href="qh-optc.htm#Wn">Wn</a>', '<a href="qh-optc.htm#Un">Un</a>'.
-'<a href="qh-optc.htm#An">A-n</a>', '<a href="qh-optc.htm#Cn">C-n</a>',
-'<a href="qh-optc.htm#An2">An</a>', '<a href="qh-optc.htm#Cn2">Cn</a>',
-and '<a href="qh-optq.htm#Qx">Qx</a>', may have large effects on
-Qhull performance. You will need to experiment to find the best
-combination for your application. </p>
-
-<p>The verify option ('<a href="qh-optt.htm#Tv">Tv</a>') checks
-every point after the hull is complete. If facet merging is used,
-it checks that every point is inside every facet. This can take a
-very long time if there are many points and many facets. You can
-interrupt the verify without losing your output. If facet merging
-is not used and there are many points and facets, Qhull uses a
-directed search instead of an exhaustive search. This should be
-fast enough for most point sets. Directed search is not used for
-facet merging because directed search was already used for
-updating the facets' outer planes.</p>
-
-<p>The check-frequently option ('<a href="qh-optt.htm#Tc">Tc</a>')
-becomes expensive as the dimension increases. The verify option
-('<a href="qh-optt.htm#Tv">Tv</a>') performs many of the same
-checks before outputting the results.</p>
-
-<p>Options '<a href="qh-optq.htm#Q0">Q0</a>' (no pre-merging), '<a
-href="qh-optq.htm#Q3">Q3</a>' (no checks for redundant vertices),
-'<a href="qh-optq.htm#Q5">Q5</a>' (no updates for outer planes),
-and '<a href="qh-optq.htm#Q8">Q8</a>' (no near-interior points)
-increase Qhull's speed. The corresponding operations may not be
-needed in your application.</p>
-
-<p>In 2-d and 3-d, a partial hull may be faster to produce.
-Option '<a href="qh-optq.htm#QGn">QgGn</a>' only builds facets
-visible to point n. Option '<a href="qh-optq.htm#QVn">QgVn</a>'
-only builds facets that contain point n. In higher-dimensions,
-this does not reduce the number of facets.</p>
-
-<p><tt>User.h</tt> includes a number of performance-related
-constants. Changes may improve Qhull performance on your data
-sets. To understand their effect on performance, you will need to
-read the corresponding code. </p>
-
-<p>GNU <tt>gprof</tt> reports that the dominate cost for 3-d
-convex hull of cosperical points is qh_distplane(), mainly called
-from qh_findbestnew(). The dominate cost for 3-d Delaunay triangulation
-is creating new facets in qh_addpoint(), while qh_distplane() remains
-the most expensive function.
-
-</p>
-<h2><a href="#TOC">»</a><a name="library">Calling Qhull from
-your program</a></h2>
-
-<p><b>Warning:</b> Qhull was not designed for calling from other
-programs. There is neither API nor Qhull classes.
-It can be done, but it takes work and head scratching.
-You will need to understand the data structures and read the code.
-Most users will find it easier to call Qhull as an external
-command.
-
-<p>For examples of calling Qhull, see GNU Octave's
-<a href=http://octave.sourceforge.net/index/analysis.html#Geometry>computational geometry code</a>,
-and Qhull's
-<a href=../src/user_eg.c>user_eg.c</a>,
-<a href=../src/user_eg2.c>user_eg2.c</a>,
-<a href=../src/user.c>user.c</a>, and
-<a href=../src/qhull_interface.cpp>qhull_interface.cpp</a>.
-Qhull's programs use the same library:
-<a href=../src/unix.c>unix.c</a>,
-<a href=../src/qconvex.c>qconvex.c</a>,
-<a href=../src/qdelaun.c>qdelaun.c</a>,
-<a href=../src/qhalf.c>qhalf.c</a>, and
-<a href=../src/qvoronoi.c>qvoronoi.c</a>.
-
-<p>The <a href=http://www.boost.org/libs/graph/doc/table_of_contents.html>BGL</a>
-Boost Graph Library [aka GGCL] provides C++ classes for graph data structures
-and algorithms [Dr. Dobb's 9/00 p. 29-38; OOPSLA '99 p. 399-414]. It is modelled after the
-Standard Template Library. It would provide a good interface to Qhull.
-If you are interested in adapting BGL to Qhull, please contact
-<a href="mailto:bradb@qhull.org">bradb@qhull.org</a>.
-
-<p>See <a href="../src/index.htm">Qhull functions, macros, and data
-structures</a> for internal documentation of Qhull. The
-documentation provides an overview and index. To use the library
-you will need to read and understand the code. For most users, it
-is better to write data to a file, call the qhull program, and
-read the results from the output file.</p>
-
-<p>When you read the code, be aware of the macros "qh"
-and "qhstat", e.g., "qh hull_dim". They are
-defined in <tt>qhull.h</tt>. They allow the global data
-structures to be pre-allocated (faster access) or dynamically
-allocated (allows multiple copies). </p>
-
-<p>Qhull's <tt>Makefile</tt> produces a library, <tt>libqhull.a</tt>,
-for inclusion in your programs. First review <tt>qhull.h</tt>.
-This defines the data structures used by Qhull and provides
-prototypes for the top-level functions.
-Most users will only need qhull.h in their programs. For
-example, the Qhull program is defined with <tt>qhull.h</tt> and <tt>unix.c</tt>.
-To access all functions, use <tt>qhull_a.h</tt>. Include the file
-with "<tt>#include <qhull/qhull_a.h>".</tt> This
-avoids potential name conflicts.</p>
-
-<p>If you use the Qhull library, you are on your own as far as
-bugs go. Start with small examples for which you know the output.
-If you get a bug, try to duplicate it with the Qhull program. The
-'<a href="qh-optt.htm#Tc">Tc</a>' option will catch many problems
-as they occur. When an error occurs, use '<a
-href="qh-optt.htm#Tn">T4</a> <a href="qh-optt.htm#TPn">TPn</a>'
-to trace from the last point added to the hull. Compare your
-trace with the trace output from the Qhull program.</p>
-
-<p>Errors in the Qhull library are more likely than errors in the
-Qhull program. These are usually due to feature interactions that
-do not occur in the Qhull program. Please report all errors that
-you find in the Qhull library. Please include suggestions for
-improvement. </p>
-
-<h3><a href="#TOC">»</a><a name="mem">sets and quick memory
-allocation</a></h3>
-
-<p>You can use <tt>mem.c</tt> and<tt> qset.c</tt> individually. <tt>Mem.c
-</tt>implements quick-fit memory allocation. It is faster than
-malloc/free in applications that allocate and deallocate lots of
-memory. </p>
-
-<p><tt>Qset.c</tt> implements sets and related collections. It's
-the inner loop of Qhull, so speed is more important than
-abstraction. Set iteration is particularly fast. <tt>qset.c</tt>
-just includes the functions needed for Qhull. </p>
-
-<h3><a href="#TOC">»</a><a name="dids">Delaunay triangulations
-and point indices</a></h3>
-
-<p>Here some unchecked code to print the point indices of each
-Delaunay triangle. Use option 'QJ' if you want to avoid
-non-simplicial facets. Note that upper Delaunay regions are
-skipped. These facets correspond to the furthest-site Delaunay
-triangulation. </p>
-
-<blockquote>
- <pre>
- facetT *facet;
- vertexT *vertex, **vertexp;
-
- FORALLfacets {
- if (!facet->upperdelaunay) {
- printf ("%d", qh_setsize (facet->vertices);
- FOREACHvertex_(facet->vertices)
- printf (" %d", qh_pointid (vertex->point));
- printf ("\n");
- }
- }
-
-</pre>
-</blockquote>
-
-<h3><a href="#TOC">»</a><a name="findfacet">locate a facet with
-qh_findbestfacet()</a></h3>
-
-<p>The routine qh_findbestfacet in <tt>poly2.c</tt> is
-particularly useful. It uses a directed search to locate the
-facet that is furthest below a point. For Delaunay
-triangulations, this facet is the Delaunay triangle that contains
-the lifted point. For convex hulls, the distance of a point to
-the convex hull is either the distance to this facet or the
-distance to a subface of the facet.</p>
-
-<blockquote>
-<p><b>Warning:</b> If triangulated output ('<a href=qh-optq.htm#Qt>Qt</a>') and
-the best facet is triangulated, qh_findbestfacet() returns one of
-the corresponding 'tricoplanar' facets. The actual best facet may be a different
-tricoplanar facet.
-<p>
-See qh_nearvertex() in poly2.c for sample code to visit each
-tricoplanar facet. To identify the correct tricoplanar facet,
-see Devillers, et. al., [<a href="index.htm#devi01">'01</a>]
-and Mucke, et al [<a href="index.htm#muck96">'96</a>]. If you
-implement this test in general dimension, please notify
-<a href="mailto:qhull@qhull.org">qhull@qhull.org</a>.
-</blockquote>
-
-<p>qh_findbestfacet performs an exhaustive search if its directed
-search returns a facet that is above the point. This occurs when
-the point is inside the hull or if the curvature of the convex
-hull is less than the curvature of a sphere centered at the point
-(e.g., a point near a lens-shaped convex hull). When the later
-occurs, the distance function is bimodal and a directed search
-may return a facet on the far side of the convex hull. </p>
-
-<p>Algorithms that retain the previously constructed hulls
-usually avoid an exhaustive search for the best facet. You may
-use a hierarchical decomposition of the convex hull [Dobkin and
-Kirkpatrick <a href="index.htm#dob-kir90">'90</a>]. </p>
-
-<p>To use qh_findbestfacet with Delaunay triangulations, lift the
-point to a paraboloid by summing the squares of its coordinates
-(see qh_setdelaunay in geom2.c). Do not scale the input with
-options 'Qbk', 'QBk', 'QbB' or 'Qbb'. See Mucke, et al [<a
-href="index.htm#muck96">'96</a>] for a good point location
-algorithm.</p>
-
-<p>The intersection of a ray with the convex hull may be found by
-locating the facet closest to a distant point on the ray.
-Intersecting the ray with the facet's hyperplane gives a new
-point to test. </p>
-
-<h3><a href="#TOC">»</a><a name="inc">on-line construction with
-qh_addpoint()</a></h3>
-
-<p>The Qhull library may be used for the on-line construction of
-convex hulls, Delaunay triangulations, and halfspace
-intersections about a point. It may be slower than implementations that retain
-intermediate convex hulls (e.g., Clarkson's <a
-href="http://netlib.bell-labs.com/netlib/voronoi/hull.html">hull
-program</a>). These implementations always use a directed search.
-For the on-line construction of convex hulls and halfspace
-intersections, Qhull may use an exhaustive search
-(qh_findbestfacet). </p>
-
-<p>You may use qh_findbestfacet and qh_addpoint (<tt>qhull.c</tt>) to add a point to
-a convex hull. Do not modify the point's coordinates since
-qh_addpoint does not make a copy of the coordinates. For Delaunay
-triangulations, you need to lift the point to a paraboloid by
-summing the squares of the coordinates (see qh_setdelaunay in
-geom2.c). Do not scale the input with options 'Qbk', 'QBk', 'QbB'
-or 'Qbb'. Do not deallocate the point's coordinates. You need to
-provide a facet that is below the point (<a href="#findfacet">qh_findbestfacet</a>).
-</p>
-
-<p>You can not delete points. Another limitation is that Qhull
-uses the initial set of points to determine the maximum roundoff
-error (via the upper and lower bounds for each coordinate). </p>
-
-<p>For many applications, it is better to rebuild the hull from
-scratch for each new point. This is especially true if the point
-set is small or if many points are added at a time.</p>
-
-<p>Calling qh_addpoint from your program may be slower than
-recomputing the convex hull with qh_qhull. This is especially
-true if the added points are not appended to the qh first_point
-array. In this case, Qhull must search a set to determine a
-point's ID. [R. Weber] </p>
-
-<p>See user_eg.c for examples of the on-line construction of
-convex hulls, Delaunay triangulations, and halfspace
-intersections. The outline is: </p>
-
-<blockquote>
- <pre>
-initialize qhull with an initial set of points
-qh_qhull();
-
-for each additional point p
- append p to the end of the point array or allocate p separately
- lift p to the paraboloid by calling qh_setdelaunay
- facet= qh_findbestfacet (p, !qh_ALL, &bestdist, &isoutside);
- if (isoutside)
- if (!qh_addpoint (point, facet, False))
- break; /* user requested an early exit with 'TVn' or 'TCn' */
-
-call qh_check_maxout() to compute outer planes
-terminate qhull</pre>
-</blockquote>
-
-<h3><a href="#TOC">»</a><a name="constrained">Constrained
-Delaunay triangulation </a></h3>
-
-<p>With a fair amount of work, Qhull is suitable for constrained
-Delaunay triangulation. See Shewchuk, ACM Symposium on
-Computational Geometry, Minneapolis 1998.</p>
-
-<p>Here's a quick way to add a constraint to a Delaunay
-triangulation: subdivide the constraint into pieces shorter than
-the minimum feature separation. You will need an independent
-check of the constraint in the output since the minimum feature
-separation may be incorrect. [H. Geron] </p>
-
-<h3><A href="#TOC">»</A><a name="tricoplanar">Tricoplanar facets and option 'Qt'</h3>
-
-<p>Option '<a href=qh-optq.htm#Qt>Qt</a>' triangulates non-simplicial
-facets (e.g., a square facet in 3-d or a cubical facet in 4-d).
-All facets share the same apex (i.e., the first vertex in facet->vertices).
-For each triangulated facet, Qhull
-sets facet->tricoplanar true and copies facet->center, facet->normal, facet->offset, and facet->maxoutside. One of
-the facets owns facet->normal; its facet->keepcentrum is true.
-If facet->isarea is false, facet->triowner points to the owning
-facet.
-
-<p>Qhull sets facet->degenerate if the facet's vertices belong
-to the same ridge of the non-simplicial facet.
-
-<p>To visit each tricoplanar facet of a non-simplicial facet,
-either visit all neighbors of the apex or recursively visit
-all neighbors of a tricoplanar facet. The tricoplanar facets
-will have the same facet->center.</p>
-
-<p>See <a href=../src/io.c#detvridge>qh_detvridge</a> for an example of ignoring tricoplanar facets.</p>
-
-<h3><a href="#TOC">»</a><a name="vertices">Voronoi vertices of a
-region</a></h3>
-
-<p>The following code iterates over all Voronoi vertices for each
-Voronoi region. Qhull computes Voronoi vertices from the convex
-hull that corresponds to a Delaunay triangulation. An input site
-corresponds to a vertex of the convex hull and a Voronoi vertex
-corresponds to an adjacent facet. A facet is
-"upperdelaunay" if it corresponds to a Voronoi vertex
-"at-infinity". Qhull uses qh_printvoronoi in <tt>io.c</tt>
-for '<a href=qvoronoi.htm>qvoronoi</a> <a href="qh-opto.htm#o">o'</a> </p>
-
-<blockquote>
- <pre>
-/* please review this code for correctness */
-qh_setvoronoi_all();
-FORALLvertices {
- site_id = qh_pointid (vertex->point);
- if (qh hull_dim == 3)
- qh_order_vertexneighbors(vertex);
- infinity_seen = 0;
- FOREACHneighbor_(vertex) {
- if (neighbor->upperdelaunay) {
- if (!infinity_seen) {
- infinity_seen = 1;
- ... process a Voronoi vertex "at infinity" ...
- }
- }else {
- voronoi_vertex = neighbor->center;
- ... your code goes here ...
- }
- }
-}
-</pre>
-</blockquote>
-
-<h3><a href="#TOC">»</a><a name="ridge">Voronoi vertices of a
-ridge</a></h3>
-
-<p>Qhull uses qh_printvdiagram() in io.c to print the ridges of a
-Voronoi diagram for option '<a href="qh-optf.htm#Fv2">Fv</a>'.
-The helper function qh_eachvoronoi() does the real work. It calls
-the callback 'printvridge' for each ridge of the Voronoi diagram.
-</p>
-
-<p>You may call qh_printvdiagram2(), qh_eachvoronoi(), or
-qh_eachvoronoi_all() with your own function. If you do not need
-the total number of ridges, you can skip the first call to
-qh_printvdiagram2(). See qh_printvridge() and qh_printvnorm() in
-io.c for examples. </p>
-
-<h3><a href="#TOC">»</a><a name="vneighbor">vertex neighbors of
-a vertex</a></h3>
-
-<p>To visit all of the vertices that share an edge with a vertex:
-</p>
-
-<ul>
- <li>Generate neighbors for each vertex with
- qh_vertexneighbors in <tt>poly2.c</tt>. </li>
- <li>For simplicial facets, visit the vertices of each
- neighbor </li>
- <li>For non-simplicial facets, <ul>
- <li>Generate ridges for neighbors with qh_makeridges
- in <tt>merge.c</tt>. </li>
- <li>Generate ridges for a vertex with qh_vertexridges
- in <tt>merge.c</tt>. </li>
- <li>Visit the vertices of these ridges. </li>
- </ul>
- </li>
-</ul>
-
-<p>For non-simplicial facets, the ridges form a simplicial
-decomposition of the (d-2)-faces between each pair of facets --
-if you need 1-faces, you probably need to generate the full face
-graph of the convex hull. </p>
-
-<h2><a href="#TOC">»</a><a name="enhance">Enhancements to Qhull </a></h2>
-
-<p>There are many ways in which Qhull can be improved. </p>
-
-<pre>Here is a partial list:
- - fix finddelaunay() in user_eg.c for tricoplanar facets
- - write a BGL, C++ interface to Qhull
- http://www.boost.org/libs/graph/doc/table_of_contents.html
- - change qh_save_qhull to swap the qhT structure instead of using pointers
- - change error handling and tracing to be independent of 'qh ferr'
- - determine the maximum width for a given set of parameters
- - prove that directed search locates all coplanar facets
- - in high-d merging, can a loop of facets become disconnected?
- - find a way to improve inner hulls in 5-d and higher
- - determine the best policy for facet visibility ('<a
-href="qh-optc.htm#Vn">Vn</a>')
- - determine the limitations of '<a href="qh-optq.htm#Qg">Qg</a>'
-
-Precision improvements:
- - For 'Qt', resolve cross-linked, butterfly ridges.
- May allow retriangulation in qh_addpoint().
- - for Delaunay triangulations ('d' or 'v') under joggled input ('QJ'),
- remove vertical facets whose lowest vertex may be coplanar with convex hull
- - review use of 'Qbb' with 'd QJ'. Is MAXabs_coord better than MAXwidth?
- - check Sugihara and Iri's better in-sphere test [Canadian
- Conf. on Comp. Geo., 1989; Univ. of Tokyo RMI 89-05]
- - replace centrum with center of mass and facet area
- - handle numeric overflow in qh_normalize and elsewhere
- - merge flipped facets into non-flipped neighbors.
- currently they merge into best neighbor (appears ok)
- - determine min norm for Cramer's rule (qh_sethyperplane_det). It looks high.
- - improve facet width for very narrow distributions
-
-New features:
- - implement Matlab's tsearch() using Qhull
- - compute volume of Voronoi regions. You need to determine the dual face
- graph in all dimensions [see Clarkson's hull program]
- - compute alpha shapes [see Clarkson's hull program]
- - implement deletion of Delaunay vertices
- see Devillers, ACM Symposium on Computational Geometry, Minneapolis 1999.
- - compute largest empty circle [see O'Rourke, chapter 5.5.3] [Hase]
- - list redundant (i.e., coincident) vertices [Spitz]
- - implement Mucke, et al, ['96] for point location in Delaunay triangulations
- - implement convex hull of moving points
- - implement constrained Delaunay diagrams
- see Shewchuk, ACM Symposium on Computational Geometry, Minneapolis 1998.
- - estimate outer volume of hull
- - automatically determine lower dimensional hulls
- - allow "color" data for input points
- need to insert a coordinate for Delaunay triangulations
-
-Input/output improvements:
- - Support the VTK Visualization Toolkit, http://www.kitware.com/vtk.html
- - generate output data array for Qhull library [Gautier]
- - need improved DOS window with screen fonts, scrollbar, cut/paste
- - generate Geomview output for Voronoi ridges and unbounded rays
- - generate Geomview output for halfspace intersection
- - generate Geomview display of furthest-site Voronoi diagram
- - use '<a href="qh-optg.htm#GDn">GDn</a>' to view 5-d facets in 4-d
- - convert Geomview output for other 3-d viewers
- - add interactive output option to avoid recomputing a hull
- - orient vertex neighbors for '<a href="qh-optf.htm#Fv">Fv</a>' in 3-d and 2-d
- - track total number of ridges for summary and logging
-
-Performance improvements:
- - optimize Qhull for 2-d Delaunay triangulations
- - use O'Rourke's <a href="index.htm#orou94">'94</a> vertex->duplicate_edge
- - add bucketing
- - better to specialize all of the code (ca. 2-3x faster w/o merging)
- - use updated LU decomposition to speed up hyperplane construction
- - [Gill et al. 1974, Math. Comp. 28:505-35]
- - construct hyperplanes from the corresponding horizon/visible facets
- - for merging in high d, do not use vertex->neighbors
-
-</pre>
-
-<p>Please let us know about your applications and improvements. </p>
-<!-- Navigation links -->
-<hr>
-
-<p><b>Up:</b> <a href="http://www.qhull.org">Home
-page for Qhull</a> <br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual: Table of
-Contents</a><br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a><br>
-<b>To:</b> <a href="#TOC">Qhull internals</a>: Table of Contents <br>
-<b>Dn:</b> <a href="../src/index.htm">Qhull functions</a>, macros, and data
-structures <!-- GC common information -->
-
-<hr>
-
-<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
-align="middle" width="40" height="40"></a><i>The Geometry Center
-Home Page </i></p>
-
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see changes.txt <!-- hhmts end --> </p>
-</body>
-</html>
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-<html>
-
-<head>
-<title>Qhull precision options</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a></p>
-
-<hr>
-<!-- Main text of document -->
-<h1><a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
-src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
-height="100"></a> Qhull precision options</h1>
-
-This section lists the precision options for Qhull. These options are
-indicated by an upper-case letter followed by a number.
-
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-
-<hr>
-
-<p><a href="index.htm#TOC">»</a> <a href="qh-quick.htm#programs">Programs</a>
-<a name="prec">•</a> <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a></p>
-
-<h2>Precision options</h2>
-
-<p>Most users will not need to set these options. They are best
-used for <a href="qh-impre.htm#approximate">approximating</a> a
-convex hull. They may also be used for testing Qhull's handling
-of precision errors.</p>
-
-<p>By default, Qhull uses options '<a href="#C0">C-0</a>' for
-2-d, 3-d and 4-d, and '<a href="qh-optq.htm#Qx">Qx</a>' for 5-d
-and higher. These options use facet merging to handle precision
-errors. You may also use joggled input '<a href="qh-optq.htm#QJn">QJ</a>'
-to avoid precision problems.
-For more information see <a
-href="qh-impre.htm">Imprecision in Qhull</a>.</p>
-
-<dl compact>
- <dt> </dt>
- <dd><b>General</b></dd>
- <dt><a href="#Cn2">Cn</a></dt>
- <dd>centrum radius for post-merging</dd>
- <dt><a href="#Cn">C-n</a></dt>
- <dd>centrum radius for pre-merging</dd>
- <dt><a href="#An2">An</a></dt>
- <dd>cosine of maximum angle for post-merging</dd>
- <dt><a href="#An">A-n</a></dt>
- <dd>cosine of maximum angle for pre-merging</dd>
- <dt><a href="qh-optq.htm#Qx">Qx</a></dt>
- <dd>exact pre-merges (allows coplanar facets)</dd>
- <dt><a href="#C0">C-0</a></dt>
- <dd>handle all precision errors</dd>
- <dt><a href="#Wn">Wn</a></dt>
- <dd>min distance above plane for outside points</dd>
-</dl>
-
-<dl compact>
- <dt> </dt>
- <dd><b>Experimental</b></dd>
- <dt><a href="#Un">Un</a></dt>
- <dd>max distance below plane for a new, coplanar point</dd>
- <dt><a href="#En">En</a></dt>
- <dd>max roundoff error for distance computation</dd>
- <dt><a href="#Vn">Vn</a></dt>
- <dd>min distance above plane for a visible facet</dd>
- <dt><a href="#Rn">Rn</a></dt>
- <dd>randomly perturb computations by a factor of [1-n,1+n]</dd>
-</dl>
-
-<dl compact>
-</dl>
-
-<hr>
-
-<h3><a href="#prec">»</a><a name="An">A-n - cosine of maximum
-angle for pre-merging.</a></h3>
-
-<p>Pre-merging occurs while Qhull constructs the hull. It is
-indicated by '<a href="#Cn">C-n</a>', 'A-n', or '<a
-href="qh-optq.htm#Qx">Qx</a>'.</p>
-
-<p>If the angle between a pair of facet normals is greater than <i>n</i>,
-Qhull merges one of the facets into a neighbor. It selects the
-facet that is closest to a neighboring facet.</p>
-
-<p>For example, option 'A-0.99' merges facets during the
-construction of the hull. If the cosine of the angle between
-facets is greater than 0.99, one or the other facet is merged.
-Qhull accounts for the maximum roundoff error.</p>
-
-<p>If 'A-n' is set without '<a href="#Cn">C-n</a>', then '<a
-href="#C0">C-0</a>' is automatically set. </p>
-
-<p>In 5-d and higher, you should set '<a href="qh-optq.htm#Qx">Qx</a>'
-along with 'A-n'. It skips merges of coplanar facets until after
-the hull is constructed and before '<a href="#An2">An</a>' and '<a
-href="#Cn2">Cn</a>' are checked. </p>
-
-<h3><a href="#prec">»</a><a name="An2">An - cosine of maximum angle for
-post-merging.</a></h3>
-
-<p>Post merging occurs after the hull is constructed. For
-example, option 'A0.99' merges a facet if the cosine of the angle
-between facets is greater than 0.99. Qhull accounts for the
-maximum roundoff error.</p>
-
-<p>If 'An' is set without '<a href="#Cn2">Cn</a>', then '<a
-href="#Cn2">C0</a>' is automatically set. </p>
-
-<h3><a href="#prec">»</a><a name="C0">C-0 - handle all precision
-errors </a></h3>
-
-<p>Qhull handles precision errors by merging facets. The 'C-0'
-option handles all precision errors in 2-d, 3-d, and 4-d. It is
-set by default. It may be used in higher dimensions, but
-sometimes the facet width grows rapidly. It is usually better to
-use '<a href="qh-optq.htm#Qx">Qx</a>' in 5-d and higher.
-Use '<a href="qh-optq.htm#QJn">QJ</a>' to joggle the input
-instead of merging facets.
-Use '<a
-href="qh-optq.htm#Q0">Q0</a>' to turn both options off.</p>
-
-<p>Qhull optimizes 'C-0' ("_zero-centrum") by testing
-vertices instead of centrums for adjacent simplices. This may be
-slower in higher dimensions if merges decrease the number of
-processed points. The optimization may be turned off by setting a
-small value such as 'C-1e-30'. See <a href="qh-impre.htm">How
-Qhull handles imprecision</a>.</p>
-
-<h3><a href="#prec">»</a><a name="Cn">C-n - centrum radius for
-pre-merging</a></h3>
-
-<p>Pre-merging occurs while Qhull constructs the hull. It is
-indicated by 'C-n', '<a href="#An">A-n</a>', or '<a
-href="qh-optq.htm#Qx">Qx</a>'.</p>
-
-<p>The <i>centrum</i> of a facet is a point on the facet for
-testing facet convexity. It is the average of the vertices
-projected to the facet's hyperplane. Two adjacent facets are
-convex if each centrum is clearly below the other facet. </p>
-
-<p>If adjacent facets are non-convex, one of the facets is merged
-into a neighboring facet. Qhull merges the facet that is closest
-to a neighboring facet. </p>
-
-<p>For option 'C-n', <i>n</i> is the centrum radius. For example,
-'C-0.001' merges facets whenever the centrum is less than 0.001
-from a neighboring hyperplane. Qhull accounts for roundoff error
-when testing the centrum.</p>
-
-<p>In 5-d and higher, you should set '<a href="qh-optq.htm#Qx">Qx</a>'
-along with 'C-n'. It skips merges of coplanar facets until after
-the hull is constructed and before '<a href="#An2">An</a>' and '<a
-href="#Cn2">Cn</a>' are checked. </p>
-
-<h3><a href="#prec">»</a><a name="Cn2">Cn - centrum radius for
-post-merging</a></h3>
-
-<p>Post-merging occurs after Qhull constructs the hull. It is
-indicated by '<a href="#Cn2">Cn</a>' or '<a href="#An2">An</a>'. </p>
-
-<p>For option '<a href="#Cn2">Cn</a>', <i>n</i> is the centrum
-radius. For example, 'C0.001' merges facets when the centrum is
-less than 0.001 from a neighboring hyperplane. Qhull accounts for
-roundoff error when testing the centrum.</p>
-
-<p>Both pre-merging and post-merging may be defined. If only
-post-merging is used ('<a href="qh-optq.htm#Q0">Q0</a>' with
-'Cn'), Qhull may fail to produce a hull due to precision errors
-during the hull's construction.</p>
-
-<h3><a href="#prec">»</a><a name="En">En - max roundoff error
-for distance computations</a></h3>
-
-<p>This allows the user to change the maximum roundoff error
-computed by Qhull. The value computed by Qhull may be overly
-pessimistic. If 'En' is set too small, then the output may not be
-convex. The statistic "max. distance of a new vertex to a
-facet" (from option '<a href="qh-optt.htm#Ts">Ts</a>') is a
-reasonable upper bound for the actual roundoff error. </p>
-
-<h3><a href="#prec">»</a><a name="Rn">Rn - randomly perturb
-computations </a></h3>
-
-<p>This option perturbs every distance, hyperplane, and angle
-computation by up to <i>(+/- n * max_coord)</i>. It simulates the
-effect of roundoff errors. Unless '<a href="#En">En</a>' is
-explicitly set, it is adjusted for 'Rn'. The command 'qhull Rn'
-will generate a convex hull despite the perturbations. See the <a
-href="qh-eg.htm#merge">Examples </a>section for an example.</p>
-
-<p>Options 'Rn C-n' have the effect of '<a href="#Wn">W2n</a>'
-and '<a href="#Cn">C-2n</a>'. To use time as the random number
-seed, use option '<a href="qh-optq.htm#QRn">QR-1</a>'.</p>
-
-<h3><a href="#prec">»</a><a name="Un">Un - max distance for a
-new, coplanar point </a></h3>
-
-<p>This allows the user to set coplanarity. When pre-merging ('<a
-href="#Cn">C-n </a>', '<a href="#An">A-n</a>' or '<a
-href="qh-optq.htm#Qx">Qx</a>'), Qhull merges a new point into any
-coplanar facets. The default value for 'Un' is '<a href="#Vn">Vn</a>'.</p>
-
-<h3><a href="#prec">»</a><a name="Vn">Vn - min distance for a
-visible facet </a></h3>
-
-<p>This allows the user to set facet visibility. When adding a
-point to the convex hull, Qhull determines all facets that are
-visible from the point. A facet is visible if the distance from
-the point to the facet is greater than 'Vn'.</p>
-
-<p>Without merging, the default value for 'Vn' is the roundoff
-error ('<a href="#En">En</a>'). With merging, the default value
-is the pre-merge centrum ('<a href="#Cn">C-n</a>') in 2-d or 3-d,
-or three times that in other dimensions. If the outside width is
-specified with option '<a href="#Wn">Wn </a>', the maximum,
-default value for 'Vn' is '<a href="#Wn">Wn</a>'.</p>
-
-<p>Qhull warns if 'Vn' is greater than '<a href="#Wn">Wn</a>' and
-furthest outside ('<a href="qh-optq.htm#Qf">Qf</a>') is not
-selected; this combination usually results in flipped facets
-(i.e., reversed normals).</p>
-
-<h3><a href="#prec">»</a><a name="Wn">Wn - min distance above
-plane for outside points</a></h3>
-
-<p>Points are added to the convex hull only if they are clearly
-outside of a facet. A point is outside of a facet if its distance
-to the facet is greater than 'Wn'. Without pre-merging, the
-default value for 'Wn' is '<a href="#En">En </a>'. If the user
-specifies pre-merging and does not set 'Wn', than 'Wn' is set to
-the maximum of '<a href="#Cn">C-n</a>' and <i>maxcoord*(1 - </i><a
-href="#An"><i>A-n</i></a><i>)</i>.</p>
-
-<p>This option is good for <a href="qh-impre.htm#approximate">approximating</a>
-a convex hull.</p>
-
-<p>Options '<a href="qh-optq.htm#Qc">Qc</a>' and '<a
-href="qh-optq.htm#Qi">Qi</a>' use the minimum vertex to
-distinguish coplanar points from interior points.</p>
-<!-- Navigation links -->
-<hr>
-
-<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a></p>
-<!-- GC common information -->
-<hr>
-
-<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
-align="middle" width="40" height="40"></a><i>The Geometry Center
-Home Page </i></p>
-
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qh-optf.htm b/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qh-optf.htm
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--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qh-optf.htm
+++ /dev/null
@@ -1,719 +0,0 @@
-<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
-<html>
-
-<head>
-<title>Qhull format options (F)</title>
-</head>
-
-<body><!-- Navigation links -->
-<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <A href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <A href="qh-quick.htm#programs">Programs</a>
-• <A href="qh-quick.htm#options">Options</a>
-• <A href="qh-opto.htm#output">Output</a>
-• <A href="qh-optf.htm#format">Formats</a>
-• <A href="qh-optg.htm#geomview">Geomview</a>
-• <A href="qh-optp.htm#print">Print</a>
-• <A href="qh-optq.htm#qhull">Qhull</a>
-• <A href="qh-optc.htm#prec">Precision</a>
-• <A href="qh-optt.htm#trace">Trace</a></p>
-<hr>
-<!-- Main text of document -->
-<h1><a
- href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><IMG
- align=middle alt=[delaunay] height=100
- src="qh--dt.gif" width=100 ></a> Qhull format options (F)</h1>
-
-<p>This section lists the format options for Qhull. These options
-are indicated by 'F' followed by a letter. See <A
- href="qh-opto.htm#output" >Output</a>, <A href="qh-optp.htm#print">Print</a>,
-and <A href="qh-optg.htm#geomview">Geomview</a> for other output
-options. </p>
-
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-
-<hr>
-
-<p><A href="index.htm#TOC">»</a> <A href="qh-quick.htm#programs">Programs</a>
-<a name="format">•</a> <A href="qh-quick.htm#options">Options</a>
-• <A href="qh-opto.htm#output">Output</a>
-• <A href="qh-optf.htm#format">Formats</a>
-• <A href="qh-optg.htm#geomview">Geomview</a>
-• <A href="qh-optp.htm#print">Print</a>
-• <A href="qh-optq.htm#qhull">Qhull</a>
-• <A href="qh-optc.htm#prec">Precision</a>
-• <A href="qh-optt.htm#trace">Trace</a></p>
-
-<h2>Additional input & output formats</h2>
-
-<p>These options allow for automatic processing of Qhull output.
-Options '<A href="qh-opto.htm#i">i</a>', '<A href="qh-opto.htm#o">o</a>',
-'<A href="qh-opto.htm#n">n</a>', and '<A href="qh-opto.htm#p">p</a>'
-may also be used.</p>
-
-<dl compact>
- <dt>
- <dd><b>Summary and control</b>
- <dt><A href="#FA">FA</a>
- <dd>compute total area and volume for option '<A
- href="qh-opto.htm#s">s</a>'
-
- <dt><A href="#FV">FV</a>
- <dd>print average vertex (interior point for '<A
- href="qhalf.htm">qhalf</a>')
- <dt><A href="#FQ">FQ</a>
- <dd>print command for qhull and input
- <dt><A href="#FO">FO</a>
- <dd>print options to stderr or stdout
- <dt><A href="#FS">FS</a>
- <dd>print sizes: total area and volume
- <dt><A href="#Fs">Fs</a>
- <dd>print summary: dim, #points, total vertices and
- facets, #vertices, #facets, max outer and inner plane
- <dt><A href="#Fd">Fd</a>
- <dd>use format for input (offset first)
- <dt><A href="#FD">FD</a>
- <dd>use cdd format for normals (offset first)
- <dt><a href="#FM">FM</a>
- <dd>print Maple output (2-d and 3-d)
- <dt>
- <dt>
- <dd><b>Facets, points, and vertices</b>
- <dt><A href="#Fa">Fa</a>
- <dd>print area for each facet
- <dt><A href="#FC">FC</a>
- <dd>print centrum for each facet
- <dt><A href="#Fc">Fc</a>
- <dd>print coplanar points for each facet
- <dt><A href="#Fx">Fx</a>
- <dd>print extreme points (i.e., vertices) of convex hull.
-
- <dt><A href="#FF">FF</a>
- <dd>print facets w/o ridges
- <dt><A href="#FI">FI</a>
- <dd>print ID for each facet
- <dt><A href="#Fi">Fi</a>
- <dd>print inner planes for each facet
- <dt><A href="#Fm">Fm</a>
- <dd>print merge count for each facet (511 max)
- <dt><A href="#FP">FP</a>
- <dd>print nearest vertex for coplanar points
- <dt><A href="#Fn">Fn</a>
- <dd>print neighboring facets for each facet
- <dt><A href="#FN">FN</a>
- <dd>print neighboring facets for each point
- <dt><A href="#Fo">Fo</a>
- <dd>print outer planes for each facet
- <dt><A href="#Ft">Ft</a>
- <dd>print triangulation with added points
- <dt><A href="#Fv">Fv</a>
- <dd>print vertices for each facet
- <dt>
- <dt>
- <dd><b>Delaunay, Voronoi, and halfspace</b>
- <dt><A href="#Fx">Fx</a>
- <dd>print extreme input sites of Delaunay triangulation
- or Voronoi diagram.
- <dt><A href="#Fp">Fp</a>
- <dd>print points at halfspace intersections
- <dt><A href="#Fi2">Fi</a>
- <dd>print separating hyperplanes for inner, bounded
- Voronoi regions
- <dt><A href="#Fo2">Fo</a>
- <dd>print separating hyperplanes for outer, unbounded
- Voronoi regions
- <dt><A href="#Fv2">Fv</a>
- <dd>print Voronoi diagram as ridges for each input pair
- <dt><A href="#FC">FC</a>
- <dd>print Voronoi vertex ("center") for each facet</dd>
-</dl>
-
-<hr>
-
-<h3><A href="#format">»</a><a name="Fa">Fa - print area for each
-facet </a></h3>
-
-<p>The first line is the number of facets. The remaining lines
-are the area for each facet, one facet per line. See '<A
- href="#FA" >FA</a>' for computing the total area and volume.</p>
-
-<p>Use '<A href="qh-optp.htm#PAn">PAn</a>' for printing the n
-largest facets. Use option '<A href="qh-optp.htm#PFn">PFn</a>'
-for printing facets larger than <i>n</i>.</p>
-
-<p>For Delaunay triangulations, the area is the area of each
-Delaunay triangle. For Voronoi vertices, the area is the area of
-the dual facet to each vertex. </p>
-
-<p>Qhull uses the centrum and ridges to triangulate
-non-simplicial facets. The area for non-simplicial facets is the
-sum of the areas for each triangle. It is an approximation of the
-actual area. The ridge's vertices are projected to the facet's
-hyperplane. If a vertex is far below a facet (qh_WIDEcoplanar in <tt>user.h</tt>),
-the corresponding triangles are ignored.</p>
-
-<p>For non-simplicial facets, vertices are often below the
-facet's hyperplane. If so, the approximation is less than the
-actual value and it may be significantly less. </p>
-
-<h3><A href="#format">»</a><a name="FA">FA - compute total area
-and volume for option 's' </a></h3>
-
-<p>With option 'FA', Qhull includes the total area and volume in
-the summary ('<A href="qh-opto.htm#s">s</a>'). If facets are
-merged, the area and volume are approximations. Option 'FA' is
-automatically set for options '<A href="#Fa">Fa </a>', '<A
- href="qh-optp.htm#PAn" >PAn</a>', and '<A href="qh-optp.htm#PFn">PFn</a>'.
-</p>
-
-<p>With '<A href="qdelaun.htm">qdelaunay</a> <A
- href="qh-opto.htm#s" >s</a> FA', Qhull computes the total area of
-the Delaunay triangulation. This equals the volume of the convex
-hull of the data points. With options '<A href="qdelau_f.htm">qdelaunay Qu</a>
-<A href="qh-opto.htm#s">s</a> FA', Qhull computes the
-total area of the furthest-site Delaunay triangulation. This
-equals of the total area of the Delaunay triangulation. </p>
-
-<p>See '<A href="#Fa">Fa</a>' for further details. </p>
-
-<h3><A href="#format">»</a><a name="Fc">Fc - print coplanar
-points for each facet </a></h3>
-
-<p>The output starts with the number of facets. Then each facet
-is printed one per line. Each line is the number of coplanar
-points followed by the point ids. </p>
-
-<p>By default, option 'Fc' reports coplanar points
-('<A href="qh-optq.htm#Qc">Qc</a>'). You may also use
-option '<A href="qh-optq.htm#Qi">Qi</a>'. Options 'Qi Fc' prints
-interior points while 'Qci Fc' prints both coplanar and interior
-points.
-
-<p>Each coplanar point or interior point is assigned to the
-facet it is furthest above (resp., least below). </p>
-
-<p>Use 'Qc <A href="qh-opto.htm#p">p</a>' to print vertex and
-coplanar point coordinates. Use '<A href="qh-optf.htm#Fv">Fv</a>'
-to print vertices. </p>
-
-<h3><A href="#format">»</a><a name="FC">FC - print centrum or
-Voronoi vertex for each facet </a></h3>
-
-<p>The output starts with the dimension followed by the number of
-facets. Then each facet centrum is printed, one per line. For
-<A href="qvoronoi.htm">qvoronoi</a>, Voronoi vertices are
-printed instead. </p>
-
-<h3><A href="#format">»</a><a name="Fd">Fd - use cdd format for
-input </a></h3>
-
-<p>The input starts with comments. The first comment is reported
-in the summary. Data starts after a "begin" line. The
-next line is the number of points followed by the dimension plus
-one and "real" or "integer". Then the points
-are listed with a leading "1" or "1.0". The
-data ends with an "end" line.</p>
-
-<p>For halfspaces ('<A href="qhalf.htm">qhalf</a> Fd'),
-the input format is the same. Each halfspace starts with its
-offset. The signs of the offset and coefficients are the
-opposite of Qhull's
-convention. The first two lines of the input may be an interior
-point in '<A href="#FV">FV</a>' format.</p>
-
-<h3><A href="#format">»</a><a name="FD">FD - use cdd format for
-normals </a></h3>
-
-<p>Option 'FD' prints normals ('<A href="qh-opto.htm#n">n</a>', '<A
- href="#Fo" >Fo</a>', '<A href="#Fi">Fi</a>') or points ('<A
- href="qh-opto.htm#p" >p</a>') in cdd format. The first line is the
-command line that invoked Qhull. Data starts with a
-"begin" line. The next line is the number of normals or
-points followed by the dimension plus one and "real".
-Then the normals or points are listed with the offset before the
-coefficients. The offset for points is 1.0. For normals,
-the offset and coefficients use the opposite sign from Qhull.
-The data ends with an "end" line.</p>
-
-<h3><A href="#format">»</a><a name="FF">FF - print facets w/o
-ridges </a></h3>
-
-<p>Option 'FF' prints all fields of all facets (as in '<A
- href="qh-opto.htm#f" >f</a>') without printing the ridges. This is
-useful in higher dimensions where a facet may have many ridges.
-For simplicial facets, options 'FF' and '<A href="qh-opto.htm#f">f
-</a>' are equivalent.</p>
-
-<h3><A href="#format">»</a><a name="Fi">Fi - print inner planes
-for each facet </a></h3>
-
-<p>The first line is the dimension plus one. The second line is
-the number of facets. The remainder is one inner plane per line.
-The format is the same as option '<A href="qh-opto.htm#n">n</a>'.</p>
-
-<p>The inner plane is a plane that is below the facet's vertices.
-It is an offset from the facet's hyperplane. It includes a
-roundoff error for computing the vertex distance.</p>
-
-<p>Note that the inner planes for Geomview output ('<A
- href="qh-optg.htm#Gi" >Gi</a>') include an additional offset for
-vertex visualization and roundoff error. </p>
-
-<h3><A href="#format">»</a><a name="Fi2">Fi - print separating
-hyperplanes for inner, bounded Voronoi regions</a></h3>
-
-<p>With <A href="qvoronoi.htm" >qvoronoi</a>, 'Fi' prints the
-separating hyperplanes for inner, bounded regions of the Voronoi
-diagram. The first line is the number of ridges. Then each
-hyperplane is printed, one per line. A line starts with the
-number of indices and floats. The first pair of indices indicates
-an adjacent pair of input sites. The next <i>d</i> floats are the
-normalized coefficients for the hyperplane, and the last float is
-the offset. The hyperplane is oriented toward '<A
- href="qh-optq.htm#QVn" >QVn</a>' (if defined), or the first input
-site of the pair. </p>
-
-<p>Use '<A href="qh-optf.htm#Fo2">Fo</a>' for unbounded regions,
-and '<A href="qh-optf.htm#Fv2">Fv</a>' for the corresponding
-Voronoi vertices. </p>
-
-<p>Use '<A href="qh-optt.htm#Tv">Tv</a>' to verify that the
-hyperplanes are perpendicular bisectors. It will list relevant
-statistics to stderr. The hyperplane is a perpendicular bisector
-if the midpoint of the input sites lies on the plane, all Voronoi
-vertices in the ridge lie on the plane, and the angle between the
-input sites and the plane is ninety degrees. This is true if all
-statistics are zero. Roundoff and computation errors make these
-non-zero. The deviations appear to be largest when the
-corresponding Delaunay triangles are large and thin; for example,
-the Voronoi diagram of nearly cospherical points. </p>
-
-<h3><A href="#format">»</a><a name="FI">FI - print ID for each
-facet </a></h3>
-
-<p>Print facet identifiers. These are used internally and listed
-with options '<A href="qh-opto.htm#f">f</a>' and '<A href="#FF">FF</a>'.
-Options '<A href="#Fn">Fn </a>' and '<A href="#FN">FN</a>' use
-facet identifiers for negative indices. </p>
-
-<h3><A href="#format">»</a><a name="Fm">Fm - print merge count
-for each facet </a></h3>
-
-<p>The first line is the number of facets. The remainder is the
-number of merges for each facet, one per line. At most 511 merges
-are reported for a facet. See '<A href="qh-optp.htm#PMn">PMn</a>'
-for printing the facets with the most merges. </p>
-
-<h3><a href="#format">»</a><a name="FM">FM - print Maple
-output </a></h3>
-
-<p>Qhull writes a Maple file for 2-d and 3-d convex hulls,
-2-d and 3-d halfspace intersections,
-and 2-d Delaunay triangulations. Qhull produces a 2-d
-or 3-d plot.
-
-<p><i>Warning</i>: This option has not been tested in Maple.
-
-<p>[From T. K. Abraham with help from M. R. Feinberg and N. Platinova.]
-The following steps apply while working within the
-Maple worksheet environment :
-<ol>
-<li>Generate the data and store it as an array . For example, in 3-d, data generated
-in Maple is of the form : x[i],y[i],z[i]
-<p>
-<li>Create a single variable and assign the entire array of data points to this variable.
-Use the "seq" command within square brackets as shown in the following example.
-(The square brackets are essential for the rest of the steps to work.)
-<p>
->data:=[seq([x[i],y[i],z[i]],i=1..n)]:# here n is the number of data points
-
-<li>Next we need to write the data to a file to be read by qhull. Before
-writing the data to a file, make sure that the qhull executable files and
-the data file lie in the same subdirectory. If the executable files are
-stored in the "C:\qhull3.1\" subdirectory, then save the file in the same
-subdirectory, say "C:\qhull3.1\datafile.txt". For the sake of integrity of
-the data file , it is best to first ensure that the data file does not
-exist before writing into the data file. This can be done by running a
-delete command first . To write the data to the file, use the "writedata"
-and the "writedata[APPEND]" commands as illustrated in the following example :
-<p>
->system("del c:\\qhull3.1\\datafile.txt");#To erase any previous versions of the file
-<br>>writedata("c:\\qhull3.1\\datafile.txt ",[3, nops(data)]);#writing in qhull format
-<br>>writedata[APPEND]("c:\\ qhull3.1\\datafile.txt ", data);#writing the data points
-<li>
-Use the 'FM' option to produce Maple output. Store the output as a ".mpl" file.
-For example, using the file we created above, we type the following (in DOS environment)
-<p>
-qconvex s FM <datafile.txt >dataplot.mpl
-
-<li>
-To read 3-d output in Maple, we use the 'read' command followed by
-a 'display3d' command. For example (in Maple environment):
-<p>
->with(plots):
-<br>>read `c:\\qhull3.1\\dataplot.mpl`:#IMPORTANT - Note that the punctuation mark used is ' and NOT '. The correct punctuation mark is the one next to the key for "1" (not the punctuation mark near the enter key)
-<br>> qhullplot:=%:
-<br>> display3d(qhullplot);
-</ol>
-
-<p>For Delaunay triangulation orthogonal projection is better.
-
-<p>For halfspace intersections, Qhull produces the dual
-convex hull.
-
-<p>See <a href="qh-faq.htm#math">Is Qhull available for Maple?</a>
-for other URLs.
-
-<h3><A href="#format">»</a><a name="Fn">Fn - print neighboring
-facets for each facet </a></h3>
-
-<p>The output starts with the number of facets. Then each facet
-is printed one per line. Each line is the number of neighbors
-followed by an index for each neighbor. The indices match the
-other facet output formats.</p>
-
-<p>A negative index indicates an unprinted facet due to printing
-only good facets ('<A href="qh-optp.htm#Pg">Pg</a>', <A href="qdelaun.htm" >qdelaunay</a>,
-<A href="qvoronoi.htm" >qvoronoi</a>). It
-is the negation of the facet's ID (option '<A href="#FI">FI</a>').
-For example, negative indices are used for facets "at
-infinity" in the Delaunay triangulation.</p>
-
-<h3><A href="#format">»</a><a name="FN">FN - print neighboring
-facets for each point </a></h3>
-
-<p>The first line is the number of points. Then each point is
-printed, one per line. For unassigned points (either interior or
-coplanar), the line is "0". For assigned coplanar
-points ('<A href="qh-optq.htm#Qc">Qc</a>'), the line is
-"1" followed by the index of the facet that is furthest
-below the point. For assigned interior points ('<A
- href="qh-optq.htm#Qi" >Qi</a>'), the line is "1"
-followed by the index of the facet that is least above the point.
-For vertices that do not belong to good facet, the line is
-"0"</p>
-
-<p>For vertices of good facets, the line is the number of
-neighboring facets followed by the facet indices. The indices
-correspond to the other '<A href="#format">F</a>' formats. In 4-d
-and higher, the facets are sorted by index. In 3-d, the facets
-are in adjacency order (not oriented).</p>
-
-<p>A negative index indicates an unprinted facet due to printing
-only good facets (<A href="qdelaun.htm" >qdelaunay</a>,
-<A href="qvoronoi.htm" >qvoronoi</a>, '<A href="qh-optp.htm#Pdk">Pdk</a>',
-'<A href="qh-optp.htm#Pg">Pg</a>'). It is the negation of the
-facet's ID ('<A href="#FI"> FI</a>'). For example, negative
-indices are used for facets "at infinity" in the
-Delaunay triangulation.</p>
-
-<p>For Voronoi vertices, option 'FN' lists the vertices of the
-Voronoi region for each input site. Option 'FN' lists the regions
-in site ID order. Option 'FN' corresponds to the second half of
-option '<A href="qh-opto.htm#o">o</a>'. To convert from 'FN' to '<A
- href="qh-opto.htm#o" >o</a>', replace negative indices with zero
-and increment non-negative indices by one. </p>
-
-<p>If you are using the <A href="qh-in.htm#library">Qhull
-library</a>, option 'FN' has the side effect of reordering the
-neighbors for a vertex </p>
-
-<h3><A href="#format">»</a><a name="Fo">Fo - print outer planes
-for each facet </a></h3>
-
-<p>The first line is the dimension plus one. The second line is
-the number of facets. The remainder is one outer plane per line.
-The format is the same as option '<A href="qh-opto.htm#n">n</a>'.</p>
-
-<p>The outer plane is a plane that is above all points. It is an
-offset from the facet's hyperplane. It includes a roundoff error
-for computing the point distance. When testing the outer plane
-(e.g., '<A href="qh-optt.htm#Tv">Tv</a>'), another roundoff error
-should be added for the tested point.</p>
-
-<p>If outer planes are not checked ('<A href="qh-optq.htm#Q5">Q5</a>')
-or not computed (!qh_MAXoutside), the maximum, computed outside
-distance is used instead. This can be much larger than the actual
-outer planes.</p>
-
-<p>Note that the outer planes for Geomview output ('<A
- href="qh-optg.htm#G" >G</a>') include an additional offset for
-vertex/point visualization, 'lines closer,' and roundoff error.</p>
-
-<h3><A href="#format">»</a><a name="Fo2">Fo - print separating
-hyperplanes for outer, unbounded Voronoi regions</a></h3>
-
-<p>With <A href="qvoronoi.htm" >qvoronoi</a>, 'Fo' prints the
-separating hyperplanes for outer, unbounded regions of the
-Voronoi diagram. The first line is the number of ridges. Then
-each hyperplane is printed, one per line. A line starts with the
-number of indices and floats. The first pair of indices indicates
-an adjacent pair of input sites. The next <i>d</i> floats are the
-normalized coefficients for the hyperplane, and the last float is
-the offset. The hyperplane is oriented toward '<A
- href="qh-optq.htm#QVn" >QVn</a>' (if defined), or the first input
-site of the pair. </p>
-
-<p>Option 'Fo' gives the hyperplanes for the unbounded rays of
-the unbounded regions of the Voronoi diagram. Each hyperplane
-goes through the midpoint of the corresponding input sites. The
-rays are directed away from the input sites. </p>
-
-<p>Use '<A href="qh-optf.htm#Fi2">Fi</a>' for bounded regions,
-and '<A href="qh-optf.htm#Fv2">Fv</a>' for the corresponding
-Voronoi vertices. Use '<A href="qh-optt.htm#Tv">Tv</a>' to verify
-that the corresponding Voronoi vertices lie on the hyperplane. </p>
-
-<h3><A href="#format">»</a><a name="FO">FO - print list of
-selected options </a></h3>
-
-<p>Lists selected options and default values to stderr.
-Additional 'FO's are printed to stdout. </p>
-
-<h3><A href="#format">»</a><a name="Fp">Fp - print points at
-halfspace intersections</a></h3>
-
-<p>The first line is the number of intersection points. The
-remainder is one intersection point per line. A intersection
-point is the intersection of <i>d</i> or more halfspaces from
-'<A href="qhalf.htm">qhalf</a>'. It corresponds to a
-facet of the dual polytope. The "infinity" point
-[-10.101,-10.101,...] indicates an unbounded intersection.</p>
-
-<p>If [x,y,z] are the dual facet's normal coefficients and <i>b<0</i>
-is its offset, the halfspace intersection occurs at
-[x/-b,y/-b,z/-b] plus the interior point. If <i>b>=0</i>, the
-halfspace intersection is unbounded. </p>
-
-<h3><A href="#format">»</a><a name="FP">FP - print nearest
-vertex for coplanar points </a></h3>
-
-<p>The output starts with the number of coplanar points. Then
-each coplanar point is printed one per line. Each line is the
-point ID of the closest vertex, the point ID of the coplanar
-point, the corresponding facet ID, and the distance. Sort the
-lines to list the coplanar points nearest to each vertex. </p>
-
-<p>Use options '<A href="qh-optq.htm#Qc">Qc</a>' and/or '<A
- href="qh-optq.htm#Qi" >Qi</a>' with 'FP'. Options 'Qc FP' prints
-coplanar points while 'Qci FP' prints coplanar and interior
-points. Option 'Qc' is automatically selected if 'Qi' is not
-selected.
-
-<p>For Delaunay triangulations (<A href="qdelaun.htm" >qdelaunay</a>
-or <A href="qvoronoi.htm" >qvoronoi</a>), a coplanar point is nearly
-incident to a vertex. The distance is the distance in the
-original point set.</p>
-
-<p>If imprecision problems are severe, Qhull will delete input
-sites when constructing the Delaunay triangulation. Option 'FP' will
-list these points along with coincident points.</p>
-
-<p>If there are many coplanar or coincident points and non-simplicial
-facets are triangulated ('<A href="qh-optq.htm#Qt">Qt</a>'), option
-'FP' may be inefficient. It redetermines the original vertex set
-for each coplanar point.</p>
-
-<h3><A href="#format">»</a><a name="FQ">FQ - print command for
-qhull and input </a></h3>
-
-<p>Prints qhull and input command, e.g., "rbox 10 s | qhull
-FQ". Option 'FQ' may be repeated multiple times.</p>
-
-<h3><A href="#format">»</a><a name="Fs">Fs - print summary</a></h3>
-
-<p>The first line consists of number of integers ("10")
-followed by the:
-<ul>
-<li>dimension
-<li>number of points
-<li>number of vertices
-<li>number of facets
-<li>number of vertices selected for output
-<li>number of facets selected for output
-<li>number of coplanar points for selected facets
-<li>number of nonsimplicial or merged facets selected for
- output
-<LI>number of deleted vertices</LI>
-<LI>number of triangulated facets ('<A href="qh-optq.htm#Qt">Qt</a>')</LI>
-</ul>
-
-<p>The second line consists of the number of reals
-("2") followed by the:
-<ul>
-<li>maximum offset to an outer plane
-<li>minimum offset to an inner plane.</li>
-</ul>
-Roundoff and joggle are included.
-<P></P>
-
-<p>For Delaunay triangulations and Voronoi diagrams, the
-number of deleted vertices should be zero. If greater than zero, then the
-input is highly degenerate and coplanar points are not necessarily coincident
-points. For example, <tt>'RBOX 1000 s W1e-13 t995138628 | QHULL d Qbb'</tt> reports
-deleted vertices; the input is nearly cospherical.</p>
-
-<P>Later versions of Qhull may produce additional integers or reals.</P>
-
-<h3><A href="#format">»</a><a name="FS">FS - print sizes</a></h3>
-
-<p>The first line consists of the number of integers
-("0"). The second line consists of the number of reals
-("2"), followed by the total facet area, and the total
-volume. Later versions of Qhull may produce additional integers
-or reals.</p>
-
-<p>The total volume measures the volume of the intersection of
-the halfspaces defined by each facet. It is computed from the
-facet area. Both area and volume are approximations for
-non-simplicial facets. See option '<A href="#Fa">Fa </a>' for
-further notes. </p>
-
-<h3><A href="#format">»</a><a name="Ft">Ft - print triangulation</a></h3>
-
-<p>Prints a triangulation with added points for non-simplicial
-facets. The output is </p>
-
-<ul>
- <li>The first line is the dimension
- <li>The second line is the number of points, the number
- of facets, and the number of ridges.
- <li>All of the input points follow, one per line.
- <li>The centrums follow, one per non-simplicial facet
- <li>Then the facets follow as a list of point indices
- preceded by the number of points. The simplices are
- oriented. </li>
-</ul>
-
-<p>For convex hulls with simplicial facets, the output is the
-same as option '<A href="qh-opto.htm#o">o</a>'.</p>
-
-<p>The added points are the centrums of the non-simplicial
-facets. Except for large facets, the centrum is the average
-vertex coordinate projected to the facet's hyperplane. Large
-facets may use an old centrum to avoid recomputing the centrum
-after each merge. In either case, the centrum is clearly below
-neighboring facets. See <A href="qh-impre.htm">Precision issues</a>.
-</p>
-
-<p>The new simplices will not be clearly convex with their
-neighbors and they will not satisfy the Delaunay property. They
-may even have a flipped orientation. Use triangulated input ('<A
- href="qh-optq.htm#Qt">Qt</a>') for Delaunay triangulations.
-
-<p>For Delaunay triangulations with simplicial facets, the output is the
-same as option '<A href="qh-opto.htm#o">o</a>' without the lifted
-coordinate. Since 'Ft' is invalid for merged Delaunay facets, option
-'Ft' is not available for qdelaunay or qvoronoi. It may be used with
-joggled input ('<A href="qh-optq.htm#QJn" >QJ</a>') or triangulated output ('<A
- href="qh-optq.htm#Qt" >Qt</a>'), for example, rbox 10 c G 0.01 | qhull d QJ Ft</p>
-
-<p>If you add a point-at-infinity with '<A href="qh-optq.htm#Qz">Qz</a>',
-it is printed after the input sites and before any centrums. It
-will not be used in a Delaunay facet.</p>
-
-<h3><A href="#format">»</a><a name="Fv">Fv - print vertices for
-each facet</a></h3>
-
-<p>The first line is the number of facets. Then each facet is
-printed, one per line. Each line is the number of vertices
-followed by the corresponding point ids. Vertices are listed in
-the order they were added to the hull (the last one added is the
-first listed). Similar to option '<A href="qh-opto.htm#i">i</a>'.</p>
-
-<h3><A href="#format">»</a><a name="Fv2">Fv - print Voronoi
-diagram</a></h3>
-
-<p>With <A href="qvoronoi.htm" >qvoronoi</a>, 'Fv' prints the
-Voronoi diagram or furthest-site Voronoi diagram. The first line
-is the number of ridges. Then each ridge is printed, one per
-line. The first number is the count of indices. The second pair
-of indices indicates a pair of input sites. The remaining indices
-list the corresponding ridge of Voronoi vertices. Vertex 0 is the
-vertex-at-infinity. It indicates an unbounded ray. </p>
-
-<p>All vertices of a ridge are coplanar. If the ridge is
-unbounded, add the midpoint of the pair of input sites. The
-unbounded ray is directed from the Voronoi vertices to infinity. </p>
-
-<p>Use '<A href="qh-optf.htm#Fo2">Fo</a>' for separating
-hyperplanes of outer, unbounded regions. Use '<A
- href="qh-optf.htm#Fi2" >Fi</a>' for separating hyperplanes of
-inner, bounded regions. </p>
-
-<p>Option 'Fv' does not list ridges that require more than one
-midpoint. For example, the Voronoi diagram of cospherical points
-lists zero ridges (e.g., 'rbox 10 s | qvoronoi Fv Qz').
-Other examples are the Voronoi diagrams of a rectangular mesh
-(e.g., 'rbox 27 M1,0 | qvoronoi Fv') or a point set with
-a rectangular corner (e.g.,
-'rbox P4,4,4 P4,2,4 P2,4,4 P4,4,2 10 | qvoronoi Fv').
-Both cases miss unbounded rays at the corners.
-To determine these ridges, surround the points with a
-large cube (e.g., 'rbox 10 s c G2.0 | qvoronoi Fv Qz').
-Please report any other cases that are missed. If you
-can formally describe these cases or
-write code to handle them, please send email to <A
- href="mailto:qhull@qhull.org" >qhull@qhull.org</a>. </p>
-
-<h3><A href="#format">»</a><a name="FV">FV - print average
-vertex </a></h3>
-
-<p>The average vertex is the average of all vertex coordinates.
-It is an interior point for halfspace intersection. The first
-line is the dimension and "1"; the second line is the
-coordinates. For example,</p>
-
-<blockquote>
- <p>qconvex FV <A
- href="qh-opto.htm#n">n</a> | qhalf <A href="#Fp">Fp</a></p>
-</blockquote>
-
-<p>prints the extreme points of the original point set (roundoff
-included). </p>
-
-<h3><A href="#format">»</a><a name="Fx">Fx - print extreme
-points (vertices) of convex hulls and Delaunay triangulations</a></h3>
-
-<p>The first line is the number of points. The following lines
-give the index of the corresponding points. The first point is
-'0'. </p>
-
-<p>In 2-d, the extreme points (vertices) are listed in
-counterclockwise order (by qh_ORIENTclock in user.h). </p>
-
-<p>In 3-d and higher convex hulls, the extreme points (vertices)
-are sorted by index. This is the same order as option '<A
- href="qh-opto.htm#p" >p</a>' when it doesn't include coplanar or
-interior points. </p>
-
-<p>For Delaunay triangulations, 'Fx' lists the extreme
-points of the input sites (i.e., the vertices of their convex hull). The points
-are unordered. <!-- Navigation links --> </p>
-
-<hr>
-
-<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <A href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <A href="qh-quick.htm#programs">Programs</a>
-• <A href="qh-quick.htm#options">Options</a>
-• <A href="qh-opto.htm#output">Output</a>
-• <A href="qh-optf.htm#format">Formats</a>
-• <A href="qh-optg.htm#geomview">Geomview</a>
-• <A href="qh-optp.htm#print">Print</a>
-• <A href="qh-optq.htm#qhull">Qhull</a>
-• <A href="qh-optc.htm#prec">Precision</a>
-• <A href="qh-optt.htm#trace">Trace</a></p><!-- GC common information -->
-<hr>
-
-<p><a href="http://www.geom.uiuc.edu/"><IMG align=middle
- height=40 src="qh--geom.gif" width=40 ></a><i>The Geometry Center
-Home Page </i></p>
-
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created:
-Sept. 25, 1995 --- <!-- hhmts start -->Last modified: see top
-<!-- hhmts end --> </p>
-</body>
-</html>
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qh-optg.htm b/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qh-optg.htm
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--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qh-optg.htm
+++ /dev/null
@@ -1,271 +0,0 @@
-<html>
-
-<head>
-<title>Qhull Geomview options (G)</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-
-<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a></p>
-
-<hr>
-<!-- Main text of document -->
-
-<h1><a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
-src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
-height="100"></a> Qhull Geomview options (G)</h1>
-
-This section lists the Geomview options for Qhull. These options are
-indicated by 'G' followed by a letter. See
-<a href="qh-opto.htm#output">Output</a>, <a href="qh-optp.htm#print">Print</a>,
-and <a href="qh-optf.htm#format">Format</a> for other output options.
-
-
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-
-<hr>
-
-<p><a href="index.htm#TOC">»</a> <a href="qh-quick.htm#programs">Programs</a>
-<a name="geomview">•</a> <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a></p>
-
-<h2>Geomview output options</h2>
-
-<p><a href="http://www.geomview.org">Geomview</a> is the graphical
-viewer for visualizing Qhull output in 2-d, 3-d and 4-d.</p>
-
-<p>Geomview displays each facet of the convex hull. The color of
-a facet is determined by the coefficients of the facet's normal
-equation. For imprecise hulls, Geomview displays the inner and
-outer hull. Geomview can also display points, ridges, vertices,
-coplanar points, and facet intersections. </p>
-
-<p>For 2-d Delaunay triangulations, Geomview displays the
-corresponding paraboloid. Geomview displays the 2-d Voronoi
-diagram. For halfspace intersections, it displays the
-dual convex hull. </p>
-
-<dl compact>
- <dt> </dt>
- <dd><b>General</b></dd>
- <dt><a href="#G">G</a></dt>
- <dd>display Geomview output</dd>
- <dt><a href="#Gt">Gt</a></dt>
- <dd>display transparent 3-d Delaunay triangulation</dd>
- <dt><a href="#GDn">GDn</a></dt>
- <dd>drop dimension n in 3-d and 4-d output </dd>
-
- <dt> </dt>
- <dt> </dt>
- <dd><b>Specific</b></dd>
- <dt><a href="#Ga">Ga</a></dt>
- <dd>display all points as dots</dd>
- <dt><a href="#Gc">Gc</a></dt>
- <dd>display centrums (2-d, 3-d)</dd>
- <dt><a href="#Gp">Gp</a></dt>
- <dd>display coplanar points and vertices as radii</dd>
- <dt><a href="#Gh">Gh</a></dt>
- <dd>display hyperplane intersections</dd>
- <dt><a href="#Gi">Gi</a></dt>
- <dd>display inner planes only (2-d, 3-d)</dd>
- <dt><a href="#Go">Go</a></dt>
- <dd>display outer planes only (2-d, 3-d)</dd>
- <dt><a href="#Gr">Gr</a></dt>
- <dd>display ridges (3-d)</dd>
- <dt><a href="#Gv">Gv</a></dt>
- <dd>display vertices as spheres</dd>
- <dt><a href="#Gn">Gn</a></dt>
- <dd>do not display planes</dd>
-
-</dl>
-
-<hr>
-
-<h3><a href="#geomview">»</a><a name="G">G - produce output for
-viewing with Geomview</a></h3>
-
-<p>By default, option 'G' displays edges in 2-d, outer planes in
-3-d, and ridges in 4-d.</p>
-
-<p>A ridge can be explicit or implicit. An explicit ridge is a <i>(d-1)</i>-dimensional
-simplex between two facets. In 4-d, the explicit ridges are
-triangles. An implicit ridge is the topological intersection of
-two neighboring facets. It is the union of explicit ridges.</p>
-
-<p>For non-simplicial 4-d facets, the explicit ridges can be
-quite complex. When displaying a ridge in 4-d, Qhull projects the
-ridge's vertices to one of its facets' hyperplanes. Use '<a
-href="#Gh">Gh</a>' to project ridges to the intersection of both
-hyperplanes. This usually results in a cleaner display. </p>
-
-<p>For 2-d Delaunay triangulations, Geomview displays the
-corresponding paraboloid. Geomview displays the 2-d Voronoi
-diagram. For halfspace intersections, it displays the
-dual convex hull.
-
-<h3><a href="#geomview">»</a><a name="Ga">Ga - display all
-points as dots </a></h3>
-
-<p>Each input point is displayed as a green dot.</p>
-
-<h3><a href="#geomview">»</a><a name="Gc">Gc - display centrums
-(3-d) </a></h3>
-
-<p>The centrum is defined by a green radius sitting on a blue
-plane. The plane corresponds to the facet's hyperplane. If you
-sight along a facet's hyperplane, you will see that all
-neighboring centrums are below the facet. The radius is defined
-by '<a href="qh-optc.htm#Cn">C-n</a>' or '<a
-href="qh-optc.htm#Cn2">Cn</a>'.</p>
-
-<h3><a href="#geomview">»</a><a name="GDn">GDn - drop dimension
-n in 3-d and 4-d output </a></h3>
-
-<p>The result is a 2-d or 3-d object. In 4-d, this corresponds to
-viewing the 4-d object from the nth axis without perspective.
-It's best to view 4-d objects in pieces. Use the '<a
-href="qh-optp.htm#Pdk">Pdk</a>' '<a href="qh-optp.htm#Pg">Pg</a>'
-'<a href="qh-optp.htm#PG">PG</a>' '<a href="qh-optq.htm#QGn">QGn</a>'
-and '<a href="qh-optq.htm#QVn">QVn</a>' options to select a few
-facets. If one of the facets is perpendicular to an axis, then
-projecting along that axis will show the facet exactly as it is
-in 4-d. If you generate many facets, use Geomview's <tt>ginsu</tt>
-module to view the interior</p>
-
-<p>To view multiple 4-d dimensions at once, output the object
-without 'GDn' and read it with Geomview's <tt>ndview</tt>. As you
-rotate the object in one set of dimensions, you can see how it
-changes in other sets of dimensions.</p>
-
-<p>For additional control over 4-d objects, output the object
-without 'GDn' and read it with Geomview's <tt>4dview</tt>. You
-can slice the object along any 4-d plane. You can also flip the
-halfspace that's deleted when slicing. By combining these
-features, you can get some interesting cross sections.</p>
-
-<h3><a href="#geomview">»</a><a name="Gh">Gh - display
-hyperplane intersections (3-d, 4-d)</a></h3>
-
-<p>In 3-d, the intersection is a black line. It lies on two
-neighboring hyperplanes, c.f., the blue squares associated with
-centrums ('<a href="#Gc">Gc </a>'). In 4-d, the ridges are
-projected to the intersection of both hyperplanes. If you turn on
-edges (Geomview's 'appearances' menu), each triangle corresponds
-to one ridge. The ridges may overlap each other.</p>
-
-<h3><a href="#geomview">»</a><a name="Gi">Gi - display inner
-planes only (2-d, 3-d)</a></h3>
-
-<p>The inner plane of a facet is below all of its vertices. It is
-parallel to the facet's hyperplane. The inner plane's color is
-the opposite of the outer plane's color, i.e., <i>[1-r,1-g,1-b] </i>.
-Its edges are determined by the vertices.</p>
-
-<h3><a href="#geomview">»</a><a name="Gn">Gn - do not display
-planes </a></h3>
-
-<p>By default, Geomview displays the precise plane (no merging)
-or both inner and output planes (if merging). If merging,
-Geomview does not display the inner plane if the the difference
-between inner and outer is too small.</p>
-
-<h3><a href="#geomview">»</a><a name="Go">Go - display outer
-planes only (2-d, 3-d)</a></h3>
-
-<p>The outer plane of a facet is above all input points. It is
-parallel to the facet's hyperplane. Its color is determined by
-the facet's normal, and its edges are determined by the vertices.</p>
-
-<h3><a href="#geomview">»</a><a name="Gp">Gp - display coplanar
-points and vertices as radii </a></h3>
-
-<p>Coplanar points ('<a href="qh-optq.htm#Qc">Qc</a>'), interior
-points ('<a href="qh-optq.htm#Qi">Qi</a>'), outside points ('<a
-href="qh-optt.htm#TCn">TCn</a>' or '<a href="qh-optt.htm#TVn">TVn</a>'),
-and vertices are displayed as red and yellow radii. The radii are
-perpendicular to the corresponding facet. Vertices are aligned
-with an interior point. The radii define a ball which corresponds
-to the imprecision of the point. The imprecision is the maximum
-of the roundoff error, the centrum radius, and <i>maxcoord * (1 -
-</i><a href="qh-optc.htm#An"><i>A-n</i></a><i>)</i>. It is at
-least 1/20'th of the maximum coordinate, and ignores post merging
-if pre-merging is done.</p>
-
-<p>If '<a href="qh-optg.htm#Gv">Gv</a>' (print vertices as
-spheres) is also selected, option 'Gp' displays coplanar
-points as radii. Select options <a href="qh-optq.htm#Qc">Qc</a>'
-and/or '<a href="qh-optq.htm#Qi">Qi</a>'. Options 'Qc Gpv' displays
-coplanar points while 'Qci Gpv' displays coplanar and interior
-points. Option 'Qc' is automatically selected if 'Qi' is not
-selected with options 'Gpv'.
-
-<h3><a href="#geomview">»</a><a name="Gr">Gr - display ridges
-(3-d) </a></h3>
-
-<p>A ridge connects the two vertices that are shared by
-neighboring facets. It is displayed in green. A ridge is the
-topological edge between two facets while the hyperplane
-intersection is the geometric edge between two facets. Ridges are
-always displayed in 4-d.</p>
-
-<h3><a href="#geomview">»</a><a name="Gt">Gt - transparent 3-d
-Delaunay </a></h3>
-
-<p>A 3-d Delaunay triangulation looks like a convex hull with
-interior facets. Option 'Gt' removes the outside ridges to reveal
-the outermost facets. It automatically sets options '<a
-href="#Gr">Gr</a>' and '<a href="#GDn">GDn</a>'. See example <a
-href="qh-eg.htm#17f">eg.17f.delaunay.3</a>.</p>
-
-<h3><a href="#geomview">»</a><a name="Gv">Gv - display vertices
-as spheres (2-d, 3-d)</a></h3>
-
-<p>The radius of the sphere corresponds to the imprecision of the
-data. See '<a href="#Gp">Gp</a>' for determining the radius.</p>
-
-<!-- Navigation links -->
-
-<hr>
-
-<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a></p>
-<!-- GC common information -->
-
-<hr>
-
-<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
-align="middle" width="40" height="40"></a><i>The Geometry Center
-Home Page </i></p>
-
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qh-opto.htm b/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qh-opto.htm
deleted file mode 100644
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--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qh-opto.htm
+++ /dev/null
@@ -1,343 +0,0 @@
-<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
-<html>
-
-<head>
-<title>Qhull output options</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a></p>
-
-<hr>
-<!-- Main text of document -->
-<h1><a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
-src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
-height="100"></a> Qhull output options</h1>
-
-<p>This section lists the output options for Qhull. These options
-are indicated by lower case characters. See <a
-href="qh-optf.htm#format">Formats</a>, <a
-href="qh-optp.htm#print">Print</a>, and <a
-href="qh-optg.htm#geomview">Geomview</a> for other output
-options. </p>
-
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-
-<hr>
-
-<p><a href="index.htm#TOC">»</a> <a href="qh-quick.htm#programs">Programs</a>
-<a name="output">•</a> <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a></p>
-
-<h2>Output options</h2>
-
-<p>Qhull prints its output to standard out. All output is printed
-text. The default output is a summary (option '<a href="#s">s</a>').
-Other outputs may be specified as follows. </p>
-
-<dl compact>
- <dt><a href="#f">f</a></dt>
- <dd>print all fields of all facets</dd>
- <dt><a href="#n">n</a></dt>
- <dd>print hyperplane normals with offsets</dd>
- <dt><a href="#m">m</a></dt>
- <dd>print Mathematica output (2-d and 3-d)</dd>
- <dt><a href="#o">o</a></dt>
- <dd>print OFF file format (dim, points and facets)</dd>
- <dt><a href="#s">s</a></dt>
- <dd>print summary to stderr</dd>
- <dt><a href="#p">p</a></dt>
- <dd>print vertex and point coordinates</dd>
- <dt><a href="#i">i</a></dt>
- <dd>print vertices incident to each facet </dd>
- <dt> </dt>
- <dt> </dt>
- <dd><b>Related options</b></dd>
- <dt><a href="qh-optf.htm#format">F</a></dt>
- <dd>additional input/output formats</dd>
- <dt><a href="qh-optg.htm#geomview">G</a></dt>
- <dd>Geomview output</dd>
- <dt><a href="qh-optp.htm#print">P</a></dt>
- <dd>Print options</dd>
- <dt><a href="qh-optf.htm#Ft">Ft</a></dt>
- <dd>print triangulation with added points</dd>
- <dt> </dt>
-</dl>
-
-<hr>
-
-<h3><a href="#output">»</a><a name="f">f - print all fields of
-all facets </a></h3>
-
-<p>Print <a href=../src/qhull.h#facetT>all fields</a> of all facets.
-The facet is the primary <a href=index.htm#structure>data structure</a> for
-Qhull.
-
-<p>Option 'f' is for
-debugging. Most of the fields are available via the '<a
-href="qh-optf.htm#format">F</a>' options. If you need specialized
-information from Qhull, you can use the <a
-href="qh-in.htm#library">Qhull library</a>.</p>
-
-<p>Use the '<a href="qh-optf.htm#FF">FF</a>' option to print the
-facets but not the ridges. </p>
-
-<h3><a href="#output">»</a><a name="i">i - print vertices
-incident to each facet </a></h3>
-
-<p>The first line is the number of facets. The remaining lines
-list the vertices for each facet, one facet per line. The indices
-are 0-relative indices of the corresponding input points. The
-facets are oriented. Option '<a href="qh-optf.htm#Fv">Fv</a>'
-displays an unoriented list of vertices with a vertex count per
-line. Options '<a href="qh-opto.htm#o">o</a>' and '<a
-href="qh-optf.htm#Ft">Ft</a>' displays coordinates for each
-vertex prior to the vertices for each facet. </p>
-
-<p>Simplicial facets (e.g., triangles in 3-d) consist of <i>d</i>
-vertices. Non-simplicial facets in 3-d consist of 4 or more
-vertices. For example, a facet of a cube consists of 4 vertices.</p>
-
-<p>For 4-d and higher convex hulls and 3-d and higher Delaunay
-triangulations, <i>d</i> vertices are listed for all facets. A
-non-simplicial facet is triangulated with its centrum and each
-ridge. The index of the centrum is higher than any input point.
-Use option '<a href="qh-optf.htm#Fv">Fv</a>' to list the vertices
-of non-simplicial facets as is. Use option '<a
-href="qh-optf.htm#Ft">Ft</a>' to print the coordinates of the
-centrums as well as those of the input points. </p>
-
-<h3><a href="#output">»</a><a name="m">m - print Mathematica
-output </a></h3>
-
-<p>Qhull writes a Mathematica file for 2-d and 3-d convex hulls,
-2-d and 3-d halfspace intersections,
-and 2-d Delaunay triangulations. Qhull produces a list of
-objects that you can assign to a variable in Mathematica, for
-example: "<tt>list= << <outputfilename> </tt>".
-If the object is 2-d, it can be visualized by "<tt>Show[Graphics[list]]
-</tt>". For 3-d objects the command is "<tt>Show[Graphics3D[list]]
-</tt>". Now the object can be manipulated by commands of the
-form <tt>"Show[%, <parametername> ->
-<newvalue>]</tt>". </p>
-
-<p>For Delaunay triangulation orthogonal projection is better.
-This can be specified, for example, by "<tt>BoxRatios:
-Show[%, BoxRatios -> {1, 1, 1e-8}]</tt>". To see the
-meaningful side of the 3-d object used to visualize 2-d Delaunay,
-you need to change the viewpoint: "<tt>Show[%, ViewPoint
--> {0, 0, -1}]</tt>". By specifying different viewpoints
-you can slowly rotate objects. </p>
-
-<p>For halfspace intersections, Qhull produces the dual
-convex hull.
-
-<p>See <a href="qh-faq.htm#math">Is Qhull available for Mathematica?</a>
-for URLs.
-
-<h3><a href="#output">»</a><a name="n">n - print hyperplane
-normals with offsets </a></h3>
-
-<p>The first line is the dimension plus one. The second line is
-the number of facets. The remaining lines are the normals for
-each facet, one normal per line. The facet's offset follows its
-normal coefficients.</p>
-
-<p>The normals point outward, i.e., the convex hull satisfies <i>Ax
-<= -b </i>where <i>A</i> is the matrix of coefficients and <i>b</i>
-is the vector of offsets.</p>
-
-<p>If cdd output is specified ('<a href="qh-optf.htm#FD">FD</a>'),
-Qhull prints the command line, the keyword "begin", the
-number of facets, the dimension (plus one), the keyword
-"real", and the normals for each facet. The facet's
-negative offset precedes its normal coefficients (i.e., if the
-origin is an interior point, the offset is positive). Qhull ends
-the output with the keyword "end". </p>
-
-<h3><a href="#output">»</a><a name="o">o - print OFF file format
-</a></h3>
-
-<p>The output is: </p>
-
-<ul>
- <li>The first line is the dimension </li>
- <li>The second line is the number of points, the number of
- facets, and the number of ridges. </li>
- <li>All of the input points follow, one per line. </li>
- <li>Then Qhull prints the vertices for each facet. Each facet
- is on a separate line. The first number is the number of
- vertices. The remainder is the indices of the
- corresponding points. The vertices are oriented in 2-d,
- 3-d, and in simplicial facets. </li>
-</ul>
-
-<p>Option '<a href="qh-optf.htm#Ft">Ft</a>' prints the same
-information with added points for non-simplicial facets.</p>
-
-<p>Option '<a href="qh-opto.htm#i">i</a>' displays vertices
-without the point coordinates. Option '<a href="qh-opto.htm#p">p</a>'
-displays the point coordinates without vertex and facet information.</p>
-
-<p>In 3-d, Geomview can load the file directly if you delete the
-first line (e.g., by piping through '<tt>tail +2</tt>').</p>
-
-<p>For Voronoi diagrams (<a href=qvoronoi.htm>qvoronoi</a>), option
-'o' prints Voronoi vertices and Voronoi regions instead of input
-points and facets. The first vertex is the infinity vertex
-[-10.101, -10.101, ...]. Then, option 'o' lists the vertices in
-the Voronoi region for each input site. The regions appear in
-site ID order. In 2-d, the vertices of a Voronoi region are
-sorted by adjacency (non-oriented). In 3-d and higher, the
-Voronoi vertices are sorted by index. See the '<a
-href="qh-optf.htm#FN">FN</a>' option for listing Voronoi regions
-without listing Voronoi vertices.</p>
-
-<p>If you are using the Qhull library, options 'v o' have the
-side effect of reordering the neighbors for a vertex.</p>
-
-<h3><a href="#output">»</a><a name="p">p - print vertex and
-point coordinates </a></h3>
-
-<p>The first line is the dimension. The second line is the number
-of vertices. The remaining lines are the vertices, one vertex per
-line. A vertex consists of its point coordinates</p>
-
-<p>With the '<a href="qh-optg.htm#Gc">Gc</a>' and '<a
-href="qh-optg.htm#Gi">Gi</a>' options, option 'p' also prints
-coplanar and interior points respectively.</p>
-
-<p>For <a href=qvoronoi.htm>qvoronoi</a>, it prints the
-coordinates of each Voronoi vertex.</p>
-
-<p>For <a href=qdelaun.htm>qdelaunay</a>, it prints the
-input sites as lifted to a paraboloid. For <a href=qhalf.htm>qhalf</a>
-it prints the dual points. For both, option 'p' is the same as the first
-section of option '<a href="qh-opto.htm#o">o</a>'.</p>
-
-<p>Use '<a href="qh-optf.htm#Fx">Fx</a>' to list the point ids of
-the extreme points (i.e., vertices). </p>
-
-<p>If a subset of the facets is selected ('<a
-href="qh-optp.htm#Pdk">Pdk</a>', '<a href="qh-optp.htm#PDk">PDk</a>',
-'<a href="qh-optp.htm#Pg">Pg</a>' options), option 'p' only
-prints vertices and points associated with those facets.</p>
-
-<p>If cdd-output format is selected ('<a href="qh-optf.htm#FD">FD</a>'),
-the first line is "begin". The second line is the
-number of vertices, the dimension plus one, and "real".
-The vertices follow with a leading "1". Output ends
-with "end". </p>
-
-<h3><a href="#output">»</a><a name="s">s - print summary to
-stderr </a></h3>
-
-<p>The default output of Qhull is a summary to stderr. Options '<a
-href="qh-optf.htm#FS">FS</a>' and '<a href="qh-optf.htm#Fs">Fs</a>'
-produce the same information for programs. <b>Note</b>: Windows 95 and 98
-treats stderr the same as stdout. Use option '<a href="qh-optt.htm#TO">TO file</a>' to separate
-stderr and stdout.</p>
-
-<p>The summary lists the number of input points, the dimension,
-the number of vertices in the convex hull, and the number of
-facets in the convex hull. It lists the number of selected
-("good") facets for options '<a href="qh-optp.htm#Pg">Pg</a>',
-'<a href="qh-optp.htm#Pdk">Pdk</a>', <a href=qdelaun.htm>qdelaunay</a>,
-or <a href=qvoronoi.htm>qvoronoi</a> (Delaunay triangulations only
-use the lower half of a convex hull). It lists the number of
-coplanar points. For Delaunay triangulations without '<a
-href="qh-optq.htm#Qc">Qc</a>', it lists the total number of
-coplanar points. It lists the number of simplicial facets in
-the output.</p>
-
-<p>The terminology depends on the output structure. </p>
-
-<p>The summary lists these statistics:</p>
-
-<ul>
- <li>number of points processed by Qhull </li>
- <li>number of hyperplanes created</li>
- <li>number of distance tests (not counting statistics,
- summary, and checking) </li>
- <li>number of merged facets (if any)</li>
- <li>number of distance tests for merging (if any)</li>
- <li>CPU seconds to compute the hull</li>
- <li>the maximum joggle for '<a href="qh-optq.htm#QJn">QJ</a>'<br>
- or, the probability of precision errors for '<a
- href="qh-optq.htm#QJn">QJ</a> <a href="qh-optt.htm#TRn">TRn</a>'
- </li>
- <li>total area and volume (if computed, see '<a
- href="qh-optf.htm#FS">FS</a>' '<a href="qh-optf.htm#FA">FA</a>'
- '<a href="qh-optf.htm#Fa">Fa</a>' '<a
- href="qh-optp.htm#PAn">PAn</a>')</li>
- <li>max. distance of a point above a facet (if non-zero)</li>
- <li>max. distance of a vertex below a facet (if non-zero)</li>
-</ul>
-
-<p>The statistics include intermediate hulls. For example 'rbox d
-D4 | qhull' reports merged facets even though the final hull is
-simplicial. </p>
-
-<p>Qhull starts counting CPU seconds after it has read and
-projected the input points. It stops counting before producing
-output. In the code, CPU seconds measures the execution time of
-function qhull() in <tt>qhull.c</tt>. If the number of CPU
-seconds is clearly wrong, check qh_SECticks in <tt>user.h</tt>. </p>
-
-<p>The last two figures measure the maximum distance from a point
-or vertex to a facet. They are not printed if less than roundoff
-or if not merging. They account for roundoff error in computing
-the distance (c.f., option '<a href="qh-optc.htm#Rn">Rn</a>').
-Use '<a href="qh-optf.htm#Fs">Fs</a>' to report the maximum outer
-and inner plane. </p>
-
-<p>A number may appear in parentheses after the maximum distance
-(e.g., 2.1x). It is the ratio between the maximum distance and
-the worst-case distance due to merging two simplicial facets. It
-should be small for 2-d, 3-d, and 4-d, and for higher dimensions
-with '<a href="qh-optq.htm#Qx">Qx</a>'. It is not printed if less
-than 0.05. </p>
-<!-- Navigation links -->
-<hr>
-
-<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a></p>
-<!-- GC common information -->
-<hr>
-
-<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
-align="middle" width="40" height="40"></a><i>The Geometry Center
-Home Page </i></p>
-
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qh-optp.htm b/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qh-optp.htm
deleted file mode 100644
index fccb87bccb1f2f621048d8e6c111ab41c88fd35b..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qh-optp.htm
+++ /dev/null
@@ -1,249 +0,0 @@
-<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
-<html>
-
-<head>
-<title>Qhull print options (P)</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a></p>
-
-<hr>
-<!-- Main text of document -->
-<h1><a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
-src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
-height="100"></a> Qhull print options (P)</h1>
-
-This section lists the print options for Qhull. These options are
-indicated by 'P' followed by a letter. See
-<a href="qh-opto.htm#output">Output</a>, <a href="qh-optg.htm#geomview">Geomview</a>,
-and <a href="qh-optf.htm#format">Format</a> for other output options.
-
-
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-
-<hr>
-
-<p><a href="index.htm#TOC">»</a> <a href="qh-quick.htm#programs">Programs</a>
-<a name="print">•</a> <a href="qh-quick.htm#options">Options</a> • <a
-href="qh-opto.htm#output">Output</a> • <a
-href="qh-optf.htm#format">Formats</a> • <a
-href="qh-optg.htm#geomview">Geomview</a> • <a href="#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a> • <a
-href="qh-optc.htm#prec">Precision</a> • <a
-href="qh-optt.htm#trace">Trace</a></p>
-
-<h2>Print options</h2>
-<blockquote>
-<dl compact>
- <dt> </dt>
- <dd><b>General</b></dd>
- <dt><a href="#Pp">Pp</a></dt>
- <dd>do not report precision problems </dd>
- <dt><a href="#Po">Po</a></dt>
- <dd>force output despite precision problems</dd>
- <dt><a href="#Po2">Po</a></dt>
- <dd>if error, output neighborhood of facet</dd>
- <dt> </dt>
- <dt> </dt>
- <dd><b>Select</b></dd>
- <dt><a href="#Pdk">Pdk:n</a></dt>
- <dd>print facets with normal[k] >= n (default 0.0)</dd>
- <dt><a href="#PDk">PDk:n</a></dt>
- <dd>print facets with normal[k] <= n </dd>
- <dt><a href="#PFn">PFn</a></dt>
- <dd>print facets whose area is at least n</dd>
- <dt><a href="#Pg">Pg</a></dt>
- <dd>print good facets only (needs '<a href="qh-optq.htm#QGn">QGn</a>'
- or '<a href="qh-optq.htm#QVn">QVn </a>')</dd>
- <dt><a href="#PMn">PMn</a></dt>
- <dd>print n facets with most merges</dd>
- <dt><a href="#PAn">PAn</a></dt>
- <dd>print n largest facets by area</dd>
- <dt><a href="#PG">PG</a></dt>
- <dd>print neighbors of good facets</dd>
-</dl>
-</blockquote>
-<hr>
-
-<h3><a href="#print">»</a><a name="PAn">PAn - keep n largest
-facets by area</a></h3>
-
-<p>The <i>n</i> largest facets are marked good for printing. This
-may be useful for <a href="qh-impre.htm#approximate">approximating
-a hull</a>. Unless '<a href="#PG">PG</a>' is set, '<a href="#Pg">Pg</a>'
-is automatically set. </p>
-
-<h3><a href="#print">»</a><a name="Pdk">Pdk:n - print facet if
-normal[k] >= n </a></h3>
-
-<p>For a given output, print only those facets with <i>normal[k] >= n</i>
-and <i>drop</i> the others. For example, 'Pd0:0.5' prints facets with <i>normal[0]
->= 0.5 </i>. The default value of <i>n</i> is zero. For
-example in 3-d, 'Pd0d1d2' prints facets in the positive octant.
-<p>
-If no facets match, the closest facet is returned.</p>
-<p>
-On Windows 95, do not combine multiple options. A 'd' is considered
-part of a number. For example, use 'Pd0:0.5 Pd1:0.5' instead of
-'Pd0:0.5d1:0.5'.
-
-<h3><a href="#print">»</a><a name="PDk">PDk:n - print facet if
-normal[k] <= n</a></h3>
-
-<p>For a given output, print only those facets with <i>normal[k] <= n</i>
-and <i>drop</i> the others.
-For example, 'PD0:0.5' prints facets with <i>normal[0]
-<= 0.5 </i>. The default value of <i>n</i> is zero. For
-example in 3-d, 'PD0D1D2' displays facets in the negative octant.
-<p>
-If no facets match, the closest facet is returned.</p>
-
-<p>In 2-d, 'd G PD2' displays the Delaunay triangulation instead
-of the corresponding paraboloid. </p>
-
-<p>Be careful of placing 'Dk' or 'dk' immediately after a real
-number. Some compilers treat the 'D' as a double precision
-exponent. </p>
-
-<h3><a href="#print">»</a><a name="PFn">PFn - keep facets whose
-area is at least n</a></h3>
-
-<p>The facets with area at least <i>n</i> are marked good for
-printing. This may be useful for <a
-href="qh-impre.htm#approximate">approximating a hull</a>. Unless
-'<a href="#PG">PG</a>' is set, '<a href="#Pg">Pg</a>' is
-automatically set. </p>
-
-<h3><a href="#print">»</a><a name="Pg">Pg - print good facets </a></h3>
-
-<p>Qhull can mark facets as "good". This is used to</p>
-
-<ul>
- <li>mark the lower convex hull for Delaunay triangulations
- and Voronoi diagrams</li>
- <li>mark the facets that are visible from a point (the '<a
- href="qh-optq.htm#QGn">QGn </a>' option)</li>
- <li>mark the facets that contain a point (the '<a
- href="qh-optq.htm#QVn">QVn</a>' option).</li>
- <li>indicate facets with a large enough area (options '<a
- href="#PAn">PAn</a>' and '<a href="#PFn">PFn</a>')</li>
-</ul>
-
-<p>Option '<a href="#Pg">Pg</a>' only prints good facets that
-also meet '<a href="#Pdk">Pdk</a>' and '<a href="#PDk">PDk</a>'
-options. It is automatically set for options '<a href="#PAn">PAn</a>',
-'<a href="#PFn">PFn </a>', '<a href="qh-optq.htm#QGn">QGn</a>',
-and '<a href="qh-optq.htm#QVn">QVn</a>'.</p>
-
-<h3><a href="#print">»</a><a name="PG">PG - print neighbors of
-good facets</a></h3>
-
-<p>Option 'PG' can be used with or without option '<a href="#Pg">Pg</a>'
-to print the neighbors of good facets. For example, options '<a
-href="qh-optq.htm#QGn">QGn</a>' and '<a href="qh-optq.htm#QVn">QVn</a>'
-print the horizon facets for point <i>n. </i></p>
-
-<h3><a href="#print">»</a><a name="PMn">PMn - keep n facets with
-most merges</a></h3>
-
-<p>The n facets with the most merges are marked good for
-printing. This may be useful for <a
-href="qh-impre.htm#approximate">approximating a hull</a>. Unless
-'<a href="#PG">PG</a>' is set, '<a href="#Pg">Pg</a>' is
-automatically set. </p>
-
-<p>Use option '<a href="qh-optf.htm#Fm">Fm</a>' to print merges
-per facet.
-
-<h3><a href="#print">»</a><a name="Po">Po - force output despite
-precision problems</a></h3>
-
-<p>Use options 'Po' and '<a href="qh-optq.htm#Q0">Q0</a>' if you
-can not merge facets, triangulate the output ('<a href="qh-optq.htm#Qt">Qt</a>'),
-or joggle the input (<a href="qh-optq.htm#QJn">QJ</a>).
-
-<p>Option 'Po' can not force output when
-duplicate ridges or duplicate facets occur. It may produce
-erroneous results. For these reasons, merged facets, joggled input, or <a
-href="qh-impre.htm#exact">exact arithmetic</a> are better.</p>
-
-<p>If you need a simplicial Delaunay triangulation, use
-joggled input '<a href="qh-optq.htm#QJn">QJ</a>' or triangulated
-output '<a
-href="qh-optf.htm#Ft">Ft</a>'.
-
-<p>Option 'Po' may be used without '<a href="qh-optq.htm#Q0">Q0</a>'
-to remove some steps from Qhull or to output the neighborhood of
-an error.</p>
-
-<p>Option 'Po' may be used with option '<a href="qh-optq.htm#Q5">Q5</a>')
-to skip qh_check_maxout (i.e., do not determine the maximum outside distance).
-This can save a significant amount of time.
-
-<p>If option 'Po' is used,</p>
-
-<ul>
- <li>most precision errors allow Qhull to continue. </li>
- <li>verify ('<a href="qh-optt.htm#Tv">Tv</a>') does not check
- coplanar points.</li>
- <li>points are not partitioned into flipped facets and a
- flipped facet is always visible to a point. This may
- delete flipped facets from the output. </li>
-</ul>
-
-<h3><a href="#print">»</a><a name="Po2">Po - if error, output
-neighborhood of facet</a></h3>
-
-<p>If an error occurs before the completion of Qhull and tracing
-is not active, 'Po' outputs a neighborhood of the erroneous
-facets (if any). It uses the current output options.</p>
-
-<p>See '<a href="qh-optp.htm#Po">Po</a>' - force output despite
-precision problems.
-
-<h3><a href="#print">»</a><a name="Pp">Pp - do not report
-precision problems </a></h3>
-
-<p>With option 'Pp', Qhull does not print statistics about
-precision problems, and it removes some of the warnings. It
-removes the narrow hull warning.</p>
-
-<!-- Navigation links -->
-<hr>
-
-<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a></p>
-<!-- GC common information -->
-<hr>
-
-<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
-align="middle" width="40" height="40"></a><i>The Geometry Center
-Home Page </i></p>
-
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qh-optq.htm b/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qh-optq.htm
deleted file mode 100644
index 69dbc0a4a941b76b890d85bc2c97974e24c8fea4..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qh-optq.htm
+++ /dev/null
@@ -1,696 +0,0 @@
-<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
-<html>
-
-<head>
-<title>Qhull control options (Q)</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a></p>
-
-<hr>
-<!-- Main text of document -->
-<h1><a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
-src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
-height="100"></a> Qhull control options (Q)</h1>
-
-<p>This section lists the control options for Qhull. These
-options are indicated by 'Q' followed by a letter. </p>
-
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-
-<hr>
-
-<p><a href="index.htm#TOC">»</a> <a href="qh-quick.htm#programs">Programs</a>
-<a name="qhull">•</a> <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a></p>
-
-<h2>Qhull control options</h2>
-
-<dl compact>
- <dt> </dt>
- <dd><b>General</b></dd>
- <dt><a href="#Qu">Qu</a></dt>
- <dd>compute upper hull for furthest-site Delaunay
- triangulation </dd>
- <dt><a href="#Qc">Qc</a></dt>
- <dd>keep coplanar points with nearest facet</dd>
- <dt><a href="#Qi">Qi</a></dt>
- <dd>keep interior points with nearest facet</dd>
- <dt><a href="#QJn">QJ</a></dt>
- <dd>joggled input to avoid precision problems</dd>
- <dt><a href="#Qt">Qt</a></dt>
- <dd>triangulated output</dd>
- <dt> </dt>
- <dt> </dt>
- <dd><b>Precision handling</b></dd>
- <dt><a href="#Qz">Qz</a></dt>
- <dd>add a point-at-infinity for Delaunay triangulations</dd>
- <dt><a href="#Qx">Qx</a></dt>
- <dd>exact pre-merges (allows coplanar facets)</dd>
- <dt><a href="#Qs">Qs</a></dt>
- <dd>search all points for the initial simplex</dd>
- <dt><a href="#Qbb">Qbb</a></dt>
- <dd>scale last coordinate to [0,m] for Delaunay</dd>
- <dt><a href="#Qv">Qv</a></dt>
- <dd>test vertex neighbors for convexity</dd>
- <dt> </dt>
- <dt> </dt>
- <dd><b>Transform input</b></dd>
- <dt><a href="#Qb0">Qbk:0Bk:0</a></dt>
- <dd>drop dimension k from input</dd>
- <dt><a href="#QRn">QRn</a></dt>
- <dd>random rotation (n=seed, n=0 time, n=-1 time/no rotate)</dd>
- <dt><a href="#Qbk">Qbk:n</a></dt>
- <dd>scale coord[k] to low bound of n (default -0.5)</dd>
- <dt><a href="#QBk">QBk:n</a></dt>
- <dd>scale coord[k] to upper bound of n (default 0.5)</dd>
- <dt><a href="#QbB">QbB</a></dt>
- <dd>scale input to fit the unit cube</dd>
- <dt> </dt>
- <dt> </dt>
- <dd><b>Select facets</b></dd>
- <dt><a href="#QVn">QVn</a></dt>
- <dd>good facet if it includes point n, -n if not</dd>
- <dt><a href="#QGn">QGn</a></dt>
- <dd>good facet if visible from point n, -n for not visible</dd>
- <dt><a href="#Qg">Qg</a></dt>
- <dd>only build good facets (needs '<a href="#QGn">QGn</a>', '<a
- href="#QVn">QVn </a>', or '<a href="qh-optp.htm#Pdk">Pdk</a>')</dd>
- <dt> </dt>
- <dt> </dt>
- <dd><b>Experimental</b></dd>
- <dt><a href="#Q4">Q4</a></dt>
- <dd>avoid merging old facets into new facets</dd>
- <dt><a href="#Q5">Q5</a></dt>
- <dd>do not correct outer planes at end of qhull</dd>
- <dt><a href="#Q3">Q3</a></dt>
- <dd>do not merge redundant vertices</dd>
- <dt><a href="#Q6">Q6</a></dt>
- <dd>do not pre-merge concave or coplanar facets</dd>
- <dt><a href="#Q0">Q0</a></dt>
- <dd>do not pre-merge facets with 'C-0' or 'Qx'</dd>
- <dt><a href="#Q8">Q8</a></dt>
- <dd>ignore near-interior points</dd>
- <dt><a href="#Q2">Q2</a></dt>
- <dd>merge all non-convex at once instead of independent sets</dd>
- <dt><a href="#Qf">Qf</a></dt>
- <dd>partition point to furthest outside facet</dd>
- <dt><a href="#Q7">Q7</a></dt>
- <dd>process facets depth-first instead of breadth-first</dd>
- <dt><a href="#Q9">Q9</a></dt>
- <dd>process furthest of furthest points</dd>
- <dt><a href="#Q10">Q10</a></dt>
- <dd>no special processing for narrow distributions</dd>
- <dt><a href="#Q11">Q11</a></dt>
- <dd>copy normals and recompute centrums for tricoplanar facets</dd>
- <dt><a href="#Qm">Qm</a></dt>
- <dd>process points only if they would increase the max. outer
- plane </dd>
- <dt><a href="#Qr">Qr</a></dt>
- <dd>process random outside points instead of furthest one</dd>
- <dt><a href="#Q1">Q1</a></dt>
- <dd>sort merges by type instead of angle</dd>
-</dl>
-
-<hr>
-
-<h3><a href="#qhull">»</a><a name="Qbb">Qbb - scale the last
-coordinate to [0,m] for Delaunay</a></h3>
-
-<p>After scaling with option 'Qbb', the lower bound of the last
-coordinate will be 0 and the upper bound will be the maximum
-width of the other coordinates. Scaling happens after projecting
-the points to a paraboloid and scaling other coordinates. </p>
-
-<p>Option 'Qbb' is automatically set for <a href=qdelaun.htm>qdelaunay</a>
-and <a href=qvoronoi.htm>qvoronoi</a>. Option 'Qbb' is automatically set for joggled input '<a
-href="qh-optq.htm#QJn">QJ</a>'. </p>
-
-<p>Option 'Qbb' should be used for Delaunay triangulations with
-integer coordinates. Since the last coordinate is the sum of
-squares, it may be much larger than the other coordinates. For
-example, <tt>rbox 10000 D2 B1e8 | qhull d</tt> has precision
-problems while <tt>rbox 10000 D2 B1e8 | qhull d Qbb</tt> is OK. </p>
-
-<h3><a href="#qhull">»</a><a name="QbB">QbB - scale the input to
-fit the unit cube</a></h3>
-
-<p>After scaling with option 'QbB', the lower bound will be -0.5
-and the upper bound +0.5 in all dimensions. For different bounds
-change qh_DEFAULTbox in <tt>user.h</tt> (0.5 is best for <a
-href="index.htm#geomview">Geomview</a>).</p>
-
-<p>For Delaunay and Voronoi diagrams, scaling happens after
-projection to the paraboloid. Under precise arithmetic, scaling
-does not change the topology of the convex hull. Scaling may
-reduce precision errors if coordinate values vary widely.</p>
-
-<h3><a href="#qhull">»</a><a name="Qbk">Qbk:n - scale coord[k]
-to low bound</a></h3>
-
-<p>After scaling, the lower bound for dimension k of the input
-points will be n. 'Qbk' scales coord[k] to -0.5. </p>
-
-<h3><a href="#qhull">»</a><a name="QBk">QBk:n - scale coord[k]
-to upper bound </a></h3>
-
-<p>After scaling, the upper bound for dimension k of the input
-points will be n. 'QBk' scales coord[k] to 0.5. </p>
-
-<h3><a href="#qhull">»</a><a name="Qb0">Qbk:0Bk:0 - drop
-dimension k from the input points</a></h3>
-
-<p>Drop dimension<em> k </em>from the input points. For example,
-'Qb1:0B1:0' deletes the y-coordinate from all input points. This
-allows the user to take convex hulls of sub-dimensional objects.
-It happens before the Delaunay and Voronoi transformation.
-It happens after the halfspace transformation for both the data
-and the feasible point.</p>
-
-<h3><a href="#qhull">»</a><a name="Qc">Qc - keep coplanar points
-with nearest facet </a></h3>
-
-<p>During construction of the hull, a point is coplanar if it is
-between '<a href="qh-optc.htm#Wn">Wn</a>' above and '<a
-href="qh-optc.htm#Un">Un</a>' below a facet's hyperplane. A
-different definition is used for output from Qhull. </p>
-
-<p>For output, a coplanar point is above the minimum vertex
-(i.e., above the inner plane). With joggle ('<a
-href="qh-optq.htm#QJn">QJ</a>'), a coplanar point includes points
-within one joggle of the inner plane. </p>
-
-<p>With option 'Qc', output formats '<a href="qh-opto.htm#p">p </a>',
-'<a href="qh-opto.htm#f">f</a>', '<a href="qh-optg.htm#Gp">Gp</a>',
-'<a href="qh-optf.htm#Fc">Fc</a>', '<a href="qh-optf.htm#FN">FN</a>',
-and '<a href="qh-optf.htm#FP">FP</a>' will print the coplanar
-points. With options 'Qc <a href="#Qi">Qi</a>' these outputs
-include the interior points.</p>
-
-<p>For Delaunay triangulations (<a href=qdelaun.htm>qdelaunay</a>
-or <a href=qvoronoi.htm>qvoronoi</a>), a coplanar point is a point
-that is nearly incident to a vertex. All input points are either
-vertices of the triangulation or coplanar.</p>
-
-<p>Qhull stores coplanar points with a facet. While constructing
-the hull, it retains all points within qh_RATIOnearInside
-(user.h) of a facet. In qh_check_maxout(), it uses these points
-to determine the outer plane for each facet. With option 'Qc',
-qh_check_maxout() retains points above the minimum vertex for the
-hull. Other points are removed. If qh_RATIOnearInside is wrong or
-if options '<a href="#Q5">Q5</a> <a href="#Q8">Q8</a>' are set, a
-coplanar point may be missed in the output (see <a
-href="qh-impre.htm#limit">Qhull limitations</a>).</p>
-
-<h3><a href="#qhull">»</a><a name="Qf">Qf - partition point to
-furthest outside facet </a></h3>
-
-<p>After adding a new point to the convex hull, Qhull partitions
-the outside points and coplanar points of the old, visible
-facets. Without the '<a href="qh-opto.htm#f">f </a>' option and
-merging, it assigns a point to the first facet that it is outside
-('<a href="qh-optc.htm#Wn">Wn</a>'). When merging, it assigns a
-point to the first facet that is more than several times outside
-(see qh_DISToutside in user.h).</p>
-
-<p>If option 'Qf' is selected, Qhull performs a directed search
-(no merging) or an exhaustive search (merging) of new facets.
-Option 'Qf' may reduce precision errors if pre-merging does not
-occur.</p>
-
-<p>Option '<a href="#Q9">Q9</a>' processes the furthest of all
-furthest points.</p>
-
-<h3><a href="#qhull">»</a><a name="Qg">Qg - only build good
-facets (needs 'QGn' 'QVn' or 'Pdk') </a></h3>
-
-<p>Qhull has several options for defining and printing good
-facets. With the '<a href="#Qg">Qg</a>' option, Qhull will only
-build those facets that it needs to determine the good facets in
-the output. This may speed up Qhull in 2-d and 3-d. It is
-useful for furthest-site Delaunay
-triangulations (<a href=qdelau_f.htm>qdelaunay Qu</a>,
-invoke with 'qhull d Qbb <a href="#Qu">Qu</a> Qg').
-It is not effective in higher
-dimensions because many facets see a given point and contain a
-given vertex. It is not guaranteed to work for all combinations.</p>
-
-<p>See '<a href="#QGn">QGn</a>', '<a href="#QVn">QVn</a>', and '<a
-href="qh-optp.htm#Pdk">Pdk</a>' for defining good facets, and '<a
-href="qh-optp.htm#Pg">Pg</a>' and '<a href="qh-optp.htm#PG">PG</a>'
-for printing good facets and their neighbors. If pre-merging ('<a
-href="qh-optc.htm#Cn">C-n</a>') is not used and there are
-coplanar facets, then 'Qg Pg' may produce a different result than
-'<a href="qh-optp.htm#Pg">Pg</a>'. </p>
-
-<h3><a href="#qhull">»</a><a name="QGn">QGn - good facet if
-visible from point n, -n for not visible </a></h3>
-
-<p>With option 'QGn', a facet is good (see '<a href="#Qg">Qg</a>'
-and '<a href="qh-optp.htm#Pg">Pg</a>') if it is visible from
-point n. If <i>n < 0</i>, a facet is good if it is not visible
-from point n. Point n is not added to the hull (unless '<a
-href="qh-optt.htm#TCn">TCn</a>' or '<a href="qh-optt.htm#TPn">TPn</a>').</p>
-
-<p>With <a href="rbox.htm">rbox</a>, use the 'Pn,m,r' option
-to define your point; it will be point 0 ('QG0'). </p>
-
-<h3><a href="#qhull">»</a><a name="Qi">Qi - keep interior points
-with nearest facet </a></h3>
-
-<p>Normally Qhull ignores points that are clearly interior to the
-convex hull. With option 'Qi', Qhull treats interior points the
-same as coplanar points. Option 'Qi' does not retain coplanar
-points. You will probably want '<a href="#Qc">Qc </a>' as well. </p>
-
-<p>Option 'Qi' is automatically set for '<a href=qdelaun.htm>qdelaunay</a>
-<a href="#Qc">Qc</a>' and '<a href=qvoronoi.htm>qvoronoi</a>
-<a href="#Qc">Qc</a>'. If you use
-'<a href=qdelaun.htm>qdelaunay</a> Qi' or '<a href=qvoronoi.htm>qvoronoi</a>
-Qi', option '<a href="qh-opto.htm#s">s</a>' reports all nearly
-incident points while option '<a href="qh-optf.htm#Fs">Fs</a>'
-reports the number of interior points (should always be zero).</p>
-
-<p>With option 'Qi', output formats '<a href="qh-opto.htm#p">p</a>',
-'<a href="qh-opto.htm#f">f</a>','<a href="qh-optg.htm#Gp">Gp</a>',
-'<a href="qh-optf.htm#Fc">Fc</a>', '<a href="qh-optf.htm#FN">FN</a>',
-and '<a href="qh-optf.htm#FP">FP</a>' include interior points. </p>
-
-<h3><a href="#qhull">»</a><a name="QJ">QJ</a> or <a name="QJn">QJn</a> - joggled
-input to avoid precision errors</a></h3>
-
-<p>Option 'QJ' or 'QJn' joggles each input coordinate by adding a
-random number in the range [-n,n]. If a precision error occurs,
-It tries again. If precision errors still occur, Qhull increases <i>n</i>
-ten-fold and tries again. The maximum value for increasing <i>n</i>
-is 0.01 times the maximum width of the input. Option 'QJ' selects
-a default value for <i>n</i>. <a href="../src/user.h#JOGGLEdefault">User.h</a>
-defines these parameters and a maximum number of retries. See <a
-href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p>
-
-<p>Option 'QJ' also sets '<a href="qh-optq.htm#Qbb">Qbb</a>' for
-Delaunay triangulations and Voronoi diagrams. It does not set
-'Qbb' if '<a href="qh-optq.htm#Qbk">Qbk:n</a>' or '<a
-href="qh-optq.htm#QBk">QBk:n</a>' are set. </p>
-
-<p>If 'QJn' is set, Qhull does not merge facets unless requested
-to. All facets are simplicial (triangular in 2-d). This may be
-important for your application. You may also use triangulated output
-('<a href="qh-optq.htm#Qt">Qt</a>') or Option '<a href="qh-optf.htm#Ft">Ft</a>'.
-
-<p>Qhull adjusts the outer and inner planes for 'QJn' ('<a
-href="qh-optf.htm#Fs">Fs</a>'). They are increased by <i>sqrt(d)*n</i>
-to account for the maximum distance between a joggled point and
-the corresponding input point. Coplanar points ('<a
-href="qh-optq.htm#Qc">Qc</a>') require an additional <i>sqrt(d)*n</i>
-since vertices and coplanar points may be joggled in opposite
-directions. </p>
-
-<p>For Delaunay triangulations (<a href=qdelaun.htm>qdelaunay</a>)
-and Voronoi diagrams (<a href=qvoronoi.htm>qvoronoi</a>), joggle
-happens before lifting the input sites to a paraboloid. Instead of
-'QJ', you may use triangulated output ('<a
-href="qh-optq.htm#Qt">Qt</a>')</p>
-
-<p>By default, 'QJn' uses a fixed random number seed. To use time
-as the random number seed, select '<a href="qh-optq.htm#QRn">QR-1</a>'.
-The summary ('<a href="qh-opto.htm#s">s</a>') will show the
-selected seed as 'QR-n'.
-
-<p>With 'QJn', Qhull does not error on degenerate hyperplane
-computations. Except for Delaunay and Voronoi computations, Qhull
-does not error on coplanar points. </p>
-
-<p>Use option '<a href="qh-optf.htm#FO">FO</a>' to display the
-selected options. Option 'FO' displays the joggle and the joggle
-seed. If Qhull restarts, it will redisplay the options. </p>
-
-<p>Use option '<a href="qh-optt.htm#TRn">TRn</a>' to estimate the
-probability that Qhull will fail for a given 'QJn'.
-
-<h3><a href="#qhull">»</a><a name="Qm">Qm - only process points
-that increase the maximum outer plane </a></h3>
-
-<p>Qhull reports the maximum outer plane in its summary ('<a
-href="qh-opto.htm#s">s</a>'). With option 'Qm', Qhull does not
-process points that are below the current, maximum outer plane.
-This is equivalent to always adjusting '<a href="qh-optc.htm#Wn">Wn
-</a>' to the maximum distance of a coplanar point to a facet. It
-is ignored for points above the upper convex hull of a Delaunay
-triangulation. Option 'Qm' is no longer important for merging.</p>
-
-<h3><a href="#qhull">»</a><a name="Qr">Qr - process random
-outside points instead of furthest ones </a></h3>
-
-<p>Normally, Qhull processes the furthest point of a facet's
-outside points. Option 'Qr' instead selects a random outside
-point for processing. This makes Qhull equivalent to the
-randomized incremental algorithms.</p>
-
-<p>The original randomization algorithm by Clarkson and Shor [<a
-href="index.htm#cla-sho89">'89</a>] used a conflict list which
-is equivalent to Qhull's outside set. Later randomized algorithms
-retained the previously constructed facets. </p>
-
-<p>To compare Qhull to the randomized algorithms with option
-'Qr', compare "hyperplanes constructed" and
-"distance tests". Qhull does not report CPU time
-because the randomization is inefficient. </p>
-
-<h3><a href="#qhull">»</a><a name="QRn">QRn - random rotation </a></h3>
-
-<p>Option 'QRn' randomly rotates the input. For Delaunay
-triangulations (<a href=qdelaun.htm>qdelaunay</a> or <a href=qvoronoi.htm>qvoronoi</a>),
-it rotates the lifted points about
-the last axis. </p>
-
-<p>If <em>n=0</em>, use time as the random number seed. If <em>n>0</em>,
-use n as the random number seed. If <em>n=-1</em>, don't rotate
-but use time as the random number seed. If <em>n<-1</em>,
-don't rotate but use <em>n</em> as the random number seed. </p>
-
-<h3><a href="#qhull">»</a><a name="Qs">Qs - search all points
-for the initial simplex </a></h3>
-
-<p>Qhull constructs an initial simplex from <i>d+1</i> points. It
-selects points with the maximum and minimum coordinates and
-non-zero determinants. If this fails, it searches all other
-points. In 8-d and higher, Qhull selects points with the minimum
-x or maximum coordinate (see qh_initialvertices in <tt>poly2.c </tt>).
-It rejects points with nearly zero determinants. This should work
-for almost all input sets.</p>
-
-<p>If Qhull can not construct an initial simplex, it reports a
-descriptive message. Usually, the point set is degenerate and one
-or more dimensions should be removed ('<a href="#Qb0">Qbk:0Bk:0</a>').
-If not, use option 'Qs'. It performs an exhaustive search for the
-best initial simplex. This is expensive is high dimensions. </p>
-
-<h3><a href="#qhull">»</a><a name="Qt">Qt - triangulated output</a></h3>
-
-<p>By default, qhull merges facets to handle precision errors. This
-produces non-simplicial facets (e.g., the convex hull of a cube has 6 square
-facets). Each facet is non-simplicial because it has four vertices.
-
-<p>Use option 'Qt' to triangulate all non-simplicial facets before generating
-results. Alternatively, use joggled input ('<a href="#QJn">QJ</a>') to
-prevent non-simplical facets. Unless '<a href="qh-optp.htm#Pp">Pp</a>' is set,
-qhull produces a warning if 'QJ' and 'Qt' are used together.
-
-<p>Option 'Qt' may produce degenerate facets with zero area.</p>
-
-<p>Facet area and hull volumes may differ with and without
-'Qt'. The triangulations are different and different triangles
-may be ignored due to precision errors.
-
-<p>With sufficient merging, the ridges of a non-simplicial facet may share more than two neighboring facets. If so, their triangulation ('<a href="#Qt">Qt</a>') will fail since two facets have the same vertex set. </p>
-
-<h3><a href="#qhull">»</a><a name="Qu">Qu - compute upper hull
-for furthest-site Delaunay triangulation </a></h3>
-
-<p>When computing a Delaunay triangulation (<a href=qdelaun.htm>qdelaunay</a>
-or <a href=qvoronoi.htm>qvoronoi</a>),
-Qhull computes both the the convex hull of points on a
-paraboloid. It normally prints facets of the lower hull. These
-correspond to the Delaunay triangulation. With option 'Qu', Qhull
-prints facets of the upper hull. These correspond to the <a
-href="qdelau_f.htm">furthest-site Delaunay triangulation</a>
-and the <a href="qvoron_f.htm">furthest-site Voronoi diagram</a>.</p>
-
-<p>Option 'qhull d Qbb Qu <a href="#Qg">Qg</a>' may improve the speed of option
-'Qu'. If you use the Qhull library, a faster method is 1) use
-Qhull to compute the convex hull of the input sites; 2) take the
-extreme points (vertices) of the convex hull; 3) add one interior
-point (e.g.,
-'<a href="qh-optf.htm#FV">FV</a>', the average of <em>d</em> extreme points); 4) run
-'qhull d Qbb Qu' or 'qhull v Qbb Qu' on these points.</p>
-
-<h3><a href="#qhull">»</a><a name="Qv">Qv - test vertex
-neighbors for convexity </a></h3>
-
-<p>Normally, Qhull tests all facet neighbors for convexity.
-Non-neighboring facets which share a vertex may not satisfy the
-convexity constraint. This occurs when a facet undercuts the
-centrum of another facet. They should still be convex. Option
-'Qv' extends Qhull's convexity testing to all neighboring facets
-of each vertex. The extra testing occurs after the hull is
-constructed.. </p>
-
-<h3><a href="#qhull">»</a><a name="QVn">QVn - good facet if it
-includes point n, -n if not </a></h3>
-
-<p>With option 'QVn', a facet is good ('<a href="#Qg">Qg</a>',
-'<a href="qh-optp.htm#Pg">Pg</a>') if one of its vertices is
-point n. If <i>n<0</i>, a good facet does not include point n.
-
-<p>If options '<a href="qh-optp.htm#PG">PG</a>'
-and '<a href="#Qg">Qg</a>' are not set, option '<a href="qh-optp.htm#Pg">Pg</a>'
-(print only good)
-is automatically set.
-</p>
-
-<p>Option 'QVn' behaves oddly with options '<a href="qh-optf.htm#Fx">Fx</a>'
-and '<a href=qvoronoi.htm>qvoronoi</a> <a href="qh-optf.htm#Fv2">Fv</a>'.
-
-<p>If used with option '<a href="#Qg">Qg</a>' (only process good facets), point n is
-either in the initial simplex or it is the first
-point added to the hull. Options 'QVn Qg' require either '<a href="#QJn">QJ</a>' or
-'<a href="#Q0">Q0</a>' (no merging).</p>
-
-<h3><a href="#qhull">»</a><a name="Qx">Qx - exact pre-merges
-(allows coplanar facets) </a></h3>
-
-<p>Option 'Qx' performs exact merges while building the hull.
-Option 'Qx' is set by default in 5-d and higher. Use option '<a
-href="#Q0">Q0</a>' to not use 'Qx' by default. Unless otherwise
-specified, option 'Qx' sets option '<a href="qh-optc.htm#C0">C-0</a>'.
-</p>
-
-<p>The "exact" merges are merging a point into a
-coplanar facet (defined by '<a href="qh-optc.htm#Vn">Vn </a>', '<a
-href="qh-optc.htm#Un">Un</a>', and '<a href="qh-optc.htm#Cn">C-n</a>'),
-merging concave facets, merging duplicate ridges, and merging
-flipped facets. Coplanar merges and angle coplanar merges ('<a
-href="qh-optc.htm#An">A-n</a>') are not performed. Concavity
-testing is delayed until a merge occurs.</p>
-
-<p>After the hull is built, all coplanar merges are performed
-(defined by '<a href="qh-optc.htm#Cn">C-n</a>' and '<a
-href="qh-optc.htm#An">A-n</a>'), then post-merges are performed
-(defined by '<a href="qh-optc.htm#Cn2">Cn</a>' and '<a
-href="qh-optc.htm#An2">An</a>'). If facet progress is logged ('<a
-href="qh-optt.htm#TFn">TFn</a>'), Qhull reports each phase and
-prints intermediate summaries and statistics ('<a
-href="qh-optt.htm#Ts">Ts</a>'). </p>
-
-<p>Without 'Qx' in 5-d and higher, options '<a
-href="qh-optc.htm#Cn">C-n</a>' and '<a href="qh-optc.htm#An">A-n</a>'
-may merge too many facets. Since redundant vertices are not
-removed effectively, facets become increasingly wide. </p>
-
-<p>Option 'Qx' may report a wide facet. With 'Qx', coplanar
-facets are not merged. This can produce a "dent" in an
-intermediate hull. If a point is partitioned into a dent and it
-is below the surrounding facets but above other facets, one or
-more wide facets will occur. In practice, this is unlikely. To
-observe this effect, run Qhull with option '<a href="#Q6">Q6</a>'
-which doesn't pre-merge concave facets. A concave facet makes a
-large dent in the intermediate hull.</p>
-
-<p>Option 'Qx' may set an outer plane below one of the input
-points. A coplanar point may be assigned to the wrong facet
-because of a "dent" in an intermediate hull. After
-constructing the hull, Qhull double checks all outer planes with
-qh_check_maxout in <tt>poly2.c </tt>. If a coplanar point is
-assigned to the wrong facet, qh_check_maxout may reach a local
-maximum instead of locating all coplanar facets. This appears to
-be unlikely.</p>
-
-<h3><a href="#qhull">»</a><a name="Qz">Qz - add a
-point-at-infinity for Delaunay triangulations</a></h3>
-
-<p>Option 'Qz' adds a point above the paraboloid of lifted sites
-for a Delaunay triangulation. It allows the Delaunay
-triangulation of cospherical sites. It reduces precision errors
-for nearly cospherical sites.</p>
-
-<h3><a href="#qhull">»</a><a name="Q0">Q0 - no merging with C-0
-and Qx</a></h3>
-
-<p>Turn off default merge options '<a href="qh-optc.htm#C0">C-0</a>'
-and '<a href="#Qx">Qx</a>'. </p>
-
-<p>With 'Q0' and without other pre-merge options, Qhull ignores
-precision issues while constructing the convex hull. This may
-lead to precision errors. If so, a descriptive warning is
-generated. See <a href="qh-impre.htm">Precision issues</a>.</p>
-
-<h3><a href="#qhull">»</a><a name="Q1">Q1 - sort merges by type
-instead of angle </a></h3>
-
-<p>Qhull sorts the coplanar facets before picking a subset of the
-facets to merge. It merges concave and flipped facets first. Then
-it merges facets that meet at a steep angle. With 'Q1', Qhull
-sorts merges by type (coplanar, angle coplanar, concave) instead
-of by angle. This may make the facets wider. </p>
-
-<h3><a href="#qhull">»</a><a name="Q2">Q2 - merge all non-convex
-at once instead of independent sets </a></h3>
-
-<p>With 'Q2', Qhull merges all facets at once instead of
-performing merges in independent sets. This may make the facets
-wider. </p>
-
-<h3><a href="#qhull">»</a><a name="Q3">Q3 - do not merge
-redundant vertices </a></h3>
-
-<p>With 'Q3', Qhull does not remove redundant vertices. In 6-d
-and higher, Qhull never removes redundant vertices (since
-vertices are highly interconnected). Option 'Q3' may be faster,
-but it may result in wider facets. Its effect is easiest to see
-in 3-d and 4-d.</p>
-
-<h3><a href="#qhull">»</a><a name="Q4">Q4 - avoid merging </a>old
-facets into new facets</h3>
-
-<p>With 'Q4', Qhull avoids merges of an old facet into a new
-facet. This sometimes improves facet width and sometimes makes it
-worse. </p>
-
-<h3><a href="#qhull">»</a><a name="Q5">Q5 - do not correct outer
-planes at end of qhull </a></h3>
-
-<p>When merging facets or approximating a hull, Qhull tests
-coplanar points and outer planes after constructing the hull. It
-does this by performing a directed search (qh_findbest in <tt>geom.c</tt>).
-It includes points that are just inside the hull. </p>
-
-<p>With options 'Q5' or '<a href="qh-optp.htm#Po">Po</a>', Qhull
-does not test outer planes. The maximum outer plane is used
-instead. Coplanar points ('<a href="#Qc">Qc</a>') are defined by
-'<a href="qh-optc.htm#Un">Un</a>'. An input point may be outside
-of the maximum outer plane (this appears to be unlikely). An
-interior point may be above '<a href="qh-optc.htm#Un">Un</a>'
-from a hyperplane.</p>
-
-<p>Option 'Q5' may be used if outer planes are not needed. Outer
-planes are needed for options '<a href="qh-opto.htm#s">s</a>', '<a
-href="qh-optg.htm#G">G</a>', '<a href="qh-optg.htm#Go">Go </a>',
-'<a href="qh-optf.htm#Fs">Fs</a>', '<a href="qh-optf.htm#Fo">Fo</a>',
-'<a href="qh-optf.htm#FF">FF</a>', and '<a href="qh-opto.htm#f">f</a>'.</p>
-
-<h3><a href="#qhull">»</a><a name="Q6">Q6 - do not pre-merge
-concave or coplanar facets </a></h3>
-
-<p>With 'Q6', Qhull does not pre-merge concave or coplanar
-facets. This demonstrates the effect of "dents" when
-using '<a href="#Qx">Qx</a>'. </p>
-
-<h3><a href="#qhull">»</a><a name="Q7">Q7 - depth-first
-processing instead of breadth-first </a></h3>
-
-<p>With 'Q7', Qhull processes facets in depth-first order instead
-of breadth-first order. This may increase the locality of
-reference in low dimensions. If so, Qhull may be able to use
-virtual memory effectively. </p>
-
-<p>In 5-d and higher, many facets are visible from each
-unprocessed point. So each iteration may access a large
-proportion of allocated memory. This makes virtual memory
-ineffectual. Once real memory is used up, Qhull will spend most
-of its time waiting for I/O.</p>
-
-<p>Under 'Q7', Qhull runs slower and the facets may be wider. </p>
-
-<h3><a href="#qhull">»</a><a name="Q8">Q8 - ignore near-interior
-points </a></h3>
-
-<p>With 'Q8' and merging, Qhull does not process interior points
-that are near to a facet (as defined by qh_RATIOnearInside in
-user.h). This avoids partitioning steps. It may miss a coplanar
-point when adjusting outer hulls in qh_check_maxout(). The best
-value for qh_RATIOnearInside is not known. Options 'Q8 <a
-href="#Qc">Qc</a>' may be sufficient. </p>
-
-<h3><a href="#qhull">»</a><a name="Q9">Q9 - process furthest of
-furthest points </a></h3>
-
-<p>With 'Q9', Qhull processes the furthest point of all outside
-sets. This may reduce precision problems. The furthest point of
-all outside sets is not necessarily the furthest point from the
-convex hull.</p>
-
-<h3><a href="#qhull">»</a><a name="Q10">Q10 - no special processing
-for narrow distributions</a></h3>
-
-<p>With 'Q10', Qhull does not special-case narrow distributions.
-See <a href=qh-impre.htm#limit>Limitations of merged facets</a> for
-more information.
-
-<h3><a href="#qhull">»</a><a name="Q11">Q11 - copy normals and recompute
-centrums for
-tricoplanar facets</a></h3>
-
-Option '<a href="#Qt">Qt</a>' triangulates non-simplicial facets
-into "tricoplanar" facets.
-Normally tricoplanar facets share the same normal, centrum, and
-Voronoi vertex. They can not be merged or replaced. With
-option 'Q11', Qhull duplicates the normal and Voronoi vertex.
-It recomputes the centrum.
-
-<p>Use 'Q11' if you use the Qhull library to add points
-incrementally and call qh_triangulate() after each point.
-Otherwise, Qhull will report an error when it tries to
-merge and replace a tricoplanar facet.
-
-<p>With sufficient merging and new points, option 'Q11' may
-lead to precision problems such
-as duplicate ridges and concave facets. For example, if qh_triangulate()
-is added to qh_addpoint(), RBOX 1000 s W1e-12 t1001813667 P0 | QHULL d Q11 Tv,
-reports an error due to a duplicate ridge.
-
-<!-- Navigation links -->
-<hr>
-
-<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a></p>
-<!-- GC common information -->
-<hr>
-
-<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
-align="middle" width="40" height="40"></a><i>The Geometry Center
-Home Page </i></p>
-
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
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@@ -1,275 +0,0 @@
-<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
-<html>
-
-<head>
-<title>Qhull trace options (T)</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a></p>
-
-<hr>
-<!-- Main text of document -->
-<h1><a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
-src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
-height="100"></a> Qhull trace options (T)</h1>
-
-This section lists the trace options for Qhull. These options are
-indicated by 'T' followed by a letter.
-
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-
-<hr>
-
-<p><a href="index.htm#TOC">»</a> <a href="qh-quick.htm#programs">Programs</a>
-<a name="trace">•</a> <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a></p>
-
-<h2>Trace options</h2>
-
-<dl compact>
- <dt> </dt>
- <dd><b>General</b></dd>
- <dt><a href="#Tz">Tz</a></dt>
- <dd>output error information to stdout instead of stderr</dd>
- <dt><a href="#TI">TI file</a></dt>
- <dd>input data from a file</dd>
- <dt><a href="#TO">TO file</a></dt>
- <dd>output results to a file</dd>
- <dt><a href="#Ts">Ts</a></dt>
- <dd>print statistics</dd>
- <dt><a href="#TFn">TFn</a></dt>
- <dd>report progress whenever n or more facets created</dd>
- <dt><a href="#TRn">TRn</a></dt>
- <dd>rerun qhull n times</dd>
- <dt><a href="#Tv">Tv</a></dt>
- <dd>verify result: structure, convexity, and point inclusion</dd>
-
- <dt> </dt>
- <dt> </dt>
- <dd><b>Debugging</b></dd>
- <dt><a href="#Tc">Tc</a></dt>
- <dd>check frequently during execution</dd>
- <dt><a href="#TVn2">TVn</a></dt>
- <dd>stop qhull after adding point n </dd>
- <dt><a href="#TCn">TCn</a></dt>
- <dd>stop qhull after building cone for point n</dd>
- <dt><a href="#TVn">TV-n</a></dt>
- <dd>stop qhull before adding point n</dd>
- <dt><a href="#Tn">T4</a></dt>
- <dd>trace at level n, 4=all, 5=mem/gauss, -1= events</dd>
- <dt><a href="#TWn">TWn</a></dt>
- <dd>trace merge facets when width > n</dd>
- <dt><a href="#TMn">TMn</a></dt>
- <dd>turn on tracing at merge n</dd>
- <dt><a href="#TPn">TPn</a></dt>
- <dd>turn on tracing when point n added to hull</dd>
-</dl>
-
-<hr>
-
-<h3><a href="#trace">»</a><a name="Tc">Tc - check frequently
-during execution </a></h3>
-
-<p>Qhull includes frequent checks of its data structures. Option
-'Tc' will catch most inconsistency errors. It is slow and should
-not be used for production runs. Option '<a href="#Tv">Tv</a>'
-performs the same checks after the hull is constructed.</p>
-
-<h3><a href="#trace">»</a><a name="TCn">TCn - stop qhull after
-building cone for point n</a></h3>
-
-<p>Qhull builds a cone from the point to its horizon facets.
-Option 'TCn' stops Qhull just after building the cone. The output
-for '<a href="qh-opto.htm#f">f</a>' includes the cone and the old
-hull.'. </p>
-
-<h3><a href="#trace">»</a><a name="TFn">TFn - report summary
-whenever n or more facets created </a></h3>
-
-<p>Option 'TFn' reports progress whenever more than n facets are
-created. The test occurs just before adding a new point to the
-hull. During post-merging, 'TFn' reports progress after more than
-<i>n/2</i> merges. </p>
-
-<h3><a href="#trace">»</a><a name="TI">TI file - input data from file</a></h3>
-
-<p>Input data from 'file' instead of stdin. The filename may not
-contain spaces or use single quotes.
-You may use I/O redirection
-instead (e.g., 'rbox 10 | qdelaunay >results').</P>
-
-<h3><a href="#trace">»</a><a name="TMn">TMn - turn on tracing at
-merge n </a></h3>
-
-<p>Turn on tracing at n'th merge. </p>
-
-<h3><a href="#trace">»</a><a name="Tn">Tn - trace at level n</a></h3>
-
-<p>Qhull includes full execution tracing. 'T-1' traces events.
-'T1' traces the overall execution of the program. 'T2' and 'T3'
-trace overall execution and geometric and topological events.
-'T4' traces the algorithm. 'T5' includes information about memory
-allocation and Gaussian elimination. 'T1' is useful for logging
-progress of Qhull in high dimensions.</p>
-
-<p>Option 'Tn' can produce large amounts of output. Use options '<a
-href="#TPn">TPn</a>', '<a href="#TWn">TWn</a>', and '<a href="#TMn">TMn</a>' to selectively
-turn on tracing. Since all errors report the last processed
-point, option '<a href="#TPn">TPn</a>' is particularly useful.</p>
-
-<p>Different executions of the same program may produce different
-traces and different results. The reason is that Qhull uses hashing
-to match ridges of non-simplicial facets. For performance reasons,
-the hash computation uses
-memory addresses which may change across executions.
-
-<h3><a href="#trace">»</a><a name="TO">TO file - output results to file</a></h3>
-
-<p>Redirect stdout to 'file'. The filename may be enclosed in
-single quotes. Unix and Windows NT users may use I/O redirection
-instead (e.g., 'rbox 10 | qdelaunay >results').</P>
-<p>
-Windows95 users should always use 'TO file'. If they use I/O redirection,
-error output is not sent to the console. Qhull uses single quotes instead
-of double quotes because a missing double quote can
-freeze Windows95 (e.g., do not run, rbox 10 | qhull TO "x)</p>
-<p>
-
-<h3><a href="#trace">»</a><a name="TPn">TPn - turn on tracing
-when point n added to hull </a></h3>
-
-<p>Option 'TPn' turns on tracing when point n is added to
-the hull. It also traces partitions of point n. This option
-reduces the output size when tracing. It is the normal
-method to determine the cause of a Qhull error. All Qhull errors
-report the last point added.
-
-<p>Use options 'TPn <a href="qh-optt.htm#TVn">TVn</a>' to
-trace the addition of point n to the convex hull and stop when done.</p>
-
-<p>If used with option '<a href="qh-optt.htm#TWn">TWn</a>',
-'TPn' turns off tracing after adding point n to the hull.
-Use options 'TPn TWn' to
-trace the addition of point n to the convex hull, partitions
-of point n, and wide merges.</p>
-
-<h3><a href="#trace">»</a><a name="TRn">TRn - rerun qhull n times</a></h3>
-
-<p>Option 'TRn' reruns Qhull n times. It is usually used
-with '<a href="qh-optq.htm#QJn">QJn</a>' to determine the probability
-that a given joggle will fail. The summary
-('<a href="qh-opto.htm#s">s</a>') lists the failure
-rate and the precision errors that occurred.
-Option '<a href="#Ts">Ts</a>' will report statistics for
-all of the runs. Trace and output options only apply to the last
-run. An event trace, '<a href="#Tn">T-1</a>' reports events for all runs.
-
-<p>Tracing applies to the last run of Qhull. If an error
-is reported, the options list the run number as "_run".
-To trace this run, set 'TRn' to the same value.</p>
-
-<h3><a href="#trace">»</a><a name="Ts">Ts - print statistics </a></h3>
-
-<p>Option 'Ts' collects statistics and prints them to stderr. For
-Delaunay triangulations, the angle statistics are restricted to
-the lower or upper envelope.</p>
-
-<h3><a href="#trace">»</a><a name="Tv">Tv - verify result:
-structure, convexity, and point inclusion </a></h3>
-
-<p>Option 'Tv' checks the topological structure, convexity, and
-point inclusion. If precision problems occurred, facet convexity
-is tested whether or not 'Tv' is selected. Option 'Tv' does not
-check point inclusion if forcing output with '<a
-href="qh-optp.htm#Po">Po</a>', or if '<a href="qh-optq.htm#Q5">Q5</a>'
-is set. </p>
-
-<p>The convex hull of a set of points is the smallest polytope
-that includes the points. Option 'Tv' tests point inclusion.
-Qhull verifies that all points are below all outer planes
-(facet->maxoutside). Point inclusion is exhaustive if merging
-or if the facet-point product is small enough; otherwise Qhull
-verifies each point with a directed search (qh_findbest). To
-force an exhaustive test when using option '<a
-href="qh-optc.htm#C0">C-0</a>' (default), use 'C-1e-30' instead. </p>
-
-<p>Point inclusion testing occurs after producing output. It
-prints a message to stderr unless option '<a
-href="qh-optp.htm#Pp">Pp</a>' is used. This allows the user to
-interrupt Qhull without changing the output. </p>
-
-<p>With '<a href=qvoronoi.htm>qvoronoi</a> <a href="qh-optf.htm#Fi2">Fi</a>'
-and '<a href=qvoronoi.htm>qvoronoi</a> <a href="qh-optf.htm#Fo2">Fo</a>',
-option 'Tv' collects statistics that verify all Voronoi vertices lie
-on the separating hyperplane, and for bounded regions, all
-separating hyperplanes are perpendicular bisectors.
-
-<h3><a href="#trace">»</a><a name="TVn">TV-n - stop qhull before
-adding point n</a></h3>
-
-<p>Qhull adds one point at a time to the convex hull. See <a
-href="qh-eg.htm#how">how Qhull adds a point</a>. Option 'TV-n'
-stops Qhull just before adding a new point. Output shows the hull
-at this time.</p>
-
-<h3><a href="#trace">»</a><a name="TVn2">TVn - stop qhull after
-adding point n</a></h3>
-
-<p>Option 'TVn' stops Qhull after it has added point n. Output
-shows the hull at this time.</p>
-
-<h3><a href="#trace">»</a><a name="TWn">TWn - trace merge facets
-when width > n </a></h3>
-
-<p>Along with TMn, this option allows the user to determine the
-cause of a wide merge.</p>
-<h3><a href="#trace">»</a><a name="Tz">Tz - send all output to
-stdout </a></h3>
-
-<p>Redirect stderr to stdout. </p>
-
-<!-- Navigation links -->
-<hr>
-
-<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a></p>
-<!-- GC common information -->
-<hr>
-
-<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
-align="middle" width="40" height="40"></a><i>The Geometry Center
-Home Page </i></p>
-
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
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-<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
-<html>
-
-<head>
-<title>Qhull quick reference</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<p><a name="TOC"><b>Up:</b></a> <a href="http://www.qhull.org">Home
-page for Qhull</a> <br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a> <br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a> <br>
-<b>To:</b> <a href="qh-in.htm#TOC">Qhull internals</a><br>
-<b>To:</b> <a href="../src/index.htm">Qhull functions</a>, macros, and data structures<br>
-<b>To:</b> <a href="../src/index.htm#TOC">Qhull files</a><br>
-<b>To:</b> <a href="../src/qh-geom.htm">Geom</a> • <a href="../src/qh-globa.htm">Global</a>
-• <a href="../src/qh-io.htm">Io</a> • <a href="../src/qh-mem.htm">Mem</a>
-• <a href="../src/qh-merge.htm">Merge</a> • <a href="../src/qh-poly.htm">Poly</a>
-• <a href="../src/qh-qhull.htm">Qhull</a> • <a href="../src/qh-set.htm">Set</a>
-• <a href="../src/qh-stat.htm">Stat</a> • <a href="../src/qh-user.htm">User</a>
-</p>
-
-<hr>
-<!-- Main text of document -->
-<h1><a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html"><img
-src="qh--cone.gif" alt="[cone]" align="middle" width="100"
-height="100"></a> Qhull quick reference</h1>
-
-This section lists all programs and options in Qhull.
-
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-
-<p>
-<a name="programs"> </a>
-<hr>
-<b>Qhull programs</b>
-<p><a href="#TOC">»</a> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a></p>
-
-<dl>
- <dt><a href="qconvex.htm">qconvex</a> -- convex hull</dt>
- <dd><a href="qconvex.htm#synopsis">sy</a>nopsis • <a
- href="qconvex.htm#input">in</a>put • <a
- href="qconvex.htm#outputs">ou</a>tputs • <a
- href="qconvex.htm#controls">co</a>ntrols • <a
- href="qconvex.htm#graphics">gr</a>aphics • <a
- href="qconvex.htm#notes">no</a>tes • <a
- href="qconvex.htm#conventions">co</a>nventions • <a
- href="qconvex.htm#options">op</a>tions</dd>
- <dt> </dt>
- <dt><a href="qdelaun.htm">qdelaunay</a> -- Delaunay triangulation</dt>
- <dd><a href="qdelaun.htm#synopsis">sy</a>nopsis • <a
- href="qdelaun.htm#input">in</a>put • <a
- href="qdelaun.htm#outputs">ou</a>tputs • <a
- href="qdelaun.htm#controls">co</a>ntrols • <a
- href="qdelaun.htm#graphics">gr</a>aphics • <a
- href="qdelaun.htm#notes">no</a>tes • <a
- href="qdelaun.htm#conventions">co</a>nventions • <a
- href="qdelaun.htm#options">op</a>tions</dd>
- <dt> </dt>
- <dt><a href="qdelau_f.htm">qdelaunay Qu</a> -- furthest-site Delaunay triangulation</dt>
- <dd><a href="qdelau_f.htm#synopsis">sy</a>nopsis • <a
- href="qdelau_f.htm#input">in</a>put • <a
- href="qdelau_f.htm#outputs">ou</a>tputs • <a
- href="qdelau_f.htm#controls">co</a>ntrols • <a
- href="qdelau_f.htm#graphics">gr</a>aphics • <a
- href="qdelau_f.htm#notes">no</a>tes • <a
- href="qdelau_f.htm#conventions">co</a>nventions • <a
- href="qdelau_f.htm#options">op</a>tions</dd>
- <dt> </dt>
- <dt><a href="qhalf.htm">qhalf</a> -- halfspace intersection about a point</dt>
- <dd><a href="qhalf.htm#synopsis">sy</a>nopsis • <a
- href="qhalf.htm#input">in</a>put • <a
- href="qhalf.htm#outputs">ou</a>tputs • <a
- href="qhalf.htm#controls">co</a>ntrols • <a
- href="qhalf.htm#graphics">gr</a>aphics • <a
- href="qhalf.htm#notes">no</a>tes • <a
- href="qhalf.htm#conventions">co</a>nventions • <a
- href="qhalf.htm#options">op</a>tions</dd>
- <dt> </dt>
- <dt><a href="qvoronoi.htm">qvoronoi</a> -- Voronoi diagram</dt>
- <dd><a href="qvoronoi.htm#synopsis">sy</a>nopsis • <a
- href="qvoronoi.htm#input">in</a>put • <a
- href="qvoronoi.htm#outputs">ou</a>tputs •
- <a href="qvoronoi.htm#controls">co</a>ntrols • <a
- href="qvoronoi.htm#graphics">gr</a>aphics • <a
- href="qvoronoi.htm#notes">no</a>tes • <a
- href="qvoronoi.htm#conventions">co</a>nventions • <a
- href="qvoronoi.htm#options">op</a>tions</dd>
- <dt> </dt>
- <dt><a href="qvoron_f.htm">qvoronoi Qu</a> -- furthest-site Voronoi diagram</dt>
- <dd><a href="qvoron_f.htm#synopsis">sy</a>nopsis • <a
- href="qvoron_f.htm#input">in</a>put • <a
- href="qvoron_f.htm#outputs">ou</a>tputs • <a
- href="qvoron_f.htm#controls">co</a>ntrols • <a
- href="qvoron_f.htm#graphics">gr</a>aphics • <a
- href="qvoron_f.htm#notes">no</a>tes • <a
- href="qvoron_f.htm#conventions">co</a>nventions • <a
- href="qvoron_f.htm#options">op</a>tions</dd>
- <dt> </dt>
- <dt><a href="rbox.htm">rbox</a> -- generate point distributions for qhull</dt>
- <dd><a href="rbox.htm#synopsis">sy</a>nopsis • <a
- href="rbox.htm#outputs">ou</a>tputs • <a
- href="rbox.htm#examples">ex</a>amples • <a
- href="rbox.htm#notes">no</a>tes • <a
- href="rbox.htm#options">op</a>tions</dd>
- <dt> </dt>
- <dt><a href="qhull.htm">qhull</a> -- convex hull and related structures</dt>
- <dd><a href="qhull.htm#synopsis">sy</a>nopsis • <a
- href="qhull.htm#input">in</a>put • <a
- href="qhull.htm#outputs">ou</a>tputs • <a
- href="qhull.htm#controls">co</a>ntrols • <a
- href="qhull.htm#options">op</a>tions</dd>
- </dl>
-<a name="options"> </a>
-<hr>
-<b>Qhull options</b>
-
-<p><a href="#TOC">»</a> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a></p>
-
-<p><table>
-<!-- Note: keep all lines the same for easy reorganization -->
-<tr>
-<td><nobr>'<a href=qh-optf.htm#Fa>Fa</a>'
-Farea
-</nobr></td><td><nobr>'<a href=qh-optf.htm#FA>FA</a>'
-FArea-total
-</nobr></td><td><nobr>'<a href=qh-optf.htm#Fc>Fc</a>'
-Fcoplanars
-</nobr></td><td><nobr>'<a href=qh-optf.htm#FC>FC</a>'
-FCentrums
-
-</nobr></td></tr><tr>
-<td><nobr>'<a href=qh-optf.htm#Fd>Fd</a>'
-Fd-cdd-in
-</nobr></td><td><nobr>'<a href=qh-optf.htm#FD>FD</a>'
-FD-cdd-out
-</nobr></td><td><nobr>'<a href=qh-optf.htm#FF>FF</a>'
-FF-dump-xridge
-</nobr></td><td><nobr>'<a href=qh-optf.htm#Fi>Fi</a>'
-Finner
-
-</nobr></td></tr><tr>
-<td><nobr>'<a href=qh-optf.htm#Fi2>Fi</a>'
-Finner_bounded
-</nobr></td><td><nobr>'<a href=qh-optf.htm#FI>FI</a>'
-FIDs
-</nobr></td><td><nobr>'<a href=qh-optf.htm#Fm>Fm</a>'
-Fmerges
-</nobr></td><td><nobr>'<a href=qh-optf.htm#FM>FM</a>'
-FMaple
-
-</nobr></td></tr><tr>
-<td><nobr>'<a href=qh-optf.htm#Fn>Fn</a>'
-Fneighbors
-</nobr></td><td><nobr>'<a href=qh-optf.htm#FN>FN</a>'
-FNeigh-vertex
-</nobr></td><td><nobr>'<a href=qh-optf.htm#Fo>Fo</a>'
-Fouter
-</nobr></td><td><nobr>'<a href=qh-optf.htm#Fo2>Fo</a>'
-Fouter_unbounded
-
-</nobr></td></tr><tr>
-<td><nobr>'<a href=qh-optf.htm#FO>FO</a>'
-FOptions
-</nobr></td><td><nobr>'<a href=qh-optf.htm#Fp>Fp</a>'
-Fpoint-intersect
-</nobr></td><td><nobr>'<a href=qh-optf.htm#FP>FP</a>'
-FPoint_near
-</nobr></td><td><nobr>'<a href=qh-optf.htm#FQ>FQ</a>'
-FQhull
-
-</nobr></td></tr><tr>
-<td><nobr>'<a href=qh-optf.htm#Fs>Fs</a>'
-Fsummary
-</nobr></td><td><nobr>'<a href=qh-optf.htm#FS>FS</a>'
-FSize
-</nobr></td><td><nobr>'<a href=qh-optf.htm#Ft>Ft</a>'
-Ftriangles
-</nobr></td><td><nobr>'<a href=qh-optf.htm#Fv>Fv</a>'
-Fvertices
-
-</nobr></td></tr><tr>
-<td><nobr>'<a href=qh-optf.htm#Fv2>Fv</a>'
-Fvoronoi
-</nobr></td><td><nobr>'<a href=qh-optf.htm#FV>FV</a>'
-FVertex-ave
-</nobr></td><td><nobr>'<a href=qh-optf.htm#Fx>Fx</a>'
-Fxtremes
-</nobr></td><td colspan=2><nobr>
-<a href=qh-impre.htm#joggle>Merged facets or joggled input</a>
-
-</nobr></td></tr>
-<tr><td> </td></tr><tr>
-<td><nobr>'<a href=qh-optp.htm#PAn>PAn</a>'
-PArea-keep
-</nobr></td><td><nobr>'<a href=qh-optp.htm#Pdk>Pdk:n</a>'
-Pdrop_low
-</nobr></td><td><nobr>'<a href=qh-optp.htm#PDk>PDk:n</a>'
-Pdrop_high
-</nobr></td><td><nobr>'<a href=qh-optp.htm#Pg>Pg</a>'
-Pgood
-
-</nobr></td></tr><tr>
-<td><nobr>'<a href=qh-optp.htm#PFn>PFn</a>'
-PFacet_area_keep
-</nobr></td><td><nobr>'<a href=qh-optp.htm#PG>PG</a>'
-PGood_neighbors
-</nobr></td><td><nobr>'<a href=qh-optp.htm#PMn>PMn</a>'
-PMerge-keep
-</nobr></td><td><nobr>'<a href=qh-optp.htm#Po>Po</a>'
-Poutput_forced
-
-</nobr></td></tr><tr>
-<td><nobr>'<a href=qh-optp.htm#Po2>Po</a>'
-Poutput_error
-</nobr></td><td><nobr>'<a href=qh-optp.htm#Pp>Pp</a>'
-Pprecision_not
-
-</nobr></td></tr>
-<tr><td> </td></tr><tr>
-<td><nobr>'<a href=qhull.htm#outputs>d</a>'
-delaunay
-</nobr></td><td><nobr>'<a href=qhull.htm#outputs>v</a>'
-voronoi
-</nobr></td><td><nobr>'<a href=qh-optg.htm>G</a>'
-Geomview
-</nobr></td><td><nobr>'<a href=qhull.htm#outputs>H</a>'
-Halfspace
-
-</nobr></td></tr><tr>
-<td><nobr>'<a href=qh-opto.htm#f>f</a>'
-facet_dump
-</nobr></td><td><nobr>'<a href=qh-opto.htm#i>i</a>'
-incidences
-</nobr></td><td><nobr>'<a href=qh-opto.htm#m>m</a>'
-mathematica
-</nobr></td><td><nobr>'<a href=qh-opto.htm#n>n</a>'
-normals
-
-</nobr></td></tr><tr>
-<td><nobr>'<a href=qh-opto.htm#o>o</a>'
-OFF_format
-</nobr></td><td><nobr>'<a href=qh-opto.htm#p>p</a>'
-points
-</nobr></td><td><nobr>'<a href=qh-opto.htm#s>s</a>'
-summary
-
-</nobr></td></tr>
-<tr><td> </td></tr><tr>
-<td><nobr>'<a href=qh-optg.htm#Gv>Gv</a>'
-Gvertices
-</nobr></td><td><nobr>'<a href=qh-optg.htm#Gp>Gp</a>'
-Gpoints
-</nobr></td><td><nobr>'<a href=qh-optg.htm#Ga>Ga</a>'
-Gall_points
-</nobr></td><td><nobr>'<a href=qh-optg.htm#Gn>Gn</a>'
-Gno_planes
-
-</nobr></td></tr><tr>
-<td><nobr>'<a href=qh-optg.htm#Gi>Gi</a>'
-Ginner
-</nobr></td><td><nobr>'<a href=qh-optg.htm#Gc>Gc</a>'
-Gcentrums
-</nobr></td><td><nobr>'<a href=qh-optg.htm#Gh>Gh</a>'
-Ghyperplanes
-</nobr></td><td><nobr>'<a href=qh-optg.htm#Gr>Gr</a>'
-Gridges
-
-</nobr></td></tr><tr>
-<td><nobr>'<a href=qh-optg.htm#Go>Go</a>'
-Gouter
-</nobr></td><td><nobr>'<a href=qh-optg.htm#GDn>GDn</a>'
-GDrop_dim
-</nobr></td><td><nobr>'<a href=qh-optg.htm#Gt>Gt</a>'
-Gtransparent
-
-</nobr></td></tr>
-<tr><td> </td></tr><tr>
-<td><nobr>'<a href=qh-optt.htm#Tn>T4</a>'
-T4_trace
-</nobr></td><td><nobr>'<a href=qh-optt.htm#Tc>Tc</a>'
-Tcheck_often
-</nobr></td><td><nobr>'<a href=qh-optt.htm#Ts>Ts</a>'
-Tstatistics
-</nobr></td><td><nobr>'<a href=qh-optt.htm#Tv>Tv</a>'
-Tverify
-
-</nobr></td></tr><tr>
-<td><nobr>'<a href=qh-optt.htm#Tz>Tz</a>'
-Tz_stdout
-</nobr></td><td><nobr>'<a href=qh-optt.htm#TFn>TFn</a>'
-TFacet_log
-<td><nobr>'<a href=qh-optt.htm#TI>TI file</a>'
-TInput_file
-</nobr></td><td><nobr>'<a href=qh-optt.htm#TPn>TPn</a>'
-TPoint_trace
-
-</nobr></td></tr><tr>
-<td><nobr>'<a href=qh-optt.htm#TMn>TMn</a>'
-TMerge_trace
-</nobr></td><td><nobr>'<a href=qh-optt.htm#TO>TO file</a>'
-TOutput_file
-</nobr></td><td><nobr>'<a href=qh-optt.htm#TRn>TRn</a>'
-TRerun
-</nobr></td><td><nobr>'<a href=qh-optt.htm#TWn>TWn</a>'
-TWide_trace
-
-</nobr></td></tr><tr>
-<td><nobr>'<a href=qh-optt.htm#TVn>TV-n</a>'
-TVertex_stop_before
-</nobr></td></tr><tr>
-<td><nobr>'<a href=qh-optt.htm#TVn2>TVn</a>'
-TVertex_stop_after
-</nobr></td><td><nobr>'<a href=qh-optt.htm#TCn>TCn</a>'
-TCone_stop_after
-
-</nobr></td></tr>
-<tr><td> </td></tr><tr>
-<td><nobr>'<a href=qh-optc.htm#An>A-n</a>'
-Angle_max_pre
-</nobr></td><td><nobr>'<a href=qh-optc.htm#An2>An</a>'
-Angle_max_post
-</nobr></td><td><nobr>'<a href=qh-optc.htm#C0>C-0</a>'
-Centrum_roundoff
-</nobr></td><td><nobr>'<a href=qh-optc.htm#Cn>C-n</a>'
-Centrum_size_pre
-
-</nobr></td></tr><tr>
-<td><nobr>'<a href=qh-optc.htm#Cn2>Cn</a>'
-Centrum_size_post
-</nobr></td><td><nobr>'<a href=qh-optc.htm#En>En</a>'
-Error_round
-</nobr></td><td><nobr>'<a href=qh-optc.htm#Rn>Rn</a>'
-Random_dist
-</nobr></td><td><nobr>'<a href=qh-optc.htm#Vn>Vn</a>'
-Visible_min
-
-</nobr></td></tr><tr>
-<td><nobr>'<a href=qh-optc.htm#Un>Un</a>'
-Ucoplanar_max
-</nobr></td><td><nobr>'<a href=qh-optc.htm#Wn>Wn</a>'
-Wide_outside
-
-</nobr></td></tr>
-<tr><td> </td></tr><tr>
-<td><nobr>'<a href=qh-optq.htm#Qbk>Qbk:n</a>'
-Qbound_low
-</nobr></td><td><nobr>'<a href=qh-optq.htm#QBk>QBk:n</a>'
-QBound_high
-</nobr></td><td><nobr>'<a href=qh-optq.htm#Qb0>Qbk:0Bk:0</a>'
-Qbound_drop
-</nobr></td><td><nobr>'<a href=qh-optq.htm#QbB>QbB</a>'
-QbB-scale-box
-
-</nobr></td></tr><tr>
-<td><nobr>'<a href=qh-optq.htm#Qbb>Qbb</a>'
-Qbb-scale-last
-</nobr></td><td><nobr>'<a href=qh-optq.htm#Qc>Qc</a>'
-Qcoplanar
-</nobr></td><td><nobr>'<a href=qh-optq.htm#Qf>Qf</a>'
-Qfurthest
-</nobr></td><td><nobr>'<a href=qh-optq.htm#Qg>Qg</a>'
-Qgood_only
-
-</nobr></td></tr><tr>
-<td><nobr>'<a href=qh-optq.htm#QGn>QGn</a>'
-QGood_point
-</nobr></td><td><nobr>'<a href=qh-optq.htm#Qi>Qi</a>'
-Qinterior
-</nobr></td><td><nobr>'<a href=qh-optq.htm#Qm>Qm</a>'
-Qmax_out
-</nobr></td><td><nobr>'<a href=qh-optq.htm#QJn>QJn</a>'
-QJoggle
-
-</nobr></td></tr><tr>
-<td><nobr>'<a href=qh-optq.htm#Qr>Qr</a>'
-Qrandom
-</nobr></td><td><nobr>'<a href=qh-optq.htm#QRn>QRn</a>'
-QRotate
-</nobr></td><td><nobr>'<a href=qh-optq.htm#Qs>Qs</a>'
-Qsearch_1st
-</nobr></td><td><nobr>'<a href=qh-optq.htm#Qt>Qt</a>'
-Qtriangulate
-
-</nobr></td></tr><tr>
-<td><nobr>'<a href=qh-optq.htm#Qu>Qu</a>'
-QupperDelaunay
-</nobr><td><nobr>'<a href=qh-optq.htm#QVn>QVn</a>'
-QVertex_good
-</nobr></td><td><nobr>'<a href=qh-optq.htm#Qv>Qv</a>'
-Qvneighbors
-</nobr></td><td><nobr>'<a href=qh-optq.htm#Qx>Qx</a>'
-Qxact_merge
-
-</nobr></td></tr><tr>
-<td><nobr>'<a href=qh-optq.htm#Qz>Qz</a>'
-Qzinfinite
-
-</nobr></td></tr>
-<tr><td> </td></tr><tr>
-<td><nobr>'<a href=qh-optq.htm#Q0>Q0</a>'
-Q0_no_premerge
-</nobr></td><td><nobr>'<a href=qh-optq.htm#Q1>Q1</a>'
-Q1_no_angle
-</nobr></td><td><nobr>'<a href=qh-optq.htm#Q2>Q2</a>'
-Q2_no_independ
-</nobr></td><td><nobr>'<a href=qh-optq.htm#Q3>Q3</a>'
-Q3_no_redundant
-
-</nobr></td></tr><tr>
-<td><nobr>'<a href=qh-optq.htm#Q4>Q4</a>'
-Q4_no_old
-</nobr></td><td><nobr>'<a href=qh-optq.htm#Q5>Q5</a>'
-Q5_no_check_out
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-<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
-<html>
-
-<head>
-<title>qhalf -- halfspace intersection about a point</title>
-</head>
-
-<body>
-<!-- Navigation links -->
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-<b>To:</b> <a href="#synopsis">sy</a>nopsis
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-<!-- Main text of document -->
-<h1><a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/half.html"><img
-src="qh--half.gif" alt="[halfspace]" align="middle" width="100"
-height="100"></a>qhalf -- halfspace intersection about a point</h1>
-
-<p>The intersection of a set of halfspaces is a polytope. The
-polytope may be unbounded. See Preparata & Shamos [<a
-href="index.htm#pre-sha85">'85</a>] for a discussion. In low
-dimensions, halfspace intersection may be used for linear
-programming. </p>
-
-<blockquote>
-<dl compact>
- <dt><b>Example:</b> rbox c | qconvex <a href="qh-optf.htm#FQ">FQ</a> <a href="qh-optf.htm#FV">FV</a>
- <a href="qh-opto.htm#n">n</a> | qhalf <a
- href="qh-optf.htm#Fp">Fp</a></dt>
- <dd>Print the intersection of the facets of a cube. <tt>rbox c</tt>
- generates the vertices of a cube. <tt>qconvex FV n</tt> returns of average
- of the cube's vertices (in this case, the origin) and the halfspaces
- that define the cube. <tt>qhalf Fp</tt> computes the intersection of
- the halfspaces about the origin. The intersection is the vertices
- of the original cube.</dd>
-
- <dt><p><b>Example:</b> rbox c d G0.55 | qconvex <a href="qh-optf.htm#FQ">FQ</a> <a href="qh-optf.htm#FV">FV</a>
- <a href="qh-opto.htm#n">n</a> | qhalf <a
- href="qh-optf.htm#Fp">Fp</a></dt>
- <dd>Print the intersection of the facets of a cube and a diamond. There
- are 24 facets and 14 intersection points. Four facets define each diamond
- vertext. Six facets define each cube vertex.
- </dd>
-
- <dt><p><b>Example:</b> rbox c d G0.55 | qconvex <a href="qh-optf.htm#FQ">FQ</a> <a href="qh-optf.htm#FV">FV</a>
- <a href="qh-opto.htm#n">n</a> | qhalf <a
- href="qh-optf.htm#Fp">Fp</a>
- <a href="qh-optq.htm#Qt">Qt</a></dt>
- <dd>Same as above except triangulate before computing
- the intersection points. Three facets define each intersection
- point. There are two duplicates of the diamond and four duplicates of the cube.
- </dd>
-</dl>
-</blockquote>
-
-<p>Qhull computes a halfspace intersection by the geometric
-duality between points and halfspaces.
-See <a href="qh-eg.htm#half">halfspace examples</a>,
-<a href="#notes">qhalf notes</a>, and
-option 'p' of <a href="#outputs">qhalf outputs</a>. </p>
-
-<p>By default, halfspace intersections may be defined by more than
-<i>d</i> halfspaces. See the previous cube and diamond example.
-This is the expected output for halfspace intersection.
-
-<p>You can try triangulated output and joggled input. It demonstrates
-that triangulated output is more accurate than joggled input.
-
-<p>If you use '<a href="qh-optq.htm#Qt">Qt</a>' (triangulated output), all
-halfspace intersections are simplicial (e.g., three halfspaces per
-intersection in 3-d). In 3-d, if more than three halfspaces intersect
-at the same point, triangulated output will produce
-duplicate intersections, one for each additional halfspace. See the previous
-cube and diamond example.</p>
-
-<p>If you use '<a href="qh-optq.htm#QJn">QJ</a>' (joggled input), all halfspace
-intersections are simplicial. This may lead to nearly identical
-intersections. For example, replace 'Qt' with 'QJ' above and
-compare the duplicated intersections.
-See <a
-href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p>
-
-<p>The 'qhalf' program is equivalent to
-'<a href=qhull.htm#outputs>qhull H</a>' in 2-d to 4-d, and
-'<a href=qhull.htm#outputs>qhull H</a> <a href=qh-optq.htm#Qx>Qx</a>'
-in 5-d and higher. It disables the following Qhull
-<a href=qh-quick.htm#options>options</a>: <i>d n v Qbb QbB Qf Qg Qm
-Qr QR Qv Qx Qz TR E V Fa FA FC FD FS Ft FV Gt Q0,etc</i>.
-
-
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-<hr>
-
-<h3><a href="#TOP">»</a><a name="synopsis">qhalf synopsis</a></h3>
-<pre>
-qhalf- halfspace intersection about a point.
- input (stdin): [dim, 1, interior point]
- dim+1, n
- halfspace coefficients + offset
- comments start with a non-numeric character
-
-options (qhalf.htm):
- Hn,n - specify coordinates of interior point
- Qt - triangulated output
- QJ - joggle input instead of merging facets
- Tv - verify result: structure, convexity, and redundancy
- . - concise list of all options
- - - one-line description of all options
-
-output options (subset):
- s - summary of results (default)
- Fp - intersection coordinates
- Fv - non-redundant halfspaces incident to each intersection
- Fx - non-redundant halfspaces
- o - OFF file format (dual convex hull)
- G - Geomview output (dual convex hull)
- m - Mathematica output (dual convex hull)
- QVn - print intersections for halfspace n, -n if not
- TO file - output results to file, may be enclosed in single quotes
-
-examples:
- rbox d | qconvex n | qhalf s H0,0,0 Fp
- rbox c | qconvex FV n | qhalf s i
- rbox c | qconvex FV n | qhalf s o
-</pre>
-
-<h3><a href="#TOP">»</a><a name="input">qhalf input</a></h3>
-
-<blockquote>
-<p>The input data on <tt>stdin</tt> consists of:</p>
-<ul>
- <li>[optional] interior point
- <ul>
- <li>dimension
- <li>1
- <li>coordinates of interior point
- </ul>
- <li>dimension + 1
- <li>number of halfspaces</li>
- <li>halfspace coefficients followed by offset</li>
-</ul>
-
-<p>Use I/O redirection (e.g., qhalf < data.txt), a pipe (e.g., rbox c | qconvex FV n | qhalf),
-or the '<a href=qh-optt.htm#TI>TI</a>' option (e.g., qhalf TI data.txt).
-
-<p>Qhull needs an interior point to compute the halfspace
-intersection. An interior point is inside all of the halfspaces <i>Hx+b
-<= 0</i>. The interior point may be in the input. If not, option
-'Hn,n' defines the interior point as
-[n,n,0,...] where <em>0</em> is the default coordinate (e.g.,
-'H0' is the origin). Use linear programming if you do not know
-the interior point (see <a href="#notes">halfspace notes</a>),</p>
-
-<p>The input to qhalf is a set of halfspaces. Each halfspace is defined by
-<em>d</em> coefficients followed by a signed offset. This defines
-a linear inequality. The coefficients define a vector that is
-normal to the halfspace. The vector may have any length. If it
-has length one, the offset is the distance from the origin to the
-halfspace's boundary. </p>
-
-<p>This is the same format used for output options '<a
-href="qh-opto.htm#n">n</a>', '<a href="qh-optf.htm#Fo">Fo</a>',
-and '<a href="qh-optf.htm#Fi">Fi</a>'. Use option '<a
-href="qh-optf.htm#Fd">Fd</a>' to use cdd format for the
-halfspaces.</p>
-
-<p>For example, here is the input for computing the intersection
-of halfplanes that form a cube.</p>
-
-<blockquote>
- <p>rbox c | qconvex FQ FV n TO data </p>
- <pre>
-RBOX c | QCONVEX FQ FV n
-3 1
- 0 0 0
-4
-6
- 0 0 -1 -0.5
- 0 -1 0 -0.5
- 1 0 0 -0.5
- -1 0 0 -0.5
- 0 1 0 -0.5
- 0 0 1 -0.5
-</pre>
- <p>qhalf s Fp < data </p>
- <pre>
-
-Halfspace intersection by the convex hull of 6 points in 3-d:
-
- Number of halfspaces: 6
- Number of non-redundant halfspaces: 6
- Number of intersection points: 8
-
-Statistics for: RBOX c | QCONVEX FQ FV n | QHALF s Fp
-
- Number of points processed: 6
- Number of hyperplanes created: 11
- Number of distance tests for qhull: 11
- Number of merged facets: 1
- Number of distance tests for merging: 45
- CPU seconds to compute hull (after input): 0
-
-3
-3
-8
- -0.5 0.5 0.5
- 0.5 0.5 0.5
- -0.5 0.5 -0.5
- 0.5 0.5 -0.5
- 0.5 -0.5 0.5
- -0.5 -0.5 0.5
- -0.5 -0.5 -0.5
- 0.5 -0.5 -0.5
-</pre>
-</blockquote>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="outputs">qhalf outputs</a></h3>
-<blockquote>
-
-<p>The following options control the output for halfspace
-intersection.</p>
-<blockquote>
-<dl compact>
- <dt> </dt>
- <dd><b>Intersections</b></dd>
- <dt><a href="qh-optf.htm#FN">FN</a></dt>
- <dd>list intersection points for each non-redundant
- halfspace. The first line
- is the number of non-redundant halfspaces. Each remaining
- lines starts with the number of intersection points. For the cube
- example, each halfspace has four intersection points.</dd>
- <dt><a href="qh-optf.htm#Fn">Fn</a></dt>
- <dd>list neighboring intersections for each intersection point. The first line
- is the number of intersection points. Each remaining line
- starts with the number of neighboring intersections. For the cube
- example, each intersection point has three neighboring intersections.
- In 3-d, a non-simplicial intersection has more than three neighboring
- intersections. Use option '<a href="qh-optq.htm#QJn">QJ</a>' to
- avoid non-simplicial intersections.
- </dd>
- <dt><a href="qh-optf.htm#Fp">Fp</a></dt>
- <dd>print intersection coordinates. The first line is the dimension and the
- second line is the number of intersection points. The following lines are the
- coordinates of each intersection.</dd>
- <dt><a href="qh-optf.htm#FI">FI</a></dt>
- <dd>list intersection IDs. The first line is the number of
- intersections. The IDs follow, one per line.</dd>
- <dt> </dt>
- <dt> </dt>
- <dd><b>Halfspaces</b></dd>
- <dt><a href="qh-optf.htm#Fx">Fx</a></dt>
- <dd>list non-redundant halfspaces. The first line is the number of
- non-redundant halfspaces. The other lines list one halfspace per line.
- A halfspace is <i>non-redundant</i> if it
- defines a facet of the intersection. Redundant halfspaces are ignored. For
- the cube example, all of the halfspaces are non-redundant.
- </dd>
- <dt><a href="qh-optf.htm#Fv">Fv</a></dt>
- <dd>list non-redundant halfspaces incident to each intersection point.
- The first line is the number of
- non-redundant halfspaces. Each remaining line starts with the number
- of non-redundant halfspaces. For the
- cube example, each intersection is incident to three halfspaces.</dd>
- <dt><a href="qh-opto.htm#i">i</a></dt>
- <dd>list non-redundant halfspaces incident to each intersection point. The first
- line is the number of intersection points. Each remaining line
- lists the incident, non-redundant halfspaces. For the
- cube example, each intersection is incident to three halfspaces.
- </dd>
- <dt><a href="qh-optf.htm#Fc">Fc</a></dt>
- <dd>list coplanar halfspaces for each intersection point. The first line is
- the number of intersection points. Each remaining line starts with
- the number of coplanar halfspaces. A coplanar halfspace is listed for
- one intersection point even though it is coplanar to multiple intersection
- points.</dd>
- <dt><a href="qh-optq.htm#Qc">Qi</a> <a href="qh-optf.htm#Fc">Fc</a></dt>
- <dd>list redundant halfspaces for each intersection point. The first line is
- the number of intersection points. Each remaining line starts with
- the number of redundant halfspaces. Use options '<a href="qh-optq.htm#Qc">Qc</a> Qi Fc' to list
- coplanar and redundant halfspaces.</dd>
-
- <dt> </dt>
- <dt> </dt>
- <dd><b>General</b></dd>
- <dt><a href="qh-opto.htm#s">s</a></dt>
- <dd>print summary for the halfspace intersection. Use '<a
- href="qh-optf.htm#Fs">Fs</a>' if you need numeric data.</dd>
- <dt><a href="qh-opto.htm#o">o</a></dt>
- <dd>print vertices and facets of the dual convex hull. The
- first line is the dimension. The second line is the number of
- vertices, facets, and ridges. The vertex
- coordinates are next, followed by the facets, one per line.</dd>
- <dt><a href="qh-opto.htm#p">p</a></dt>
- <dd>print vertex coordinates of the dual convex hull. Each vertex corresponds
- to a non-redundant halfspace. Its coordinates are the negative of the hyperplane's coefficients
- divided by the offset plus the inner product of the coefficients and
- the interior point (-c/(b+a.p).
- Options 'p <a href="qh-optq.htm#Qc">Qc</a>' includes coplanar halfspaces.
- Options 'p <a href="qh-optq.htm#Qi">Qi</a>' includes redundant halfspaces.</dd>
- <dt><a href="qh-opto.htm#m">m</a></dt>
- <dd>Mathematica output for the dual convex hull in 2-d or 3-d.</dd>
- <dt><a href="qh-optf.htm#FM">FM</a></dt>
- <dd>Maple output for the dual convex hull in 2-d or 3-d.</dd>
- <dt><a href="qh-optg.htm#G">G</a></dt>
- <dd>Geomview output for the dual convex hull in 2-d, 3-d, or 4-d.</dd>
- </dl>
-</blockquote>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="controls">qhalf controls</a></h3>
-<blockquote>
-
-<p>These options provide additional control:</p>
-
-<blockquote>
-<dl compact>
- <dt><a href="qh-optq.htm#Qt">Qt</a></dt>
- <dd>triangulated output. If a 3-d intersection is defined by more than
- three hyperplanes, Qhull produces duplicate intersections -- one for
- each extra hyperplane.</dd>
- <dt><a href="qh-optq.htm#QJn">QJ</a></dt>
- <dd>joggle the input instead of merging facets. In 3-d, this guarantees that
- each intersection is defined by three hyperplanes.</dd>
- <dt><a href="qh-opto.htm#f">f </a></dt>
- <dd>facet dump. Print the data structure for each intersection (i.e.,
- facet)</dd>
- <dt><a href="qh-optt.htm#TFn">TFn</a></dt>
- <dd>report summary after constructing <em>n</em>
- intersections</dd>
- <dt><a href="qh-optq.htm#QVn">QVn</a></dt>
- <dd>select intersection points for halfspace <em>n</em>
- (marked 'good')</dd>
- <dt><a href="qh-optq.htm#QGn">QGn</a></dt>
- <dd>select intersection points that are visible to halfspace <em>n</em>
- (marked 'good'). Use <em>-n</em> for the remainder.</dd>
- <dt><a href="qh-optq.htm#Qb0">Qbk:0Bk:0</a></dt>
- <dd>remove the k-th coordinate from the input. This computes the
- halfspace intersection in one lower dimension.</dd>
- <dt><a href="qh-optt.htm#Tv">Tv</a></dt>
- <dd>verify result</dd>
- <dt><a href="qh-optt.htm#TO">TI file</a></dt>
- <dd>input data from file. The filename may not use spaces or quotes.</dd>
- <dt><a href="qh-optt.htm#TO">TO file</a></dt>
- <dd>output results to file. Use single quotes if the filename
- contains spaces (e.g., <tt>TO 'file with spaces.txt'</tt></dd>
- <dt><a href="qh-optq.htm#Qs">Qs</a></dt>
- <dd>search all points for the initial simplex. If Qhull can
- not construct an initial simplex, it reports a
-descriptive message. Usually, the point set is degenerate and one
-or more dimensions should be removed ('<a href="qh-optq.htm#Qb0">Qbk:0Bk:0</a>').
-If not, use option 'Qs'. It performs an exhaustive search for the
-best initial simplex. This is expensive is high dimensions.</dd>
-</dl>
-</blockquote>
-
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="graphics">qhalf graphics</a></h3>
-<blockquote>
-
-<p>To view the results with Geomview, compute the convex hull of
-the intersection points ('qhull FQ H0 Fp | qhull G'). See <a
-href="qh-eg.htm#half">Halfspace examples</a>.</p>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="notes">qhalf notes</a></h3>
-<blockquote>
-
-<p>If you do not know an interior point for the halfspaces, use
-linear programming to find one. Assume, <em>n</em> halfspaces
-defined by: <em>aj*x1+bj*x2+cj*x3+dj>=0, j=1..n</em>. Perform
-the following linear program: </p>
-
-<blockquote>
- <p>max(x5) aj*x1+bj*x2+cj*x3+dj*x4-x5>=0, j=1..n</p>
-</blockquote>
-
-<p>Then, if <em>[x1,x2,x3,x4,x5]</em> is an optimal solution with
-<em>x4,x5>0</em> we get: </p>
-
-<blockquote>
- <p>aj*(x1/x4)+bj*(x2/x4)+cj*(x3/x4)+dj>=(x5/x4)>0,
- j=1..n </p>
-</blockquote>
-
-<p>and conclude that the point <em>[x1/x4,x2/x4,x3/x4]</em> is in
-the interior of all the halfspaces. Note that <em>x5</em> is
-optimal, so this point is "way in" the interior (good
-for precision errors).</p>
-
-<p>After finding an interior point, the rest of the intersection
-algorithm is from Preparata & Shamos [<a
-href="index.htm#pre-sha85">'85</a>, p. 316, "A simple case
-..."]. Translate the halfspaces so that the interior point
-is the origin. Calculate the dual polytope. The dual polytope is
-the convex hull of the vertices dual to the original faces in
-regard to the unit sphere (i.e., halfspaces at distance <em>d</em>
-from the origin are dual to vertices at distance <em>1/d</em>).
-Then calculate the resulting polytope, which is the dual of the
-dual polytope, and translate the origin back to the interior
-point [S. Spitz and S. Teller].</p>
-
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="conventions">qhalf
-conventions</a></h3>
-<blockquote>
-
-<p>The following terminology is used for halfspace intersection
-in Qhull. This is the hardest structure to understand. The
-underlying structure is a convex hull with one vertex per
-non-redundant halfspace. See <a href="#conventions">convex hull
-conventions</a> and <a href="index.htm#structure">Qhull's data structures</a>.</p>
-
-<ul>
- <li><em>interior point</em> - a point in the intersection of
- the halfspaces. Qhull needs an interior point to compute
- the intersection. See <a href="#input">halfspace input</a>.</li>
- <li><em>halfspace</em> - <em>d</em> coordinates for the
- normal and a signed offset. The distance to an interior
- point is negative.</li>
- <li><em>non-redundant halfspace</em> - a halfspace that
- defines an output facet</li>
- <li><em>vertex</em> - a dual vertex in the convex hull
- corresponding to a non-redundant halfspace</li>
- <li><em>coplanar point</em> - the dual point corresponding to
- a similar halfspace</li>
- <li><em>interior point</em> - the dual point corresponding to
- a redundant halfspace</li>
- <li><em>intersection point</em>- the intersection of <em>d</em>
- or more non-redundant halfspaces</li>
- <li><em>facet</em> - a dual facet in the convex hull
- corresponding to an intersection point</li>
- <li><em>non-simplicial facet</em> - more than <em>d</em>
- halfspaces intersect at a point</li>
- <li><em>good facet</em> - an intersection point that
- satisfies restriction '<a href="qh-optq.htm#QVn">QVn</a>',
- etc.</li>
-</ul>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="options">qhalf options</a></h3>
-
-<pre>
-qhalf- compute the intersection of halfspaces about a point
- http://www.qhull.org
-
-input (stdin):
- optional interior point: dimension, 1, coordinates
- first lines: dimension+1 and number of halfspaces
- other lines: halfspace coefficients followed by offset
- comments: start with a non-numeric character
-
-options:
- Hn,n - specify coordinates of interior point
- Qt - triangulated ouput
- QJ - joggle input instead of merging facets
- Qc - keep coplanar halfspaces
- Qi - keep other redundant halfspaces
-
-Qhull control options:
- QJn - randomly joggle input in range [-n,n]
- Qbk:0Bk:0 - remove k-th coordinate from input
- Qs - search all halfspaces for the initial simplex
- QGn - print intersection if redundant to halfspace n, -n for not
- QVn - print intersections for halfspace n, -n if not
-
-Trace options:
- T4 - trace at level n, 4=all, 5=mem/gauss, -1= events
- Tc - check frequently during execution
- Ts - print statistics
- Tv - verify result: structure, convexity, and redundancy
- Tz - send all output to stdout
- TFn - report summary when n or more facets created
- TI file - input data from file, no spaces or single quotes
- TO file - output results to file, may be enclosed in single quotes
- TPn - turn on tracing when halfspace n added to intersection
- TMn - turn on tracing at merge n
- TWn - trace merge facets when width > n
- TVn - stop qhull after adding halfspace n, -n for before (see TCn)
- TCn - stop qhull after building cone for halfspace n (see TVn)
-
-Precision options:
- Cn - radius of centrum (roundoff added). Merge facets if non-convex
- An - cosine of maximum angle. Merge facets if cosine > n or non-convex
- C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
- Rn - randomly perturb computations by a factor of [1-n,1+n]
- Un - max distance below plane for a new, coplanar halfspace
- Wn - min facet width for outside halfspace (before roundoff)
-
-Output formats (may be combined; if none, produces a summary to stdout):
- f - facet dump
- G - Geomview output (dual convex hull)
- i - non-redundant halfspaces incident to each intersection
- m - Mathematica output (dual convex hull)
- o - OFF format (dual convex hull: dimension, points, and facets)
- p - vertex coordinates of dual convex hull (coplanars if 'Qc' or 'Qi')
- s - summary (stderr)
-
-More formats:
- Fc - count plus redundant halfspaces for each intersection
- - Qc (default) for coplanar and Qi for other redundant
- Fd - use cdd format for input (homogeneous with offset first)
- FF - facet dump without ridges
- FI - ID of each intersection
- Fm - merge count for each intersection (511 max)
- FM - Maple output (dual convex hull)
- Fn - count plus neighboring intersections for each intersection
- FN - count plus intersections for each non-redundant halfspace
- FO - options and precision constants
- Fp - dim, count, and intersection coordinates
- FP - nearest halfspace and distance for each redundant halfspace
- FQ - command used for qhalf
- Fs - summary: #int (8), dim, #halfspaces, #non-redundant, #intersections
- for output: #non-redundant, #intersections, #coplanar
- halfspaces, #non-simplicial intersections
- #real (2), max outer plane, min vertex
- Fv - count plus non-redundant halfspaces for each intersection
- Fx - non-redundant halfspaces
-
-Geomview output (2-d, 3-d and 4-d; dual convex hull)
- Ga - all points (i.e., transformed halfspaces) as dots
- Gp - coplanar points and vertices as radii
- Gv - vertices (i.e., non-redundant halfspaces) as spheres
- Gi - inner planes (i.e., halfspace intersections) only
- Gn - no planes
- Go - outer planes only
- Gc - centrums
- Gh - hyperplane intersections
- Gr - ridges
- GDn - drop dimension n in 3-d and 4-d output
-
-Print options:
- PAn - keep n largest facets (i.e., intersections) by area
- Pdk:n- drop facet if normal[k] <= n (default 0.0)
- PDk:n- drop facet if normal[k] >= n
- Pg - print good facets (needs 'QGn' or 'QVn')
- PFn - keep facets whose area is at least n
- PG - print neighbors of good facets
- PMn - keep n facets with most merges
- Po - force output. If error, output neighborhood of facet
- Pp - do not report precision problems
-
- . - list of all options
- - - one line descriptions of all options
-</pre>
-
-<!-- Navigation links -->
-<hr>
-
-<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
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-• <a href="qh-optf.htm#format">Formats</a>
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-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a><br>
-<b>To:</b> <a href="#synopsis">sy</a>nopsis
-• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
-• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
-• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
-• <a href="#options">op</a>tions
-<!-- GC common information -->
-<hr>
-
-<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
-align="middle" width="40" height="40"></a><i>The Geometry Center
-Home Page </i></p>
-
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
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-<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
-<html>
-
-<head>
-<title>qhull -- convex hull and related structures</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<p><b><a name="TOP">Up</a></b><b>:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a><br>
-<b>To:</b> <a href="#synopsis">sy</a>nopsis • <a href="#input">in</a>put
-• <a href="#outputs">ou</a>tputs • <a href="#controls">co</a>ntrols
-• <a href="#options">op</a>tions
-<hr>
-<!-- Main text of document -->
-<h1><a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html"><img
-src="qh--cone.gif" alt="[cone]" align="middle" width="100"
-height="100"></a>qhull -- convex hull and related structures</h1>
-
-<p>The convex hull of a set of points is the smallest convex set
-containing the points. The Delaunay triangulation and furthest-site
-Delaunay triangulation are equivalent to a convex hull in one
-higher dimension. Halfspace intersection about a point is
-equivalent to a convex hull by polar duality.
-
-<p>The <tt>qhull</tt> program provides options to build these
-structures and to experiment with the process. Use the
-<a href=qconvex.htm>qconvex</a>,
-<a href=qdelaun.htm>qdelaunay</a>, <a href=qhalf.htm>qhalf</a>,
-and <a href=qvoronoi.htm>qvoronoi</a> programs
-to build specific structures. You may use <tt>qhull</tt> instead.
-It takes the same options and uses the same code.
-<blockquote>
-<dl>
- <dt><b>Example:</b> rbox 1000 D3 | qhull
- <a href="qh-optc.htm#Cn">C-1e-4</a>
- <a href="qh-optf.htm#FO">FO</a>
- <a href="qh-optt.htm#Ts">Ts</a>
- </dt>
- <dd>Compute the 3-d convex hull of 1000 random
- points.
- Centrums must be 10^-4 below neighboring
- hyperplanes. Print the options and precision constants.
- When done, print statistics. These options may be
- used with any of the Qhull programs.</dd>
- <dt> </dt>
- <dt><b>Example:</b> rbox 1000 D3 | qhull <a href=qhull.htm#outputs>d</a>
- <a href="qh-optq.htm#Qbb">Qbb</a>
- <a href="qh-optc.htm#Rn">R1e-4</a>
- <a href="qh-optq.htm#Q0">Q0</a></dt>
- <dd>Compute the 3-d Delaunay triangulation of 1000 random
- points. Randomly perturb all calculations by
- [0.9999,1.0001]. Do not correct precision problems.
- This leads to serious precision errors.</dd>
-</dl>
-</blockquote>
-<p>Use the following equivalences when calling <tt>qhull</tt> in 2-d to 4-d (a 3-d
-Delaunay triangulation is a 4-d convex hull):
-<blockquote>
-<ul>
-<li>
-<a href="qconvex.htm">qconvex</a> == qhull
-<li>
-<a href=qdelaun.htm>qdelaunay</a> == qhull d <a href="qh-optq.htm#Qbb">Qbb</a>
-<li>
-<a href=qhalf.htm>qhalf</a> == qhull H
-<li>
-<a href=qvoronoi.htm>qvoronoi</a> == qhull v <a href="qh-optq.htm#Qbb">Qbb</a>
-</ul>
-</blockquote>
-
-<p>Use the following equivalences when calling <tt>qhull</tt> in 5-d and higher (a 4-d
-Delaunay triangulation is a 5-d convex hull):
-<blockquote>
-<ul>
-<li>
-<a href="qconvex.htm">qconvex</a> == qhull <a href="qh-optq.htm#Qx">Qx</a>
-<li>
-<a href=qdelaun.htm>qdelaunay</a> == qhull d <a href="qh-optq.htm#Qbb">Qbb</a> <a href="qh-optq.htm#Qx">Qx</a>
-<li>
-<a href=qhalf.htm>qhalf</a> == qhull H <a href="qh-optq.htm#Qx">Qx</a>
-<li>
-<a href=qvoronoi.htm>qvoronoi</a> == qhull v <a href="qh-optq.htm#Qbb">Qbb</a> <a href="qh-optq.htm#Qx">Qx</a>
-</ul>
-</blockquote>
-
-
-<p>By default, Qhull merges coplanar facets. For example, the convex
-hull of a cube's vertices has six facets.
-
-<p>If you use '<a href="qh-optq.htm#Qt">Qt</a>' (triangulated output),
-all facets will be simplicial (e.g., triangles in 2-d). For the cube
-example, it will have 12 facets. Some facets may be
-degenerate and have zero area.
-
-<p>If you use '<a href="qh-optq.htm#QJn">QJ</a>' (joggled input),
-all facets will be simplicial. The corresponding vertices will be
-slightly perturbed. Joggled input is less accurate that triangulated
-output.See <a
-href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p>
-
-<p>The output for 4-d convex hulls may be confusing if the convex
-hull contains non-simplicial facets (e.g., a hypercube). See
-<a href=qh-faq.htm#extra>Why
-are there extra points in a 4-d or higher convex hull?</a><br>
-</p>
-
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-
-<hr>
-
-<h3><a href="#TOP">»</a><a name="synopsis">qhull synopsis</a></h3>
-<pre>
-qhull- compute convex hulls and related structures.
- input (stdin): dimension, n, point coordinates
- comments start with a non-numeric character
- halfspace: use dim+1 and put offsets after coefficients
-
-options (qh-quick.htm):
- d - Delaunay triangulation by lifting points to a paraboloid
- d Qu - furthest-site Delaunay triangulation (upper convex hull)
- v - Voronoi diagram as the dual of the Delaunay triangulation
- v Qu - furthest-site Voronoi diagram
- H1,1 - Halfspace intersection about [1,1,0,...] via polar duality
- Qt - triangulated output
- QJ - joggle input instead of merging facets
- Tv - verify result: structure, convexity, and point inclusion
- . - concise list of all options
- - - one-line description of all options
-
-Output options (subset):
- s - summary of results (default)
- i - vertices incident to each facet
- n - normals with offsets
- p - vertex coordinates (if 'Qc', includes coplanar points)
- if 'v', Voronoi vertices
- Fp - halfspace intersections
- Fx - extreme points (convex hull vertices)
- FA - compute total area and volume
- o - OFF format (if 'v', outputs Voronoi regions)
- G - Geomview output (2-d, 3-d and 4-d)
- m - Mathematica output (2-d and 3-d)
- QVn - print facets that include point n, -n if not
- TO file- output results to file, may be enclosed in single quotes
-
-examples:
- rbox c d D2 | qhull Qc s f Fx | more rbox 1000 s | qhull Tv s FA
- rbox 10 D2 | qhull d QJ s i TO result rbox 10 D2 | qhull v Qbb Qt p
- rbox 10 D2 | qhull d Qu QJ m rbox 10 D2 | qhull v Qu QJ o
- rbox c | qhull n rbox c | qhull FV n | qhull H Fp
- rbox d D12 | qhull QR0 FA rbox c D7 | qhull FA TF1000
- rbox y 1000 W0 | qhull rbox 10 | qhull v QJ o Fv
-</pre>
-
-<h3><a href="#TOP">»</a><a name="input">qhull input</a></h3>
-<blockquote>
-
-<p>The input data on <tt>stdin</tt> consists of:</p>
-<ul>
- <li>dimension
- <li>number of points</li>
- <li>point coordinates</li>
-</ul>
-
-<p>Use I/O redirection (e.g., qhull < data.txt), a pipe (e.g., rbox 10 | qhull),
-or the '<a href=qh-optt.htm#TI>TI</a>' option (e.g., qhull TI data.txt).
-
-<p>Comments start with a non-numeric character. Error reporting is
-simpler if there is one point per line. Dimension
-and number of points may be reversed. For halfspace intersection,
-an interior point may be prepended (see <a href=qhalf.htm#input>qhalf input</a>).
-
-<p>Here is the input for computing the convex
-hull of the unit cube. The output is the normals, one
-per facet.</p>
-
-<blockquote>
- <p>rbox c > data </p>
- <pre>
-3 RBOX c
-8
- -0.5 -0.5 -0.5
- -0.5 -0.5 0.5
- -0.5 0.5 -0.5
- -0.5 0.5 0.5
- 0.5 -0.5 -0.5
- 0.5 -0.5 0.5
- 0.5 0.5 -0.5
- 0.5 0.5 0.5
-</pre>
- <p>qhull s n < data</p>
- <pre>
-
-Convex hull of 8 points in 3-d:
-
- Number of vertices: 8
- Number of facets: 6
- Number of non-simplicial facets: 6
-
-Statistics for: RBOX c | QHULL s n
-
- Number of points processed: 8
- Number of hyperplanes created: 11
- Number of distance tests for qhull: 35
- Number of merged facets: 6
- Number of distance tests for merging: 84
- CPU seconds to compute hull (after input): 0.081
-
-4
-6
- 0 0 -1 -0.5
- 0 -1 0 -0.5
- 1 0 0 -0.5
- -1 0 0 -0.5
- 0 1 0 -0.5
- 0 0 1 -0.5
-</pre>
-</blockquote>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="outputs">qhull outputs</a></h3>
-<blockquote>
-
-<p>These options control the output of qhull. They may be used
-individually or together.</p>
-<blockquote>
-<dl compact>
- <dt> </dt>
- <dd><b>General</b></dd>
- <dt><a name="d">qhull d</a></dt>
- <dd>compute the convex hull of the input points.
- See <a href=qconvex.htm>qconvex</a>.</dd>
- <dt><a name="d">qhull d Qbb</a></dt>
- <dd>compute the Delaunay triangulation by lifting the points
- to a paraboloid. Use option '<a href="qh-optq.htm#Qbb">Qbb</a>'
- to scale the paraboloid and improve numeric precision.
- See <a href=qdelaun.htm>qdelaunay</a>.</dd>
- <dt><a name="v">qhull v Qbb</a></dt>
- <dd>compute the Voronoi diagram by computing the Delaunay
- triangulation. Use option '<a href="qh-optq.htm#Qbb">Qbb</a>'
- to scale the paraboloid and improve numeric precision.
- See <a href=qvoronoi.htm>qvoronoi</a>.</dd>
- <dt><a name="H">qhull H</a></dt>
- <dd>compute the halfspace intersection about a point via polar
- duality. See <a href=qhalf.htm>qhalf</a>.</dd>
-</dl>
-</blockquote>
-
-<p>For a full list of output options see
-<blockquote>
-<ul>
- <li><a href="qh-opto.htm#output">Output</a> formats</li>
- <li><a href="qh-optf.htm#format">Additional</a> I/O
- formats</li>
- <li><a href="qh-optg.htm#geomview">Geomview</a>
- output options</li>
- <li><a href="qh-optp.htm#print">Print</a> options</li>
-</ul>
-</blockquote>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="controls">qhull controls</a></h3>
-<blockquote>
-
-<p>For a full list of control options see
-<blockquote>
-<ul>
- <li><a href="qh-optq.htm#qhull">Qhull</a> control
- options</li>
- <li><a href="qh-optc.htm#prec">Precision</a> options</li>
- <li><a href="qh-optt.htm#trace">Trace</a> options</li>
-</ul>
-</blockquote>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="options">qhull options</a></h3>
-
-<pre>
-qhull- compute convex hulls and related structures.
- http://www.qhull.org
-
-input (stdin):
- first lines: dimension and number of points (or vice-versa).
- other lines: point coordinates, best if one point per line
- comments: start with a non-numeric character
- halfspaces: use dim plus one and put offset after coefficients.
- May be preceded by a single interior point ('H').
-
-options:
- d - Delaunay triangulation by lifting points to a paraboloid
- d Qu - furthest-site Delaunay triangulation (upper convex hull)
- v - Voronoi diagram (dual of the Delaunay triangulation)
- v Qu - furthest-site Voronoi diagram
- Hn,n,... - halfspace intersection about point [n,n,0,...]
- Qt - triangulated output
- QJ - joggle input instead of merging facets
- Qc - keep coplanar points with nearest facet
- Qi - keep interior points with nearest facet
-
-Qhull control options:
- Qbk:n - scale coord k so that low bound is n
- QBk:n - scale coord k so that upper bound is n (QBk is 0.5)
- QbB - scale input to unit cube centered at the origin
- Qbb - scale last coordinate to [0,m] for Delaunay triangulations
- Qbk:0Bk:0 - remove k-th coordinate from input
- QJn - randomly joggle input in range [-n,n]
- QRn - random rotation (n=seed, n=0 time, n=-1 time/no rotate)
- Qf - partition point to furthest outside facet
- Qg - only build good facets (needs 'QGn', 'QVn', or 'PdD')
- Qm - only process points that would increase max_outside
- Qr - process random outside points instead of furthest ones
- Qs - search all points for the initial simplex
- Qu - for 'd' or 'v', compute upper hull without point at-infinity
- returns furthest-site Delaunay triangulation
- Qv - test vertex neighbors for convexity
- Qx - exact pre-merges (skips coplanar and anglomaniacs facets)
- Qz - add point-at-infinity to Delaunay triangulation
- QGn - good facet if visible from point n, -n for not visible
- QVn - good facet if it includes point n, -n if not
- Q0 - turn off default p remerge with 'C-0'/'Qx'
- Q1 - sort merges by type instead of angle
- Q2 - merge all non-convex at once instead of independent sets
- Q3 - do not merge redundant vertices
- Q4 - avoid old>new merges
- Q5 - do not correct outer planes at end of qhull
- Q6 - do not pre-merge concave or coplanar facets
- Q7 - depth-first processing instead of breadth-first
- Q8 - do not process near-inside points
- Q9 - process furthest of furthest points
- Q10 - no special processing for narrow distributions
- Q11 - copy normals and recompute centrums for tricoplanar facets
-
-Towpaths Trace options:
- T4 - trace at level n, 4=all, 5=mem/gauss, -1= events
- Tc - check frequently during execution
- Ts - print statistics
- Tv - verify result: structure, convexity, and point inclusion
- Tz - send all output to stdout
- TFn - report summary when n or more facets created
- TI file - input data from file, no spaces or single quotes
- TO file - output results to file, may be enclosed in single quotes
- TPn - turn on tracing when point n added to hull
- TMn - turn on tracing at merge n
- TWn - trace merge facets when width > n
- TRn - rerun qhull n times. Use with 'QJn'
- TVn - stop qhull after adding point n, -n for before (see TCn)
- TCn - stop qhull after building cone for point n (see TVn)
-
-Precision options:
- Cn - radius of centrum (roundoff added). Merge facets if non-convex
- An - cosine of maximum angle. Merge facets if cosine > n or non-convex
- C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
- En - max roundoff error for distance computation
- Rn - randomly perturb computations by a factor of [1-n,1+n]
- Vn - min distance above plane for a visible facet (default 3C-n or En)
- Un - max distance below plane for a new, coplanar point (default Vn)
- Wn - min facet width for outside point (before roundoff, default 2Vn)
-
-Output formats (may be combined; if none, produces a summary to stdout):
- f - facet dump
- G - Geomview output (see below)
- i - vertices incident to each facet
- m - Mathematica output (2-d and 3-d)
- o - OFF format (dim, points and facets; Voronoi regions)
- n - normals with offsets
- p - vertex coordinates or Voronoi vertices (coplanar points if 'Qc')
- s - summary (stderr)
-
-More formats:
- Fa - area for each facet
- FA - compute total area and volume for option 's'
- Fc - count plus coplanar points for each facet
- use 'Qc' (default) for coplanar and 'Qi' for interior
- FC - centrum or Voronoi center for each facet
- Fd - use cdd format for input (homogeneous with offset first)
- FD - use cdd format for numeric output (offset first)
- FF - facet dump without ridges
- Fi - inner plane for each facet
- for 'v', separating hyperplanes for bounded Voronoi regions
- FI - ID of each facet
- Fm - merge count for each facet (511 max)
- FM - Maple output (2-d and 3-d)
- Fn - count plus neighboring facets for each facet
- FN - count plus neighboring facets for each point
- Fo - outer plane (or max_outside) for each facet
- for 'v', separating hyperplanes for unbounded Voronoi regions
- FO - options and precision constants
- Fp - dim, count, and intersection coordinates (halfspace only)
- FP - nearest vertex and distance for each coplanar point
- FQ - command used for qhull
- Fs - summary: #int (8), dimension, #points, tot vertices, tot facets,
- output: #vertices, #facets, #coplanars, #nonsimplicial
- #real (2), max outer plane, min vertex
- FS - sizes: #int (0)
- #real(2) tot area, tot volume
- Ft - triangulation with centrums for non-simplicial facets (OFF format)
- Fv - count plus vertices for each facet
- for 'v', Voronoi diagram as Voronoi vertices for pairs of sites
- FV - average of vertices (a feasible point for 'H')
- Fx - extreme points (in order for 2-d)
-
-Geomview options (2-d, 3-d, and 4-d; 2-d Voronoi)
- Ga - all points as dots
- Gp - coplanar points and vertices as radii
- Gv - vertices as spheres
- Gi - inner planes only
- Gn - no planes
- Go - outer planes only
- Gc - centrums
- Gh - hyperplane intersections
- Gr - ridges
- GDn - drop dimension n in 3-d and 4-d output
- Gt - for 3-d 'd', transparent outer ridges
-
-Print options:
- PAn - keep n largest facets by area
- Pdk:n - drop facet if normal[k] <= n (default 0.0)
- PDk:n - drop facet if normal[k] >= n
- Pg - print good facets (needs 'QGn' or 'QVn')
- PFn - keep facets whose area is at least n
- PG - print neighbors of good facets
- PMn - keep n facets with most merges
- Po - force output. If error, output neighborhood of facet
- Pp - do not report precision problems
-
- . - list of all options
- - - one line descriptions of all options
-</pre>
-
-<!-- Navigation links -->
-<hr>
-
-<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a><br>
-<b>To:</b> <a href="#synopsis">sy</a>nopsis • <a href="#input">in</a>put
-• <a href="#outputs">ou</a>tputs • <a href="#controls">co</a>ntrols
-• <a href="#options">op</a>tions
-<!-- GC common information -->
-<hr>
-
-<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
-align="middle" width="40" height="40"></a><i>The Geometry Center
-Home Page </i></p>
-
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qhull.man b/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qhull.man
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-./" This is the Unix manual page for qhull, written in nroff, the standard
-./" manual formatter for Unix systems. To format it, type
-./"
-./" nroff -man qhull.man
-./"
-./" This will print a formatted copy to standard output. If you want
-./" to ensure that the output is plain ASCII, free of any control
-./" characters that nroff uses for underlining etc, pipe the output
-./" through "col -b":
-./"
-./" nroff -man qhull.man | col -b
-./"
-./" Warning: a leading quote "'" or dot "." will not format correctly
-./"
-.TH qhull 1 "2003/12/30" "Geometry Center"
-.SH NAME
-qhull \- convex hull, Delaunay triangulation, Voronoi diagram,
-halfspace intersection about a point, hull volume, facet area
-.SH SYNOPSIS
-.nf
-qhull- compute convex hulls and related structures
- input (stdin): dimension, #points, point coordinates
- first comment (non-numeric) is listed in the summary
- halfspace: use dim plus one with offsets after coefficients
-
-options (qh-quick.htm):
- d - Delaunay triangulation by lifting points to a paraboloid
- v - Voronoi diagram via the Delaunay triangulation
- H1,1 - Halfspace intersection about [1,1,0,...]
- d Qu - Furthest-site Delaunay triangulation (upper convex hull)
- v Qu - Furthest-site Voronoi diagram
- Qt - triangulated output
- QJ - Joggle the input to avoid precision problems
- . - concise list of all options
- - - one-line description of all options
-
-Output options (subset):
- FA - compute total area and volume
- Fx - extreme points (convex hull vertices)
- G - Geomview output (2-d, 3-d and 4-d)
- Fp - halfspace intersection coordinates
- m - Mathematica output (2-d and 3-d)
- n - normals with offsets
- o - OFF file format (if Voronoi, outputs regions)
- TO file- output results to file, may be enclosed in single quotes
- f - print all fields of all facets
- s - summary of results (default)
- Tv - verify result: structure, convexity, and point inclusion
- p - vertex coordinates (centers for Voronoi)
- i - vertices incident to each facet
-
-example:
- rbox 1000 s | qhull Tv s FA
-.fi
-
- - html manual: index.htm
- - installation: README.txt
- - see also: COPYING.txt, REGISTER.txt, Changes.txt
- - WWW: <http://www.qhull.org>
- - CVS: <http://savannah.gnu.org/projects/qhull/>
- - mirror: <http://www6.uniovi.es/ftp/pub/mirrors/geom.umn.edu/software/ghindex.html>
- - news: <http://www.qhull.org/news>
- - Geomview: <http://www.geomview.org>
- - news group: <news:comp.graphics.algorithms>
- - FAQ: <http://exaflop.org/docs/cgafaq/cga6.html>
- - email: qhull@qhull.org
- - bug reports: qhull_bug@qhull.org
-
-The sections are:
- - INTRODUCTION
- - DESCRIPTION, a description of Qhull
- - IMPRECISION, how Qhull handles imprecision
- - OPTIONS
- - Input and output options
- - Additional input/output formats
- - Precision options
- - Geomview options
- - Print options
- - Qhull options
- - Trace options
- - BUGS
- - E-MAIL
- - SEE ALSO
- - AUTHORS
- - ACKNOWLEGEMENTS
-
-This man page briefly describes all Qhull options. Please report
-any mismatches with Qhull's html manual (index.htm).
-
-.PP
-.SH INTRODUCTION
-Qhull is a general dimension code for computing convex hulls, Delaunay
-triangulations, Voronoi diagram, furthest-site Voronoi diagram,
-furthest-site Delaunay triangulations, and
-halfspace intersections about a point. It implements the Quickhull algorithm for
-computing the convex hull. Qhull handles round-off errors from floating
-point arithmetic. It can approximate a convex hull.
-
-The program includes options for hull volume, facet area, partial hulls,
-input transformations, randomization, tracing, multiple output formats, and
-execution statistics. The program can be called from within your application.
-You can view the results in 2-d, 3-d and 4-d with Geomview.
-.PP
-.SH DESCRIPTION
-.PP
-The format of input is the following: first line contains the dimension,
-second line contains the number of input points, and point coordinates follow.
-The dimension and number of points can be reversed.
-Comments and line breaks are ignored. A comment starts with a
-non-numeric character and continues to the end of line. The first comment
-is reported in summaries and statistics.
-Error reporting is
-better if there is one point per line.
-.PP
-The default printout option is a short summary. There are many
-other output formats.
-.PP
-Qhull implements the Quickhull algorithm for convex hull. This algorithm combines
-the 2-d Quickhull algorithm with the n-d beneath-beyond algorithm
-[c.f., Preparata & Shamos '85].
-It is similar to the randomized algorithms of Clarkson and
-others [Clarkson et al. '93]. The main
-advantages of Quickhull are output sensitive performance, reduced
-space requirements, and automatic handling of precision problems.
-.PP
-The data structure produced by Qhull consists of vertices, ridges, and facets.
-A vertex is a point of the input set. A ridge is a set of d vertices
-and two neighboring facets. For example in 3-d, a ridge is an edge of the
-polyhedron. A facet is a set of ridges, a set of neighboring facets, a set
-of incident vertices, and a hyperplane equation. For simplicial facets, the
-ridges are defined by the vertices and neighboring facets. When Qhull
-merges two facets, it produces a non-simplicial
-facet. A non-simplicial facet has more than d neighbors and may share more than
-one ridge with a neighbor.
-.PP
-.SH IMPRECISION
-.PP
-Since Qhull uses floating point arithmetic, roundoff error may occur for each
-calculation. This causes problems
-for most geometric algorithms.
-.PP
-Qhull automatically sets option 'C-0' in 2-d, 3-d, and 4-d, or
-option 'Qx' in 5-d and higher. These options handle precision problems
-by merging facets. Alternatively, use option 'QJ' to joggle the
-input.
-.PP
-With 'C-0', Qhull merges non-convex
-facets while constructing the hull. The remaining facets are
-clearly convex. With 'Qx', Qhull merges
-coplanar horizon facets, flipped facets, concave facets and
-duplicated ridges. It merges coplanar facets after constructing
-the hull.
-With 'Qx', coplanar points may be missed, but it
-appears to be unlikely.
-.PP
-To guarantee triangular output, joggle the input with option 'QJ'. Facet
-merging will not occur.
-.SH OPTIONS
-.PP
-To get a list of the most important options, execute 'qhull' by itself.
-To get a complete list of options,
-execute 'qhull -'.
-To get a complete, concise list of options, execute 'qhull .'.
-
-Options can be in any order.
-Capitalized options take an argument (except 'PG' and 'F' options).
-Single letters are used for output formats and precision constants. The
-other options are grouped into menus for other output formats ('F'),
-Geomview output ('G'),
-printing ('P'), Qhull control ('Q'), and tracing ('T').
-.TP
-Main options:
-.TP
-default
-Compute the convex hull of the input points. Report a summary of
-the result.
-.TP
-d
-Compute the Delaunay triangulation by lifting the input points to a
-paraboloid. The 'o' option prints the input points and facets.
-The 'QJ' option guarantees triangular output. The 'Ft'
-option prints a triangulation. It adds points (the centrums) to non-simplicial
-facets.
-.TP
-v
-Compute the Voronoi diagram from the Delaunay triangulation.
-The 'p' option prints the Voronoi vertices.
-The 'o' option prints the Voronoi vertices and the
-vertices in each Voronoi region. It lists regions in
-site ID order.
-The 'Fv' option prints each ridge of the Voronoi diagram.
-The first or zero'th vertex
-indicates the infinity vertex. Its coordinates are
-qh_INFINITE (-10.101). It indicates unbounded Voronoi
-regions or degenerate Delaunay triangles.
-.TP
-Hn,n,...
-Compute halfspace intersection about [n,n,0,...].
-The input is a set of halfspaces
-defined in the same format as 'n', 'Fo', and 'Fi'.
-Use 'Fp' to print the intersection points. Use 'Fv'
-to list the intersection points for each halfspace. The
-other output formats display the dual convex hull.
-
-The point [n,n,n,...] is a feasible point for the halfspaces, i.e.,
-a point that is inside all
-of the halfspaces (Hx+b <= 0). The default coordinate value is 0.
-
-The input may start with a feasible point. If so, use 'H' by itself.
-The input starts with a feasible point when the first number is the dimension,
-the second number is "1", and the coordinates complete a line. The 'FV'
-option produces a feasible point for a convex hull.
-.TP
-d Qu
-Compute the furthest-site Delaunay triangulation from the upper
-convex hull. The 'o' option prints the input points and facets.
-The 'QJ' option guarantees triangular otuput. You can also use
-'Ft' to triangulate via the centrums of non-simplicial
-facets.
-.TP
-v Qu
-Compute the furthest-site Voronoi diagram.
-The 'p' option prints the Voronoi vertices.
-The 'o' option prints the Voronoi vertices and the
-vertices in each Voronoi region.
-The 'Fv' option prints each ridge of the Voronoi diagram.
-The first or zero'th vertex
-indicates the infinity vertex at infinity. Its coordinates are
-qh_INFINITE (-10.101). It indicates unbounded Voronoi regions
-and degenerate Delaunay triangles.
-.PP
-.TP
-Input/Output options:
-.TP
-f
-Print out all facets and all fields of each facet.
-.TP
-G
-Output the hull in Geomview format. For imprecise hulls,
-Geomview displays the inner and outer hull. Geomview can also
-display points, ridges, vertices, coplanar points, and
-facet intersections. See below for a list of options.
-
-For Delaunay triangulations, 'G' displays the
-corresponding paraboloid. For halfspace intersection, 'G' displays the
-dual polytope.
-.TP
-i
-Output the incident vertices for each facet.
-Qhull prints the number of facets followed by the
-vertices of each facet. One facet is printed per line. The numbers
-are the 0-relative indices of the corresponding input points.
-The facets
-are oriented.
-
-In 4-d and higher,
-Qhull triangulates non-simplicial facets. Each apex (the first vertex) is
-a created point that corresponds to the facet's centrum. Its index is greater
-than the indices of the input points. Each base
-corresponds to a simplicial ridge between two facets.
-To print the vertices without triangulation, use option 'Fv'.
-.TP
-m
-Output the hull in Mathematica format. Qhull writes a Mathematica file for 2-d and 3-d
-convex hulls and for 2-d Delaunay triangulations. Qhull produces a list of objects
-that you can assign to a variable in Mathematica, for example:
-"list= << <outputfilename> ". If the object is 2-d, it can be
-visualized by "Show[Graphics[list]] ". For 3-d objects the command is
-"Show[Graphics3D[list]]".
-.TP
-n
-Output the normal equation for each facet.
-Qhull prints the dimension (plus one), the number of facets,
-and the normals for each facet. The facet's offset follows its
-normal coefficients.
-.TP
-o
-Output the facets in OFF file format.
-Qhull prints the dimension, number of points, number
-of facets, and number of ridges. Then it prints the coordinates of
-the input points and the vertices for each facet. Each facet is on
-a separate line. The first number is the number of vertices. The
-remainder are the indices of the corresponding points. The vertices are
-oriented in 2-d, 3-d, and in simplicial facets.
-
-For 2-d Voronoi diagrams,
-the vertices are sorted by adjacency, but not oriented. In 3-d and higher,
-the Voronoi vertices are sorted by index.
-See the 'v' option for more information.
-.TP
-p
-Output the coordinates of each vertex point.
-Qhull prints the dimension, the number of points,
-and the coordinates for each vertex.
-With the 'Gc' and 'Gi' options, it also prints coplanar
-and interior points. For Voronoi diagrams, it prints the coordinates
-of each Voronoi vertex.
-.TP
-s
-Print a summary to stderr. If no output options
-are specified at all, a summary goes to stdout. The summary lists
-the number of input points, the dimension, the number of vertices
-in the convex hull, the number of facets in the convex hull, the
-number of good facets (if 'Pg'), and statistics.
-
-The last two statistics (if needed) measure the maximum distance
-from a point or vertex to a
-facet. The number in parenthesis (e.g., 2.1x) is the ratio between the
-maximum distance and the worst-case distance due to merging
-two simplicial facets.
-.PP
-.TP
-Precision options
-.TP
-An
-Maximum angle given as a cosine. If the angle between a pair of facet
-normals
-is greater than n, Qhull merges one of the facets into a neighbor.
-If 'n' is negative, Qhull tests angles after adding
-each point to the hull (pre-merging).
-If 'n' is positive, Qhull tests angles after
-constructing the hull (post-merging).
-Both pre- and post-merging can be defined.
-
-Option 'C0' or 'C-0' is set if the corresponding 'Cn' or 'C-n'
-is not set. If 'Qx'
-is set, then 'A-n' and 'C-n' are checked after the hull is constructed
-and before 'An' and 'Cn' are checked.
-.TP
-Cn
-Centrum radius.
-If a centrum is less than n below a neighboring facet, Qhull merges one
-of the facets.
-If 'n' is negative or '-0', Qhull tests and merges facets after adding
-each point to the hull. This is called "pre-merging". If 'n' is positive,
-Qhull tests for convexity after constructing the hull ("post-merging").
-Both pre- and post-merging can be defined.
-
-For 5-d and higher, 'Qx' should be used
-instead of 'C-n'. Otherwise, most or all facets may be merged
-together.
-.TP
-En
-Maximum roundoff error for distance computations.
-.TP
-Rn
-Randomly perturb distance computations up to +/- n * max_coord.
-This option perturbs every distance, hyperplane, and angle computation.
-To use time as the random number seed, use option 'QR-1'.
-.TP
-Vn
-Minimum distance for a facet to be visible.
-A facet is visible if the distance from the point to the
-facet is greater than 'Vn'.
-
-Without merging, the default value for 'Vn' is the round-off error ('En').
-With merging, the default value is the pre-merge centrum ('C-n') in 2-d or
-3--d, or three times that in other dimensions. If the outside width
-is specified ('Wn'), the maximum, default value for 'Vn' is 'Wn'.
-.TP
-Un
-Maximum distance below a facet for a point to be coplanar to the facet. The
-default value is 'Vn'.
-.TP
-Wn
-Minimum outside width of the hull. Points are added to the convex hull
-only if they are clearly outside of a facet. A point is outside of a
-facet if its distance to the facet is greater than 'Wn'. The normal
-value for 'Wn' is 'En'. If the user specifies pre-merging and
-does not set 'Wn', than 'Wn' is set
-to the premerge 'Cn' and maxcoord*(1-An).
-.PP
-.TP
-Additional input/output formats
-.TP
-Fa
-Print area for each facet.
-For Delaunay triangulations, the area is the area of the triangle.
-For Voronoi diagrams, the area is the area of the dual facet.
-Use 'PAn' for printing the n largest facets, and option 'PFn' for
-printing facets larger than 'n'.
-
-The area for non-simplicial facets is the sum of the
-areas for each ridge to the centrum. Vertices far below
-the facet's hyperplane are ignored.
-The reported area may be significantly less than the actual area.
-.TP
-FA
-Compute the total area and volume for option 's'. It is an approximation
-for non-simplicial facets (see 'Fa').
-.TP
-Fc
-Print coplanar points for each facet. The output starts with the
-number of facets. Then each facet is printed one per line. Each line
-is the number of coplanar points followed by the point ids.
-Option 'Qi' includes the interior points. Each coplanar point (interior point) is
-assigned to the facet it is furthest above (resp., least below).
-.TP
-FC
-Print centrums for each facet. The output starts with the
-dimension followed by the number of facets.
-Then each facet centrum is printed, one per line.
-.TP
-Fd
-Read input in cdd format with homogeneous points.
-The input starts with comments. The first comment is reported in
-the summary.
-Data starts after a "begin" line. The next line is the number of points
-followed by the dimension+1 and "real" or "integer". Then the points
-are listed with a leading "1" or "1.0". The data ends with an "end" line.
-
-For halfspaces ('Fd Hn,n,...'), the input format is the same. Each halfspace
-starts with its offset. The sign of the offset is the opposite of Qhull's
-convention.
-.TP
-FD
-Print normals ('n', 'Fo', 'Fi') or points ('p') in cdd format.
-The first line is the command line that invoked Qhull.
-Data starts with a "begin" line. The next line is the number of normals or points
-followed by the dimension+1 and "real". Then the normals or points
-are listed with the offset before the coefficients. The offset for points is
-1.0. The offset for normals has the opposite sign.
-The data ends with an "end" line.
-.TP
-FF
-Print facets (as in 'f') without printing the ridges.
-.TP
-Fi
-Print inner planes for each facet. The inner plane is below all vertices.
-.TP
-Fi
-Print separating hyperplanes for bounded, inner regions of the Voronoi
-diagram. The first line is the number
-of ridges. Then each hyperplane is printed, one per line. A line starts
-with the number of indices and floats. The first pair lists
-adjacent input
-sites, the next d floats are the normalized coefficients for the hyperplane,
-and the last float is the offset. The hyperplane is oriented toward
-'QVn' (if defined), or the first input site of the pair. Use 'Tv' to
-verify that the hyperplanes are perpendicular bisectors. Use 'Fo' for
-unbounded regions, and 'Fv' for the corresponding Voronoi vertices.
-.TP
-FI
-Print facet identifiers.
-.TP
-Fm
-Print number of merges for each facet. At most 511 merges are reported for
-a facet. See 'PMn' for printing the facets with the most merges.
-.TP
-FM
-Output the hull in Maple format. Qhull writes a Maple
-file for 2-d and 3-d
-convex hulls and for 2-d Delaunay triangulations. Qhull produces a '.mpl'
-file for displaying with display3d().
-.TP
-Fn
-Print neighbors for each facet. The output starts with the number of facets.
-Then each facet is printed one per line. Each line
-is the number of neighbors followed by an index for each neighbor. The indices
-match the other facet output formats.
-
-A negative index indicates an unprinted
-facet due to printing only good facets ('Pg'). It is the negation of the facet's
-ID (option 'FI').
-For example, negative indices are used for facets
-"at infinity" in the Delaunay triangulation.
-.TP
-FN
-Print vertex neighbors or coplanar facet for each point.
-The first line is the number
-of points. Then each point is printed, one per line. If the
-point is coplanar, the line is "1" followed by the facet's ID.
-If the point is
-not a selected vertex, the line is "0".
-Otherwise, each line is the number of
-neighbors followed by the corresponding facet indices (see 'Fn').
-.TP
-Fo
-Print outer planes for each facet in the same format as 'n'.
-The outer plane is above all points.
-.TP
-Fo
-Print separating hyperplanes for unbounded, outer regions of the Voronoi
-diagram. The first line is the number
-of ridges. Then each hyperplane is printed, one per line. A line starts
-with the number of indices and floats. The first pair lists
-adjacent input
-sites, the next d floats are the normalized coefficients for the hyperplane,
-and the last float is the offset. The hyperplane is oriented toward
-'QVn' (if defined), or the first input site of the pair. Use 'Tv' to
-verify that the hyperplanes are perpendicular bisectors. Use 'Fi' for
-bounded regions, and 'Fv' for the corresponding Voronoi vertices.
-.TP
-FO
-List all options to stderr, including the default values. Additional 'FO's
-are printed to stdout.
-.TP
-Fp
-Print points for halfspace intersections (option 'Hn,n,...'). Each
-intersection corresponds to a facet of the dual polytope.
-The "infinity" point [-10.101,-10.101,...]
-indicates an unbounded intersection.
-.TP
-FP
-For each coplanar point ('Qc') print the point ID of the nearest vertex,
-the point ID, the facet ID, and the distance.
-.TP
-FQ
-Print command used for qhull and input.
-.TP
-Fs
-Print a summary. The first line consists of the number of integers ("8"),
-followed by the dimension, the number of points, the number of vertices,
-the number of facets, the number of vertices selected for output, the
-number of facets selected for output, the number of coplanar points selected
-for output, number of simplicial, unmerged facets in output
-
-The second line consists of the number of reals ("2"),
-followed by the maxmimum offset to an outer plane and and minimum offset to
-an inner plane. Roundoff is included. Later
-versions of Qhull may produce additional integers or reals.
-.TP
-FS
-Print the size of the hull. The first line consists of the number of integers ("0").
-The second line consists of the number of reals ("2"),
-followed by the total facet area, and the total volume.
-Later
-versions of Qhull may produce additional integers or reals.
-
-The total volume measures the volume
-of the intersection of the halfspaces defined by each facet.
-Both area and volume are
-approximations for non-simplicial facets. See option 'Fa'.
-.TP
-Ft
-Print a triangulation with added points for non-simplicial
-facets. The first line is the dimension and the second line is the
-number of points and the number of facets. The points follow, one
-per line, then the facets follow as a list of point indices. With option
-'Qz', the
-points include the point-at-infinity.
-.TP
-Fv
-Print vertices for each facet. The first line is the number
-of facets. Then each facet is printed, one per line. Each line is
-the number of vertices followed by the corresponding point ids. Vertices
-are listed in the order they were added to the hull (the last one is first).
-.TP
-Fv
-Print all ridges of a Voronoi diagram. The first line is the number
-of ridges. Then each ridge is printed, one per line. A line starts
-with the number of indices. The first pair lists adjacent input
-sites, the remaining indices list Voronoi vertices. Vertex '0' indicates
-the vertex-at-infinity (i.e., an unbounded ray). In 3-d, the vertices
-are listed in order. See 'Fi' and 'Fo' for separating hyperplanes.
-.TP
-FV
-Print average vertex. The average vertex is a feasible point
-for halfspace intersection.
-.TP
-Fx
-List extreme points (vertices) of the convex hull. The first line
-is the number of points. The other lines give the indices of the
-corresponding points. The first point is '0'. In 2-d, the points
-occur in counter-clockwise order; otherwise they occur in input order.
-For Delaunay triangulations, 'Fx' lists the extreme points of the
-input sites. The points are unordered.
-.PP
-.TP
-Geomview options
-.TP
-G
-Produce a file for viewing with Geomview. Without other options,
-Qhull displays edges in 2-d, outer planes in 3-d, and ridges in 4-d.
-A ridge can be
-explicit or implicit. An explicit ridge is a dim-1 dimensional simplex
-between two facets.
-In 4-d, the explicit ridges are triangles.
-When displaying a ridge in 4-d, Qhull projects the ridge's vertices to
-one of its facets' hyperplanes.
-Use 'Gh' to
-project ridges to the intersection of both hyperplanes.
-.TP
-Ga
-Display all input points as dots.
-.TP
-Gc
-Display the centrum for each facet in 3-d. The centrum is defined by a
-green radius sitting on a blue plane. The plane corresponds to the
-facet's hyperplane.
-The radius is defined by 'C-n' or 'Cn'.
-.TP
-GDn
-Drop dimension n in 3-d or 4-d. The result is a 2-d or 3-d object.
-.TP
-Gh
-Display hyperplane intersections in 3-d and 4-d. In 3-d, the
-intersection is a black line. It lies on two neighboring hyperplanes
-(c.f., the blue squares associated with centrums ('Gc')). In 4-d,
-the ridges are projected to the intersection of both hyperplanes.
-.TP
-Gi
-Display inner planes in 2-d and 3-d. The inner plane of a facet
-is below all of its vertices. It is parallel to the facet's hyperplane.
-The inner plane's color is the opposite (1-r,1-g,1-b) of the outer
-plane. Its edges are determined by the vertices.
-.TP
-Gn
-Do not display inner or outer planes. By default,
-Geomview displays the precise plane (no merging) or both
-inner and output planes (merging). Under merging, Geomview does
-not display the inner plane if the
-the difference between inner and outer is too small.
-.TP
-Go
-Display outer planes in 2-d and 3-d. The outer plane of a facet
-is above all input points. It is parallel to the facet's hyperplane.
-Its color is determined by the facet's normal, and its
-edges are determined by the vertices.
-.TP
-Gp
-Display coplanar points and vertices as radii. A radius defines a ball
-which corresponds to the imprecision of the point. The imprecision is
-the maximum of the roundoff error, the centrum radius, and maxcoord *
-(1-An). It is at least 1/20'th of the maximum coordinate,
-and ignores post-merging if pre-merging is done.
-.TP
-Gr
-Display ridges in 3-d. A ridge connects the two vertices that are shared
-by neighboring facets. Ridges are always displayed in 4-d.
-.TP
-Gt
-A 3-d Delaunay triangulation looks like a convex hull with interior
-facets. Option 'Gt' removes the outside ridges to reveal the outermost
-facets. It automatically sets options 'Gr' and 'GDn'.
-.TP
-Gv
-Display vertices as spheres. The radius of the sphere corresponds to
-the imprecision of the data. See 'Gp' for determining the radius.
-.PP
-.TP
-Print options
-.TP
-PAn
-Only the n largest facets are marked good for printing.
-Unless 'PG' is set, 'Pg' is automatically set.
-.TP
-Pdk:n
-Drop facet from output if normal[k] <= n. The option 'Pdk' uses the
-default value of 0 for n.
-.TP
-PDk:n
-Drop facet from output if normal[k] >= n. The option 'PDk' uses the
-default value of 0 for n.
-.TP
-PFn
-Only facets with area at least 'n' are marked good for printing.
-Unless 'PG' is set, 'Pg' is automatically set.
-.TP
-Pg
-Print only good facets. A good facet is either visible from a point
-(the 'QGn' option) or includes a point (the 'QVn' option). It also meets the
-requirements of 'Pdk' and 'PDk' options. Option 'Pg' is automatically
-set for options 'PAn' and 'PFn'.
-.TP
-PG
-Print neighbors of good facets.
-.TP
-PMn
-Only the n facets with the most merges are marked good for printing.
-Unless 'PG' is set, 'Pg' is automatically set.
-.TP
-Po
-Force output despite precision problems. Verify ('Tv') does not check
-coplanar points.
-Flipped facets are reported and concave facets are counted.
-If 'Po' is used, points are not
-partitioned into flipped facets and a flipped facet is always visible
-to a point.
-Also, if an error occurs before the completion of Qhull and tracing is
-not active, 'Po' outputs a neighborhood of the erroneous facets
-(if any).
-.TP
-Pp
-Do not report precision problems.
-.PP
-.TP
-Qhull control options
-.TP
-Qbk:0Bk:0
-Drop dimension k from the input points. This allows the user to
-take convex hulls of sub-dimensional objects. It happens before
-the Delaunay and Voronoi transformation.
-.TP
-QbB
-Scale the input points to fit the unit cube. After scaling, the lower
-bound will be -0.5 and the upper bound +0.5 in all dimensions.
-For Delaunay and
-Voronoi diagrams, scaling happens after projection to the paraboloid.
-Under precise
-arithmetic, scaling does not change the topology of the convex hull.
-.TP
-Qbb
-Scale the last coordinate to [0, m] where m is the maximum absolute
-value of the other coordinates. For Delaunay and
-Voronoi diagrams, scaling happens after projection to the paraboloid.
-It reduces roundoff error for inputs with integer coordinates.
-Under precise
-arithmetic, scaling does not change the topology of the convex hull.
-.TP
-Qbk:n
-Scale the k'th coordinate of the input points. After scaling, the lower
-bound of the input points will be n. 'Qbk' scales to -0.5.
-.TP
-QBk:n
-Scale the k'th coordinate of the input points. After scaling, the upper
-bound will be n. 'QBk' scales to +0.5.
-.TP
-Qc
-Keep coplanar points with the nearest facet. Output
-formats 'p', 'f', 'Gp', 'Fc', 'FN', and 'FP' will print the points.
-.TP
-Qf
-Partition points to the furthest outside facet.
-.TP
-Qg
-Only build good facets. With the 'Qg' option, Qhull will only build
-those facets that it needs to determine the good facets in the output.
-See 'QGn', 'QVn', and 'PdD' for defining good facets, and 'Pg' and 'PG'
-for printing good facets and their neighbors.
-.TP
-QGn
-A facet is good (see 'Qg' and 'Pg') if it is visible from point n. If n < 0, a facet is
-good if it is not visible from point n. Point n is not added to the
-hull (unless 'TCn' or 'TPn').
-With rbox, use the 'Pn,m,r' option to define your point; it
-will be point 0 (QG0).
-.TP
-Qi
-Keep interior points with the nearest facet.
-Output formats 'p', 'f', 'Gp', 'FN', 'FP', and 'Fc' will print the points.
-.TP
-QJn
-Joggle each input coordinate by adding a random number in [-n,n]. If a
-precision error occurs, then qhull increases n and tries again. It does
-not increase n beyond a certain value, and it stops after a certain number
-of attempts [see user.h]. Option 'QJ'
-selects a default value for n. The output will be simplicial. For
-Delaunay triangulations, 'QJn' sets 'Qbb' to scale the last coordinate
-(not if 'Qbk:n' or 'QBk:n' is set). See also 'Qt'.
-.TP
-Qm
-Only process points that would otherwise increase max_outside. Other
-points are treated as coplanar or interior points.
-.TP
-Qr
-Process random outside points instead of furthest ones. This makes
-Qhull equivalent to the randomized incremental algorithms. CPU time
-is not reported since the randomization is inefficient.
-.TP
-QRn
-Randomly rotate the input points. If n=0, use time as the random number seed.
-If n>0, use n as the random number seed. If n=-1, don't rotate but use
-time as the random number seed. For Delaunay triangulations ('d' and 'v'),
-rotate about the last axis.
-.TP
-Qs
-Search all points for the initial simplex.
-.TP
-Qt
-Triangulated output. Triangulate all non-simplicial facets. See also 'QJ'.
-.TP
-Qv
-Test vertex neighbors for convexity after post-merging.
-To use the 'Qv' option, you also need to set a merge option
-(e.g., 'Qx' or 'C-0').
-.TP
-QVn
-A good facet (see 'Qg' and 'Pg') includes point n. If n<0, then a good facet does not
-include point n. The point is either in the initial simplex or it
-is the first point added to the hull. Option 'QVn' may not be used with merging.
-.TP
-Qx
-Perform exact merges while building the hull. The "exact" merges
-are merging a point into a coplanar facet (defined by 'Vn', 'Un',
-and 'C-n'), merging concave facets, merging duplicate ridges, and
-merging flipped facets. Coplanar merges and angle coplanar merges ('A-n')
-are not performed. Concavity testing is delayed until a merge occurs.
-
-After
-the hull is built, all coplanar merges are performed (defined by 'C-n'
-and 'A-n'), then post-merges are performed
-(defined by 'Cn' and 'An').
-.TP
-Qz
-Add a point "at infinity" that is above the paraboloid for Delaunay triangulations
-and Voronoi diagrams. This reduces precision problems and allows the triangulation
-of cospherical points.
-.PP
-.TP
-Qhull experiments and speedups
-.TP
-Q0
-Turn off pre-merging as a default option.
-With 'Q0'/'Qx' and without explicit pre-merge options, Qhull
-ignores precision issues while constructing the convex hull. This
-may lead to precision errors. If so, a descriptive warning is
-generated.
-.TP
-Q1
-With 'Q1', Qhull sorts merges by type (coplanar, angle coplanar, concave)
-instead of by angle.
-.TP
-Q2
-With 'Q2', Qhull merges all facets at once instead of using
-independent sets of merges and then retesting.
-.TP
-Q3
-With 'Q3', Qhull does not remove redundant vertices.
-.TP
-Q4
-With 'Q4', Qhull avoids merges of an old facet into a new facet.
-.TP
-Q5
-With 'Q5', Qhull does not correct outer planes at the end. The
-maximum outer plane is used instead.
-.TP
-Q6
-With 'Q6', Qhull does not pre-merge concave or coplanar facets.
-.TP
-Q7
-With 'Q7', Qhull processes facets in depth-first order instead of
-breadth-first order.
-.TP
-Q8
-With 'Q8' and merging, Qhull does not retain near-interior points for adjusting
-outer planes. 'Qc' will probably retain
-all points that adjust outer planes.
-.TP
-Q9
-With 'Q9', Qhull processes the furthest of all outside sets at each iteration.
-.TP
-Q10
-With 'Q10', Qhull does not use special processing for narrow distributions.
-.TP
-Q11
-With 'Q11', Qhull copies normals and recompute centrums for tricoplanar facets.
-.PP
-.TP
-Trace options
-.TP
-Tn
-Trace at level n. Qhull includes full execution tracing. 'T-1'
-traces events. 'T1' traces
-the overall execution of the program. 'T2' and 'T3' trace overall
-execution and geometric and topological events. 'T4' traces the
-algorithm. 'T5' includes information about memory allocation and
-Gaussian elimination.
-.TP
-Tc
-Check frequently during execution. This will catch most inconsistency
-errors.
-.TP
-TCn
-Stop Qhull after building the cone of new facets for point n. The
-output for 'f' includes the cone and the old hull.
-See also 'TVn'.
-.TP
-TFn
-Report progress whenever more than n facets are created
-During post-merging, 'TFn'
-reports progress after more than n/2 merges.
-.TP
-TI file
-Input data from 'file'. The filename may not include spaces or
-quotes.
-.TP
-TO file
-Output results to 'file'. The name may be enclosed in single
-quotes.
-.TP
-TPn
-Turn on tracing when point n is added to the hull. Trace
-partitions of point n. If used with TWn, turn off
-tracing after adding point n to the hull.
-.TP
-TRn
-Rerun qhull n times. Usually used with 'QJn' to determine the
-probability that a given joggle will fail.
-.TP
-Ts
-Collect statistics and print to stderr at the end of execution.
-.TP
-Tv
-Verify the convex hull. This checks the topological structure, facet
-convexity, and point inclusion.
-If precision problems occurred, facet convexity is tested whether or
-not 'Tv' is selected.
-Option 'Tv' does not check point inclusion if forcing output with 'Po',
-or if 'Q5' is set.
-
-For point inclusion testing, Qhull verifies that all points are below
-all outer planes (facet->maxoutside). Point inclusion is exhaustive
-if merging or if the facet-point product is small enough;
-otherwise Qhull verifies each point with a directed
-search (qh_findbest).
-
-Point inclusion testing occurs after producing output. It prints
-a message to stderr unless option 'Pp' is used. This
-allows the user to interrupt Qhull without changing the output.
-.TP
-TVn
-Stop Qhull after adding point n. If n < 0, stop Qhull before adding
-point n. Output shows the hull at this time. See also 'TCn'
-.TP
-TMn
-Turn on tracing at n'th merge.
-.TP
-TWn
-Trace merge facets when the width is greater than n.
-.TP
-Tz
-Redirect stderr to stdout.
-.PP
-.SH BUGS
-Please report bugs to Brad Barber at qhull_bug@qhull.org.
-
-If Qhull does not compile, it is due to an incompatibility between your
-system and ours. The first thing to check is that your compiler is
-ANSI standard. If it is, check the man page for the best options, or
-find someone to help you. If you locate the cause of your problem,
-please send email since it might help others.
-
-If Qhull compiles but crashes on the test case (rbox D4), there's
-still incompatibility between your system and ours. Typically it's
-been due to mem.c and memory alignment. You can use qh_NOmem in mem.h
-to turn off memory management. Please let us know if you figure out
-how to fix these problems.
-
-If you do find a problem, try to simplify it before reporting the
-error. Try different size inputs to locate the smallest one that
-causes an error. You're welcome to hunt through the code using the
-execution trace as a guide. This is especially true if you're
-incorporating Qhull into your own program.
-
-When you do report an error, please attach a data set to the
-end of your message. This allows us to see the error for ourselves.
-Qhull is maintained part-time.
-.PP
-.SH E-MAIL
-Please send correspondence to qhull@qhull.org and report bugs to
-qhull_bug@qhull.org. Let us know how you use Qhull. If you
-mention it in a paper, please send the reference and an abstract.
-
-If you would like to get Qhull announcements (e.g., a new version)
-and news (any bugs that get fixed, etc.), let us know and we will add you to
-our mailing list. If you would like to communicate with other
-Qhull users, we will add you to the qhull_users alias.
-For Internet news about geometric algorithms and convex hulls, look at
-comp.graphics.algorithms and sci.math.num-analysis
-
-.SH SEE ALSO
-rbox(1)
-
-Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa,
-"The Quickhull Algorithm for Convex Hulls," ACM
-Trans. on Mathematical Software, Dec. 1996.
-http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p469-barber/
-http://citeseer.nj.nec.com/83502.html
-
-Clarkson, K.L., K. Mehlhorn, and R. Seidel, "Four results on randomized
-incremental construction," Computational Geometry: Theory and Applications,
-vol. 3, p. 185-211, 1993.
-
-Preparata, F. and M. Shamos, Computational
-Geometry, Springer-Verlag, New York, 1985.
-
-.PP
-.SH AUTHORS
-.nf
- C. Bradford Barber Hannu Huhdanpaa
- bradb@qhull.org hannu@qhull.org
-
- c/o The Geometry Center
- University of Minnesota
- 400 Lind Hall
- 207 Church Street S.E.
- Minneapolis, MN 55455
-
-.fi
-
-.SH ACKNOWLEDGEMENTS
-
-A special thanks to Albert Marden, Victor Milenkovic, the Geometry Center,
-Harvard University, and Endocardial Solutions, Inc. for supporting this work.
-
-The software was developed under National Science Foundation grants
-NSF/DMS-8920161 and NSF-CCR-91-15793 750-7504. David Dobkin guided
-the original work at Princeton University.
-If you find it useful, please let us know.
-
-The Geometry Center is supported by grant DMS-8920161 from the National
-Science Foundation, by grant DOE/DE-FG02-92ER25137 from the Department
-of Energy, by the University of Minnesota, and by Minnesota Technology, Inc.
-
-Qhull is available from http://www.qhull.org
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qhull.txt b/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qhull.txt
deleted file mode 100644
index f3b2f88f7db800a691935555888372bc4bb8e059..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qhull.txt
+++ /dev/null
@@ -1,1263 +0,0 @@
-
-
-
-qhull(1) qhull(1)
-
-
-NAME
- qhull - convex hull, Delaunay triangulation, Voronoi dia-
- gram, halfspace intersection about a point, hull volume, facet area
-
-SYNOPSIS
- qhull- compute convex hulls and related structures
- input (stdin): dimension, #points, point coordinates
- first comment (non-numeric) is listed in the summary
- halfspace: use dim plus one with offsets after coefficients
-
- options (qh-quick.htm):
- d - Delaunay triangulation by lifting points to a paraboloid
- v - Voronoi diagram via the Delaunay triangulation
- H1,1 - Halfspace intersection about [1,1,0,...]
- d Qu - Furthest-site Delaunay triangulation (upper convex hull)
- v Qu - Furthest-site Voronoi diagram
- QJ - Joggle the input to avoid precision problems
- . - concise list of all options
- - - one-line description of all options
-
- Output options (subset):
- FA - compute total area and volume
- Fx - extreme points (convex hull vertices)
- G - Geomview output (2-d, 3-d and 4-d)
- Fp - halfspace intersection coordinates
- m - Mathematica output (2-d and 3-d)
- n - normals with offsets
- o - OFF file format (if Voronoi, outputs regions)
- TO file- output results to file, may be enclosed in single quotes
- f - print all fields of all facets
- s - summary of results (default)
- Tv - verify result: structure, convexity, and point inclusion
- p - vertex coordinates
- i - vertices incident to each facet
-
- example:
- rbox 1000 s | qhull Tv s FA
-
- - html manual: index.htm
- - installation: README.txt
- - see also: COPYING.txt, REGISTER.txt, Changes.txt
- - WWW: <http://www.qhull.org>
- - CVS: <http://savannah.gnu.org/projects/qhull/>
- - mirror: <http://www6.uniovi.es/ftp/pub/mirrors/geom.umn.edu/software/ghindex.html>
- - news: <http://www.qhull.org/news>
- - Geomview: <http://www.geomview.org>
- - news group: <news:comp.graphics.algorithms>
- - FAQ: <http://exaflop.org/docs/cgafaq/cga6.html>
- - email: qhull@qhull.org
- - bug reports: qhull_bug@qhull.org
-
-
-
-
-Geometry Center 2003/12/30 1
-
-
-
-
-
-qhull(1) qhull(1)
-
-
- The sections are:
- - INTRODUCTION
- - DESCRIPTION, a description of Qhull
- - IMPRECISION, how Qhull handles imprecision
- - OPTIONS
- - Input and output options
- - Additional input/output formats
- - Precision options
- - Geomview options
- - Print options
- - Qhull options
- - Trace options
- - BUGS
- - E-MAIL
- - SEE ALSO
- - AUTHORS
- - ACKNOWLEGEMENTS
-
- This man page briefly describes all Qhull options. Please
- report any mismatches with Qhull's html manual (qh-
- man.htm).
-
-
-
-INTRODUCTION
- Qhull is a general dimension code for computing convex
- hulls, Delaunay triangulations, Voronoi diagram, furthest-
- site Voronoi diagram, furthest-site Delaunay triangula-
- tions, and halfspace intersections about a point. It
- implements the Quickhull algorithm for computing the con-
- vex hull. Qhull handles round-off errors from floating
- point arithmetic. It can approximate a convex hull.
-
- The program includes options for hull volume, facet area,
- partial hulls, input transformations, randomization, trac-
- ing, multiple output formats, and execution statistics.
- The program can be called from within your application.
- You can view the results in 2-d, 3-d and 4-d with
- Geomview.
-
-
-DESCRIPTION
- The format of input is the following: first line contains
- the dimension, second line contains the number of input
- points, and point coordinates follow. The dimension and
- number of points can be reversed. Comments and line
- breaks are ignored. A comment starts with a non-numeric
- character and continues to the end of line. The first
- comment is reported in summaries and statistics. Error
- reporting is better if there is one point per line.
-
- The default printout option is a short summary. There are
- many other output formats.
-
-
-
-
-Geometry Center 2003/12/30 2
-
-
-
-
-
-qhull(1) qhull(1)
-
-
- Qhull implements the Quickhull algorithm for convex hull.
- This algorithm combines the 2-d Quickhull algorithm with
- the n-d beneath-beyond algorithm [c.f., Preparata & Shamos
- '85]. It is similar to the randomized algorithms of
- Clarkson and others [Clarkson et al. '93]. The main
- advantages of Quickhull are output sensitive performance,
- reduced space requirements, and automatic handling of pre-
- cision problems.
-
- The data structure produced by Qhull consists of vertices,
- ridges, and facets. A vertex is a point of the input set.
- A ridge is a set of d vertices and two neighboring facets.
- For example in 3-d, a ridge is an edge of the polyhedron.
- A facet is a set of ridges, a set of neighboring facets, a
- set of incident vertices, and a hyperplane equation. For
- simplicial facets, the ridges are defined by the vertices
- and neighboring facets. When Qhull merges two facets, it
- produces a non-simplicial facet. A non-simplicial facet
- has more than d neighbors and may share more than one
- ridge with a neighbor.
-
-
-IMPRECISION
- Since Qhull uses floating point arithmetic, roundoff error
- may occur for each calculation. This causes problems for
- most geometric algorithms.
-
- Qhull automatically sets option 'C-0' in 2-d, 3-d, and
- 4-d, or option 'Qx' in 5-d and higher. These options han-
- dle precision problems by merging facets. Alternatively,
- use option 'QJ' to joggle the input.
-
- With 'C-0', Qhull merges non-convex facets while con-
- structing the hull. The remaining facets are clearly con-
- vex. With 'Qx', Qhull merges coplanar horizon facets,
- flipped facets, concave facets and duplicated ridges. It
- merges coplanar facets after constructing the hull. With
- 'Qx', coplanar points may be missed, but it appears to be
- unlikely.
-
- To guarantee triangular output, joggle the input with
- option 'QJ'. Facet merging will not occur.
-
-OPTIONS
- To get a list of the most important options, execute
- 'qhull' by itself. To get a complete list of options,
- execute 'qhull -'. To get a complete, concise list of
- options, execute 'qhull .'.
-
- Options can be in any order. Capitalized options take an
- argument (except 'PG' and 'F' options). Single letters
- are used for output formats and precision constants. The
- other options are grouped into menus for other output for-
- mats ('F'), Geomview output ('G'), printing ('P'), Qhull
-
-
-
-Geometry Center 2003/12/30 3
-
-
-
-
-
-qhull(1) qhull(1)
-
-
- control ('Q'), and tracing ('T').
-
- Main options:
-
- default
- Compute the convex hull of the input points.
- Report a summary of the result.
-
- d Compute the Delaunay triangulation by lifting the
- input points to a paraboloid. The 'o' option
- prints the input points and facets. The 'QJ'
- option guarantees triangular output. The 'Ft'
- option prints a triangulation. It adds points (the
- centrums) to non-simplicial facets.
-
- v Compute the Voronoi diagram from the Delaunay tri-
- angulation. The 'p' option prints the Voronoi ver-
- tices. The 'o' option prints the Voronoi vertices
- and the vertices in each Voronoi region. It lists
- regions in site id order. The 'Fv' option prints
- each ridge of the Voronoi diagram. The first or
- zero'th vertex indicates the infinity vertex. Its
- coordinates are qh_INFINITE (-10.101). It indi-
- cates unbounded Voronoi regions or degenerate
- Delaunay triangles.
-
- Hn,n,...
- Compute halfspace intersection about [n,n,0,...].
- The input is a set of halfspaces defined in the
- same format as 'n', 'Fo', and 'Fi'. Use 'Fp' to
- print the intersection points. Use 'Fv' to list
- the intersection points for each halfspace. The
- other output formats display the dual convex hull.
-
- The point [n,n,n,...] is a feasible point for the
- halfspaces, i.e., a point that is inside all of the
- halfspaces (Hx+b <= 0). The default coordinate
- value is 0.
-
- The input may start with a feasible point. If so,
- use 'H' by itself. The input starts with a feasi-
- ble point when the first number is the dimension,
- the second number is "1", and the coordinates com-
- plete a line. The 'FV' option produces a feasible
- point for a convex hull.
-
- d Qu Compute the furthest-site Delaunay triangulation
- from the upper convex hull. The 'o' option prints
- the input points and facets. The 'QJ' option guar-
- antees triangular otuput. You can also use facets.
-
- v Qu Compute the furthest-site Voronoi diagram. The 'p'
- option prints the Voronoi vertices. The 'o' option
- prints the Voronoi vertices and the vertices in
-
-
-
-Geometry Center 2003/12/30 4
-
-
-
-
-
-qhull(1) qhull(1)
-
-
- each Voronoi region. The 'Fv' option prints each
- ridge of the Voronoi diagram. The first or zero'th
- vertex indicates the infinity vertex at infinity.
- Its coordinates are qh_INFINITE (-10.101). It
- indicates unbounded Voronoi regions and degenerate
- Delaunay triangles.
-
- Qt Triangulated output.
-
-
- Input/Output options:
-
- f Print out all facets and all fields of each facet.
-
- G Output the hull in Geomview format. For imprecise
- hulls, Geomview displays the inner and outer hull.
- Geomview can also display points, ridges, vertices,
- coplanar points, and facet intersections. See
- below for a list of options.
-
- For Delaunay triangulations, 'G' displays the cor-
- responding paraboloid. For halfspace intersection,
- 'G' displays the dual polytope.
-
- i Output the incident vertices for each facet. Qhull
- prints the number of facets followed by the ver-
- tices of each facet. One facet is printed per
- line. The numbers are the 0-relative indices of
- the corresponding input points. The facets are
- oriented.
-
- In 4-d and higher, Qhull triangulates non-simpli-
- cial facets. Each apex (the first vertex) is a
- created point that corresponds to the facet's cen-
- trum. Its index is greater than the indices of the
- input points. Each base corresponds to a simpli-
- cial ridge between two facets. To print the ver-
- tices without triangulation, use option 'Fv'.
-
- m Output the hull in Mathematica format. Qhull
- writes a Mathematica file for 2-d and 3-d convex
- hulls and for 2-d Delaunay triangulations. Qhull
- produces a list of objects that you can assign to a
- variable in Mathematica, for example: "list= <<
- <outputfilename> ". If the object is 2-d, it can be
- visualized by "Show[Graphics[list]] ". For 3-d
- objects the command is "Show[Graphics3D[list]]".
-
- n Output the normal equation for each facet. Qhull
- prints the dimension (plus one), the number of
- facets, and the normals for each facet. The
- facet's offset follows its normal coefficients.
-
- o Output the facets in OFF file format. Qhull prints
- the dimension, number of points, number of facets,
- and number of ridges. Then it prints the
-
-
-
-Geometry Center 2003/12/30 5
-
-
-
-
-
-qhull(1) qhull(1)
-
-
- coordinates of the input points and the vertices
- for each facet. Each facet is on a separate line.
- The first number is the number of vertices. The
- remainder are the indices of the corresponding
- points. The vertices are oriented in 2-d, 3-d, and
- in simplicial facets.
-
- For 2-d Voronoi diagrams, the vertices are sorted
- by adjacency, but not oriented. In 3-d and higher,
- the Voronoi vertices are sorted by index. See the
- 'v' option for more information.
-
- p Output the coordinates of each vertex point. Qhull
- prints the dimension, the number of points, and the
- coordinates for each vertex. With the 'Gc' and
- 'Gi' options, it also prints coplanar and interior
- points. For Voronoi diagrams, it prints the coor-
- dinates of each Voronoi vertex.
-
- s Print a summary to stderr. If no output options
- are specified at all, a summary goes to stdout.
- The summary lists the number of input points, the
- dimension, the number of vertices in the convex
- hull, the number of facets in the convex hull, the
- number of good facets (if 'Pg'), and statistics.
-
- The last two statistics (if needed) measure the
- maximum distance from a point or vertex to a facet.
- The number in parenthesis (e.g., 2.1x) is the ratio
- between the maximum distance and the worst-case
- distance due to merging two simplicial facets.
-
-
- Precision options
-
- An Maximum angle given as a cosine. If the angle
- between a pair of facet normals is greater than n, Qhull
- merges one of the facets into a neighbor. If 'n'
- is negative, Qhull tests angles after adding each
- point to the hull (pre-merging). If 'n' is posi-
- tive, Qhull tests angles after constructing the
- hull (post-merging). Both pre- and post-merging
- can be defined.
-
- Option 'C0' or 'C-0' is set if the corresponding
- 'Cn' or 'C-n' is not set. If 'Qx' is set, then 'A-
- n' and 'C-n' are checked after the hull is con-
- structed and before 'An' and 'Cn' are checked.
-
- Cn Centrum radius. If a centrum is less than n below
- a neighboring facet, Qhull merges one of the
- facets. If 'n' is negative or '-0', Qhull tests
- and merges facets after adding each point to the
- hull. This is called "pre-merging". If 'n' is
-
-
-
-Geometry Center 2003/12/30 6
-
-
-
-
-
-qhull(1) qhull(1)
-
-
- positive, Qhull tests for convexity after con-
- structing the hull ("post-merging"). Both pre- and
- post-merging can be defined.
-
- For 5-d and higher, 'Qx' should be used instead of
- 'C-n'. Otherwise, most or all facets may be merged
- together.
-
- En Maximum roundoff error for distance computations.
-
- Rn Randomly perturb distance computations up to +/- n
- * max_coord. This option perturbs every distance,
- hyperplane, and angle computation. To use time as
- the random number seed, use option 'QR-1'.
-
- Vn Minimum distance for a facet to be visible. A
- facet is visible if the distance from the point to
- the facet is greater than 'Vn'.
-
- Without merging, the default value for 'Vn' is the
- round-off error ('En'). With merging, the default
- value is the pre-merge centrum ('C-n') in 2-d or
- 3--d, or three times that in other dimensions. If
- the outside width is specified ('Wn'), the maximum,
- default value for 'Vn' is 'Wn'.
-
- Un Maximum distance below a facet for a point to be
- coplanar to the facet. The default value is 'Vn'.
-
- Wn Minimum outside width of the hull. Points are
- added to the convex hull only if they are clearly
- outside of a facet. A point is outside of a facet
- if its distance to the facet is greater than 'Wn'.
- The normal value for 'Wn' is 'En'. If the user
- specifies pre-merging and does not set 'Wn', than
- 'Wn' is set to the premerge 'Cn' and maxco-
- ord*(1-An).
-
-
- Additional input/output formats
-
- Fa Print area for each facet. For Delaunay triangula-
- tions, the area is the area of the triangle. For
- Voronoi diagrams, the area is the area of the dual
- facet. Use 'PAn' for printing the n largest
- facets, and option 'PFn' for printing facets larger
- than 'n'.
-
- The area for non-simplicial facets is the sum of
- the areas for each ridge to the centrum. Vertices
- far below the facet's hyperplane are ignored. The
- reported area may be significantly less than the
- actual area.
-
-
-
-
-Geometry Center 2003/12/30 7
-
-
-
-
-
-qhull(1) qhull(1)
-
-
- FA Compute the total area and volume for option 's'.
- It is an approximation for non-simplicial facets
- (see 'Fa').
-
- Fc Print coplanar points for each facet. The output
- starts with the number of facets. Then each facet
- is printed one per line. Each line is the number
- of coplanar points followed by the point ids.
- Option 'Qi' includes the interior points. Each
- coplanar point (interior point) is assigned to the
- facet it is furthest above (resp., least below).
-
- FC Print centrums for each facet. The output starts
- with the dimension followed by the number of
- facets. Then each facet centrum is printed, one
- per line.
-
- Fd Read input in cdd format with homogeneous points.
- The input starts with comments. The first comment
- is reported in the summary. Data starts after a
- "begin" line. The next line is the number of
- points followed by the dimension+1 and "real" or
- "integer". Then the points are listed with a
- leading "1" or "1.0". The data ends with an "end"
- line.
-
- For halfspaces ('Fd Hn,n,...'), the input format is
- the same. Each halfspace starts with its offset.
- The sign of the offset is the opposite of Qhull's
- convention.
-
- FD Print normals ('n', 'Fo', 'Fi') or points ('p') in
- cdd format. The first line is the command line
- that invoked Qhull. Data starts with a "begin"
- line. The next line is the number of normals or
- points followed by the dimension+1 and "real".
- Then the normals or points are listed with the
- offset before the coefficients. The offset for
- points is 1.0. The offset for normals has the
- opposite sign. The data ends with an "end" line.
-
- FF Print facets (as in 'f') without printing the
- ridges.
-
- Fi Print inner planes for each facet. The inner plane
- is below all vertices.
-
- Fi Print separating hyperplanes for bounded, inner
- regions of the Voronoi diagram. The first line is
- the number of ridges. Then each hyperplane is
- printed, one per line. A line starts with the num-
- ber of indices and floats. The first pair lists
- adjacent input sites, the next d floats are the
- normalized coefficients for the hyperplane, and the
-
-
-
-Geometry Center 2003/12/30 8
-
-
-
-
-
-qhull(1) qhull(1)
-
-
- last float is the offset. The hyperplane is ori-
- ented toward verify that the hyperplanes are per-
- pendicular bisectors. Use 'Fo' for unbounded
- regions, and 'Fv' for the corresponding Voronoi
- vertices.
-
- FI Print facet identifiers.
-
- Fm Print number of merges for each facet. At most 511
- merges are reported for a facet. See 'PMn' for
- printing the facets with the most merges.
-
- FM Output the hull in Maple format. See 'm'
-
- Fn Print neighbors for each facet. The output starts
- with the number of facets. Then each facet is
- printed one per line. Each line is the number of
- neighbors followed by an index for each neighbor.
- The indices match the other facet output formats.
-
- A negative index indicates an unprinted facet due
- to printing only good facets ('Pg'). It is the
- negation of the facet's id (option 'FI'). For
- example, negative indices are used for facets "at
- infinity" in the Delaunay triangulation.
-
- FN Print vertex neighbors or coplanar facet for each
- point. The first line is the number of points.
- Then each point is printed, one per line. If the
- point is coplanar, the line is "1" followed by the
- facet's id. If the point is not a selected vertex,
- the line is "0". Otherwise, each line is the num-
- ber of neighbors followed by the corresponding
- facet indices (see 'Fn').
-
- Fo Print outer planes for each facet in the same for-
- mat as 'n'. The outer plane is above all points.
-
- Fo Print separating hyperplanes for unbounded, outer
- regions of the Voronoi diagram. The first line is
- the number of ridges. Then each hyperplane is
- printed, one per line. A line starts with the num-
- ber of indices and floats. The first pair lists
- adjacent input sites, the next d floats are the
- normalized coefficients for the hyperplane, and the
- last float is the offset. The hyperplane is ori-
- ented toward verify that the hyperplanes are per-
- pendicular bisectors. Use 'Fi' for bounded
- regions, and 'Fv' for the corresponding Voronoi
- vertices.
-
- FO List all options to stderr, including the default
- values. Additional 'FO's are printed to stdout.
-
- Fp Print points for halfspace intersections (option
- 'Hn,n,...'). Each intersection corresponds to a
-
-
-
-Geometry Center 2003/12/30 9
-
-
-
-qhull(1) qhull(1)
-
-
- facet of the dual polytope. The "infinity" point
- [-10.101,-10.101,...] indicates an unbounded
- intersection.
-
- FP For each coplanar point ('Qc') print the point id
- of the nearest vertex, the point id, the facet id,
- and the distance.
-
- FQ Print command used for qhull and input.
-
- Fs Print a summary. The first line consists of the
- number of integers ("7"), followed by the dimen-
- sion, the number of points, the number of vertices,
- the number of facets, the number of vertices
- selected for output, the number of facets selected
- for output, the number of coplanar points selected
- for output.
-
- The second line consists of the number of reals
- ("2"), followed by the maxmimum offset to an outer
- plane and and minimum offset to an inner plane.
- Roundoff is included. Later versions of Qhull may
- produce additional integers or reals.
-
- FS Print the size of the hull. The first line con-
- sists of the number of integers ("0"). The second
- line consists of the number of reals ("2"), fol-
- lowed by the total facet area, and the total vol-
- ume. Later versions of Qhull may produce addi-
- tional integers or reals.
-
- The total volume measures the volume of the inter-
- section of the halfspaces defined by each facet.
- Both area and volume are approximations for non-
- simplicial facets. See option 'Fa'.
-
- Ft Print a triangulation with added points for non-
- simplicial facets. The first line is the dimension
- and the second line is the number of points and the
- number of facets. The points follow, one per line,
- then the facets follow as a list of point indices.
- With option points include the point-at-infinity.
-
- Fv Print vertices for each facet. The first line is
- the number of facets. Then each facet is printed,
- one per line. Each line is the number of vertices
- followed by the corresponding point ids. Vertices
- are listed in the order they were added to the hull
- (the last one is first).
-
- Fv Print all ridges of a Voronoi diagram. The first
- line is the number of ridges. Then each ridge is
- printed, one per line. A line starts with the num-
- ber of indices. The first pair lists adjacent
-
-
-
-Geometry Center 2003/12/30 10
-
-
-
-
-
-qhull(1) qhull(1)
-
-
- input sites, the remaining indices list Voronoi
- vertices. Vertex '0' indicates the vertex-at-
- infinity (i.e., an unbounded ray). In 3-d, the
- vertices are listed in order. See 'Fi' and 'Fo'
- for separating hyperplanes.
-
- FV Print average vertex. The average vertex is a fea-
- sible point for halfspace intersection.
-
- Fx List extreme points (vertices) of the convex hull.
- The first line is the number of points. The other
- lines give the indices of the corresponding points.
- The first point is '0'. In 2-d, the points occur
- in counter-clockwise order; otherwise they occur in
- input order. For Delaunay triangulations, 'Fx'
- lists the extreme points of the input sites. The
- points are unordered.
-
-
- Geomview options
-
- G Produce a file for viewing with Geomview. Without
- other options, Qhull displays edges in 2-d, outer
- planes in 3-d, and ridges in 4-d. A ridge can be
- explicit or implicit. An explicit ridge is a dim-1
- dimensional simplex between two facets. In 4-d,
- the explicit ridges are triangles. When displaying
- a ridge in 4-d, Qhull projects the ridge's vertices
- to one of its facets' hyperplanes. Use 'Gh' to
- project ridges to the intersection of both hyper-
- planes.
-
- Ga Display all input points as dots.
-
- Gc Display the centrum for each facet in 3-d. The
- centrum is defined by a green radius sitting on a
- blue plane. The plane corresponds to the facet's
- hyperplane. The radius is defined by 'C-n' or
- 'Cn'.
-
- GDn Drop dimension n in 3-d or 4-d. The result is a
- 2-d or 3-d object.
-
- Gh Display hyperplane intersections in 3-d and 4-d.
- In 3-d, the intersection is a black line. It lies
- on two neighboring hyperplanes (c.f., the blue
- squares associated with centrums ('Gc')). In 4-d,
- the ridges are projected to the intersection of
- both hyperplanes.
-
- Gi Display inner planes in 2-d and 3-d. The inner
- plane of a facet is below all of its vertices. It
- is parallel to the facet's hyperplane. The inner
- plane's color is the opposite (1-r,1-g,1-b) of the
-
-
-
-Geometry Center 2003/12/30 11
-
-
-
-
-
-qhull(1) qhull(1)
-
-
- outer plane. Its edges are determined by the ver-
- tices.
-
- Gn Do not display inner or outer planes. By default,
- Geomview displays the precise plane (no merging) or
- both inner and output planes (merging). Under
- merging, Geomview does not display the inner plane
- if the the difference between inner and outer is
- too small.
-
- Go Display outer planes in 2-d and 3-d. The outer
- plane of a facet is above all input points. It is
- parallel to the facet's hyperplane. Its color is
- determined by the facet's normal, and its edges are
- determined by the vertices.
-
- Gp Display coplanar points and vertices as radii. A
- radius defines a ball which corresponds to the
- imprecision of the point. The imprecision is the
- maximum of the roundoff error, the centrum radius,
- and maxcoord * (1-An). It is at least 1/20'th of
- the maximum coordinate, and ignores post-merging if
- pre-merging is done.
-
- Gr Display ridges in 3-d. A ridge connects the two
- vertices that are shared by neighboring facets.
- Ridges are always displayed in 4-d.
-
- Gt A 3-d Delaunay triangulation looks like a convex
- hull with interior facets. Option 'Gt' removes the
- outside ridges to reveal the outermost facets. It
- automatically sets options 'Gr' and 'GDn'.
-
- Gv Display vertices as spheres. The radius of the
- sphere corresponds to the imprecision of the data.
- See 'Gp' for determining the radius.
-
-
- Print options
-
- PAn Only the n largest facets are marked good for
- printing. Unless 'PG' is set, 'Pg' is automati-
- cally set.
-
- Pdk:n Drop facet from output if normal[k] <= n. The
- option 'Pdk' uses the default value of 0 for n.
-
- PDk:n Drop facet from output if normal[k] >= n. The
- option 'PDk' uses the default value of 0 for n.
-
- PFn Only facets with area at least 'n' are marked good
- for printing. Unless 'PG' is set, 'Pg' is automat-
- ically set.
-
-
-
-
-Geometry Center 2003/12/30 12
-
-
-
-
-
-qhull(1) qhull(1)
-
-
- Pg Print only good facets. A good facet is either
- visible from a point (the 'QGn' option) or includes
- a point (the 'QVn' option). It also meets the
- requirements of 'Pdk' and 'PDk' options. Option
- 'Pg' is automatically set for options 'PAn' and
- 'PFn'.
-
- PG Print neighbors of good facets.
-
- PMn Only the n facets with the most merges are marked
- good for printing. Unless 'PG' is set, 'Pg' is
- automatically set.
-
- Po Force output despite precision problems. Verify ('Tv') does not check
- coplanar points. Flipped facets are reported and
- concave facets are counted. If 'Po' is used,
- points are not partitioned into flipped facets and
- a flipped facet is always visible to a point.
- Also, if an error occurs before the completion of
- Qhull and tracing is not active, 'Po' outputs a
- neighborhood of the erroneous facets (if any).
-
- Pp Do not report precision problems.
-
-
- Qhull control options
-
- Qbk:0Bk:0
- Drop dimension k from the input points. This
- allows the user to take convex hulls of sub-dimen-
- sional objects. It happens before the Delaunay and
- Voronoi transformation.
-
- QbB Scale the input points to fit the unit cube. After
- scaling, the lower bound will be -0.5 and the upper
- bound +0.5 in all dimensions. For Delaunay and
- Voronoi diagrams, scaling happens after projection
- to the paraboloid. Under precise arithmetic, scal-
- ing does not change the topology of the convex
- hull.
-
- Qbb Scale the last coordinate to [0, m] where m is the
- maximum absolute value of the other coordinates.
- For Delaunay and Voronoi diagrams, scaling happens
- after projection to the paraboloid. It reduces
- roundoff error for inputs with integer coordinates.
- Under precise arithmetic, scaling does not change
- the topology of the convex hull.
-
- Qbk:n Scale the k'th coordinate of the input points.
- After scaling, the lower bound of the input points
- will be n. 'Qbk' scales to -0.5.
-
-
-
-Geometry Center 2003/12/30 13
-
-
-
-
-
-qhull(1) qhull(1)
-
-
- QBk:n Scale the k'th coordinate of the input points.
- After scaling, the upper bound will be n. 'QBk'
- scales to +0.5.
-
- Qc Keep coplanar points with the nearest facet. Out-
- put formats 'p', 'f', 'Gp', 'Fc', 'FN', and 'FP'
- will print the points.
-
- Qf Partition points to the furthest outside facet.
-
- Qg Only build good facets. With the 'Qg' option,
- Qhull will only build those facets that it needs to
- determine the good facets in the output. See
- 'QGn', 'QVn', and 'PdD' for defining good facets,
- and 'Pg' and 'PG' for printing good facets and
- their neighbors.
-
- QGn A facet is good (see 'Qg' and 'Pg') if it is visi-
- ble from point n. If n < 0, a facet is good if it
- is not visible from point n. Point n is not added
- to the hull (unless 'TCn' or 'TPn'). With rbox,
- use the 'Pn,m,r' option to define your point; it
- will be point 0 (QG0).
-
- Qi Keep interior points with the nearest facet. Out-
- put formats 'p', 'f', 'Gp', 'FN', 'FP', and 'Fc'
- will print the points.
-
- QJn Joggle each input coordinate by adding a random
- number in [-n,n]. If a precision error occurs,
- then qhull increases n and tries again. It does
- not increase n beyond a certain value, and it stops
- after a certain number of attempts [see user.h].
- Option 'QJ' selects a default value for n. The
- output will be simplicial. For Delaunay triangula-
- tions, 'QJn' sets 'Qbb' to scale the last coordi-
- nate (not if 'Qbk:n' or 'QBk:n' is set). See also
- 'Qt'.
-
- Qm Only process points that would otherwise increase
- max_outside. Other points are treated as coplanar
- or interior points.
-
- Qr Process random outside points instead of furthest
- ones. This makes Qhull equivalent to the random-
- ized incremental algorithms. CPU time is not
- reported since the randomization is inefficient.
-
- QRn Randomly rotate the input points. If n=0, use time
- as the random number seed. If n>0, use n as the
- random number seed. If n=-1, don't rotate but use
- time as the random number seed. For Delaunay tri-
- angulations ('d' and 'v'), rotate about the last
- axis.
-
-
-
-
-Geometry Center 2003/12/30 14
-
-
-
-
-
-qhull(1) qhull(1)
-
-
- Qs Search all points for the initial simplex.
-
- Qt Triangulated output. Triangulate non-simplicial
- facets.
-
- Qv Test vertex neighbors for convexity after post-
- merging. To use the 'Qv' option, you also need to
- set a merge option (e.g., 'Qx' or 'C-0').
-
- QVn A good facet (see 'Qg' and 'Pg') includes point n.
- If n<0, then a good facet does not include point n.
- The point is either in the initial simplex or it is
- the first point added to the hull. Option 'QVn'
- may not be used with merging.
-
- Qx Perform exact merges while building the hull. The
- "exact" merges are merging a point into a coplanar
- facet (defined by 'Vn', 'Un', and 'C-n'), merging
- concave facets, merging duplicate ridges, and merg-
- ing flipped facets. Coplanar merges and angle
- coplanar merges ('A-n') are not performed. Concav-
- ity testing is delayed until a merge occurs.
-
- After the hull is built, all coplanar merges are
- performed (defined by 'C-n' and 'A-n'), then post-
- merges are performed (defined by 'Cn' and 'An').
-
- Qz Add a point "at infinity" that is above the
- paraboloid for Delaunay triangulations and Voronoi
- diagrams. This reduces precision problems and
- allows the triangulation of cospherical points.
-
-
- Qhull experiments and speedups
-
- Q0 Turn off pre-merging as a default option. With
- 'Q0'/'Qx' and without explicit pre-merge options,
- Qhull ignores precision issues while constructing
- the convex hull. This may lead to precision
- errors. If so, a descriptive warning is generated.
-
- Q1 With 'Q1', Qhull sorts merges by type (coplanar,
- angle coplanar, concave) instead of by angle.
-
- Q2 With 'Q2', Qhull merges all facets at once instead
- of using independent sets of merges and then
- retesting.
-
- Q3 With 'Q3', Qhull does not remove redundant ver-
- tices.
-
- Q4 With 'Q4', Qhull avoids merges of an old facet into
- a new facet.
-
- Q5 With 'Q5', Qhull does not correct outer planes at
- the end. The maximum outer plane is used instead.
-
-
-
-
-Geometry Center 2003/12/30 15
-
-
-
-
-
-qhull(1) qhull(1)
-
-
- Q6 With 'Q6', Qhull does not pre-merge concave or
- coplanar facets.
-
- Q7 With 'Q7', Qhull processes facets in depth-first
- order instead of breadth-first order.
-
- Q8 With 'Q8' and merging, Qhull does not retain near-
- interior points for adjusting outer planes. 'Qc'
- will probably retain all points that adjust outer
- planes.
-
- Q9 With 'Q9', Qhull processes the furthest of all out-
- side sets at each iteration.
-
- Q10 With 'Q10', Qhull does not use special processing
- for narrow distributions.
-
- Q11 With 'Q11', Qhull copies normals and recomputes
- centrums for tricoplanar facets.
-
- Trace options
-
- Tn Trace at level n. Qhull includes full execution
- tracing. 'T-1' traces events. 'T1' traces the
- overall execution of the program. 'T2' and 'T3'
- trace overall execution and geometric and topologi-
- cal events. 'T4' traces the algorithm. 'T5'
- includes information about memory allocation and
- Gaussian elimination.
-
- Tc Check frequently during execution. This will catch
- most inconsistency errors.
-
- TCn Stop Qhull after building the cone of new facets
- for point n. The output for 'f' includes the cone
- and the old hull. See also 'TVn'.
-
- TFn Report progress whenever more than n facets are
- created During post-merging, 'TFn' reports progress
- after more than n/2 merges.
-
- TI file
- Input data from 'file'. The filename may not include
- spaces or quotes.
-
- TO file
- Output results to 'file'. The name may be enclosed
- in single quotes.
-
- TPn Turn on tracing when point n is added to the hull.
- Trace partitions of point n. If used with TWn, turn off
- tracing after adding point n to the hull.
-
- TRn Rerun qhull n times. Usually used with 'QJn' to
- determine the probability that a given joggle will
- fail.
-
- Ts Collect statistics and print to stderr at the end
- of execution.
-
- Tv Verify the convex hull. This checks the topologi-
- cal structure, facet convexity, and point inclu-
- sion. If precision problems occurred, facet con-
- vexity is tested whether or not 'Tv' is selected.
- Option 'Tv' does not check point inclusion if
-
-
-
-Geometry Center 2003/12/30 16
-
-
-
-
-
-qhull(1) qhull(1)
-
-
- forcing output with 'Po', or if 'Q5' is set.
-
- For point inclusion testing, Qhull verifies that
- all points are below all outer planes (facet->max-
- outside). Point inclusion is exhaustive if merging
- or if the facet-point product is small enough; oth-
- erwise Qhull verifies each point with a directed
- search (qh_findbest).
-
- Point inclusion testing occurs after producing out-
- put. It prints a message to stderr unless option
- 'Pp' is used. This allows the user to interrupt
- Qhull without changing the output.
-
- TVn Stop Qhull after adding point n. If n < 0, stop
- Qhull before adding point n. Output shows the hull
- at this time. See also 'TCn'
-
- TMn Turn on tracing at n'th merge.
-
- TWn Trace merge facets when the width is greater than
- n.
-
- Tz Redirect stderr to stdout.
-
-
-BUGS
- Please report bugs to Brad Barber at
- qhull_bug@qhull.org.
-
- If Qhull does not compile, it is due to an incompatibility
- between your system and ours. The first thing to check is
- that your compiler is ANSI standard. If it is, check the
- man page for the best options, or find someone to help
- you. If you locate the cause of your problem, please send
- email since it might help others.
-
- If Qhull compiles but crashes on the test case (rbox D4),
- there's still incompatibility between your system and
- ours. Typically it's been due to mem.c and memory align-
- ment. You can use qh_NOmem in mem.h to turn off memory
- management. Please let us know if you figure out how to
- fix these problems.
-
- If you do find a problem, try to simplify it before
- reporting the error. Try different size inputs to locate
- the smallest one that causes an error. You're welcome to
- hunt through the code using the execution trace as a
- guide. This is especially true if you're incorporating
- Qhull into your own program.
-
- When you do report an error, please attach a data set to
- the end of your message. This allows us to see the error
- for ourselves. Qhull is maintained part-time.
-
-
-
-Geometry Center 2003/12/30 17
-
-
-
-
-
-qhull(1) qhull(1)
-
-
-E-MAIL
- Please send correspondence to qhull@qhull.org and
- report bugs to qhull_bug@qhull.org. Let us know how
- you use Qhull. If you mention it in a paper, please send
- the reference and an abstract.
-
- If you would like to get Qhull announcements (e.g., a new
- version) and news (any bugs that get fixed, etc.), let us
- know and we will add you to our mailing list. If you
- would like to communicate with other Qhull users, we will
- add you to the qhull_users alias. For Internet news about
- geometric algorithms and convex hulls, look at comp.graph-
- ics.algorithms and sci.math.num-analysis
-
-
-SEE ALSO
- rbox(1)
-
- Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa, "The
- Quickhull Algorithm for Convex Hulls," ACM Trans. on Math-
- ematical Software, Dec. 1996.
- http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p469-barber/
- http://citeseer.nj.nec.com/83502.html
-
-
- Clarkson, K.L., K. Mehlhorn, and R. Seidel, "Four results
- on randomized incremental construction," Computational
- Geometry: Theory and Applications, vol. 3, p. 185-211,
- 1993.
-
- Preparata, F. and M. Shamos, Computational Geometry,
- Springer-Verlag, New York, 1985.
-
-
-
-AUTHORS
- C. Bradford Barber Hannu Huhdanpaa
- bradb@qhull.org hannu@qhull.org
-
- c/o The Geometry Center
- University of Minnesota
- 400 Lind Hall
- 207 Church Street S.E.
- Minneapolis, MN 55455
-
-
-
-ACKNOWLEDGEMENTS
- A special thanks to Albert Marden, Victor Milenkovic, the
- Geometry Center, Harvard University, and Endocardial Solu-
- tions, Inc. for supporting this work.
-
- The software was developed under National Science Founda-
- tion grants NSF/DMS-8920161 and NSF-CCR-91-15793 750-7504.
-
-
-
-Geometry Center 2003/12/30 18
-
-
-
-
-
-qhull(1) qhull(1)
-
-
- David Dobkin guided the original work at Princeton Univer-
- sity. If you find it useful, please let us know.
-
- The Geometry Center is supported by grant DMS-8920161 from
- the National Science Foundation, by grant DOE/DE-
- FG02-92ER25137 from the Department of Energy, by the Uni-
- versity of Minnesota, and by Minnesota Technology, Inc.
-
- Qhull is available at http://www.qhull.org
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-
-Geometry Center 2003/12/30 19
-
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qvoron_f.htm b/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qvoron_f.htm
deleted file mode 100644
index de64310f8c0da0639bfe18e3939d653ed00b0eb4..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/qvoron_f.htm
+++ /dev/null
@@ -1,408 +0,0 @@
-<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
-<html>
-
-<head>
-<title>qvoronoi Qu -- furthest-site Voronoi diagram</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<a name="TOP"><b>Up</b></a><b>:</b>
-<a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a><br>
-<b>To:</b> <a href="#synopsis">sy</a>nopsis
-• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
-• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
-• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
-• <a href="#options">op</a>tions
-
-<hr>
-<!-- Main text of document -->
-<h1><a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
-src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
-height="100"></a>qvoronoi Qu -- furthest-site Voronoi diagram</h1>
-
-<p>The furthest-site Voronoi diagram is the furthest-neighbor map for a set of
-points. Each region contains those points that are further
-from one input site than any other input site. See the
-survey article by Aurenhammer [<a href="index.htm#aure91">'91</a>]
-and the brief introduction by O'Rourke [<a
-href="index.htm#orou94">'94</a>]. The furthest-site Voronoi diagram is the dual of the <a
-href="qdelau_f.htm">furthest-site Delaunay triangulation</a>.
-</p>
-
-<blockquote>
-<dl>
- <dt><b>Example:</b> rbox 10 D2 | qvoronoi <a
- href="qh-optq.htm#Qu">Qu</a> <a href="qh-opto.htm#s">s</a>
- <a href="qh-opto.htm#o">o</a> <a href="qh-optt.htm#TO">TO
- result</a></dt>
- <dd>Compute the 2-d, furthest-site Voronoi diagram of 10
- random points. Write a summary to the console and the Voronoi
- regions and vertices to 'result'. The first vertex of the
- result indicates unbounded regions. Almost all regions
- are unbounded.</dd>
-</dl>
-
-<dl>
- <dt><b>Example:</b> rbox r y c G1 D2 | qvoronoi <a
- href="qh-optq.htm#Qu">Qu</a>
- <a href="qh-opto.htm#s">s</a>
- <a href="qh-optf.htm#Fn">Fn</a> <a href="qh-optt.htm#TO">TO
- result</a></dt>
- <dd>Compute the 2-d furthest-site Voronoi diagram of a square
- and a small triangle. Write a summary to the console and the Voronoi
- vertices for each input site to 'result'.
- The origin is the only furthest-site Voronoi vertex. The
- negative indices indicate vertices-at-infinity.</dd>
-</dl>
-</blockquote>
-
-<p>
-Qhull computes the furthest-site Voronoi diagram via the <a href="qdelau_f.htm">
-furthest-site Delaunay triangulation</a>.
-Each furthest-site Voronoi vertex is the circumcenter of an upper
-facet of the Delaunay triangulation. Each furthest-site Voronoi
-region corresponds to a vertex of the Delaunay triangulation
-(i.e., an input site).</p>
-
-<p>See <a href="http://www.qhull.org/html/qh-faq.htm#TOC">Qhull FAQ</a> - Delaunay and
-Voronoi diagram questions.</p>
-
-<p>Options '<a href="qh-optq.htm#Qt">Qt</a>' (triangulated output)
-and '<a href="qh-optq.htm#QJn">QJ</a>' (joggled input), may produce
-unexpected results. Cocircular and cospherical input sites will
-produce duplicate or nearly duplicate furthest-site Voronoi vertices. See also <a
-href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p>
-
-<p>The 'qvonoroi' program is equivalent to
-'<a href=qhull.htm#outputs>qhull v</a> <a href=qh-optq.htm#Qbb>Qbb</a>' in 2-d to 3-d, and
-'<a href=qhull.htm#outputs>qhull v</a> <a href=qh-optq.htm#Qbb>Qbb</a> <a href=qh-optq.htm#Qx>Qx</a>'
-in 4-d and higher. It disables the following Qhull
-<a href=qh-quick.htm#options>options</a>: <i>d n m v H U Qb
-QB Qc Qf Qg Qi Qm Qr QR Qv Qx TR E V Fa FA FC Fp FS Ft FV Gt Q0,etc</i>.
-
-
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-
-<hr>
-<h3><a href="#TOP">»</a><a name="synopsis">furthest-site qvoronoi synopsis</a></h3>
-<blockquote>
-
-See <a href="qvoronoi.htm#synopsis">qvoronoi synopsis</a>. The same
-program is used for both constructions. Use option '<a href="qh-optq.htm#Qu">Qu</a>'
-for furthest-site Voronoi diagrams.
-
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="input">furthest-site qvoronoi
-input</a></h3>
-<blockquote>
-<p>The input data on <tt>stdin</tt> consists of:</p>
-<ul>
- <li>dimension
- <li>number of points</li>
- <li>point coordinates</li>
-</ul>
-
-<p>Use I/O redirection (e.g., qvoronoi Qu < data.txt), a pipe (e.g., rbox 10 | qvoronoi Qu),
-or the '<a href=qh-optt.htm#TI>TI</a>' option (e.g., qvoronoi TI data.txt Qu).
-
-<p>For example, this is a square containing four random points.
-Its furthest-site Voronoi diagram has on vertex and four unbounded,
-separating hyperplanes (i.e., the coordinate axes)
-<p>
-<blockquote>
-<tt>rbox c 4 D2 > data</tt>
-<blockquote><pre>
-2 RBOX c 4 D2
-8
--0.4999921736307369 -0.3684622117955817
-0.2556053225468894 -0.0413498678629751
-0.0327672376602583 -0.2810408135699488
--0.452955383763607 0.17886471718444
- -0.5 -0.5
- -0.5 0.5
- 0.5 -0.5
- 0.5 0.5
-</pre></blockquote>
-
-<p><tt>qvoronoi Qu s Fo < data</tt>
-<blockquote><pre>
-
-Furthest-site Voronoi vertices by the convex hull of 8 points in 3-d:
-
- Number of Voronoi regions: 8
- Number of Voronoi vertices: 1
- Number of non-simplicial Voronoi vertices: 1
-
-Statistics for: RBOX c 4 D2 | QVORONOI Qu s Fo
-
- Number of points processed: 8
- Number of hyperplanes created: 20
- Number of facets in hull: 11
- Number of distance tests for qhull: 34
- Number of merged facets: 1
- Number of distance tests for merging: 107
- CPU seconds to compute hull (after input): 0
-
-4
-5 4 5 0 1 0
-5 4 6 1 0 0
-5 5 7 1 0 0
-5 6 7 0 1 0
-</pre></blockquote>
-</blockquote>
-
-</blockquote>
-<h3><a href="#TOP">»</a> <a name="outputs">furthest-site qvoronoi
-outputs</a></h3>
-<blockquote>
-
-<p>These options control the output of furthest-site Voronoi diagrams.</p>
-<blockquote>
-
-<dl compact>
- <dt> </dt>
- <dd><b>furthest-site Voronoi vertices</b></dd>
- <dt><a href="qh-opto.htm#p">p</a></dt>
- <dd>print the coordinates of the furthest-site Voronoi vertices. The first line
- is the dimension. The second line is the number of vertices. Each
- remaining line is a furthest-site Voronoi vertex. The points-in-square example
- has one furthest-site Voronoi vertex at the origin.</dd>
- <dt><a href="qh-optf.htm#Fn">Fn</a></dt>
- <dd>list the neighboring furthest-site Voronoi vertices for each furthest-site Voronoi
- vertex. The first line is the number of Voronoi vertices. Each
- remaining line starts with the number of neighboring vertices. Negative indices (e.g., <em>-1</em>) indicate vertices
- outside of the Voronoi diagram. In the points-in-square example, the
- Voronoi vertex at the origin has four neighbors-at-infinity.</dd>
- <dt><a href="qh-optf.htm#FN">FN</a></dt>
- <dd>list the furthest-site Voronoi vertices for each furthest-site Voronoi region. The first line is
- the number of Voronoi regions. Each remaining line starts with the
- number of Voronoi vertices. Negative indices (e.g., <em>-1</em>) indicate vertices
- outside of the Voronoi diagram.
- In the points-in-square example, all regions share the Voronoi vertex
- at the origin.</dd>
-
- <dt> </dt>
- <dt> </dt>
- <dd><b>furthest-site Voronoi regions</b></dd>
- <dt><a href="qh-opto.htm#o">o</a></dt>
- <dd>print the furthest-site Voronoi regions in OFF format. The first line is the
- dimension. The second line is the number of vertices, the number
- of input sites, and "1". The third line represents the vertex-at-infinity.
- Its coordinates are "-10.101". The next lines are the coordinates
- of the furthest-site Voronoi vertices. Each remaining line starts with the number
- of Voronoi vertices in a Voronoi region. In 2-d, the vertices are
-listed in adjacency order (unoriented). In 3-d and higher, the
-vertices are listed in numeric order. In the points-in-square
- example, each unbounded region includes the Voronoi vertex at
- the origin. Lines consisting of <em>0</em> indicate
- interior input sites. </dd>
- <dt><a href="qh-optf.htm#Fi2">Fi</a></dt>
- <dd>print separating hyperplanes for inner, bounded furthest-site Voronoi
- regions. The first number is the number of separating
- hyperplanes. Each remaining line starts with <i>3+dim</i>. The
- next two numbers are adjacent input sites. The next <i>dim</i>
- numbers are the coefficients of the separating hyperplane. The
- last number is its offset. The are no bounded, separating hyperplanes
- for the points-in-square example.</dd>
- <dt><a href="qh-optf.htm#Fo2">Fo</a></dt>
- <dd>print separating hyperplanes for outer, unbounded furthest-site Voronoi
- regions. The first number is the number of separating
- hyperplanes. Each remaining line starts with <i>3+dim</i>. The
- next two numbers are adjacent input sites on the convex hull. The
- next <i>dim</i>
- numbers are the coefficients of the separating hyperplane. The
- last number is its offset. The points-in-square example has four
- unbounded, separating hyperplanes.</dd>
- <dt> </dt>
- <dt> </dt>
- <dd><b>Input sites</b></dd>
- <dt><a href="qh-optf.htm#Fv2">Fv</a></dt>
- <dd>list ridges of furthest-site Voronoi vertices for pairs of input sites. The
- first line is the number of ridges. Each remaining line starts with
- two plus the number of Voronoi vertices in the ridge. The next
- two numbers are two adjacent input sites. The remaining numbers list
- the Voronoi vertices. As with option 'o', a <em>0</em> indicates
- the vertex-at-infinity
- and an unbounded, separating hyperplane.
- The perpendicular bisector (separating hyperplane)
- of the input sites is a flat through these vertices.
- In the points-in-square example, the ridge for each edge of the square
- is unbounded.</dd>
- <dt> </dt>
- <dt> </dt>
- <dd><b>General</b></dd>
- <dt><a href="qh-opto.htm#s">s</a></dt>
- <dd>print summary of the furthest-site Voronoi diagram. Use '<a
- href="qh-optf.htm#Fs">Fs</a>' for numeric data.</dd>
- <dt><a href="qh-opto.htm#i">i</a></dt>
- <dd>list input sites for each <a href=qdelau_f.htm>furthest-site Delaunay region</a>. Use option '<a href="qh-optp.htm#Pp">Pp</a>'
- to avoid the warning. The first line is the number of regions. The
- remaining lines list the input sites for each region. The regions are
- oriented. In the points-in-square example, the square region has four
- input sites. In 3-d and higher, report cospherical sites by adding extra points.
- </dd>
- <dt><a href="qh-optg.htm#G">G</a></dt>
- <dd>Geomview output for 2-d furthest-site Voronoi diagrams.</dd>
- </dl>
-</blockquote>
-
-</blockquote>
-<h3><a href="#TOP">»</a> <a name="controls">furthest-site qvoronoi
-controls</a></h3>
-<blockquote>
-
-<p>These options provide additional control:</p>
-<blockquote>
-
-<dl compact>
- <dt><a href="qh-optq.htm#Qu">Qu</a></dt>
- <dd>must be used.</dd>
- <dt><a href="qh-optq.htm#Qt">Qt</a></dt>
- <dd>triangulated output. If a furthest-site Voronoi vertex is defined by cospherical data, Qhull
- duplicates the vertex. For example, if 2-d data is contained in a square, the output
- will contain two, identical furthest-site Voronoi vertices.</dd>
- <dt><a href="qh-optq.htm#QJn">QJ</a></dt>
- <dd>joggle the input to avoid furthest-site Voronoi vertices defined by more
- than <i>dim+1</i> points. It is less accurate than triangulated output ('Qt').
- </dd>
- <dt><a href="qh-optq.htm#QVn">QVn</a></dt>
- <dd>select furthest-site Voronoi vertices for input site <em>n</em> </dd>
- <dt><a href="qh-optt.htm#Tv">Tv</a></dt>
- <dd>verify result</dd>
- <dt><a href="qh-optt.htm#TO">TI file</a></dt>
- <dd>input data from file. The filename may not use spaces or quotes.</dd>
- <dt><a href="qh-optt.htm#TO">TO file</a></dt>
- <dd>output results to file. Use single quotes if the filename
- contains spaces (e.g., <tt>TO 'file with spaces.txt'</tt></dd>
- <dt><a href="qh-optt.htm#TFn">TFn</a></dt>
- <dd>report progress after constructing <em>n</em> facets</dd>
- <dt><a href="qh-optp.htm#PDk">PDk:1</a></dt>
- <dd>include upper and lower facets in the output. Set <em>k</em>
- to the last dimension (e.g., 'PD2:1' for 2-d inputs). </dd>
- <dt><a href="qh-opto.htm#f">f </a></dt>
- <dd>facet dump. Print the data structure for each facet (i.e.,
- furthest-site Voronoi vertex).</dd>
-</dl>
-
-</blockquote>
-</blockquote>
-<h3><a href="#TOP">»</a> <a name="graphics">furthest-site qvoronoi
-graphics</a></h3>
-<blockquote>
-<p>In 2-d, Geomview output ('<a href="qh-optg.htm#G">G</a>')
-displays a furthest-site Voronoi diagram with extra edges to
-close the unbounded furthest-site Voronoi regions. All regions
-will be unbounded. Since the points-in-box example has only
-one furthest-site Voronoi vertex, the Geomview output is one
-point.</p>
-
-<p>See the <a href="qh-eg.htm#delaunay">Delaunay and Voronoi
-examples</a> for a 2-d example. Turn off normalization (on
-Geomview's 'obscure' menu) when comparing the furthest-site
-Voronoi diagram with the corresponding Voronoi diagram. </p>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="notes">furthest-site qvoronoi
-notes</a></h3>
-<blockquote>
-
-<p>See <a href="qvoronoi.htm#notes">Voronoi notes</a>.</p>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="conventions">furthest-site qvoronoi conventions</a></h3>
-<blockquote>
-
-<p>The following terminology is used for furthest-site Voronoi
-diagrams in Qhull. The underlying structure is a furthest-site
-Delaunay triangulation from a convex hull in one higher
-dimension. Upper facets of the Delaunay triangulation correspond
-to vertices of the furthest-site Voronoi diagram. Vertices of the
-furthest-site Delaunay triangulation correspond to input sites.
-They also define regions of the furthest-site Voronoi diagram.
-All vertices are extreme points of the input sites. See <a
-href="qconvex.htm#conventions">qconvex conventions</a>, <a
-href="qdelau_f.htm#conventions">furthest-site delaunay
-conventions</a>, and <a href="index.htm#structure">Qhull's data structures</a>.</p>
-
-<ul>
- <li><em>input site</em> - a point in the input (one dimension
- lower than a point on the convex hull)</li>
- <li><em>point</em> - a point has <i>d+1</i> coordinates. The
- last coordinate is the sum of the squares of the input
- site's coordinates</li>
- <li><em>vertex</em> - a point on the upper facets of the
- paraboloid. It corresponds to a unique input site. </li>
- <li><em>furthest-site Delaunay facet</em> - an upper facet of the
- paraboloid. The last coefficient of its normal is
- clearly positive.</li>
- <li><em>furthest-site Voronoi vertex</em> - the circumcenter
- of a furthest-site Delaunay facet</li>
- <li><em>furthest-site Voronoi region</em> - the region of
- Euclidean space further from an input site than any other
- input site. Qhull lists the furthest-site Voronoi
- vertices that define each furthest-site Voronoi region.</li>
- <li><em>furthest-site Voronoi diagram</em> - the graph of the
- furthest-site Voronoi regions with the ridges (edges)
- between the regions.</li>
- <li><em>infinity vertex</em> - the Voronoi vertex for
- unbounded furthest-site Voronoi regions in '<a
- href="qh-opto.htm#o">o</a>' output format. Its
- coordinates are <em>-10.101</em>.</li>
- <li><em>good facet</em> - an furthest-site Voronoi vertex with
- optional restrictions by '<a href="qh-optq.htm#QVn">QVn</a>',
- etc.</li>
-</ul>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="options">furthest-site qvoronoi options</a></h3>
-<blockquote>
-
-See <a href="qvoronoi.htm#options">qvoronoi options</a>. The same
-program is used for both constructions. Use option '<a href="qh-optq.htm#Qu">Qu</a>'
-for furthest-site Voronoi diagrams.
-</blockquote>
-
-<!-- Navigation links -->
-<hr>
-
-<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
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-• <a href="qh-optf.htm#format">Formats</a>
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-• <a href="qh-optt.htm#trace">Trace</a><br>
-<b>To:</b> <a href="#synopsis">sy</a>nopsis
-• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
-• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
-• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
-• <a href="#options">op</a>tions
-<!-- GC common information -->
-<hr>
-
-<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
-align="middle" width="40" height="40"></a><i>The Geometry Center
-Home Page </i></p>
-
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
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-<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
-<html>
-
-<head>
-<title>qvoronoi -- Voronoi diagram</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<a name="TOP"><b>Up</b></a><b>:</b>
-<a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a><br>
-<b>To:</b> <a href="#synopsis">sy</a>nopsis
-• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
-• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
-• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
-• <a href="#options">op</a>tions
-
-<hr>
-<!-- Main text of document -->
-<h1><a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
-src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
-height="100"></a>qvoronoi -- Voronoi diagram</h1>
-
-<p>The Voronoi diagram is the nearest-neighbor map for a set of
-points. Each region contains those points that are nearer
-one input site than any other input site. It has many useful properties and applications. See the
-survey article by Aurenhammer [<a href="index.htm#aure91">'91</a>]
-and the detailed introduction by O'Rourke [<a
-href="index.htm#orou94">'94</a>]. The Voronoi diagram is the
-dual of the <a href=qdelaun.htm>Delaunay triangulation</a>. </p>
-
-<blockquote>
-<dl>
- <dt><b>Example:</b> rbox 10 D3 | qvoronoi <a href="qh-opto.htm#s">s</a>
- <a href="qh-opto.htm#o">o</a> <a href="qh-optt.htm#TO">TO
- result</a></dt>
- <dd>Compute the 3-d Voronoi diagram of 10 random points. Write a
- summary to the console and the Voronoi vertices and
- regions to 'result'. The first vertex of the result
- indicates unbounded regions.</dd>
-
- <dt> </dt>
- <dt><b>Example:</b> rbox r y c G0.1 D2 | qvoronoi
- <a href="qh-opto.htm#s">s</a>
- <a href="qh-opto.htm#o">o</a> <a href="qh-optt.htm#TO">TO
- result</a></dt>
- <dd>Compute the 2-d Voronoi diagram of a triangle and a small
- square. Write a
- summary to the console and Voronoi vertices and regions
- to 'result'. Report a single Voronoi vertex for
- cocircular input sites. The first vertex of the result
- indicates unbounded regions. The origin is the Voronoi
- vertex for the square.</dd>
-
- <dt> </dt>
- <dt><b>Example:</b> rbox r y c G0.1 D2 | qvoronoi <a href="qh-optf.htm#Fv2">Fv</a>
- <a href="qh-optt.htm#TO">TO result</a></dt>
- <dd>Compute the 2-d Voronoi diagram of a triangle and a small
- square. Write a
- summary to the console and the Voronoi ridges to
- 'result'. Each ridge is the perpendicular bisector of a
- pair of input sites. Vertex "0" indicates
- unbounded ridges. Vertex "8" is the Voronoi
- vertex for the square.</dd>
-
- <dt> </dt>
- <dt><b>Example:</b> rbox r y c G0.1 D2 | qvoronoi <a href="qh-optf.htm#Fi2">Fi</a></dt>
- <dd>Print the bounded, separating hyperplanes for the 2-d Voronoi diagram of a
- triangle and a small
- square. Note the four hyperplanes (i.e., lines) for Voronoi vertex
- "8". It is at the origin.
- </dd>
-</dl>
-</blockquote>
-
-<p>Qhull computes the Voronoi diagram via the <a href="qdelaun.htm">Delaunay
-triangulation</a>. Each Voronoi
-vertex is the circumcenter of a facet of the Delaunay
-triangulation. Each Voronoi region corresponds to a vertex (i.e., input site) of the
-Delaunay triangulation. </p>
-
-<p>Qhull outputs the Voronoi vertices for each Voronoi region. With
-option '<a href="qh-optf.htm#Fv2">Fv</a>',
-it lists all ridges of the Voronoi diagram with the corresponding
-pairs of input sites. With
-options '<a href="qh-optf.htm#Fi2">Fi</a>' and '<a href="qh-optf.htm#Fo2">Fo</a>',
-it lists the bounded and unbounded separating hyperplanes.
-You can also output a single Voronoi region
-for further processing [see <a href="#graphics">graphics</a>].</p>
-
-<p>See <a href="http://www.qhull.org/html/qh-faq.htm#TOC">Qhull FAQ</a> - Delaunay and
-Voronoi diagram questions.</p>
-
-<p>Options '<a href="qh-optq.htm#Qt">Qt</a>' (triangulated output)
-and '<a href="qh-optq.htm#QJn">QJ</a>' (joggled input) may produce
-unexpected results. Cocircular and cospherical input sites will
-produce duplicate or nearly duplicate Voronoi vertices. See also <a
-href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p>
-
-<p>The 'qvonoroi' program is equivalent to
-'<a href=qhull.htm#outputs>qhull v</a> <a href=qh-optq.htm#Qbb>Qbb</a>' in 2-d to 3-d, and
-'<a href=qhull.htm#outputs>qhull v</a> <a href=qh-optq.htm#Qbb>Qbb</a> <a href=qh-optq.htm#Qx>Qx</a>'
-in 4-d and higher. It disables the following Qhull
-<a href=qh-quick.htm#options>options</a>: <i>d n v Qbb QbB Qf Qg Qm
-Qr QR Qv Qx Qz TR E V Fa FA FC FD FS Ft FV Gt Q0,etc</i>.
-
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-
-<hr>
-<h3><a href="#TOP">»</a><a name="synopsis">qvoronoi synopsis</a></h3>
-
-<pre>
-qvoronoi- compute the Voronoi diagram.
- input (stdin): dimension, number of points, point coordinates
- comments start with a non-numeric character
-
-options (qh-voron.htm):
- Qu - compute furthest-site Voronoi diagram
- Qt - triangulated output
- QJ - joggle input instead of merging facets
- Tv - verify result: structure, convexity, and in-circle test
- . - concise list of all options
- - - one-line description of all options
-
-output options (subset):
- s - summary of results (default)
- p - Voronoi vertices
- o - OFF file format (dim, Voronoi vertices, and Voronoi regions)
- FN - count and Voronoi vertices for each Voronoi region
- Fv - Voronoi diagram as Voronoi vertices between adjacent input sites
- Fi - separating hyperplanes for bounded regions, 'Fo' for unbounded
- G - Geomview output (2-d only)
- QVn - Voronoi vertices for input point n, -n if not
- TO file- output results to file, may be enclosed in single quotes
-
-examples:
-rbox c P0 D2 | qvoronoi s o rbox c P0 D2 | qvoronoi Fi
-rbox c P0 D2 | qvoronoi Fo rbox c P0 D2 | qvoronoi Fv
-rbox c P0 D2 | qvoronoi s Qu Fv rbox c P0 D2 | qvoronoi Qu Fo
-rbox c G1 d D2 | qvoronoi s p rbox c G1 d D2 | qvoronoi Qt s p
-rbox c P0 D2 | qvoronoi s Fv QV0
-</pre>
-
-<h3><a href="#TOP">»</a><a name="input">qvoronoi input</a></h3>
-<blockquote>
-The input data on <tt>stdin</tt> consists of:
-<ul>
- <li>dimension
- <li>number of points</li>
- <li>point coordinates</li>
-</ul>
-
-<p>Use I/O redirection (e.g., qvoronoi < data.txt), a pipe (e.g., rbox 10 | qvoronoi),
-or the '<a href=qh-optt.htm#TI>TI</a>' option (e.g., qvoronoi TI data.txt).
-
-<p>For example, this is four cocircular points inside a square. Their Voronoi
-diagram has nine vertices and eight regions. Notice the Voronoi vertex
-at the origin, and the Voronoi vertices (on each axis) for the four
-sides of the square.
-<p>
-<blockquote>
-<tt>rbox s 4 W0 c G1 D2 > data</tt>
-<blockquote><pre>
-2 RBOX s 4 W0 c D2
-8
--0.4941988586954018 -0.07594397977563715
--0.06448037284989526 0.4958248496365813
-0.4911154367094632 0.09383830681375946
--0.348353580869097 -0.3586778257652367
- -1 -1
- -1 1
- 1 -1
- 1 1
-</pre></blockquote>
-
-<p><tt>qvoronoi s p < data</tt>
-<blockquote><pre>
-
-Voronoi diagram by the convex hull of 8 points in 3-d:
-
- Number of Voronoi regions: 8
- Number of Voronoi vertices: 9
- Number of non-simplicial Voronoi vertices: 1
-
-Statistics for: RBOX s 4 W0 c D2 | QVORONOI s p
-
- Number of points processed: 8
- Number of hyperplanes created: 18
- Number of facets in hull: 10
- Number of distance tests for qhull: 33
- Number of merged facets: 2
- Number of distance tests for merging: 102
- CPU seconds to compute hull (after input): 0.094
-
-2
-9
-4.217546450968612e-17 1.735507986399734
--8.402566836762659e-17 -1.364368854147395
-0.3447488772716865 -0.6395484723719818
-1.719446929853986 2.136555906154247e-17
-0.4967882915039657 0.68662371396699
--1.729928876283549 1.343733067524222e-17
--0.8906163241424728 -0.4594150543829102
--0.6656840313875723 0.5003013793414868
--7.318364664277155e-19 -1.188217818408333e-16
-</pre></blockquote>
-</blockquote>
-
-</blockquote>
-<h3><a href="#TOP">»</a> <a name="outputs">qvoronoi
-outputs</a></h3>
-<blockquote>
-
-<p>These options control the output of Voronoi diagrams.</p>
-<blockquote>
-
-<dl compact>
- <dt> </dt>
- <dd><b>Voronoi vertices</b></dd>
- <dt><a href="qh-opto.htm#p">p</a></dt>
- <dd>print the coordinates of the Voronoi vertices. The first line
- is the dimension. The second line is the number of vertices. Each
- remaining line is a Voronoi vertex.</dd>
- <dt><a href="qh-optf.htm#Fn">Fn</a></dt>
- <dd>list the neighboring Voronoi vertices for each Voronoi
- vertex. The first line is the number of Voronoi vertices. Each
- remaining line starts with the number of neighboring vertices.
- Negative vertices (e.g., <em>-1</em>) indicate vertices
- outside of the Voronoi diagram.
- In the circle-in-box example, the
- Voronoi vertex at the origin has four neighbors.</dd>
- <dt><a href="qh-optf.htm#FN">FN</a></dt>
- <dd>list the Voronoi vertices for each Voronoi region. The first line is
- the number of Voronoi regions. Each remaining line starts with the
- number of Voronoi vertices. Negative indices (e.g., <em>-1</em>) indicate vertices
- outside of the Voronoi diagram.
- In the circle-in-box example, the four bounded regions are defined by four
- Voronoi vertices.</dd>
-
- <dt> </dt>
- <dt> </dt>
- <dd><b>Voronoi regions</b></dd>
- <dt><a href="qh-opto.htm#o">o</a></dt>
- <dd>print the Voronoi regions in OFF format. The first line is the
- dimension. The second line is the number of vertices, the number
- of input sites, and "1". The third line represents the vertex-at-infinity.
- Its coordinates are "-10.101". The next lines are the coordinates
- of the Voronoi vertices. Each remaining line starts with the number
- of Voronoi vertices in a Voronoi region. In 2-d, the vertices are
-listed in adjacency order (unoriented). In 3-d and higher, the
-vertices are listed in numeric order. In the circle-in-square
- example, each bounded region includes the Voronoi vertex at
- the origin. Lines consisting of <em>0</em> indicate
- coplanar input sites or '<a href="qh-optq.htm#Qz">Qz</a>'. </dd>
- <dt><a href="qh-optf.htm#Fi2">Fi</a></dt>
- <dd>print separating hyperplanes for inner, bounded Voronoi
- regions. The first number is the number of separating
- hyperplanes. Each remaining line starts with <i>3+dim</i>. The
- next two numbers are adjacent input sites. The next <i>dim</i>
- numbers are the coefficients of the separating hyperplane. The
- last number is its offset. Use '<a href="qh-optt.htm#Tv">Tv</a>' to verify that the
-hyperplanes are perpendicular bisectors. It will list relevant
-statistics to stderr. </dd>
- <dt><a href="qh-optf.htm#Fo2">Fo</a></dt>
- <dd>print separating hyperplanes for outer, unbounded Voronoi
- regions. The first number is the number of separating
- hyperplanes. Each remaining line starts with <i>3+dim</i>. The
- next two numbers are adjacent input sites on the convex hull. The
- next <i>dim</i>
- numbers are the coefficients of the separating hyperplane. The
- last number is its offset. Use '<a href="qh-optt.htm#Tv">Tv</a>' to verify that the
-hyperplanes are perpendicular bisectors. It will list relevant
-statistics to stderr,</dd>
- <dt> </dt>
- <dt> </dt>
- <dd><b>Input sites</b></dd>
- <dt><a href="qh-optf.htm#Fv2">Fv</a></dt>
- <dd>list ridges of Voronoi vertices for pairs of input sites. The
- first line is the number of ridges. Each remaining line starts with
- two plus the number of Voronoi vertices in the ridge. The next
- two numbers are two adjacent input sites. The remaining numbers list
- the Voronoi vertices. As with option 'o', a <em>0</em> indicates
- the vertex-at-infinity
- and an unbounded, separating hyperplane.
- The perpendicular bisector (separating hyperplane)
- of the input sites is a flat through these vertices.
- In the circle-in-square example, the ridge for each edge of the square
- is unbounded.</dd>
- <dt><a href="qh-optf.htm#Fc">Fc</a></dt>
- <dd>list coincident input sites for each Voronoi vertex.
- The first line is the number of vertices. The remaining lines start with
- the number of coincident sites and deleted vertices. Deleted vertices
- indicate highly degenerate input (see'<A href="qh-optf.htm#Fs">Fs</a>').
- A coincident site is assigned to one Voronoi
- vertex. Do not use '<a href="qh-optq.htm#QJn">QJ</a>' with 'Fc'; the joggle will separate
- coincident sites.</dd>
- <dt><a href="qh-optf.htm#FP">FP</a></dt>
- <dd>print coincident input sites with distance to
- nearest site (i.e., vertex). The first line is the
- number of coincident sites. Each remaining line starts with the point ID of
- an input site, followed by the point ID of a coincident point, its vertex, and distance.
- Includes deleted vertices which
- indicate highly degenerate input (see'<A href="qh-optf.htm#Fs">Fs</a>').
- Do not use '<a href="qh-optq.htm#QJn">QJ</a>' with 'FP'; the joggle will separate
- coincident sites.</dd>
- <dt> </dt>
- <dt> </dt>
- <dd><b>General</b></dd>
- <dt><a href="qh-opto.htm#s">s</a></dt>
- <dd>print summary of the Voronoi diagram. Use '<a
- href="qh-optf.htm#Fs">Fs</a>' for numeric data.</dd>
- <dt><a href="qh-opto.htm#i">i</a></dt>
- <dd>list input sites for each <a href=qdelaun.htm>Delaunay region</a>. Use option '<a href="qh-optp.htm#Pp">Pp</a>'
- to avoid the warning. The first line is the number of regions. The
- remaining lines list the input sites for each region. The regions are
- oriented. In the circle-in-square example, the cocircular region has four
- edges. In 3-d and higher, report cospherical sites by adding extra points.
- </dd>
- <dt><a href="qh-optg.htm#G">G</a></dt>
- <dd>Geomview output for 2-d Voronoi diagrams.</dd>
- </dl>
-</blockquote>
-</blockquote>
-<h3><a href="#TOP">»</a> <a name="controls">qvoronoi
-controls</a></h3>
-<blockquote>
-
-<p>These options provide additional control:</p>
-<blockquote>
-
-<dl compact>
- <dt><a href="qh-optq.htm#Qt">Qt</a></dt>
- <dd>triangulated output. If a Voronoi vertex is defined by cospherical data, Qhull
- duplicates the vertex. For example, if the data contains a square, the output
- will contain two copies of the Voronoi vertex.</dd>
- <dt><a href="qh-optq.htm#QJn">QJ</a></dt>
- <dd>joggle the input to avoid Voronoi vertices defined by more
- than <i>dim+1</i> points. It is less accurate than triangulated output ('Qt').
- </dd>
- <dt><a href="qh-optq.htm#Qu">Qu</a></dt>
- <dd>compute the <a href="qvoron_f.htm">furthest-site Voronoi diagram</a>.</dd>
- <dt><a href="qh-optq.htm#QVn">QVn</a></dt>
- <dd>select Voronoi vertices for input site <em>n</em> </dd>
- <dt><a href="qh-optq.htm#Qz">Qz</a></dt>
- <dd>add a point above the paraboloid to reduce precision
- errors. Use it for nearly cocircular/cospherical input
- (e.g., 'rbox c | qvoronoi Qz').</dd>
- <dt><a href="qh-optt.htm#Tv">Tv</a></dt>
- <dd>verify result</dd>
- <dt><a href="qh-optt.htm#TO">TI file</a></dt>
- <dd>input data from file. The filename may not use spaces or quotes.</dd>
- <dt><a href="qh-optt.htm#TO">TO file</a></dt>
- <dd>output results to file. Use single quotes if the filename
- contains spaces (e.g., <tt>TO 'file with spaces.txt'</tt></dd>
- <dt><a href="qh-optt.htm#TFn">TFn</a></dt>
- <dd>report progress after constructing <em>n</em> facets</dd>
- <dt><a href="qh-optp.htm#PDk">PDk:1</a></dt>
- <dd>include upper and lower facets in the output. Set <em>k</em>
- to the last dimension (e.g., 'PD2:1' for 2-d inputs). </dd>
- <dt><a href="qh-opto.htm#f">f </a></dt>
- <dd>facet dump. Print the data structure for each facet (i.e.,
- Voronoi vertex).</dd>
-</dl>
-
-</blockquote>
-</blockquote>
-<h3><a href="#TOP">»</a> <a name="graphics">qvoronoi
-graphics</a></h3>
-<blockquote>
-
-<p>In 2-d, Geomview output ('<a href="qh-optg.htm#G">G</a>')
-displays a Voronoi diagram with extra edges to close the
-unbounded Voronoi regions. To view the unbounded rays, enclose
-the input points in a square.</p>
-
-<p>You can also view <i>individual</i> Voronoi regions in 3-d. To
-view the Voronoi region for site 3 in Geomview, execute</p>
-
-<blockquote>
- <p>qvoronoi <data '<a href="qh-optq.htm#QVn">QV3</a>' '<a
- href="qh-opto.htm#p">p</a>' | qconvex s G >output</p>
-</blockquote>
-
-<p>The <tt>qvoronoi</tt> command returns the Voronoi vertices
-for input site 3. The <tt>qconvex</tt> command computes their convex hull.
-This is the Voronoi region for input site 3. Its
-hyperplane normals (qconvex 'n') are the same as the separating hyperplanes
-from options '<a href="qh-optf.htm#Fi">Fi</a>'
-and '<a href="qh-optf.htm#Fo">Fo</a>' (up to roundoff error).
-
-<p>See the <a href="qh-eg.htm#delaunay">Delaunay and Voronoi
-examples</a> for 2-d and 3-d examples. Turn off normalization (on
-Geomview's 'obscure' menu) when comparing the Voronoi diagram
-with the corresponding Delaunay triangulation. </p>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="notes">qvoronoi
-notes</a></h3>
-<blockquote>
-
-<p>You can simplify the Voronoi diagram by enclosing the input
-sites in a large square or cube. This is particularly recommended
-for cocircular or cospherical input data.</p>
-
-<p>See <a href="#graphics">Voronoi graphics</a> for computing
-the convex hull of a Voronoi region. </p>
-
-<p>Voronoi diagrams do not include facets that are
-coplanar with the convex hull of the input sites. A facet is
-coplanar if the last coefficient of its normal is
-nearly zero (see <a href="../src/user.h#ZEROdelaunay">qh_ZEROdelaunay</a>).
-
-<p>Unbounded regions can be confusing. For example, '<tt>rbox c |
-qvoronoi Qz o</tt>' produces the Voronoi regions for the vertices
-of a cube centered at the origin. All regions are unbounded. The
-output is </p>
-
-<blockquote>
- <pre>3
-2 9 1
--10.101 -10.101 -10.101
- 0 0 0
-2 0 1
-2 0 1
-2 0 1
-2 0 1
-2 0 1
-2 0 1
-2 0 1
-2 0 1
-0
-</pre>
-</blockquote>
-
-<p>The first line is the dimension. The second line is the number
-of vertices and the number of regions. There is one region per
-input point plus a region for the point-at-infinity added by
-option '<a href="qh-optq.htm#Qz">Qz</a>'. The next two lines
-lists the Voronoi vertices. The first vertex is the infinity
-vertex. It is indicate by the coordinates <em>-10.101</em>. The
-second vertex is the origin. The next nine lines list the
-regions. Each region lists two vertices -- the infinity vertex
-and the origin. The last line is "0" because no region
-is associated with the point-at-infinity. A "0" would
-also be listed for nearly incident input sites. </p>
-
-<p>To use option '<a href="qh-optf.htm#Fv">Fv</a>', add an
-interior point. For example, </p>
-
-<blockquote>
- <pre>
-rbox c P0 | qvoronoi Fv
-20
-5 0 7 1 3 5
-5 0 3 1 4 5
-5 0 5 1 2 3
-5 0 1 1 2 4
-5 0 6 2 3 6
-5 0 2 2 4 6
-5 0 4 4 5 6
-5 0 8 5 3 6
-5 1 2 0 2 4
-5 1 3 0 1 4
-5 1 5 0 1 2
-5 2 4 0 4 6
-5 2 6 0 2 6
-5 3 4 0 4 5
-5 3 7 0 1 5
-5 4 8 0 6 5
-5 5 6 0 2 3
-5 5 7 0 1 3
-5 6 8 0 6 3
-5 7 8 0 3 5
-</pre>
-</blockquote>
-
-<p>The output consists of 20 ridges and each ridge lists a pair
-of input sites and a triplet of Voronoi vertices. The first eight
-ridges connect the origin ('P0'). The remainder list the edges of
-the cube. Each edge generates an unbounded ray through the
-midpoint. The corresponding separating planes ('Fo') follow each
-pair of coordinate axes. </p>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="conventions">qvoronoi conventions</a></h3>
-<blockquote>
-
-<p>The following terminology is used for Voronoi diagrams in
-Qhull. The underlying structure is a Delaunay triangulation from
-a convex hull in one higher dimension. Facets of the Delaunay
-triangulation correspond to vertices of the Voronoi diagram.
-Vertices of the Delaunay triangulation correspond to input sites.
-They also correspond to regions of the Voronoi diagram. See <a
-href="qconvex.htm#conventions">convex hull conventions</a>, <a
-href="qdelaun.htm#conventions">Delaunay conventions</a>, and
-<a href="index.htm#structure">Qhull's data structures</a>.</p>
-<blockquote>
-
-<ul>
- <li><em>input site</em> - a point in the input (one dimension
- lower than a point on the convex hull)</li>
- <li><em>point</em> - a point has <i>d+1</i> coordinates. The
- last coordinate is the sum of the squares of the input
- site's coordinates</li>
- <li><em>coplanar point</em> - a <em>nearly incident</em>
- input site</li>
- <li><em>vertex</em> - a point on the paraboloid. It
- corresponds to a unique input site. </li>
- <li><em>point-at-infinity</em> - a point added above the
- paraboloid by option '<a href="qh-optq.htm#Qz">Qz</a>'</li>
- <li><em>Delaunay facet</em> - a lower facet of the
- paraboloid. The last coefficient of its normal is
- clearly negative.</li>
- <li><em>Voronoi vertex</em> - the circumcenter of a Delaunay
- facet</li>
- <li><em>Voronoi region</em> - the Voronoi vertices for an
- input site. The region of Euclidean space nearest to an
- input site.</li>
- <li><em>Voronoi diagram</em> - the graph of the Voronoi
- regions. It includes the ridges (i.e., edges) between the
- regions.</li>
- <li><em>vertex-at-infinity</em> - the Voronoi vertex that
- indicates unbounded Voronoi regions in '<a
- href="qh-opto.htm#o">o</a>' output format. Its
- coordinates are <em>-10.101</em>.</li>
- <li><em>good facet</em> - a Voronoi vertex with optional
- restrictions by '<a href="qh-optq.htm#QVn">QVn</a>', etc.</li>
-</ul>
-
-</blockquote>
-</blockquote>
-<h3><a href="#TOP">»</a><a name="options">qvoronoi options</a></h3>
-
-<pre>
-qvoronoi- compute the Voronoi diagram
- http://www.qhull.org
-
-input (stdin):
- first lines: dimension and number of points (or vice-versa).
- other lines: point coordinates, best if one point per line
- comments: start with a non-numeric character
-
-options:
- Qu - compute furthest-site Voronoi diagram
- Qt - triangulated output
- QJ - joggle input instead of merging facets
-
-Qhull control options:
- QJn - randomly joggle input in range [-n,n]
- Qs - search all points for the initial simplex
- Qz - add point-at-infinity to Voronoi diagram
- QGn - Voronoi vertices if visible from point n, -n if not
- QVn - Voronoi vertices for input point n, -n if not
-
-Trace options:
- T4 - trace at level n, 4=all, 5=mem/gauss, -1= events
- Tc - check frequently during execution
- Ts - statistics
- Tv - verify result: structure, convexity, and in-circle test
- Tz - send all output to stdout
- TFn - report summary when n or more facets created
- TI file - input data from file, no spaces or single quotes
- TO file - output results to file, may be enclosed in single quotes
- TPn - turn on tracing when point n added to hull
- TMn - turn on tracing at merge n
- TWn - trace merge facets when width > n
- TVn - stop qhull after adding point n, -n for before (see TCn)
- TCn - stop qhull after building cone for point n (see TVn)
-
-Precision options:
- Cn - radius of centrum (roundoff added). Merge facets if non-convex
- An - cosine of maximum angle. Merge facets if cosine > n or non-convex
- C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
- Rn - randomly perturb computations by a factor of [1-n,1+n]
- Wn - min facet width for non-coincident point (before roundoff)
-
-Output formats (may be combined; if none, produces a summary to stdout):
- s - summary to stderr
- p - Voronoi vertices
- o - OFF format (dim, Voronoi vertices, and Voronoi regions)
- i - Delaunay regions (use 'Pp' to avoid warning)
- f - facet dump
-
-More formats:
- Fc - count plus coincident points (by Voronoi vertex)
- Fd - use cdd format for input (homogeneous with offset first)
- FD - use cdd format for output (offset first)
- FF - facet dump without ridges
- Fi - separating hyperplanes for bounded Voronoi regions
- FI - ID for each Voronoi vertex
- Fm - merge count for each Voronoi vertex (511 max)
- Fn - count plus neighboring Voronoi vertices for each Voronoi vertex
- FN - count and Voronoi vertices for each Voronoi region
- Fo - separating hyperplanes for unbounded Voronoi regions
- FO - options and precision constants
- FP - nearest point and distance for each coincident point
- FQ - command used for qvoronoi
- Fs - summary: #int (8), dimension, #points, tot vertices, tot facets,
- for output: #Voronoi regions, #Voronoi vertices,
- #coincident points, #non-simplicial regions
- #real (2), max outer plane and min vertex
- Fv - Voronoi diagram as Voronoi vertices between adjacent input sites
- Fx - extreme points of Delaunay triangulation (on convex hull)
-
-Geomview options (2-d only)
- Ga - all points as dots
- Gp - coplanar points and vertices as radii
- Gv - vertices as spheres
- Gi - inner planes only
- Gn - no planes
- Go - outer planes only
- Gc - centrums
- Gh - hyperplane intersections
- Gr - ridges
- GDn - drop dimension n in 3-d and 4-d output
-
-Print options:
- PAn - keep n largest Voronoi vertices by 'area'
- Pdk:n - drop facet if normal[k] <= n (default 0.0)
- PDk:n - drop facet if normal[k] >= n
- Pg - print good Voronoi vertices (needs 'QGn' or 'QVn')
- PFn - keep Voronoi vertices whose 'area' is at least n
- PG - print neighbors of good Voronoi vertices
- PMn - keep n Voronoi vertices with most merges
- Po - force output. If error, output neighborhood of facet
- Pp - do not report precision problems
-
- . - list of all options
- - - one line descriptions of all options
-</pre>
-
-<!-- Navigation links -->
-<hr>
-
-<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a><br>
-<b>To:</b> <a href="#synopsis">sy</a>nopsis
-• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
-• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
-• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
-• <a href="#options">op</a>tions
-<!-- GC common information -->
-<hr>
-
-<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
-align="middle" width="40" height="40"></a><i>The Geometry Center
-Home Page </i></p>
-
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/rbox.htm b/GraspPlanning/ExternalDependencies/qhull-2003.1/html/rbox.htm
deleted file mode 100644
index f039ead1d139ae4a889c733d5fe523b24810360e..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/rbox.htm
+++ /dev/null
@@ -1,272 +0,0 @@
-<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
-<html>
-
-<head>
-<title>rbox -- generate point distributions</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<p><b><a name="TOP">Up:</a></b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a><br>
-<b>To:</b> <a href="#synopsis">sy</a>nopsis • <a href="#outputs">ou</a>tputs
-• <a href="#examples">ex</a>amples • <a href="#notes">no</a>tes
-• <a href="#options">op</a>tions
-<hr>
-<!-- Main text of document -->
-<h1><a
-href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html"><img
-src="qh--cone.gif" alt="[CONE]" align="middle" width="100"
-height="100"></a>rbox -- generate point distributions</h1>
-
-<blockquote>
- rbox generates random or regular points according to the
- options given, and outputs the points to stdout. The
- points are generated in a cube, unless 's', 'x', or 'y'
- are given.
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="synopsis">rbox synopsis</a></h3>
-<pre>
-rbox- generate various point distributions. Default is random in cube.
-
-args (any order, space separated):
- 3000 number of random points in cube, lens, spiral, sphere or grid
- D3 dimension 3-d
- c add a unit cube to the output ('c G2.0' sets size)
- d add a unit diamond to the output ('d G2.0' sets size)
- l generate a regular 3-d spiral
- r generate a regular polygon, ('r s Z1 G0.1' makes a cone)
- s generate cospherical points
- x generate random points in simplex, may use 'r' or 'Wn'
- y same as 'x', plus simplex
- Pn,m,r add point [n,m,r] first, pads with 0
-
- Ln lens distribution of radius n. Also 's', 'r', 'G', 'W'.
- Mn,m,r lattice (Mesh) rotated by [n,-m,0], [m,n,0], [0,0,r], ...
- '27 M1,0,1' is {0,1,2} x {0,1,2} x {0,1,2}. Try 'M3,4 z'.
- W0.1 random distribution within 0.1 of the cube's or sphere's surface
- Z0.5 s random points in a 0.5 disk projected to a sphere
- Z0.5 s G0.6 same as Z0.5 within a 0.6 gap
-
- Bn bounding box coordinates, default 0.5
- h output as homogeneous coordinates for cdd
- n remove command line from the first line of output
- On offset coordinates by n
- t use time as the random number seed (default is command line)
- tn use n as the random number seed
- z print integer coordinates, default 'Bn' is 1e+06
-</pre>
-
-<h3><a href="#TOP">»</a><a name="outputs">rbox outputs</a></h3>
-<blockquote>
-
-The format of the output is the following: first line contains
- the dimension and a comment, second line contains the
- number of points, and the following lines contain the points,
- one point per line. Points are represented by their coordinate values.
-
-<p>For example, <tt>rbox c 10 D2</tt> generates
-<blockquote>
-<pre>
-2 RBOX c 10 D2
-14
--0.4999921736307369 -0.3684622117955817
-0.2556053225468894 -0.0413498678629751
-0.0327672376602583 -0.2810408135699488
--0.452955383763607 0.17886471718444
-0.1792964061529342 0.4346928963760779
--0.1164979223315585 0.01941637230982666
-0.3309653464993139 -0.4654278894564396
--0.4465383649305798 0.02970019358182344
-0.1711493843897706 -0.4923018137852678
--0.1165843490665633 -0.433157762450313
- -0.5 -0.5
- -0.5 0.5
- 0.5 -0.5
- 0.5 0.5
-</pre>
-
-</blockquote>
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="examples">rbox examples</a></h3>
-
-<pre>
- rbox 10
- 10 random points in the unit cube centered at the
- origin.
-
- rbox 10 s D2
- 10 random points on a 2-d circle.
-
- rbox 100 W0
- 100 random points on the surface of a cube.
-
- rbox 1000 s D4
- 1000 random points on a 4-d sphere.
-
- rbox c D5 O0.5
- a 5-d hypercube with one corner at the origin.
-
- rbox d D10
- a 10-d diamond.
-
- rbox x 1000 r W0
- 100 random points on the surface of a fixed simplex
-
- rbox y D12
- a 12-d simplex.
-
- rbox l 10
- 10 random points along a spiral
-
- rbox l 10 r
- 10 regular points along a spiral plus two end
- points
-
- rbox 1000 L10000 D4 s
- 1000 random points on the surface of a narrow lens.
-
- rbox 1000 L100000 s G1e-6
- 1000 random points near the edge of a narrow lens
-
- rbox c G2 d G3
- a cube with coordinates +2/-2 and a diamond with
- coordinates +3/-3.
-
- rbox 64 M3,4 z
- a rotated, {0,1,2,3} x {0,1,2,3} x {0,1,2,3} lat-
- tice (Mesh) of integer points.
-
- rbox P0 P0 P0 P0 P0
- 5 copies of the origin in 3-d. Try 'rbox P0 P0 P0
- P0 P0 | qhull QJ'.
-
- r 100 s Z1 G0.1
- two cospherical 100-gons plus another cospherical
- point.
-
- 100 s Z1
- a cone of points.
-
- 100 s Z1e-7
- a narrow cone of points with many precision errors.
-</pre>
-
-<h3><a href="#TOP">»</a><a name="notes">rbox notes</a></h3>
-<blockquote>
-Some combinations of arguments generate odd results.
-
-</blockquote>
-<h3><a href="#TOP">»</a><a name="options">rbox options</a></h3>
-
-<pre>
- n number of points
-
- Dn dimension n-d (default 3-d)
-
- Bn bounding box coordinates (default 0.5)
-
- l spiral distribution, available only in 3-d
-
- Ln lens distribution of radius n. May be used with
- 's', 'r', 'G', and 'W'.
-
- Mn,m,r lattice (Mesh) rotated by {[n,-m,0], [m,n,0],
- [0,0,r], ...}. Use 'Mm,n' for a rigid rotation
- with r = sqrt(n^2+m^2). 'M1,0' is an orthogonal
- lattice. For example, '27 M1,0' is {0,1,2} x
- {0,1,2} x {0,1,2}.
-
- s cospherical points randomly generated in a cube and
- projected to the unit sphere
-
- x simplicial distribution. It is fixed for option
- 'r'. May be used with 'W'.
-
- y simplicial distribution plus a simplex. Both 'x'
- and 'y' generate the same points.
-
- Wn restrict points to distance n of the surface of a
- sphere or a cube
-
- c add a unit cube to the output
-
- c Gm add a cube with all combinations of +m and -m to
- the output
-
- d add a unit diamond to the output.
-
- d Gm add a diamond made of 0, +m and -m to the output
-
- Pn,m,r add point [n,m,r] to the output first. Pad coordi-
- nates with 0.0.
-
- n Remove the command line from the first line of out-
- put.
-
- On offset the data by adding n to each coordinate.
-
- t use time in seconds as the random number seed
- (default is command line).
-
- tn set the random number seed to n.
-
- z generate integer coordinates. Use 'Bn' to change
- the range. The default is 'B1e6' for six-digit
- coordinates. In R^4, seven-digit coordinates will
- overflow hyperplane normalization.
-
- Zn s restrict points to a disk about the z+ axis and the
- sphere (default Z1.0). Includes the opposite pole.
- 'Z1e-6' generates degenerate points under single
- precision.
-
- Zn Gm s
- same as Zn with an empty center (default G0.5).
-
- r s D2 generate a regular polygon
-
- r s Z1 G0.1
- generate a regular cone
-</pre>
-
-<!-- Navigation links -->
-<hr>
-
-<p><b>Up:</b> <a href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
-<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
-• <a href="qh-quick.htm#options">Options</a>
-• <a href="qh-opto.htm#output">Output</a>
-• <a href="qh-optf.htm#format">Formats</a>
-• <a href="qh-optg.htm#geomview">Geomview</a>
-• <a href="qh-optp.htm#print">Print</a>
-• <a href="qh-optq.htm#qhull">Qhull</a>
-• <a href="qh-optc.htm#prec">Precision</a>
-• <a href="qh-optt.htm#trace">Trace</a><br>
-<b>To:</b> <a href="#synopsis">sy</a>nopsis • <a href="#outputs">ou</a>tputs
-• <a href="#examples">ex</a>amples • <a href="#notes">no</a>tes
-• <a href="#options">op</a>tions
-<!-- GC common information -->
-<hr>
-
-<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
-align="middle" width="40" height="40"></a><i>The Geometry Center
-Home Page </i></p>
-
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-<br>
-Created: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: August 12, 1998 <!-- hhmts end --> </p>
-</body>
-</html>
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/rbox.man b/GraspPlanning/ExternalDependencies/qhull-2003.1/html/rbox.man
deleted file mode 100644
index 84ef6e306823f040f35490304d9154faef9c2b71..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/rbox.man
+++ /dev/null
@@ -1,176 +0,0 @@
-./" This is the Unix manual page for rbox, written in nroff, the standard
-./" manual formatter for Unix systems. To format it, type
-./"
-./" nroff -man rbox.man
-./"
-./" This will print a formatted copy to standard output. If you want
-./" to ensure that the output is plain ascii, free of any control
-./" characters that nroff uses for underlining etc, pipe the output
-./" through "col -b":
-./"
-./" nroff -man rbox.man | col -b
-./"
-.TH rbox 1 "August 10, 1998" "Geometry Center"
-.SH NAME
-rbox \- generate point distributions for qhull
-.SH SYNOPSIS
-Command "rbox" (w/o arguments) lists the options.
-.SH DESCRIPTION
-.PP
-rbox generates random or regular points according to the options given, and
-outputs
-the points to stdout. The points are generated in a cube, unless 's' or
-'k' option is
-given. The format of the output is the following: first line
-contains the dimension and a comment,
-second line contains the number of points, and the
-following lines contain the points, one point per line. Points are represented
-by their coordinate values.
-.SH EXAMPLES
-.TP
-rbox 10
-10 random points in the unit cube centered at the origin.
-.TP
-rbox 10 s D2
-10 random points on a 2-d circle.
-.TP
-rbox 100 W0
-100 random points on the surface of a cube.
-.TP
-rbox 1000 s D4
-1000 random points on a 4-d sphere.
-.TP
-rbox c D5 O0.5
-a 5-d hypercube with one corner at the origin.
-.TP
-rbox d D10
-a 10-d diamond.
-.TP
-rbox x 1000 r W0
-100 random points on the surface of a fixed simplex
-.TP
-rbox y D12
-a 12-d simplex.
-.TP
-rbox l 10
-10 random points along a spiral
-.TP
-rbox l 10 r
-10 regular points along a spiral plus two end points
-.TP
-rbox 1000 L10000 D4 s
-1000 random points on the surface of a narrow lens.
-.TP
-rbox c G2 d G3
-a cube with coordinates +2/-2 and a diamond with coordinates +3/-3.
-.TP
-rbox 64 M3,4 z
-a rotated, {0,1,2,3} x {0,1,2,3} x {0,1,2,3} lattice (Mesh) of integer points.
-'rbox 64 M1,0' is orthogonal.
-.TP
-rbox P0 P0 P0 P0 P0
-5 copies of the origin in 3-d. Try 'rbox P0 P0 P0 P0 P0 | qhull QJ'.
-.TP
-r 100 s Z1 G0.1
-two cospherical 100-gons plus another cospherical point.
-.TP
-100 s Z1
-a cone of points.
-.TP
-100 s Z1e-7
-a narrow cone of points with many precision errors.
-.SH OPTIONS
-.TP
-n
-number of points
-.TP
-Dn
-dimension n-d (default 3-d)
-.TP
-Bn
-bounding box coordinates (default 0.5)
-.TP
-l
-spiral distribution, available only in 3-d
-.TP
-Ln
-lens distribution of radius n. May be used with 's', 'r', 'G', and 'W'.
-.TP
-Mn,m,r
-lattice (Mesh) rotated by {[n,-m,0], [m,n,0], [0,0,r], ...}.
-Use 'Mm,n' for a rigid rotation with r = sqrt(n^2+m^2). 'M1,0' is an
-orthogonal lattice. For example, '27 M1,0' is {0,1,2} x {0,1,2} x {0,1,2}.
-'27 M3,4 z' is a rotated integer lattice.
-.TP
-s
-cospherical points randomly generated in a cube and projected to the unit sphere
-.TP
-x
-simplicial distribution. It is fixed for option 'r'. May be used with 'W'.
-.TP
-y
-simplicial distribution plus a simplex. Both 'x' and 'y' generate the same points.
-.TP
-Wn
-restrict points to distance n of the surface of a sphere or a cube
-.TP
-c
-add a unit cube to the output
-.TP
-c Gm
-add a cube with all combinations of +m and -m to the output
-.TP
-d
-add a unit diamond to the output.
-.TP
-d Gm
-add a diamond made of 0, +m and -m to the output
-.TP
-Pn,m,r
-add point [n,m,r] to the output first. Pad coordinates with 0.0.
-.TP
-n
-Remove the command line from the first line of output.
-.TP
-On
-offset the data by adding n to each coordinate.
-.TP
-t
-use time in seconds as the random number seed (default is command line).
-.TP
-tn
-set the random number seed to n.
-.TP
-z
-generate integer coordinates. Use 'Bn' to change the range.
-The default is 'B1e6' for six-digit coordinates. In R^4, seven-digit
-coordinates will overflow hyperplane normalization.
-.TP
-Zn s
-restrict points to a disk about the z+ axis and the sphere (default Z1.0).
-Includes the opposite pole. 'Z1e-6' generates degenerate points under
-single precision.
-.TP
-Zn Gm s
-same as Zn with an empty center (default G0.5).
-.TP
-r s D2
-generate a regular polygon
-.TP
-r s Z1 G0.1
-generate a regular cone
-.SH BUGS
-Some combinations of arguments generate odd results.
-
-Report bugs to qhull_bug@qhull.org, other correspondence to qhull@qhull.org
-.SH SEE ALSO
-qhull(1)
-.SH AUTHOR
-.nf
-C. Bradford Barber
-c/o The Geometry Center
-400 Lind Hall
-207 Church Street S.E.
-Minneapolis, MN 55455
-.fi
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/rbox.txt b/GraspPlanning/ExternalDependencies/qhull-2003.1/html/rbox.txt
deleted file mode 100644
index bc459525fe97fb3ea9ac062e1eba7f7279f0e733..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/html/rbox.txt
+++ /dev/null
@@ -1,198 +0,0 @@
-
-
-
-rbox(1) rbox(1)
-
-
-NAME
- rbox - generate point distributions for qhull
-
-SYNOPSIS
- Command "rbox" (w/o arguments) lists the options.
-
-DESCRIPTION
- rbox generates random or regular points according to the
- options given, and outputs the points to stdout. The
- points are generated in a cube, unless 's' or given. The
- format of the output is the following: first line contains
- the dimension and a comment, second line contains the num-
- ber of points, and the following lines contain the points,
- one point per line. Points are represented by their coor-
- dinate values.
-
-EXAMPLES
- rbox 10
- 10 random points in the unit cube centered at the
- origin.
-
- rbox 10 s D2
- 10 random points on a 2-d circle.
-
- rbox 100 W0
- 100 random points on the surface of a cube.
-
- rbox 1000 s D4
- 1000 random points on a 4-d sphere.
-
- rbox c D5 O0.5
- a 5-d hypercube with one corner at the origin.
-
- rbox d D10
- a 10-d diamond.
-
- rbox x 1000 r W0
- 100 random points on the surface of a fixed simplex
-
- rbox y D12
- a 12-d simplex.
-
- rbox l 10
- 10 random points along a spiral
-
- rbox l 10 r
- 10 regular points along a spiral plus two end
- points
-
- rbox 1000 L10000 D4 s
- 1000 random points on the surface of a narrow lens.
-
- rbox c G2 d G3
- a cube with coordinates +2/-2 and a diamond with
-
-
-
-Geometry Center August 10, 1998 1
-
-
-
-
-
-rbox(1) rbox(1)
-
-
- coordinates +3/-3.
-
- rbox 64 M3,4 z
- a rotated, {0,1,2,3} x {0,1,2,3} x {0,1,2,3} lat-
- tice (Mesh) of integer points.
-
- rbox P0 P0 P0 P0 P0
- 5 copies of the origin in 3-d. Try 'rbox P0 P0 P0
- P0 P0 | qhull QJ'.
-
- r 100 s Z1 G0.1
- two cospherical 100-gons plus another cospherical
- point.
-
- 100 s Z1
- a cone of points.
-
- 100 s Z1e-7
- a narrow cone of points with many precision errors.
-
-OPTIONS
- n number of points
-
- Dn dimension n-d (default 3-d)
-
- Bn bounding box coordinates (default 0.5)
-
- l spiral distribution, available only in 3-d
-
- Ln lens distribution of radius n. May be used with
- 's', 'r', 'G', and 'W'.
-
- Mn,m,r lattice (Mesh) rotated by {[n,-m,0], [m,n,0],
- [0,0,r], ...}. Use 'Mm,n' for a rigid rotation
- with r = sqrt(n^2+m^2). 'M1,0' is an orthogonal
- lattice. For example, '27 M1,0' is {0,1,2} x
- {0,1,2} x {0,1,2}.
-
- s cospherical points randomly generated in a cube and
- projected to the unit sphere
-
- x simplicial distribution. It is fixed for option
- 'r'. May be used with 'W'.
-
- y simplicial distribution plus a simplex. Both 'x'
- and 'y' generate the same points.
-
- Wn restrict points to distance n of the surface of a
- sphere or a cube
-
- c add a unit cube to the output
-
- c Gm add a cube with all combinations of +m and -m to
- the output
-
-
-
-Geometry Center August 10, 1998 2
-
-
-
-
-
-rbox(1) rbox(1)
-
-
- d add a unit diamond to the output.
-
- d Gm add a diamond made of 0, +m and -m to the output
-
- Pn,m,r add point [n,m,r] to the output first. Pad coordi-
- nates with 0.0.
-
- n Remove the command line from the first line of out-
- put.
-
- On offset the data by adding n to each coordinate.
-
- t use time in seconds as the random number seed
- (default is command line).
-
- tn set the random number seed to n.
-
- z generate integer coordinates. Use 'Bn' to change
- the range. The default is 'B1e6' for six-digit
- coordinates. In R^4, seven-digit coordinates will
- overflow hyperplane normalization.
-
- Zn s restrict points to a disk about the z+ axis and the
- sphere (default Z1.0). Includes the opposite pole.
- 'Z1e-6' generates degenerate points under single
- precision.
-
- Zn Gm s
- same as Zn with an empty center (default G0.5).
-
- r s D2 generate a regular polygon
-
- r s Z1 G0.1
- generate a regular cone
-
-BUGS
- Some combinations of arguments generate odd results.
-
- Report bugs to qhull_bug@qhull.org, other correspon-
- dence to qhull@qhull.org
-
-SEE ALSO
- qhull(1)
-
-AUTHOR
- C. Bradford Barber
- c/o The Geometry Center
- 400 Lind Hall
- 207 Church Street S.E.
- Minneapolis, MN 55455
-
-
-
-
-
-
-
-Geometry Center August 10, 1998 3
-
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/geom.h b/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/geom.h
deleted file mode 100644
index 6b37268941f66df7a774ca3cdbb0fb22d89611b3..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/geom.h
+++ /dev/null
@@ -1,177 +0,0 @@
-/*<html><pre> -<a href="qh-geom.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- geom.h
- header file for geometric routines
-
- see qh-geom.htm and geom.c
-
- copyright (c) 1993-2003 The Geometry Center
-*/
-
-#ifndef qhDEFgeom
-#define qhDEFgeom 1
-
-/* ============ -macros- ======================== */
-
-/*-<a href="qh-geom.htm#TOC"
- >--------------------------------</a><a name="fabs_">-</a>
-
- fabs_(a)
- returns the absolute value of a
-*/
-#define fabs_( a ) ((( a ) < 0 ) ? -( a ):( a ))
-
-/*-<a href="qh-geom.htm#TOC"
- >--------------------------------</a><a name="fmax_">-</a>
-
- fmax_(a,b)
- returns the maximum value of a and b
-*/
-#define fmax_( a,b ) ( ( a ) < ( b ) ? ( b ) : ( a ) )
-
-/*-<a href="qh-geom.htm#TOC"
- >--------------------------------</a><a name="fmin_">-</a>
-
- fmin_(a,b)
- returns the minimum value of a and b
-*/
-#define fmin_( a,b ) ( ( a ) > ( b ) ? ( b ) : ( a ) )
-
-/*-<a href="qh-geom.htm#TOC"
- >--------------------------------</a><a name="maximize_">-</a>
-
- maximize_(maxval, val)
- set maxval to val if val is greater than maxval
-*/
-#define maximize_( maxval, val ) {if (( maxval ) < ( val )) ( maxval )= ( val );}
-
-/*-<a href="qh-geom.htm#TOC"
- >--------------------------------</a><a name="minimize_">-</a>
-
- minimize_(minval, val)
- set minval to val if val is less than minval
-*/
-#define minimize_( minval, val ) {if (( minval ) > ( val )) ( minval )= ( val );}
-
-/*-<a href="qh-geom.htm#TOC"
- >--------------------------------</a><a name="det2_">-</a>
-
- det2_(a1, a2,
- b1, b2)
-
- compute a 2-d determinate
-*/
-#define det2_( a1,a2,b1,b2 ) (( a1 )*( b2 ) - ( a2 )*( b1 ))
-
-/*-<a href="qh-geom.htm#TOC"
- >--------------------------------</a><a name="det3_">-</a>
-
- det3_(a1, a2, a3,
- b1, b2, b3,
- c1, c2, c3)
-
- compute a 3-d determinate
-*/
-#define det3_( a1,a2,a3,b1,b2,b3,c1,c2,c3 ) ( ( a1 )*det2_( b2,b3,c2,c3 ) \
- - ( b1 )*det2_( a2,a3,c2,c3 ) + ( c1 )*det2_( a2,a3,b2,b3 ) )
-
-/*-<a href="qh-geom.htm#TOC"
- >--------------------------------</a><a name="dX">-</a>
-
- dX( p1, p2 )
- dY( p1, p2 )
- dZ( p1, p2 )
-
- given two indices into rows[],
-
- compute the difference between X, Y, or Z coordinates
-*/
-#define dX( p1,p2 ) ( *( rows[p1] ) - *( rows[p2] ))
-#define dY( p1,p2 ) ( *( rows[p1]+1 ) - *( rows[p2]+1 ))
-#define dZ( p1,p2 ) ( *( rows[p1]+2 ) - *( rows[p2]+2 ))
-#define dW( p1,p2 ) ( *( rows[p1]+3 ) - *( rows[p2]+3 ))
-
-/*============= prototypes in alphabetical order, infrequent at end ======= */
-
-void qh_backnormal(realT** rows, int numrow, int numcol, boolT sign, coordT* normal, boolT* nearzero);
-void qh_distplane(pointT* point, facetT* facet, realT* dist);
-facetT* qh_findbest(pointT* point, facetT* startfacet,
- boolT bestoutside, boolT isnewfacets, boolT noupper,
- realT* dist, boolT* isoutside, int* numpart);
-facetT* qh_findbesthorizon(boolT ischeckmax, pointT* point,
- facetT* startfacet, boolT noupper, realT* bestdist, int* numpart);
-facetT* qh_findbestnew(pointT* point, facetT* startfacet, realT* dist,
- boolT bestoutside, boolT* isoutside, int* numpart);
-void qh_gausselim(realT** rows, int numrow, int numcol, boolT* sign, boolT* nearzero);
-realT qh_getangle(pointT* vect1, pointT* vect2);
-pointT* qh_getcenter(setT* vertices);
-pointT* qh_getcentrum(facetT* facet);
-realT qh_getdistance(facetT* facet, facetT* neighbor, realT* mindist, realT* maxdist);
-void qh_normalize(coordT* normal, int dim, boolT toporient);
-void qh_normalize2(coordT* normal, int dim, boolT toporient,
- realT* minnorm, boolT* ismin);
-pointT* qh_projectpoint(pointT* point, facetT* facet, realT dist);
-
-void qh_setfacetplane(facetT* newfacets);
-void qh_sethyperplane_det(int dim, coordT** rows, coordT* point0,
- boolT toporient, coordT* normal, realT* offset, boolT* nearzero);
-void qh_sethyperplane_gauss(int dim, coordT** rows, pointT* point0,
- boolT toporient, coordT* normal, coordT* offset, boolT* nearzero);
-boolT qh_sharpnewfacets(void);
-
-/*========= infrequently used code in geom2.c =============*/
-
-
-coordT* qh_copypoints(coordT* points, int numpoints, int dimension);
-void qh_crossproduct(int dim, realT vecA[3], realT vecB[3], realT vecC[3]);
-realT qh_determinant(realT** rows, int dim, boolT* nearzero);
-realT qh_detjoggle(pointT* points, int numpoints, int dimension);
-void qh_detroundoff(void);
-realT qh_detsimplex(pointT* apex, setT* points, int dim, boolT* nearzero);
-realT qh_distnorm(int dim, pointT* point, pointT* normal, realT* offsetp);
-realT qh_distround(int dimension, realT maxabs, realT maxsumabs);
-realT qh_divzero(realT numer, realT denom, realT mindenom1, boolT* zerodiv);
-realT qh_facetarea(facetT* facet);
-realT qh_facetarea_simplex(int dim, coordT* apex, setT* vertices,
- vertexT* notvertex, boolT toporient, coordT* normal, realT* offset);
-pointT* qh_facetcenter(setT* vertices);
-facetT* qh_findgooddist(pointT* point, facetT* facetA, realT* distp, facetT** facetlist);
-void qh_getarea(facetT* facetlist);
-boolT qh_gram_schmidt(int dim, realT** rows);
-boolT qh_inthresholds(coordT* normal, realT* angle);
-void qh_joggleinput(void);
-realT* qh_maxabsval(realT* normal, int dim);
-setT* qh_maxmin(pointT* points, int numpoints, int dimension);
-realT qh_maxouter(void);
-void qh_maxsimplex(int dim, setT* maxpoints, pointT* points, int numpoints, setT** simplex);
-realT qh_minabsval(realT* normal, int dim);
-int qh_mindiff(realT* vecA, realT* vecB, int dim);
-boolT qh_orientoutside(facetT* facet);
-void qh_outerinner(facetT* facet, realT* outerplane, realT* innerplane);
-coordT qh_pointdist(pointT* point1, pointT* point2, int dim);
-void qh_printmatrix(FILE* fp, char* string, realT** rows, int numrow, int numcol);
-void qh_printpoints(FILE* fp, char* string, setT* points);
-void qh_projectinput(void);
-void qh_projectpoints(signed char* project, int n, realT* points,
- int numpoints, int dim, realT* newpoints, int newdim);
-int qh_rand(void);
-void qh_srand(int seed);
-realT qh_randomfactor(void);
-void qh_randommatrix(realT* buffer, int dim, realT** row);
-void qh_rotateinput(realT** rows);
-void qh_rotatepoints(realT* points, int numpoints, int dim, realT** rows);
-void qh_scaleinput(void);
-void qh_scalelast(coordT* points, int numpoints, int dim, coordT low,
- coordT high, coordT newhigh);
-void qh_scalepoints(pointT* points, int numpoints, int dim,
- realT* newlows, realT* newhighs);
-boolT qh_sethalfspace(int dim, coordT* coords, coordT** nextp,
- coordT* normal, coordT* offset, coordT* feasible);
-coordT* qh_sethalfspace_all(int dim, int count, coordT* halfspaces, pointT* feasible);
-pointT* qh_voronoi_center(int dim, setT* points);
-
-#endif /* qhDEFgeom */
-
-
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/io.h b/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/io.h
deleted file mode 100644
index a2ca04499c442309eeddfeb3ad4557af40f3b707..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/io.h
+++ /dev/null
@@ -1,154 +0,0 @@
-/*<html><pre> -<a href="qh-io.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- io.h
- declarations of Input/Output functions
-
- see README, qhull.h and io.c
-
- copyright (c) 1993-2003, The Geometry Center
-*/
-
-#ifndef qhDEFio
-#define qhDEFio 1
-
-/*============ constants and flags ==================*/
-
-/*-<a href="qh-io.htm#TOC"
- >--------------------------------</a><a name="qh_MAXfirst">-</a>
-
- qh_MAXfirst
- maximum length of first two lines of stdin
-*/
-#define qh_MAXfirst 200
-
-/*-<a href="qh-io.htm#TOC"
- >--------------------------------</a><a name="qh_MINradius">-</a>
-
- qh_MINradius
- min radius for Gp and Gv, fraction of maxcoord
-*/
-#define qh_MINradius 0.02
-
-/*-<a href="qh-io.htm#TOC"
- >--------------------------------</a><a name="qh_GEOMepsilon">-</a>
-
- qh_GEOMepsilon
- adjust outer planes for 'lines closer' and geomview roundoff.
- This prevents bleed through.
-*/
-#define qh_GEOMepsilon 2e-3
-
-/*-<a href="qh-io.htm#TOC"
- >--------------------------------</a><a name="qh_WHITESPACE">-</a>
-
- qh_WHITESPACE
- possible values of white space
-*/
-#define qh_WHITESPACE " \n\t\v\r\f"
-
-
-/*-<a href="qh-io.htm#TOC"
- >--------------------------------</a><a name="RIDGE">-</a>
-
- qh_RIDGE
- to select which ridges to print in qh_eachvoronoi
-*/
-typedef enum
-{
- qh_RIDGEall = 0, qh_RIDGEinner, qh_RIDGEouter
-}
-qh_RIDGE;
-
-/*-<a href="qh-io.htm#TOC"
- >--------------------------------</a><a name="printvridgeT">-</a>
-
- printvridgeT
- prints results of qh_printvdiagram
-
- see:
- <a href="io.c#printvridge">qh_printvridge</a> for an example
-*/
-typedef void (*printvridgeT)(FILE* fp, vertexT* vertex, vertexT* vertexA, setT* centers, boolT unbounded);
-
-/*============== -prototypes in alphabetical order =========*/
-
-void dfacet(unsigned id);
-void dvertex(unsigned id);
-int qh_compare_facetarea(const void* p1, const void* p2);
-int qh_compare_facetmerge(const void* p1, const void* p2);
-int qh_compare_facetvisit(const void* p1, const void* p2);
-int qh_compare_vertexpoint(const void* p1, const void* p2); /* not used */
-
-void qh_countfacets(facetT* facetlist, setT* facets, boolT printall,
- int* numfacetsp, int* numsimplicialp, int* totneighborsp,
- int* numridgesp, int* numcoplanarsp, int* numnumtricoplanarsp);
-pointT* qh_detvnorm(vertexT* vertex, vertexT* vertexA, setT* centers, realT* offsetp);
-setT* qh_detvridge(vertexT* vertex);
-setT* qh_detvridge3(vertexT* atvertex, vertexT* vertex);
-int qh_eachvoronoi(FILE* fp, printvridgeT printvridge, vertexT* atvertex, boolT visitall, qh_RIDGE innerouter, boolT inorder);
-int qh_eachvoronoi_all(FILE* fp, printvridgeT printvridge, boolT isupper, qh_RIDGE innerouter, boolT inorder);
-void qh_facet2point(facetT* facet, pointT** point0, pointT** point1, realT* mindist);
-setT* qh_facetvertices(facetT* facetlist, setT* facets, boolT allfacets);
-void qh_geomplanes(facetT* facet, realT* outerplane, realT* innerplane);
-void qh_markkeep(facetT* facetlist);
-setT* qh_markvoronoi(facetT* facetlist, setT* facets, boolT printall, boolT* islowerp, int* numcentersp);
-void qh_order_vertexneighbors(vertexT* vertex);
-void qh_printafacet(FILE* fp, int format, facetT* facet, boolT printall);
-void qh_printbegin(FILE* fp, int format, facetT* facetlist, setT* facets, boolT printall);
-void qh_printcenter(FILE* fp, int format, char* string, facetT* facet);
-void qh_printcentrum(FILE* fp, facetT* facet, realT radius);
-void qh_printend(FILE* fp, int format, facetT* facetlist, setT* facets, boolT printall);
-void qh_printend4geom(FILE* fp, facetT* facet, int* num, boolT printall);
-void qh_printextremes(FILE* fp, facetT* facetlist, setT* facets, int printall);
-void qh_printextremes_2d(FILE* fp, facetT* facetlist, setT* facets, int printall);
-void qh_printextremes_d(FILE* fp, facetT* facetlist, setT* facets, int printall);
-void qh_printfacet(FILE* fp, facetT* facet);
-void qh_printfacet2math(FILE* fp, facetT* facet, int format, int notfirst);
-void qh_printfacet2geom(FILE* fp, facetT* facet, realT color[3]);
-void qh_printfacet2geom_points(FILE* fp, pointT* point1, pointT* point2,
- facetT* facet, realT offset, realT color[3]);
-void qh_printfacet3math(FILE* fp, facetT* facet, int format, int notfirst);
-void qh_printfacet3geom_nonsimplicial(FILE* fp, facetT* facet, realT color[3]);
-void qh_printfacet3geom_points(FILE* fp, setT* points, facetT* facet, realT offset, realT color[3]);
-void qh_printfacet3geom_simplicial(FILE* fp, facetT* facet, realT color[3]);
-void qh_printfacet3vertex(FILE* fp, facetT* facet, int format);
-void qh_printfacet4geom_nonsimplicial(FILE* fp, facetT* facet, realT color[3]);
-void qh_printfacet4geom_simplicial(FILE* fp, facetT* facet, realT color[3]);
-void qh_printfacetNvertex_nonsimplicial(FILE* fp, facetT* facet, int id, int format);
-void qh_printfacetNvertex_simplicial(FILE* fp, facetT* facet, int format);
-void qh_printfacetheader(FILE* fp, facetT* facet);
-void qh_printfacetridges(FILE* fp, facetT* facet);
-void qh_printfacets(FILE* fp, int format, facetT* facetlist, setT* facets, boolT printall);
-void qh_printhelp_degenerate(FILE* fp);
-void qh_printhelp_singular(FILE* fp);
-void qh_printhyperplaneintersection(FILE* fp, facetT* facet1, facetT* facet2,
- setT* vertices, realT color[3]);
-void qh_printneighborhood(FILE* fp, int format, facetT* facetA, facetT* facetB, boolT printall);
-void qh_printline3geom(FILE* fp, pointT* pointA, pointT* pointB, realT color[3]);
-void qh_printpoint(FILE* fp, char* string, pointT* point);
-void qh_printpointid(FILE* fp, char* string, int dim, pointT* point, int id);
-void qh_printpoint3(FILE* fp, pointT* point);
-void qh_printpoints_out(FILE* fp, facetT* facetlist, setT* facets, int printall);
-void qh_printpointvect(FILE* fp, pointT* point, coordT* normal, pointT* center, realT radius, realT color[3]);
-void qh_printpointvect2(FILE* fp, pointT* point, coordT* normal, pointT* center, realT radius);
-void qh_printridge(FILE* fp, ridgeT* ridge);
-void qh_printspheres(FILE* fp, setT* vertices, realT radius);
-void qh_printvdiagram(FILE* fp, int format, facetT* facetlist, setT* facets, boolT printall);
-int qh_printvdiagram2(FILE* fp, printvridgeT printvridge, setT* vertices, qh_RIDGE innerouter, boolT inorder);
-void qh_printvertex(FILE* fp, vertexT* vertex);
-void qh_printvertexlist(FILE* fp, char* string, facetT* facetlist,
- setT* facets, boolT printall);
-void qh_printvertices(FILE* fp, char* string, setT* vertices);
-void qh_printvneighbors(FILE* fp, facetT* facetlist, setT* facets, boolT printall);
-void qh_printvoronoi(FILE* fp, int format, facetT* facetlist, setT* facets, boolT printall);
-void qh_printvnorm(FILE* fp, vertexT* vertex, vertexT* vertexA, setT* centers, boolT unbounded);
-void qh_printvridge(FILE* fp, vertexT* vertex, vertexT* vertexA, setT* centers, boolT unbounded);
-void qh_produce_output(void);
-void qh_projectdim3(pointT* source, pointT* destination);
-int qh_readfeasible(int dim, char* remainder);
-coordT* qh_readpoints(int* numpoints, int* dimension, boolT* ismalloc);
-void qh_setfeasible(int dim);
-boolT qh_skipfacet(facetT* facet);
-
-#endif /* qhDEFio */
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/mem.h b/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/mem.h
deleted file mode 100644
index 3283efe89efa77d661b47bf603c50317c611d5f8..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/mem.h
+++ /dev/null
@@ -1,173 +0,0 @@
-/*<html><pre> -<a href="qh-mem.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- mem.h
- prototypes for memory management functions
-
- see qh-mem.htm, mem.c and qset.h
-
- for error handling, writes message and calls
- qh_errexit (qhmem_ERRmem, NULL, NULL) if insufficient memory
- and
- qh_errexit (qhmem_ERRqhull, NULL, NULL) otherwise
-
- copyright (c) 1993-2003, The Geometry Center
-*/
-
-#pragma once
-
-/*-<a href="qh-mem.htm#TOC"
- >-------------------------------</a><a name="NOmem">-</a>
-
- qh_NOmem
- turn off quick-fit memory allocation
-
- notes:
- mem.c implements Quickfit memory allocation for about 20% time
- savings. If it fails on your machine, try to locate the
- problem, and send the answer to qhull@qhull.org. If this can
- not be done, define qh_NOmem to use malloc/free instead.
-
- #define qh_NOmem
-*/
-
-/*-------------------------------------------
- to avoid bus errors, memory allocation must consider alignment requirements.
- malloc() automatically takes care of alignment. Since mem.c manages
- its own memory, we need to explicitly specify alignment in
- qh_meminitbuffers().
-
- A safe choice is sizeof(double). sizeof(float) may be used if doubles
- do not occur in data structures and pointers are the same size. Be careful
- of machines (e.g., DEC Alpha) with large pointers. If gcc is available,
- use __alignof__(double) or fmax_(__alignof__(float), __alignof__(void *)).
-
- see <a href="user.h#MEMalign">qh_MEMalign</a> in user.h for qhull's alignment
-*/
-
-#define qhmem_ERRmem 4 /* matches qh_ERRmem in qhull.h */
-#define qhmem_ERRqhull 5 /* matches qh_ERRqhull in qhull.h */
-
-/*-<a href="qh-mem.htm#TOC"
- >--------------------------------</a><a name="ptr_intT">-</a>
-
- ptr_intT
- for casting a void* to an integer-type
-
- notes:
- On 64-bit machines, a pointer may be larger than an 'int'.
- qh_meminit() checks that 'long' holds a 'void*'
-*/
-typedef unsigned long ptr_intT;
-
-/*-<a href="qh-mem.htm#TOC"
- >--------------------------------</a><a name="qhmemT">-</a>
-
- qhmemT
- global memory structure for mem.c
-
- notes:
- users should ignore qhmem except for writing extensions
- qhmem is allocated in mem.c
-
- qhmem could be swapable like qh and qhstat, but then
- multiple qh's and qhmem's would need to keep in synch.
- A swapable qhmem would also waste memory buffers. As long
- as memory operations are atomic, there is no problem with
- multiple qh structures being active at the same time.
- If you need separate address spaces, you can swap the
- contents of qhmem.
-*/
-typedef struct qhmemT qhmemT;
-extern qhmemT qhmem;
-
-struct qhmemT /* global memory management variables */
-{
- int BUFsize; /* size of memory allocation buffer */
- int BUFinit; /* initial size of memory allocation buffer */
- int TABLEsize; /* actual number of sizes in free list table */
- int NUMsizes; /* maximum number of sizes in free list table */
- int LASTsize; /* last size in free list table */
- int ALIGNmask; /* worst-case alignment, must be 2^n-1 */
- void** freelists; /* free list table, linked by offset 0 */
- int* sizetable; /* size of each freelist */
- int* indextable; /* size->index table */
- void* curbuffer; /* current buffer, linked by offset 0 */
- void* freemem; /* free memory in curbuffer */
- int freesize; /* size of free memory in bytes */
- void* tempstack; /* stack of temporary memory, managed by users */
- FILE* ferr; /* file for reporting errors */
- int IStracing; /* =5 if tracing memory allocations */
- int cntquick; /* count of quick allocations */
- /* remove statistics doesn't effect speed */
- int cntshort; /* count of short allocations */
- int cntlong; /* count of long allocations */
- int curlong; /* current count of inuse, long allocations */
- int freeshort; /* count of short memfrees */
- int freelong; /* count of long memfrees */
- int totshort; /* total size of short allocations */
- int totlong; /* total size of long allocations */
- int maxlong; /* maximum totlong */
- int cntlarger; /* count of setlarger's */
- int totlarger; /* total copied by setlarger */
-};
-
-
-/*==================== -macros ====================*/
-
-/*-<a href="qh-mem.htm#TOC"
- >--------------------------------</a><a name="memalloc_">-</a>
-
- qh_memalloc_(size, object, type)
- returns object of size bytes
- assumes size<=qhmem.LASTsize and void **freelistp is a temp
-*/
-
-#ifdef qh_NOmem
-#define qh_memalloc_(size, freelistp, object, type) {\
- object= (type*)qh_memalloc (size); }
-#else /* !qh_NOmem */
-
-#define qh_memalloc_(size, freelistp, object, type) {\
- freelistp= qhmem.freelists + qhmem.indextable[size];\
- if ((object= (type*)*freelistp)) {\
- qhmem.cntquick++; \
- *freelistp= *((void **)*freelistp);\
- }else object= (type*)qh_memalloc (size);}
-#endif
-
-/*-<a href="qh-mem.htm#TOC"
- >--------------------------------</a><a name="memfree_">-</a>
-
- qh_memfree_(object, size)
- free up an object
-
- notes:
- object may be NULL
- assumes size<=qhmem.LASTsize and void **freelistp is a temp
-*/
-#ifdef qh_NOmem
-#define qh_memfree_(object, size, freelistp) {\
- qh_memfree (object, size); }
-#else /* !qh_NOmem */
-
-#define qh_memfree_(object, size, freelistp) {\
- if (object) { \
- qhmem .freeshort++;\
- freelistp= qhmem.freelists + qhmem.indextable[size];\
- *((void **)object)= *freelistp;\
- *freelistp= object;}}
-#endif
-
-/*=============== prototypes in alphabetical order ============*/
-
-void* qh_memalloc(int insize);
-void qh_memfree(void* object, int size);
-void qh_memfreeshort(int* curlong, int* totlong);
-void qh_meminit(FILE* ferr);
-void qh_meminitbuffers(int tracelevel, int alignment, int numsizes,
- int bufsize, int bufinit);
-void qh_memsetup(void);
-void qh_memsize(int size);
-void qh_memstatistics(FILE* fp);
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/merge.h b/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/merge.h
deleted file mode 100644
index 8b689576dbb05d1627d116b360599a866b2cc93c..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/merge.h
+++ /dev/null
@@ -1,176 +0,0 @@
-/*<html><pre> -<a href="qh-merge.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- merge.h
- header file for merge.c
-
- see qh-merge.htm and merge.c
-
- copyright (c) 1993-2003, The Geometry Center
-*/
-
-#ifndef qhDEFmerge
-#define qhDEFmerge 1
-
-
-/*============ -constants- ==============*/
-
-/*-<a href="qh-merge.htm#TOC"
- >--------------------------------</a><a name="qh_ANGLEredundant">-</a>
-
- qh_ANGLEredundant
- indicates redundant merge in mergeT->angle
-*/
-#define qh_ANGLEredundant 6.0
-
-/*-<a href="qh-merge.htm#TOC"
- >--------------------------------</a><a name="qh_ANGLEdegen">-</a>
-
- qh_ANGLEdegen
- indicates degenerate facet in mergeT->angle
-*/
-#define qh_ANGLEdegen 5.0
-
-/*-<a href="qh-merge.htm#TOC"
- >--------------------------------</a><a name="qh_ANGLEconcave">-</a>
-
- qh_ANGLEconcave
- offset to indicate concave facets in mergeT->angle
-
- notes:
- concave facets are assigned the range of [2,4] in mergeT->angle
- roundoff error may make the angle less than 2
-*/
-#define qh_ANGLEconcave 1.5
-
-/*-<a href="qh-merge.htm#TOC"
- >--------------------------------</a><a name="MRG">-</a>
-
- MRG... (mergeType)
- indicates the type of a merge (mergeT->type)
-*/
-typedef enum /* in sort order for facet_mergeset */
-{
- MRGnone = 0,
- MRGcoplanar, /* centrum coplanar */
- MRGanglecoplanar, /* angle coplanar */
- /* could detect half concave ridges */
- MRGconcave, /* concave ridge */
- MRGflip, /* flipped facet. facet1 == facet2 */
- MRGridge, /* duplicate ridge (qh_MERGEridge) */
- /* degen and redundant go onto degen_mergeset */
- MRGdegen, /* degenerate facet (not enough neighbors) facet1 == facet2 */
- MRGredundant, /* redundant facet (vertex subset) */
- /* merge_degenredundant assumes degen < redundant */
- MRGmirror, /* mirror facet from qh_triangulate */
- ENDmrg
-} mergeType;
-
-/*-<a href="qh-merge.htm#TOC"
- >--------------------------------</a><a name="qh_MERGEapex">-</a>
-
- qh_MERGEapex
- flag for qh_mergefacet() to indicate an apex merge
-*/
-#define qh_MERGEapex True
-
-/*============ -structures- ====================*/
-
-/*-<a href="qh-merge.htm#TOC"
- >--------------------------------</a><a name="mergeT">-</a>
-
- mergeT
- structure used to merge facets
-*/
-
-typedef struct mergeT mergeT;
-struct mergeT /* initialize in qh_appendmergeset */
-{
- realT angle; /* angle between normals of facet1 and facet2 */
- facetT* facet1; /* will merge facet1 into facet2 */
- facetT* facet2;
- mergeType type;
-};
-
-
-/*=========== -macros- =========================*/
-
-/*-<a href="qh-merge.htm#TOC"
- >--------------------------------</a><a name="FOREACHmerge_">-</a>
-
- FOREACHmerge_( merges ) {...}
- assign 'merge' to each merge in merges
-
- notes:
- uses 'mergeT *merge, **mergep;'
- if qh_mergefacet(),
- restart since qh.facet_mergeset may change
- see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
-*/
-#define FOREACHmerge_( merges ) FOREACHsetelement_(mergeT, merges, merge)
-
-/*============ prototypes in alphabetical order after pre/postmerge =======*/
-
-void qh_premerge(vertexT* apex, realT maxcentrum, realT maxangle);
-void qh_postmerge(char* reason, realT maxcentrum, realT maxangle,
- boolT vneighbors);
-void qh_all_merges(boolT othermerge, boolT vneighbors);
-void qh_appendmergeset(facetT* facet, facetT* neighbor, mergeType mergetype, realT* angle);
-setT* qh_basevertices(facetT* samecycle);
-void qh_checkconnect(void /* qh new_facets */);
-boolT qh_checkzero(boolT testall);
-int qh_compareangle(const void* p1, const void* p2);
-int qh_comparemerge(const void* p1, const void* p2);
-int qh_comparevisit(const void* p1, const void* p2);
-void qh_copynonconvex(ridgeT* atridge);
-void qh_degen_redundant_facet(facetT* facet);
-void qh_degen_redundant_neighbors(facetT* facet, facetT* delfacet);
-vertexT* qh_find_newvertex(vertexT* oldvertex, setT* vertices, setT* ridges);
-void qh_findbest_test(boolT testcentrum, facetT* facet, facetT* neighbor,
- facetT** bestfacet, realT* distp, realT* mindistp, realT* maxdistp);
-facetT* qh_findbestneighbor(facetT* facet, realT* distp, realT* mindistp, realT* maxdistp);
-void qh_flippedmerges(facetT* facetlist, boolT* wasmerge);
-void qh_forcedmerges(boolT* wasmerge);
-void qh_getmergeset(facetT* facetlist);
-void qh_getmergeset_initial(facetT* facetlist);
-void qh_hashridge(setT* hashtable, int hashsize, ridgeT* ridge, vertexT* oldvertex);
-ridgeT* qh_hashridge_find(setT* hashtable, int hashsize, ridgeT* ridge,
- vertexT* vertex, vertexT* oldvertex, int* hashslot);
-void qh_makeridges(facetT* facet);
-void qh_mark_dupridges(facetT* facetlist);
-void qh_maydropneighbor(facetT* facet);
-int qh_merge_degenredundant(void);
-void qh_merge_nonconvex(facetT* facet1, facetT* facet2, mergeType mergetype);
-void qh_mergecycle(facetT* samecycle, facetT* newfacet);
-void qh_mergecycle_all(facetT* facetlist, boolT* wasmerge);
-void qh_mergecycle_facets(facetT* samecycle, facetT* newfacet);
-void qh_mergecycle_neighbors(facetT* samecycle, facetT* newfacet);
-void qh_mergecycle_ridges(facetT* samecycle, facetT* newfacet);
-void qh_mergecycle_vneighbors(facetT* samecycle, facetT* newfacet);
-void qh_mergefacet(facetT* facet1, facetT* facet2, realT* mindist, realT* maxdist, boolT mergeapex);
-void qh_mergefacet2d(facetT* facet1, facetT* facet2);
-void qh_mergeneighbors(facetT* facet1, facetT* facet2);
-void qh_mergeridges(facetT* facet1, facetT* facet2);
-void qh_mergesimplex(facetT* facet1, facetT* facet2, boolT mergeapex);
-void qh_mergevertex_del(vertexT* vertex, facetT* facet1, facetT* facet2);
-void qh_mergevertex_neighbors(facetT* facet1, facetT* facet2);
-void qh_mergevertices(setT* vertices1, setT** vertices);
-setT* qh_neighbor_intersections(vertexT* vertex);
-void qh_newvertices(setT* vertices);
-boolT qh_reducevertices(void);
-vertexT* qh_redundant_vertex(vertexT* vertex);
-boolT qh_remove_extravertices(facetT* facet);
-vertexT* qh_rename_sharedvertex(vertexT* vertex, facetT* facet);
-void qh_renameridgevertex(ridgeT* ridge, vertexT* oldvertex, vertexT* newvertex);
-void qh_renamevertex(vertexT* oldvertex, vertexT* newvertex, setT* ridges,
- facetT* oldfacet, facetT* neighborA);
-boolT qh_test_appendmerge(facetT* facet, facetT* neighbor);
-boolT qh_test_vneighbors(void /* qh newfacet_list */);
-void qh_tracemerge(facetT* facet1, facetT* facet2);
-void qh_tracemerging(void);
-void qh_updatetested(facetT* facet1, facetT* facet2);
-setT* qh_vertexridges(vertexT* vertex);
-void qh_vertexridges_facet(vertexT* vertex, facetT* facet, setT** ridges);
-void qh_willdelete(facetT* facet, facetT* replace);
-
-#endif /* qhDEFmerge */
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/poly.h b/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/poly.h
deleted file mode 100644
index 109b5b3eab4c055084faca92bd9fc8561ec59259..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/poly.h
+++ /dev/null
@@ -1,291 +0,0 @@
-/*<html><pre> -<a href="qh-poly.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- poly.h
- header file for poly.c and poly2.c
-
- see qh-poly.htm, qhull.h and poly.c
-
- copyright (c) 1993-2003, The Geometry Center
-*/
-
-#ifndef qhDEFpoly
-#define qhDEFpoly 1
-
-/*=============== constants ========================== */
-
-/*-<a href="qh-geom.htm#TOC"
- >--------------------------------</a><a name="ALGORITHMfault">-</a>
-
- ALGORITHMfault
- use as argument to checkconvex() to report errors during buildhull
-*/
-#define qh_ALGORITHMfault 0
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="DATAfault">-</a>
-
- DATAfault
- use as argument to checkconvex() to report errors during initialhull
-*/
-#define qh_DATAfault 1
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="DUPLICATEridge">-</a>
-
- DUPLICATEridge
- special value for facet->neighbor to indicate a duplicate ridge
-
- notes:
- set by matchneighbor, used by matchmatch and mark_dupridge
-*/
-#define qh_DUPLICATEridge ( facetT * ) 1L
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="MERGEridge">-</a>
-
- MERGEridge flag in facet
- special value for facet->neighbor to indicate a merged ridge
-
- notes:
- set by matchneighbor, used by matchmatch and mark_dupridge
-*/
-#define qh_MERGEridge ( facetT * ) 2L
-
-
-/*============ -structures- ====================*/
-
-/*=========== -macros- =========================*/
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FORALLfacet_">-</a>
-
- FORALLfacet_( facetlist ) { ... }
- assign 'facet' to each facet in facetlist
-
- notes:
- uses 'facetT *facet;'
- assumes last facet is a sentinel
-
- see:
- FORALLfacets
-*/
-#define FORALLfacet_( facetlist ) if ( facetlist ) for( facet=( facetlist );facet && facet->next;facet=facet->next )
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FORALLnew_facets">-</a>
-
- FORALLnew_facets { ... }
- assign 'newfacet' to each facet in qh.newfacet_list
-
- notes:
- uses 'facetT *newfacet;'
- at exit, newfacet==NULL
-*/
-#define FORALLnew_facets for( newfacet=qh newfacet_list;newfacet && newfacet->next;newfacet=newfacet->next )
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FORALLvertex_">-</a>
-
- FORALLvertex_( vertexlist ) { ... }
- assign 'vertex' to each vertex in vertexlist
-
- notes:
- uses 'vertexT *vertex;'
- at exit, vertex==NULL
-*/
-#define FORALLvertex_( vertexlist ) for ( vertex=( vertexlist );vertex && vertex->next;vertex= vertex->next )
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FORALLvisible_facets">-</a>
-
- FORALLvisible_facets { ... }
- assign 'visible' to each visible facet in qh.visible_list
-
- notes:
- uses 'vacetT *visible;'
- at exit, visible==NULL
-*/
-#define FORALLvisible_facets for (visible=qh visible_list; visible && visible->visible; visible= visible->next)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FORALLsame_">-</a>
-
- FORALLsame_( newfacet ) { ... }
- assign 'same' to each facet in newfacet->f.samecycle
-
- notes:
- uses 'facetT *same;'
- stops when it returns to newfacet
-*/
-#define FORALLsame_(newfacet) for (same= newfacet->f.samecycle; same != newfacet; same= same->f.samecycle)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FORALLsame_cycle_">-</a>
-
- FORALLsame_cycle_( newfacet ) { ... }
- assign 'same' to each facet in newfacet->f.samecycle
-
- notes:
- uses 'facetT *same;'
- at exit, same == NULL
-*/
-#define FORALLsame_cycle_(newfacet) \
- for (same= newfacet->f.samecycle; \
- same; same= (same == newfacet ? NULL : same->f.samecycle))
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHneighborA_">-</a>
-
- FOREACHneighborA_( facet ) { ... }
- assign 'neighborA' to each neighbor in facet->neighbors
-
- FOREACHneighborA_( vertex ) { ... }
- assign 'neighborA' to each neighbor in vertex->neighbors
-
- declare:
- facetT *neighborA, **neighborAp;
-
- see:
- <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
-*/
-#define FOREACHneighborA_(facet) FOREACHsetelement_(facetT, facet->neighbors, neighborA)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHvisible_">-</a>
-
- FOREACHvisible_( facets ) { ... }
- assign 'visible' to each facet in facets
-
- notes:
- uses 'facetT *facet, *facetp;'
- see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
-*/
-#define FOREACHvisible_(facets) FOREACHsetelement_(facetT, facets, visible)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHnewfacet_">-</a>
-
- FOREACHnewfacet_( facets ) { ... }
- assign 'newfacet' to each facet in facets
-
- notes:
- uses 'facetT *newfacet, *newfacetp;'
- see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
-*/
-#define FOREACHnewfacet_(facets) FOREACHsetelement_(facetT, facets, newfacet)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHvertexA_">-</a>
-
- FOREACHvertexA_( vertices ) { ... }
- assign 'vertexA' to each vertex in vertices
-
- notes:
- uses 'vertexT *vertexA, *vertexAp;'
- see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
-*/
-#define FOREACHvertexA_(vertices) FOREACHsetelement_(vertexT, vertices, vertexA)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHvertexreverse12_">-</a>
-
- FOREACHvertexreverse12_( vertices ) { ... }
- assign 'vertex' to each vertex in vertices
- reverse order of first two vertices
-
- notes:
- uses 'vertexT *vertex, *vertexp;'
- see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
-*/
-#define FOREACHvertexreverse12_(vertices) FOREACHsetelementreverse12_(vertexT, vertices, vertex)
-
-
-/*=============== prototypes poly.c in alphabetical order ================*/
-
-void qh_appendfacet(facetT* facet);
-void qh_appendvertex(vertexT* vertex);
-void qh_attachnewfacets(void);
-boolT qh_checkflipped(facetT* facet, realT* dist, boolT allerror);
-void qh_delfacet(facetT* facet);
-void qh_deletevisible(void /*qh visible_list, qh horizon_list*/);
-setT* qh_facetintersect(facetT* facetA, facetT* facetB, int* skipAp, int* skipBp, int extra);
-unsigned qh_gethash(int hashsize, setT* set, int size, int firstindex, void* skipelem);
-facetT* qh_makenewfacet(setT* vertices, boolT toporient, facetT* facet);
-void qh_makenewplanes(void /* newfacet_list */);
-facetT* qh_makenew_nonsimplicial(facetT* visible, vertexT* apex, int* numnew);
-facetT* qh_makenew_simplicial(facetT* visible, vertexT* apex, int* numnew);
-void qh_matchneighbor(facetT* newfacet, int newskip, int hashsize,
- int* hashcount);
-void qh_matchnewfacets(void);
-boolT qh_matchvertices(int firstindex, setT* verticesA, int skipA,
- setT* verticesB, int* skipB, boolT* same);
-facetT* qh_newfacet(void);
-ridgeT* qh_newridge(void);
-int qh_pointid(pointT* point);
-void qh_removefacet(facetT* facet);
-void qh_removevertex(vertexT* vertex);
-void qh_updatevertices(void);
-
-
-/*========== -prototypes poly2.c in alphabetical order ===========*/
-
-void qh_addhash(void* newelem, setT* hashtable, int hashsize, unsigned hash);
-void qh_check_bestdist(void);
-void qh_check_maxout(void);
-void qh_check_output(void);
-void qh_check_point(pointT* point, facetT* facet, realT* maxoutside, realT* maxdist, facetT** errfacet1, facetT** errfacet2);
-void qh_check_points(void);
-void qh_checkconvex(facetT* facetlist, int fault);
-void qh_checkfacet(facetT* facet, boolT newmerge, boolT* waserrorp);
-void qh_checkflipped_all(facetT* facetlist);
-void qh_checkpolygon(facetT* facetlist);
-void qh_checkvertex(vertexT* vertex);
-void qh_clearcenters(qh_CENTER type);
-void qh_createsimplex(setT* vertices);
-void qh_delridge(ridgeT* ridge);
-void qh_delvertex(vertexT* vertex);
-setT* qh_facet3vertex(facetT* facet);
-facetT* qh_findbestfacet(pointT* point, boolT bestoutside,
- realT* bestdist, boolT* isoutside);
-facetT* qh_findbestlower(facetT* upperfacet, pointT* point, realT* bestdistp, int* numpart);
-facetT* qh_findfacet_all(pointT* point, realT* bestdist, boolT* isoutside,
- int* numpart);
-int qh_findgood(facetT* facetlist, int goodhorizon);
-void qh_findgood_all(facetT* facetlist);
-void qh_furthestnext(void /* qh facet_list */);
-void qh_furthestout(facetT* facet);
-void qh_infiniteloop(facetT* facet);
-void qh_initbuild(void);
-void qh_initialhull(setT* vertices);
-setT* qh_initialvertices(int dim, setT* maxpoints, pointT* points, int numpoints);
-vertexT* qh_isvertex(pointT* point, setT* vertices);
-vertexT* qh_makenewfacets(pointT* point /*horizon_list, visible_list*/);
-void qh_matchduplicates(facetT* atfacet, int atskip, int hashsize, int* hashcount);
-void qh_nearcoplanar(void /* qh.facet_list */);
-vertexT* qh_nearvertex(facetT* facet, pointT* point, realT* bestdistp);
-int qh_newhashtable(int newsize);
-vertexT* qh_newvertex(pointT* point);
-ridgeT* qh_nextridge3d(ridgeT* atridge, facetT* facet, vertexT** vertexp);
-void qh_outcoplanar(void /* facet_list */);
-pointT* qh_point(int id);
-void qh_point_add(setT* set, pointT* point, void* elem);
-setT* qh_pointfacet(void /*qh facet_list*/);
-setT* qh_pointvertex(void /*qh facet_list*/);
-void qh_prependfacet(facetT* facet, facetT** facetlist);
-void qh_printhashtable(FILE* fp);
-void qh_printlists(void);
-void qh_resetlists(boolT stats, boolT resetVisible /*qh newvertex_list newfacet_list visible_list*/);
-void qh_setvoronoi_all(void);
-void qh_triangulate(void /*qh facet_list*/);
-void qh_triangulate_facet(facetT* facetA, vertexT** first_vertex);
-void qh_triangulate_link(facetT* oldfacetA, facetT* facetA, facetT* oldfacetB, facetT* facetB);
-void qh_triangulate_mirror(facetT* facetA, facetT* facetB);
-void qh_triangulate_null(facetT* facetA);
-void qh_vertexintersect(setT** vertexsetA, setT* vertexsetB);
-setT* qh_vertexintersect_new(setT* vertexsetA, setT* vertexsetB);
-void qh_vertexneighbors(void /*qh facet_list*/);
-boolT qh_vertexsubset(setT* vertexsetA, setT* vertexsetB);
-
-
-#endif /* qhDEFpoly */
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/qhull.h b/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/qhull.h
deleted file mode 100644
index ebc0d2becc309ea76adbd9f2d194c29b609b45df..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/qhull.h
+++ /dev/null
@@ -1,1036 +0,0 @@
-/*<html><pre> -<a href="qh-qhull.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- qhull.h
- user-level header file for using qhull.a library
-
- see qh-qhull.htm, qhull_a.h
-
- copyright (c) 1993-2003, The Geometry Center
-
- NOTE: access to qh_qh is via the 'qh' macro. This allows
- qh_qh to be either a pointer or a structure. An example
- of using qh is "qh DROPdim" which accesses the DROPdim
- field of qh_qh. Similarly, access to qh_qhstat is via
- the 'qhstat' macro.
-
- includes function prototypes for qhull.c, geom.c, global.c, io.c, user.c
-
- use mem.h for mem.c
- use qset.h for qset.c
-
- see unix.c for an example of using qhull.h
-
- recompile qhull if you change this file
-*/
-
-#ifndef qhDEFqhull
-#define qhDEFqhull 1
-
-/*=========================== -included files ==============*/
-
-#include <setjmp.h>
-#include <float.h>
-#include <time.h>
-
-#if __MWERKS__ && __POWERPC__
-#include <SIOUX.h>
-#include <Files.h>
-#include <Desk.h>
-#endif
-
-#ifndef __STDC__
-#ifndef __cplusplus
-#if !_MSC_VER
-#error Neither __STDC__ nor __cplusplus is defined. Please use strict ANSI C or C++ to compile
-#error Qhull. You may need to turn off compiler extensions in your project configuration. If
-#error your compiler is a standard C compiler, you can delete this warning from qhull.h
-#endif
-#endif
-#endif
-
-#include "user.h" /* user defineable constants */
-
-/*============ constants and basic types ====================*/
-
-extern char* qh_version; /* defined in global.c */
-
-/*-<a href="qh-geom.htm#TOC"
- >--------------------------------</a><a name="coordT">-</a>
-
- coordT
- coordinates and coefficients are stored as realT (i.e., double)
-
- notes:
- could use 'float' for data and 'double' for calculations (realT vs. coordT)
- This requires many type casts, and adjusted error bounds.
- Also C compilers may do expressions in double anyway.
-*/
-#define coordT realT
-
-/*-<a href="qh-geom.htm#TOC"
- >--------------------------------</a><a name="pointT">-</a>
-
- pointT
- a point is an array of DIM3 coordinates
-*/
-#define pointT coordT
-
-/*-<a href="qh-qhull.htm#TOC"
- >--------------------------------</a><a name="flagT">-</a>
-
- flagT
- Boolean flag as a bit
-*/
-#define flagT unsigned int
-
-/*-<a href="qh-qhull.htm#TOC"
- >--------------------------------</a><a name="boolT">-</a>
-
- boolT
- boolean value, either True or False
-
- notes:
- needed for portability
-*/
-#define boolT unsigned int
-#ifdef False
-#undef False
-#endif
-#ifdef True
-#undef True
-#endif
-#define False 0
-#define True 1
-
-/*-<a href="qh-qhull.htm#TOC"
- >--------------------------------</a><a name="CENTERtype">-</a>
-
- qh_CENTER
- to distinguish facet->center
-*/
-typedef enum
-{
- qh_ASnone = 0, qh_ASvoronoi, qh_AScentrum
-}
-qh_CENTER;
-
-/*-<a href="qh-qhull.htm#TOC"
- >--------------------------------</a><a name="qh_PRINT">-</a>
-
- qh_PRINT
- output formats for printing (qh.PRINTout).
- 'Fa' 'FV' 'Fc' 'FC'
-
-
- notes:
- some of these names are similar to qh names. The similar names are only
- used in switch statements in qh_printbegin() etc.
-*/
-typedef enum {qh_PRINTnone = 0,
- qh_PRINTarea, qh_PRINTaverage, /* 'Fa' 'FV' 'Fc' 'FC' */
- qh_PRINTcoplanars, qh_PRINTcentrums,
- qh_PRINTfacets, qh_PRINTfacets_xridge, /* 'f' 'FF' 'G' 'FI' 'Fi' 'Fn' */
- qh_PRINTgeom, qh_PRINTids, qh_PRINTinner, qh_PRINTneighbors,
- qh_PRINTnormals, qh_PRINTouter, qh_PRINTmaple, /* 'n' 'Fo' 'i' 'm' 'Fm' 'FM', 'o' */
- qh_PRINTincidences, qh_PRINTmathematica, qh_PRINTmerges, qh_PRINToff,
- qh_PRINToptions, qh_PRINTpointintersect, /* 'FO' 'Fp' 'FP' 'p' 'FQ' 'FS' */
- qh_PRINTpointnearest, qh_PRINTpoints, qh_PRINTqhull, qh_PRINTsize,
- qh_PRINTsummary, qh_PRINTtriangles, /* 'Fs' 'Ft' 'Fv' 'FN' 'Fx' */
- qh_PRINTvertices, qh_PRINTvneighbors, qh_PRINTextremes,
- qh_PRINTEND
- } qh_PRINT;
-
-/*-<a href="qh-qhull.htm#TOC"
- >--------------------------------</a><a name="qh_ALL">-</a>
-
- qh_ALL
- argument flag for selecting everything
-*/
-#define qh_ALL True
-#define qh_NOupper True /* argument for qh_findbest */
-#define qh_IScheckmax True /* argument for qh_findbesthorizon */
-#define qh_ISnewfacets True /* argument for qh_findbest */
-#define qh_RESETvisible True /* argument for qh_resetlists */
-
-/*-<a href="qh-qhull.htm#TOC"
- >--------------------------------</a><a name="qh_ERR">-</a>
-
- qh_ERR
- Qhull exit codes, for indicating errors
-*/
-#define qh_ERRnone 0 /* no error occurred during qhull */
-#define qh_ERRinput 1 /* input inconsistency */
-#define qh_ERRsingular 2 /* singular input data */
-#define qh_ERRprec 3 /* precision error */
-#define qh_ERRmem 4 /* insufficient memory, matches mem.h */
-#define qh_ERRqhull 5 /* internal error detected, matches mem.h */
-
-/* ============ -structures- ====================
- each of the following structures is defined by a typedef
- all realT and coordT fields occur at the beginning of a structure
- (otherwise space may be wasted due to alignment)
- define all flags together and pack into 32-bit number
-*/
-
-typedef struct vertexT vertexT;
-typedef struct ridgeT ridgeT;
-typedef struct facetT facetT;
-#ifndef DEFsetT
-#define DEFsetT 1
-typedef struct setT setT; /* defined in qset.h */
-#endif
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="facetT">-</a>
-
- facetT
- defines a facet
-
- notes:
- qhull() generates the hull as a list of facets.
-
- topological information:
- f.previous,next doubly-linked list of facets
- f.vertices set of vertices
- f.ridges set of ridges
- f.neighbors set of neighbors
- f.toporient True if facet has top-orientation (else bottom)
-
- geometric information:
- f.offset,normal hyperplane equation
- f.maxoutside offset to outer plane -- all points inside
- f.center centrum for testing convexity
- f.simplicial True if facet is simplicial
- f.flipped True if facet does not include qh.interior_point
-
- for constructing hull:
- f.visible True if facet on list of visible facets (will be deleted)
- f.newfacet True if facet on list of newly created facets
- f.coplanarset set of points coplanar with this facet
- (includes near-inside points for later testing)
- f.outsideset set of points outside of this facet
- f.furthestdist distance to furthest point of outside set
- f.visitid marks visited facets during a loop
- f.replace replacement facet for to-be-deleted, visible facets
- f.samecycle,newcycle cycle of facets for merging into horizon facet
-
- see below for other flags and fields
-*/
-struct facetT
-{
-#if !qh_COMPUTEfurthest
- coordT furthestdist;/* distance to furthest point of outsideset */
-#endif
-#if qh_MAXoutside
- coordT maxoutside; /* max computed distance of point to facet
- Before QHULLfinished this is an approximation
- since maxdist not always set for mergefacet
- Actual outer plane is +DISTround and
- computed outer plane is +2*DISTround */
-#endif
- coordT offset; /* exact offset of hyperplane from origin */
- coordT* normal; /* normal of hyperplane, hull_dim coefficients */
- /* if tricoplanar, shared with a neighbor */
- union /* in order of testing */
- {
- realT area; /* area of facet, only in io.c if ->isarea */
- facetT* replace; /* replacement facet if ->visible and NEWfacets
- is NULL only if qh_mergedegen_redundant or interior */
- facetT* samecycle; /* cycle of facets from the same visible/horizon intersection,
- if ->newfacet */
- facetT* newcycle; /* in horizon facet, current samecycle of new facets */
- facetT* trivisible; /* visible facet for ->tricoplanar facets during qh_triangulate() */
- facetT* triowner; /* owner facet for ->tricoplanar, !isarea facets w/ ->keepcentrum */
- } f;
- coordT* center; /* centrum for convexity, qh CENTERtype == qh_AScentrum */
- /* Voronoi center, qh CENTERtype == qh_ASvoronoi */
- /* if tricoplanar, shared with a neighbor */
- facetT* previous; /* previous facet in the facet_list */
- facetT* next; /* next facet in the facet_list */
- setT* vertices; /* vertices for this facet, inverse sorted by ID
- if simplicial, 1st vertex was apex/furthest */
- setT* ridges; /* explicit ridges for nonsimplicial facets.
- for simplicial facets, neighbors defines ridge */
- setT* neighbors; /* neighbors of the facet. If simplicial, the kth
- neighbor is opposite the kth vertex, and the first
- neighbor is the horizon facet for the first vertex*/
- setT* outsideset; /* set of points outside this facet
- if non-empty, last point is furthest
- if NARROWhull, includes coplanars for partitioning*/
- setT* coplanarset; /* set of points coplanar with this facet
- > qh.min_vertex and <= facet->max_outside
- a point is assigned to the furthest facet
- if non-empty, last point is furthest away */
- unsigned visitid; /* visit_id, for visiting all neighbors,
- all uses are independent */
- unsigned id; /* unique identifier from qh facet_id */
- unsigned nummerge: 9; /* number of merges */
-#define qh_MAXnummerge 511 /* 2^9-1, 32 flags total, see "flags:" in io.c */
- flagT tricoplanar: 1; /* True if TRIangulate and simplicial and coplanar with a neighbor */
- /* all tricoplanars share the same ->center, ->normal, ->offset, ->maxoutside */
- /* all tricoplanars share the same apex */
- /* if ->degenerate, does not span facet (one logical ridge) */
- /* one tricoplanar has ->keepcentrum and ->coplanarset */
- /* during qh_triangulate, f.trivisible points to original facet */
- flagT newfacet: 1; /* True if facet on qh newfacet_list (new or merged) */
- flagT visible: 1; /* True if visible facet (will be deleted) */
- flagT toporient: 1; /* True if created with top orientation
- after merging, use ridge orientation */
- flagT simplicial: 1; /* True if simplicial facet, ->ridges may be implicit */
- flagT seen: 1; /* used to perform operations only once, like visitid */
- flagT seen2: 1; /* used to perform operations only once, like visitid */
- flagT flipped: 1; /* True if facet is flipped */
- flagT upperdelaunay: 1; /* True if facet is upper envelope of Delaunay triangulation */
- flagT notfurthest: 1; /* True if last point of outsideset is not furthest*/
-
- /*-------- flags primarily for output ---------*/
- flagT good: 1; /* True if a facet marked good for output */
- flagT isarea: 1; /* True if facet->f.area is defined */
-
- /*-------- flags for merging ------------------*/
- flagT dupridge: 1; /* True if duplicate ridge in facet */
- flagT mergeridge: 1; /* True if facet or neighbor contains a qh_MERGEridge
- ->normal defined (also defined for mergeridge2) */
- flagT mergeridge2: 1; /* True if neighbor contains a qh_MERGEridge (mark_dupridges */
- flagT coplanar: 1; /* True if horizon facet is coplanar at last use */
- flagT mergehorizon: 1; /* True if will merge into horizon (->coplanar) */
- flagT cycledone: 1; /* True if mergecycle_all already done */
- flagT tested: 1; /* True if facet convexity has been tested (false after merge */
- flagT keepcentrum: 1; /* True if keep old centrum after a merge, or marks owner for ->tricoplanar */
- flagT newmerge: 1; /* True if facet is newly merged for reducevertices */
- flagT degenerate: 1; /* True if facet is degenerate (degen_mergeset or ->tricoplanar) */
- flagT redundant: 1; /* True if facet is redundant (degen_mergeset) */
-};
-
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="ridgeT">-</a>
-
- ridgeT
- defines a ridge
-
- notes:
- a ridge is DIM3-1 simplex between two neighboring facets. If the
- facets are non-simplicial, there may be more than one ridge between
- two facets. E.G. a 4-d hypercube has two triangles between each pair
- of neighboring facets.
-
- topological information:
- vertices a set of vertices
- top,bottom neighboring facets with orientation
-
- geometric information:
- tested True if ridge is clearly convex
- nonconvex True if ridge is non-convex
-*/
-struct ridgeT
-{
- setT* vertices; /* vertices belonging to this ridge, inverse sorted by ID
- NULL if a degen ridge (matchsame) */
- facetT* top; /* top facet this ridge is part of */
- facetT* bottom; /* bottom facet this ridge is part of */
- unsigned id: 24; /* unique identifier, =>room for 8 flags */
- flagT seen: 1; /* used to perform operations only once */
- flagT tested: 1; /* True when ridge is tested for convexity */
- flagT nonconvex: 1; /* True if getmergeset detected a non-convex neighbor
- only one ridge between neighbors may have nonconvex */
-};
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="vertexT">-</a>
-
- vertexT
- defines a vertex
-
- topological information:
- next,previous doubly-linked list of all vertices
- neighbors set of adjacent facets (only if qh.VERTEXneighbors)
-
- geometric information:
- point array of DIM3 coordinates
-*/
-struct vertexT
-{
- vertexT* next; /* next vertex in vertex_list */
- vertexT* previous; /* previous vertex in vertex_list */
- pointT* point; /* hull_dim coordinates (coordT) */
- setT* neighbors; /* neighboring facets of vertex, qh_vertexneighbors()
- inits in io.c or after first merge */
- unsigned visitid; /* for use with qh vertex_visit */
- unsigned id: 24; /* unique identifier, =>room for 8 flags */
- flagT seen: 1; /* used to perform operations only once */
- flagT seen2: 1; /* another seen flag */
- flagT delridge: 1; /* vertex was part of a deleted ridge */
- flagT deleted: 1; /* true if vertex on qh del_vertices */
- flagT newlist: 1; /* true if vertex on qh newvertex_list */
-};
-
-/*======= -global variables -qh ============================*/
-
-/*-<a href="qh-globa.htm#TOC"
- >--------------------------------</a><a name="qh">-</a>
-
- qh
- all global variables for qhull are in qh, qhmem, and qhstat
-
- notes:
- qhmem is defined in mem.h and qhstat is defined in stat.h
- Access to qh_qh is via the "qh" macro. See qh_QHpointer in user.h
-*/
-typedef struct qhT qhT;
-#if qh_QHpointer
-#define qh qh_qh->
-extern qhT* qh_qh; /* allocated in global.c */
-#else
-#define qh qh_qh.
-extern qhT qh_qh;
-#endif
-
-struct qhT
-{
-
- /*-<a href="qh-globa.htm#TOC"
- >--------------------------------</a><a name="qh-const">-</a>
-
- qh constants
- configuration flags and constants for Qhull
-
- notes:
- The user configures Qhull by defining flags. They are
- copied into qh by qh_setflags(). qh-quick.htm#options defines the flags.
- */
- boolT ALLpoints; /* true 'Qs' if search all points for initial simplex */
- boolT ANGLEmerge; /* true 'Qa' if sort potential merges by angle */
- boolT APPROXhull; /* true 'Wn' if MINoutside set */
- realT MINoutside; /* 'Wn' min. distance for an outside point */
- boolT ATinfinity; /* true 'Qz' if point num_points-1 is "at-infinity"
- for improving precision in Delaunay triangulations */
- boolT AVOIDold; /* true 'Q4' if avoid old->new merges */
- boolT BESToutside; /* true 'Qf' if partition points into best outsideset */
- boolT CDDinput; /* true 'Pc' if input uses CDD format (1.0/offset first) */
- boolT CDDoutput; /* true 'PC' if print normals in CDD format (offset first) */
- boolT CHECKfrequently; /* true 'Tc' if checking frequently */
- realT premerge_cos; /* 'A-n' cos_max when pre merging */
- realT postmerge_cos; /* 'An' cos_max when post merging */
- boolT DELAUNAY; /* true 'd' if computing DELAUNAY triangulation */
- boolT DOintersections; /* true 'Gh' if print hyperplane intersections */
- int DROPdim; /* drops dim 'GDn' for 4-d -> 3-d output */
- boolT FORCEoutput; /* true 'Po' if forcing output despite degeneracies */
- int GOODpoint; /* 1+n for 'QGn', good facet if visible/not(-) from point n*/
- pointT* GOODpointp; /* the actual point */
- boolT GOODthreshold; /* true if qh lower_threshold/upper_threshold defined
- false if qh SPLITthreshold */
- int GOODvertex; /* 1+n, good facet if vertex for point n */
- pointT* GOODvertexp; /* the actual point */
- boolT HALFspace; /* true 'Hn,n,n' if halfspace intersection */
- int IStracing; /* trace execution, 0=none, 1=least, 4=most, -1=events */
- int KEEParea; /* 'PAn' number of largest facets to keep */
- boolT KEEPcoplanar; /* true 'Qc' if keeping nearest facet for coplanar points */
- boolT KEEPinside; /* true 'Qi' if keeping nearest facet for inside points
- set automatically if 'd Qc' */
- int KEEPmerge; /* 'PMn' number of facets to keep with most merges */
- realT KEEPminArea; /* 'PFn' minimum facet area to keep */
- realT MAXcoplanar; /* 'Un' max distance below a facet to be coplanar*/
- boolT MERGEexact; /* true 'Qx' if exact merges (coplanar, degen, dupridge, flipped) */
- boolT MERGEindependent; /* true 'Q2' if merging independent sets */
- boolT MERGING; /* true if exact-, pre- or post-merging, with angle and centrum tests */
- realT premerge_centrum; /* 'C-n' centrum_radius when pre merging. Default is round-off */
- realT postmerge_centrum; /* 'Cn' centrum_radius when post merging. Default is round-off */
- boolT MERGEvertices; /* true 'Q3' if merging redundant vertices */
- realT MINvisible; /* 'Vn' min. distance for a facet to be visible */
- boolT NOnarrow; /* true 'Q10' if no special processing for narrow distributions */
- boolT NOnearinside; /* true 'Q8' if ignore near-inside points when partitioning */
- boolT NOpremerge; /* true 'Q0' if no defaults for C-0 or Qx */
- boolT ONLYgood; /* true 'Qg' if process points with good visible or horizon facets */
- boolT ONLYmax; /* true 'Qm' if only process points that increase max_outside */
- boolT PICKfurthest; /* true 'Q9' if process furthest of furthest points*/
- boolT POSTmerge; /* true if merging after buildhull (Cn or An) */
- boolT PREmerge; /* true if merging during buildhull (C-n or A-n) */
- /* NOTE: some of these names are similar to qh_PRINT names */
- boolT PRINTcentrums; /* true 'Gc' if printing centrums */
- boolT PRINTcoplanar; /* true 'Gp' if printing coplanar points */
- int PRINTdim; /* print dimension for Geomview output */
- boolT PRINTdots; /* true 'Ga' if printing all points as dots */
- boolT PRINTgood; /* true 'Pg' if printing good facets */
- boolT PRINTinner; /* true 'Gi' if printing inner planes */
- boolT PRINTneighbors; /* true 'PG' if printing neighbors of good facets */
- boolT PRINTnoplanes; /* true 'Gn' if printing no planes */
- boolT PRINToptions1st; /* true 'FO' if printing options to stderr */
- boolT PRINTouter; /* true 'Go' if printing outer planes */
- boolT PRINTprecision; /* false 'Pp' if not reporting precision problems */
- qh_PRINT PRINTout[qh_PRINTEND]; /* list of output formats to print */
- boolT PRINTridges; /* true 'Gr' if print ridges */
- boolT PRINTspheres; /* true 'Gv' if print vertices as spheres */
- boolT PRINTstatistics; /* true 'Ts' if printing statistics to stderr */
- boolT PRINTsummary; /* true 's' if printing summary to stderr */
- boolT PRINTtransparent; /* true 'Gt' if print transparent outer ridges */
- boolT PROJECTdelaunay; /* true if DELAUNAY, no readpoints() and
- need projectinput() for Delaunay in qh_init_B */
- int PROJECTinput; /* number of projected dimensions 'bn:0Bn:0' */
- boolT QUICKhelp; /* true if quick help message for degen input */
- boolT RANDOMdist; /* true if randomly change distplane and setfacetplane */
- realT RANDOMfactor; /* maximum random perturbation */
- realT RANDOMa; /* qh_randomfactor is randr * RANDOMa + RANDOMb */
- realT RANDOMb;
- boolT RANDOMoutside; /* true if select a random outside point */
- int REPORTfreq; /* buildtracing reports every n facets */
- int REPORTfreq2; /* tracemerging reports every REPORTfreq/2 facets */
- int RERUN; /* 'TRn' rerun qhull n times (qh.build_cnt) */
- int ROTATErandom; /* 'QRn' seed, 0 time, >= rotate input */
- boolT SCALEinput; /* true 'Qbk' if scaling input */
- boolT SCALElast; /* true 'Qbb' if scale last coord to max prev coord */
- boolT SETroundoff; /* true 'E' if qh DISTround is predefined */
- boolT SKIPcheckmax; /* true 'Q5' if skip qh_check_maxout */
- boolT SKIPconvex; /* true 'Q6' if skip convexity testing during pre-merge */
- boolT SPLITthresholds; /* true if upper_/lower_threshold defines a region
- used only for printing (not for qh ONLYgood) */
- int STOPcone; /* 'TCn' 1+n for stopping after cone for point n*/
- /* also used by qh_build_withresart for err exit*/
- int STOPpoint; /* 'TVn' 'TV-n' 1+n for stopping after/before(-)
- adding point n */
- int TESTpoints; /* 'QTn' num of test points after qh.num_points. Test points always coplanar. */
- boolT TESTvneighbors; /* true 'Qv' if test vertex neighbors at end */
- int TRACElevel; /* 'Tn' conditional IStracing level */
- int TRACElastrun; /* qh.TRACElevel applies to last qh.RERUN */
- int TRACEpoint; /* 'TPn' start tracing when point n is a vertex */
- realT TRACEdist; /* 'TWn' start tracing when merge distance too big */
- int TRACEmerge; /* 'TMn' start tracing before this merge */
- boolT TRIangulate; /* true 'Qt' if triangulate non-simplicial facets */
- boolT TRInormals; /* true 'Q11' if triangulate duplicates normals (sets Qt) */
- boolT UPPERdelaunay; /* true 'Qu' if computing furthest-site Delaunay */
- boolT VERIFYoutput; /* true 'Tv' if verify output at end of qhull */
- boolT VIRTUALmemory; /* true 'Q7' if depth-first processing in buildhull */
- boolT VORONOI; /* true 'v' if computing Voronoi diagram */
-
- /*--------input constants ---------*/
- realT AREAfactor; /* 1/(hull_dim-1)! for converting det's to area */
- boolT DOcheckmax; /* true if calling qh_check_maxout (qh_initqhull_globals) */
- char* feasible_string; /* feasible point 'Hn,n,n' for halfspace intersection */
- coordT* feasible_point; /* as coordinates, both malloc'd */
- boolT GETarea; /* true 'Fa', 'FA', 'FS', 'PAn', 'PFn' if compute facet area/Voronoi volume in io.c */
- boolT KEEPnearinside; /* true if near-inside points in coplanarset */
- int hull_dim; /* dimension of hull, set by initbuffers */
- int input_dim; /* dimension of input, set by initbuffers */
- int num_points; /* number of input points */
- pointT* first_point; /* array of input points, see POINTSmalloc */
- boolT POINTSmalloc; /* true if qh first_point/num_points allocated */
- pointT* input_points; /* copy of original qh.first_point for input points for qh_joggleinput */
- boolT input_malloc; /* true if qh input_points malloc'd */
- char qhull_command[256];/* command line that invoked this program */
- char rbox_command[256]; /* command line that produced the input points */
- char qhull_options[512];/* descriptive list of options */
- int qhull_optionlen; /* length of last line */
- int qhull_optionsiz; /* size of qhull_options before qh_initbuild */
- boolT VERTEXneighbors; /* true if maintaining vertex neighbors */
- boolT ZEROcentrum; /* true if 'C-0' or 'C-0 Qx'. sets ZEROall_ok */
- realT* upper_threshold; /* don't print if facet->normal[k]>=upper_threshold[k]
- must set either GOODthreshold or SPLITthreshold
- if Delaunay, default is 0.0 for upper envelope */
- realT* lower_threshold; /* don't print if facet->normal[k] <=lower_threshold[k] */
- realT* upper_bound; /* scale point[k] to new upper bound */
- realT* lower_bound; /* scale point[k] to new lower bound
- project if both upper_ and lower_bound == 0 */
-
- /*-<a href="qh-globa.htm#TOC"
- >--------------------------------</a><a name="qh-prec">-</a>
-
- qh precision constants
- precision constants for Qhull
-
- notes:
- qh_detroundoff() computes the maximum roundoff error for distance
- and other computations. It also sets default values for the
- qh constants above.
- */
- realT ANGLEround; /* max round off error for angles */
- realT centrum_radius; /* max centrum radius for convexity (roundoff added) */
- realT cos_max; /* max cosine for convexity (roundoff added) */
- realT DISTround; /* max round off error for distances, 'E' overrides */
- realT MAXabs_coord; /* max absolute coordinate */
- realT MAXlastcoord; /* max last coordinate for qh_scalelast */
- realT MAXsumcoord; /* max sum of coordinates */
- realT MAXwidth; /* max rectilinear width of point coordinates */
- realT MINdenom_1; /* min. abs. value for 1/x */
- realT MINdenom; /* use divzero if denominator < MINdenom */
- realT MINdenom_1_2; /* min. abs. val for 1/x that allows normalization */
- realT MINdenom_2; /* use divzero if denominator < MINdenom_2 */
- realT MINlastcoord; /* min. last coordinate for qh_scalelast */
- boolT NARROWhull; /* set in qh_initialhull if angle < qh_MAXnarrow */
- realT* NEARzero; /* hull_dim array for near zero in gausselim */
- realT NEARinside; /* keep points for qh_check_maxout if close to facet */
- realT ONEmerge; /* max distance for merging simplicial facets */
- realT outside_err; /* application's epsilon for coplanar points
- qh_check_bestdist() qh_check_points() reports error if point outside */
- realT WIDEfacet; /* size of wide facet for skipping ridge in
- area computation and locking centrum */
-
- /*-<a href="qh-globa.htm#TOC"
- >--------------------------------</a><a name="qh-intern">-</a>
-
- qh internal constants
- internal constants for Qhull
- */
- char qhull[sizeof("qhull")]; /* for checking ownership */
- void* old_stat; /* pointer to saved qh_qhstat, qh_save_qhull */
- jmp_buf errexit; /* exit label for qh_errexit, defined by setjmp() */
- char jmpXtra[40]; /* extra bytes in case jmp_buf is defined wrong by compiler */
- jmp_buf restartexit; /* restart label for qh_errexit, defined by setjmp() */
- char jmpXtra2[40]; /* extra bytes in case jmp_buf is defined wrong by compiler*/
- FILE* fin; /* pointer to input file, init by qh_meminit */
- FILE* fout; /* pointer to output file */
- FILE* ferr; /* pointer to error file */
- pointT* interior_point; /* center point of the initial simplex*/
- int normal_size; /* size in bytes for facet normals and point coords*/
- int center_size; /* size in bytes for Voronoi centers */
- int TEMPsize; /* size for small, temporary sets (in quick mem) */
-
- /*-<a href="qh-globa.htm#TOC"
- >--------------------------------</a><a name="qh-lists">-</a>
-
- qh facet and vertex lists
- defines lists of facets, new facets, visible facets, vertices, and
- new vertices. Includes counts, next ids, and trace ids.
- see:
- qh_resetlists()
- */
- facetT* facet_list; /* first facet */
- facetT* facet_tail; /* end of facet_list (dummy facet) */
- facetT* facet_next; /* next facet for buildhull()
- previous facets do not have outside sets
- NARROWhull: previous facets may have coplanar outside sets for qh_outcoplanar */
- facetT* newfacet_list; /* list of new facets to end of facet_list */
- facetT* visible_list; /* list of visible facets preceeding newfacet_list,
- facet->visible set */
- int num_visible; /* current number of visible facets */
- unsigned tracefacet_id; /* set at init, then can print whenever */
- facetT* tracefacet; /* set in newfacet/mergefacet, undone in delfacet*/
- unsigned tracevertex_id; /* set at buildtracing, can print whenever */
- vertexT* tracevertex; /* set in newvertex, undone in delvertex*/
- vertexT* vertex_list; /* list of all vertices, to vertex_tail */
- vertexT* vertex_tail; /* end of vertex_list (dummy vertex) */
- vertexT* newvertex_list; /* list of vertices in newfacet_list, to vertex_tail
- all vertices have 'newlist' set */
- int num_facets; /* number of facets in facet_list
- includes visble faces (num_visible) */
- int num_vertices; /* number of vertices in facet_list */
- int num_outside; /* number of points in outsidesets (for tracing and RANDOMoutside)
- includes coplanar outsideset points for NARROWhull/qh_outcoplanar() */
- int num_good; /* number of good facets (after findgood_all) */
- unsigned facet_id; /* ID of next, new facet from newfacet() */
- unsigned ridge_id; /* ID of next, new ridge from newridge() */
- unsigned vertex_id; /* ID of next, new vertex from newvertex() */
-
- /*-<a href="qh-globa.htm#TOC"
- >--------------------------------</a><a name="qh-var">-</a>
-
- qh global variables
- defines minimum and maximum distances, next visit ids, several flags,
- and other global variables.
- initialize in qh_initbuild or qh_maxmin if used in qh_buildhull
- */
- unsigned long hulltime; /* ignore time to set up input and randomize */
- /* use unsigned to avoid wrap-around errors */
- boolT ALLOWrestart; /* true if qh_precision can use qh.restartexit */
- int build_cnt; /* number of calls to qh_initbuild */
- qh_CENTER CENTERtype; /* current type of facet->center, qh_CENTER */
- int furthest_id; /* pointid of furthest point, for tracing */
- facetT* GOODclosest; /* closest facet to GOODthreshold in qh_findgood */
- realT JOGGLEmax; /* set 'QJn' if randomly joggle input */
- boolT maxoutdone; /* set qh_check_maxout(), cleared by qh_addpoint() */
- realT max_outside; /* maximum distance from a point to a facet,
- before roundoff, not simplicial vertices
- actual outer plane is +DISTround and
- computed outer plane is +2*DISTround */
- realT max_vertex; /* maximum distance (>0) from vertex to a facet,
- before roundoff, due to a merge */
- realT min_vertex; /* minimum distance (<0) from vertex to a facet,
- before roundoff, due to a merge
- if qh.JOGGLEmax, qh_makenewplanes sets it
- recomputed if qh.DOcheckmax, default -qh.DISTround */
- boolT NEWfacets; /* true while visible facets invalid due to new or merge
- from makecone/attachnewfacets to deletevisible */
- boolT findbestnew; /* true if partitioning calls qh_findbestnew */
- boolT findbest_notsharp; /* true if new facets are at least 90 degrees */
- boolT NOerrexit; /* true if qh.errexit is not available */
- realT PRINTcradius; /* radius for printing centrums */
- realT PRINTradius; /* radius for printing vertex spheres and points */
- boolT POSTmerging; /* true when post merging */
- int printoutvar; /* temporary variable for qh_printbegin, etc. */
- int printoutnum; /* number of facets printed */
- boolT QHULLfinished; /* True after qhull() is finished */
- realT totarea; /* 'FA': total facet area computed by qh_getarea */
- realT totvol; /* 'FA': total volume computed by qh_getarea */
- unsigned int visit_id; /* unique ID for searching neighborhoods, */
- unsigned int vertex_visit; /* unique ID for searching vertices */
- boolT ZEROall_ok; /* True if qh_checkzero always succeeds */
- boolT WAScoplanar; /* True if qh_partitioncoplanar (qh_check_maxout) */
-
- /*-<a href="qh-globa.htm#TOC"
- >--------------------------------</a><a name="qh-set">-</a>
-
- qh global sets
- defines sets for merging, initial simplex, hashing, extra input points,
- and deleted vertices
- */
- setT* facet_mergeset; /* temporary set of merges to be done */
- setT* degen_mergeset; /* temporary set of degenerate and redundant merges */
- setT* hash_table; /* hash table for matching ridges in qh_matchfacets
- size is setsize() */
- setT* other_points; /* additional points (first is qh interior_point) */
- setT* del_vertices; /* vertices to partition and delete with visible
- facets. Have deleted set for checkfacet */
-
- /*-<a href="qh-globa.htm#TOC"
- >--------------------------------</a><a name="qh-buf">-</a>
-
- qh global buffers
- defines buffers for maxtrix operations, input, and error messages
- */
- coordT* gm_matrix; /* (dim+1)Xdim matrix for geom.c */
- coordT** gm_row; /* array of gm_matrix rows */
- char* line; /* malloc'd input line of maxline+1 chars */
- int maxline;
- coordT* half_space; /* malloc'd input array for halfspace (qh normal_size+coordT) */
- coordT* temp_malloc; /* malloc'd input array for points */
-
- /*-<a href="qh-globa.htm#TOC"
- >--------------------------------</a><a name="qh-static">-</a>
-
- qh static variables
- defines static variables for individual functions
-
- notes:
- do not use 'static' within a function. Multiple instances of qhull
- may exist.
-
- do not assume zero initialization, 'QPn' may cause a restart
- */
- boolT ERREXITcalled; /* true during errexit (prevents duplicate calls */
- boolT firstcentrum; /* for qh_printcentrum */
- realT last_low; /* qh_scalelast parameters for qh_setdelaunay */
- realT last_high;
- realT last_newhigh;
- unsigned lastreport; /* for qh_buildtracing */
- int mergereport; /* for qh_tracemerging */
- boolT old_randomdist; /* save RANDOMdist when io, tracing, or statistics */
- int ridgeoutnum; /* number of ridges in 4OFF output */
- void* old_qhstat; /* for saving qh_qhstat in save_qhull() */
- setT* old_tempstack; /* for saving qhmem.tempstack in save_qhull */
- setT* coplanarset; /* set of coplanar facets for searching qh_findbesthorizon() */
-};
-
-/*=========== -macros- =========================*/
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="otherfacet_">-</a>
-
- otherfacet_(ridge, facet)
- return neighboring facet for a ridge in facet
-*/
-#define otherfacet_(ridge, facet) \
- (((ridge)->top == (facet)) ? (ridge)->bottom : (ridge)->top)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="getid_">-</a>
-
- getid_(p)
- return ID for facet, ridge, or vertex
- return MAXINT if NULL (-1 causes type conversion error )
-*/
-#define getid_(p) ((p) ? (p)->id : -1)
-
-/*============== FORALL macros ===================*/
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FORALLfacets">-</a>
-
- FORALLfacets { ... }
- assign 'facet' to each facet in qh.facet_list
-
- notes:
- uses 'facetT *facet;'
- assumes last facet is a sentinel
-
- see:
- FORALLfacet_( facetlist )
-*/
-#define FORALLfacets for (facet=qh facet_list;facet && facet->next;facet=facet->next)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FORALLpoints">-</a>
-
- FORALLpoints { ... }
- assign 'point' to each point in qh.first_point, qh.num_points
-
- declare:
- coordT *point, *pointtemp;
-*/
-#define FORALLpoints FORALLpoint_(qh first_point, qh num_points)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FORALLpoint_">-</a>
-
- FORALLpoint_( points, num) { ... }
- assign 'point' to each point in points array of num points
-
- declare:
- coordT *point, *pointtemp;
-*/
-#define FORALLpoint_(points, num) for(point= (points), \
- pointtemp= (points)+qh hull_dim*(num); point < pointtemp; point += qh hull_dim)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FORALLvertices">-</a>
-
- FORALLvertices { ... }
- assign 'vertex' to each vertex in qh.vertex_list
-
- declare:
- vertexT *vertex;
-
- notes:
- assumes qh.vertex_list terminated with a sentinel
-*/
-#define FORALLvertices for (vertex=qh vertex_list;vertex && vertex->next;vertex= vertex->next)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHfacet_">-</a>
-
- FOREACHfacet_( facets ) { ... }
- assign 'facet' to each facet in facets
-
- declare:
- facetT *facet, **facetp;
-
- see:
- <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
-*/
-#define FOREACHfacet_(facets) FOREACHsetelement_(facetT, facets, facet)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHneighbor_">-</a>
-
- FOREACHneighbor_( facet ) { ... }
- assign 'neighbor' to each neighbor in facet->neighbors
-
- FOREACHneighbor_( vertex ) { ... }
- assign 'neighbor' to each neighbor in vertex->neighbors
-
- declare:
- facetT *neighbor, **neighborp;
-
- see:
- <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
-*/
-#define FOREACHneighbor_(facet) FOREACHsetelement_(facetT, facet->neighbors, neighbor)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHpoint_">-</a>
-
- FOREACHpoint_( points ) { ... }
- assign 'point' to each point in points set
-
- declare:
- pointT *point, **pointp;
-
- see:
- <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
-*/
-#define FOREACHpoint_(points) FOREACHsetelement_(pointT, points, point)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHridge_">-</a>
-
- FOREACHridge_( ridges ) { ... }
- assign 'ridge' to each ridge in ridges set
-
- declare:
- ridgeT *ridge, **ridgep;
-
- see:
- <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
-*/
-#define FOREACHridge_(ridges) FOREACHsetelement_(ridgeT, ridges, ridge)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHvertex_">-</a>
-
- FOREACHvertex_( vertices ) { ... }
- assign 'vertex' to each vertex in vertices set
-
- declare:
- vertexT *vertex, **vertexp;
-
- see:
- <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
-*/
-#define FOREACHvertex_(vertices) FOREACHsetelement_(vertexT, vertices,vertex)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHfacet_i_">-</a>
-
- FOREACHfacet_i_( facets ) { ... }
- assign 'facet' and 'facet_i' for each facet in facets set
-
- declare:
- facetT *facet;
- int facet_n, facet_i;
-
- see:
- <a href="qset.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
-*/
-#define FOREACHfacet_i_(facets) FOREACHsetelement_i_(facetT, facets, facet)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHneighbor_i_">-</a>
-
- FOREACHneighbor_i_( facet ) { ... }
- assign 'neighbor' and 'neighbor_i' for each neighbor in facet->neighbors
-
- FOREACHneighbor_i_( vertex ) { ... }
- assign 'neighbor' and 'neighbor_i' for each neighbor in vertex->neighbors
-
- declare:
- facetT *neighbor;
- int neighbor_n, neighbor_i;
-
- see:
- <a href="qset.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
-*/
-#define FOREACHneighbor_i_(facet) FOREACHsetelement_i_(facetT, facet->neighbors, neighbor)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHpoint_i_">-</a>
-
- FOREACHpoint_i_( points ) { ... }
- assign 'point' and 'point_i' for each point in points set
-
- declare:
- pointT *point;
- int point_n, point_i;
-
- see:
- <a href="qset.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
-*/
-#define FOREACHpoint_i_(points) FOREACHsetelement_i_(pointT, points, point)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHridge_i_">-</a>
-
- FOREACHridge_i_( ridges ) { ... }
- assign 'ridge' and 'ridge_i' for each ridge in ridges set
-
- declare:
- ridgeT *ridge;
- int ridge_n, ridge_i;
-
- see:
- <a href="qset.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
-*/
-#define FOREACHridge_i_(ridges) FOREACHsetelement_i_(ridgeT, ridges, ridge)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHvertex_i_">-</a>
-
- FOREACHvertex_i_( vertices ) { ... }
- assign 'vertex' and 'vertex_i' for each vertex in vertices set
-
- declare:
- vertexT *vertex;
- int vertex_n, vertex_i;
-
- see:
- <a href="qset.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
- */
-#define FOREACHvertex_i_(vertices) FOREACHsetelement_i_(vertexT, vertices,vertex)
-
-/********* -qhull.c prototypes (duplicated from qhull_a.h) **********************/
-
-void qh_qhull(void);
-boolT qh_addpoint(pointT* furthest, facetT* facet, boolT checkdist);
-void qh_printsummary(FILE* fp);
-
-/********* -user.c prototypes (alphabetical) **********************/
-
-void qh_errexit(int exitcode, facetT* facet, ridgeT* ridge);
-void qh_errprint(char* string, facetT* atfacet, facetT* otherfacet, ridgeT* atridge, vertexT* atvertex);
-int qh_new_qhull(int dim, int numpoints, coordT* points, boolT ismalloc,
- char* qhull_cmd, FILE* outfile, FILE* errfile);
-void qh_printfacetlist(facetT* facetlist, setT* facets, boolT printall);
-void qh_user_memsizes(void);
-
-/***** -geom.c/geom2.c prototypes (duplicated from geom.h) ****************/
-
-facetT* qh_findbest(pointT* point, facetT* startfacet,
- boolT bestoutside, boolT newfacets, boolT noupper,
- realT* dist, boolT* isoutside, int* numpart);
-facetT* qh_findbestnew(pointT* point, facetT* startfacet,
- realT* dist, boolT bestoutside, boolT* isoutside, int* numpart);
-boolT qh_gram_schmidt(int dim, realT** rows);
-void qh_outerinner(facetT* facet, realT* outerplane, realT* innerplane);
-void qh_printsummary(FILE* fp);
-void qh_projectinput(void);
-void qh_randommatrix(realT* buffer, int dim, realT** row);
-void qh_rotateinput(realT** rows);
-void qh_scaleinput(void);
-void qh_setdelaunay(int dim, int count, pointT* points);
-coordT* qh_sethalfspace_all(int dim, int count, coordT* halfspaces, pointT* feasible);
-
-/***** -global.c prototypes (alphabetical) ***********************/
-
-unsigned long qh_clock(void);
-void qh_checkflags(char* command, char* hiddenflags);
-void qh_freebuffers(void);
-void qh_freeqhull(boolT allmem);
-void qh_init_A(FILE* infile, FILE* outfile, FILE* errfile, int argc, char* argv[]);
-void qh_init_B(coordT* points, int numpoints, int dim, boolT ismalloc);
-void qh_init_qhull_command(int argc, char* argv[]);
-void qh_initbuffers(coordT* points, int numpoints, int dim, boolT ismalloc);
-void qh_initflags(char* command);
-void qh_initqhull_buffers(void);
-void qh_initqhull_globals(coordT* points, int numpoints, int dim, boolT ismalloc);
-void qh_initqhull_mem(void);
-void qh_initqhull_start(FILE* infile, FILE* outfile, FILE* errfile);
-void qh_initthresholds(char* command);
-void qh_option(char* option, int* i, realT* r);
-#if qh_QHpointer
-void qh_restore_qhull(qhT** oldqh);
-qhT* qh_save_qhull(void);
-#endif
-
-/***** -io.c prototypes (duplicated from io.h) ***********************/
-
-void dfacet(unsigned id);
-void dvertex(unsigned id);
-void qh_printneighborhood(FILE* fp, int format, facetT* facetA, facetT* facetB, boolT printall);
-void qh_produce_output(void);
-coordT* qh_readpoints(int* numpoints, int* dimension, boolT* ismalloc);
-
-
-/********* -mem.c prototypes (duplicated from mem.h) **********************/
-
-void qh_meminit(FILE* ferr);
-void qh_memfreeshort(int* curlong, int* totlong);
-
-/********* -poly.c/poly2.c prototypes (duplicated from poly.h) **********************/
-
-void qh_check_output(void);
-void qh_check_points(void);
-setT* qh_facetvertices(facetT* facetlist, setT* facets, boolT allfacets);
-facetT* qh_findbestfacet(pointT* point, boolT bestoutside,
- realT* bestdist, boolT* isoutside);
-vertexT* qh_nearvertex(facetT* facet, pointT* point, realT* bestdistp);
-pointT* qh_point(int id);
-setT* qh_pointfacet(void /*qh.facet_list*/);
-int qh_pointid(pointT* point);
-setT* qh_pointvertex(void /*qh.facet_list*/);
-void qh_setvoronoi_all(void);
-void qh_triangulate(void /*qh facet_list*/);
-
-/********* -stat.c prototypes (duplicated from stat.h) **********************/
-
-void qh_collectstatistics(void);
-void qh_printallstatistics(FILE* fp, char* string);
-
-#endif /* qhDEFqhull */
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/qhull_a.h b/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/qhull_a.h
deleted file mode 100644
index 5d985a084ab6fd201a6864692d249972ab5cb2f7..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/qhull_a.h
+++ /dev/null
@@ -1,125 +0,0 @@
-/*<html><pre> -<a href="qh-qhull.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- qhull_a.h
- all header files for compiling qhull
-
- see qh-qhull.htm
-
- see qhull.h for user-level definitions
-
- see user.h for user-defineable constants
-
- defines internal functions for qhull.c global.c
-
- copyright (c) 1993-2003, The Geometry Center
-
- Notes: grep for ((" and (" to catch fprintf("lkasdjf");
- full parens around (x?y:z)
- use '#include qhull/qhull_a.h' to avoid name clashes
-*/
-
-#pragma once
-
-#include <stdio.h>
-#include <stdlib.h>
-#include <setjmp.h>
-#include <string.h>
-#include <math.h>
-#include <float.h> /* some compilers will not need float.h */
-#include <limits.h>
-#include <time.h>
-#include <ctype.h>
-/*** uncomment here and qset.c
- if string.h does not define memcpy()
-#include <memory.h>
-*/
-#include "qhull.h"
-#include "mem.h"
-#include "qset.h"
-#include "geom.h"
-#include "merge.h"
-#include "poly.h"
-#include "io.h"
-#include "stat.h"
-
-#if qh_CLOCKtype == 2 /* defined in user.h from qhull.h */
-#include <sys/types.h>
-#include <sys/times.h>
-#include <unistd.h>
-#endif
-
-#ifdef _MSC_VER /* Microsoft Visual C++ */
-#pragma warning( disable : 4056) /* float constant expression. Looks like a compiler bug */
-#pragma warning( disable : 4146) /* unary minus applied to unsigned type */
-#pragma warning( disable : 4244) /* conversion from 'unsigned long' to 'real' */
-#pragma warning( disable : 4305) /* conversion from 'const double' to 'float' */
-#endif
-
-/* ======= -macros- =========== */
-
-/*-<a href="qh-qhull.htm#TOC"
- >--------------------------------</a><a name="traceN">-</a>
-
- traceN((fp.ferr, "format\n", vars));
- calls fprintf if qh.IStracing >= N
-
- notes:
- removing tracing reduces code size but doesn't change execution speed
-*/
-#ifndef qh_NOtrace
-#define trace0(args) {if (qh IStracing) fprintf args;}
-#define trace1(args) {if (qh IStracing >= 1) fprintf args;}
-#define trace2(args) {if (qh IStracing >= 2) fprintf args;}
-#define trace3(args) {if (qh IStracing >= 3) fprintf args;}
-#define trace4(args) {if (qh IStracing >= 4) fprintf args;}
-#define trace5(args) {if (qh IStracing >= 5) fprintf args;}
-#else /* qh_NOtrace */
-#define trace0(args) {}
-#define trace1(args) {}
-#define trace2(args) {}
-#define trace3(args) {}
-#define trace4(args) {}
-#define trace5(args) {}
-#endif /* qh_NOtrace */
-
-/***** -qhull.c prototypes (alphabetical after qhull) ********************/
-
-void qh_qhull(void);
-boolT qh_addpoint(pointT* furthest, facetT* facet, boolT checkdist);
-void qh_buildhull(void);
-void qh_buildtracing(pointT* furthest, facetT* facet);
-void qh_build_withrestart(void);
-void qh_errexit2(int exitcode, facetT* facet, facetT* otherfacet);
-void qh_findhorizon(pointT* point, facetT* facet, int* goodvisible, int* goodhorizon);
-pointT* qh_nextfurthest(facetT** visible);
-void qh_partitionall(setT* vertices, pointT* points, int npoints);
-void qh_partitioncoplanar(pointT* point, facetT* facet, realT* dist);
-void qh_partitionpoint(pointT* point, facetT* facet);
-void qh_partitionvisible(boolT allpoints, int* numpoints);
-void qh_precision(char* reason);
-void qh_printsummary(FILE* fp);
-
-/***** -global.c internal prototypes (alphabetical) ***********************/
-
-void qh_appendprint(qh_PRINT format);
-void qh_freebuild(boolT allmem);
-void qh_freebuffers(void);
-void qh_initbuffers(coordT* points, int numpoints, int dim, boolT ismalloc);
-int qh_strtol(const char* s, char** endp);
-double qh_strtod(const char* s, char** endp);
-
-/***** -stat.c internal prototypes (alphabetical) ***********************/
-
-void qh_allstatA(void);
-void qh_allstatB(void);
-void qh_allstatC(void);
-void qh_allstatD(void);
-void qh_allstatE(void);
-void qh_allstatE2(void);
-void qh_allstatF(void);
-void qh_allstatG(void);
-void qh_allstatH(void);
-void qh_freebuffers(void);
-void qh_initbuffers(coordT* points, int numpoints, int dim, boolT ismalloc);
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/qset.h b/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/qset.h
deleted file mode 100644
index 165a84c3b361527d8478a66c829d29e49420816a..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/qset.h
+++ /dev/null
@@ -1,470 +0,0 @@
-/*<html><pre> -<a href="qh-set.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- qset.h
- header file for qset.c that implements set
-
- see qh-set.htm and qset.c
-
- only uses mem.c, malloc/free
-
- for error handling, writes message and calls
- qh_errexit (qhmem_ERRqhull, NULL, NULL);
-
- set operations satisfy the following properties:
- - sets have a max size, the actual size (if different) is stored at the end
- - every set is NULL terminated
- - sets may be sorted or unsorted, the caller must distinguish this
-
- copyright (c) 1993-2003, The Geometry Center
-*/
-
-#ifndef qhDEFset
-#define qhDEFset 1
-
-/*================= -structures- ===============*/
-
-#ifndef DEFsetT
-#define DEFsetT 1
-typedef struct setT setT; /* a set is a sorted or unsorted array of pointers */
-#endif
-
-/*-<a href="qh-set.htm#TOC"
->----------------------------------------</a><a name="setT">-</a>
-
-setT
- a set or list of pointers with maximum size and actual size.
-
-variations:
- unsorted, unique -- a list of unique pointers with NULL terminator
- user guarantees uniqueness
- sorted -- a sorted list of unique pointers with NULL terminator
- qset.c guarantees uniqueness
- unsorted -- a list of pointers terminated with NULL
- indexed -- an array of pointers with NULL elements
-
-structure for set of n elements:
-
- --------------
- | maxsize
- --------------
- | e[0] - a pointer, may be NULL for indexed sets
- --------------
- | e[1]
-
- --------------
- | ...
- --------------
- | e[n-1]
- --------------
- | e[n] = NULL
- --------------
- | ...
- --------------
- | e[maxsize] - n+1 or NULL (determines actual size of set)
- --------------
-
-*/
-
-/*-- setelemT -- internal type to allow both pointers and indices
-*/
-typedef union setelemT setelemT;
-union setelemT
-{
- void* p;
- int i; /* integer used for e[maxSize] */
-};
-
-struct setT
-{
- int maxsize; /* maximum number of elements (except NULL) */
- setelemT e[1]; /* array of pointers, tail is NULL */
- /* last slot (unless NULL) is actual size+1
- e[maxsize]==NULL or e[e[maxsize]-1]==NULL */
- /* this may generate a warning since e[] contains
- maxsize elements */
-};
-
-/*=========== -constants- =========================*/
-
-/*-<a href="qh-set.htm#TOC"
- >-----------------------------------</a><a name="SETelemsize">-</a>
-
- SETelemsize
- size of a set element in bytes
-*/
-#define SETelemsize sizeof(setelemT)
-
-
-/*=========== -macros- =========================*/
-
-/*-<a href="qh-set.htm#TOC"
- >-----------------------------------</a><a name="FOREACHsetelement_">-</a>
-
- FOREACHsetelement_(type, set, variable)
- define FOREACH iterator
-
- declare:
- assumes *variable and **variablep are declared
- no space in "variable)" [DEC Alpha cc compiler]
-
- each iteration:
- variable is set element
- variablep is one beyond variable.
-
- to repeat an element:
- variablep--; / *repeat* /
-
- at exit:
- variable is NULL at end of loop
-
- example:
- #define FOREACHfacet_( facets ) FOREACHsetelement_( facetT, facets, facet )
-
- notes:
- use FOREACHsetelement_i_() if need index or include NULLs
-
- WARNING:
- nested loops can't use the same variable (define another FOREACH)
-
- needs braces if nested inside another FOREACH
- this includes intervening blocks, e.g. FOREACH...{ if () FOREACH...} )
-*/
-#define FOREACHsetelement_(type, set, variable) \
- if (((variable= NULL), set)) for(\
- variable##p= (type **)&((set)->e[0].p); \
- (variable= *variable##p++);)
-
-/*-<a href="qh-set.htm#TOC"
- >----------------------------------------</a><a name="FOREACHsetelement_i_">-</a>
-
- FOREACHsetelement_i_(type, set, variable)
- define indexed FOREACH iterator
-
- declare:
- type *variable, variable_n, variable_i;
-
- each iteration:
- variable is set element, may be NULL
- variable_i is index, variable_n is qh_setsize()
-
- to repeat an element:
- variable_i--; variable_n-- repeats for deleted element
-
- at exit:
- variable==NULL and variable_i==variable_n
-
- example:
- #define FOREACHfacet_i_( facets ) FOREACHsetelement_i_( facetT, facets, facet )
-
- WARNING:
- nested loops can't use the same variable (define another FOREACH)
-
- needs braces if nested inside another FOREACH
- this includes intervening blocks, e.g. FOREACH...{ if () FOREACH...} )
-*/
-#define FOREACHsetelement_i_(type, set, variable) \
- if (((variable= NULL), set)) for (\
- variable##_i= 0, variable= (type *)((set)->e[0].p), \
- variable##_n= qh_setsize(set);\
- variable##_i < variable##_n;\
- variable= (type *)((set)->e[++variable##_i].p) )
-
-/*-<a href="qh-set.htm#TOC"
- >--------------------------------------</a><a name="FOREACHsetelementreverse_">-</a>
-
- FOREACHsetelementreverse_(type, set, variable)-
- define FOREACH iterator in reverse order
-
- declare:
- assumes *variable and **variablep are declared
- also declare 'int variabletemp'
-
- each iteration:
- variable is set element
-
- to repeat an element:
- variabletemp++; / *repeat* /
-
- at exit:
- variable is NULL
-
- example:
- #define FOREACHvertexreverse_( vertices ) FOREACHsetelementreverse_( vertexT, vertices, vertex )
-
- notes:
- use FOREACHsetelementreverse12_() to reverse first two elements
- WARNING: needs braces if nested inside another FOREACH
-*/
-#define FOREACHsetelementreverse_(type, set, variable) \
- if (((variable= NULL), set)) for(\
- variable##temp= qh_setsize(set)-1, variable= qh_setlast(set);\
- variable; variable= \
- ((--variable##temp >= 0) ? SETelemt_(set, variable##temp, type) : NULL))
-
-/*-<a href="qh-set.htm#TOC"
- >-----------------------------------</a><a name="FOREACHsetelementreverse12_">-</a>
-
- FOREACHsetelementreverse12_(type, set, variable)-
- define FOREACH iterator with e[1] and e[0] reversed
-
- declare:
- assumes *variable and **variablep are declared
-
- each iteration:
- variable is set element
- variablep is one after variable.
-
- to repeat an element:
- variablep--; / *repeat* /
-
- at exit:
- variable is NULL at end of loop
-
- example
- #define FOREACHvertexreverse12_( vertices ) FOREACHsetelementreverse12_( vertexT, vertices, vertex )
-
- notes:
- WARNING: needs braces if nested inside another FOREACH
-*/
-#define FOREACHsetelementreverse12_(type, set, variable) \
- if (((variable= NULL), set)) for(\
- variable##p= (type **)&((set)->e[1].p); \
- (variable= *variable##p); \
- variable##p == ((type **)&((set)->e[0].p))?variable##p += 2: \
- (variable##p == ((type **)&((set)->e[1].p))?variable##p--:variable##p++))
-
-/*-<a href="qh-set.htm#TOC"
- >-----------------------------------</a><a name="FOREACHelem_">-</a>
-
- FOREACHelem_( set )-
- iterate elements in a set
-
- declare:
- void *elem, *elemp;
-
- each iteration:
- elem is set element
- elemp is one beyond
-
- to repeat an element:
- elemp--; / *repeat* /
-
- at exit:
- elem == NULL at end of loop
-
- example:
- FOREACHelem_(set) {
-
- notes:
- WARNING: needs braces if nested inside another FOREACH
-*/
-#define FOREACHelem_(set) FOREACHsetelement_(void, set, elem)
-
-/*-<a href="qh-set.htm#TOC"
- >-----------------------------------</a><a name="FOREACHset_">-</a>
-
- FOREACHset_( set )-
- iterate a set of sets
-
- declare:
- setT *set, **setp;
-
- each iteration:
- set is set element
- setp is one beyond
-
- to repeat an element:
- setp--; / *repeat* /
-
- at exit:
- set == NULL at end of loop
-
- example
- FOREACHset_(sets) {
-
- notes:
- WARNING: needs braces if nested inside another FOREACH
-*/
-#define FOREACHset_(sets) FOREACHsetelement_(setT, sets, set)
-
-/*-<a href="qh-set.htm#TOC"
- >-----------------------------------------</a><a name="SETindex_">-</a>
-
- SETindex_( set, elem )
- return index of elem in set
-
- notes:
- for use with FOREACH iteration
-
- example:
- i= SETindex_(ridges, ridge)
-*/
-#define SETindex_(set, elem) ((void **)elem##p - (void **)&(set)->e[1].p)
-
-/*-<a href="qh-set.htm#TOC"
- >---------------------------------------</a><a name="SETref_">-</a>
-
- SETref_( elem )
- l.h.s. for modifying the current element in a FOREACH iteration
-
- example:
- SETref_(ridge)= anotherridge;
-*/
-#define SETref_(elem) (elem##p[-1])
-
-/*-<a href="qh-set.htm#TOC"
- >---------------------------------------</a><a name="SETelem_">-</a>
-
- SETelem_(set, n)
- return the n'th element of set
-
- notes:
- assumes that n is valid [0..size] and that set is defined
- use SETelemt_() for type cast
-*/
-#define SETelem_(set, n) ((set)->e[n].p)
-
-/*-<a href="qh-set.htm#TOC"
- >---------------------------------------</a><a name="SETelemt_">-</a>
-
- SETelemt_(set, n, type)
- return the n'th element of set as a type
-
- notes:
- assumes that n is valid [0..size] and that set is defined
-*/
-#define SETelemt_(set, n, type) ((type*)((set)->e[n].p))
-
-/*-<a href="qh-set.htm#TOC"
- >---------------------------------------</a><a name="SETelemaddr_">-</a>
-
- SETelemaddr_(set, n, type)
- return address of the n'th element of a set
-
- notes:
- assumes that n is valid [0..size] and set is defined
-*/
-#define SETelemaddr_(set, n, type) ((type **)(&((set)->e[n].p)))
-
-/*-<a href="qh-set.htm#TOC"
- >---------------------------------------</a><a name="SETfirst_">-</a>
-
- SETfirst_(set)
- return first element of set
-
-*/
-#define SETfirst_(set) ((set)->e[0].p)
-
-/*-<a href="qh-set.htm#TOC"
- >---------------------------------------</a><a name="SETfirstt_">-</a>
-
- SETfirstt_(set, type)
- return first element of set as a type
-
-*/
-#define SETfirstt_(set, type) ((type*)((set)->e[0].p))
-
-/*-<a href="qh-set.htm#TOC"
- >---------------------------------------</a><a name="SETsecond_">-</a>
-
- SETsecond_(set)
- return second element of set
-
-*/
-#define SETsecond_(set) ((set)->e[1].p)
-
-/*-<a href="qh-set.htm#TOC"
- >---------------------------------------</a><a name="SETsecondt_">-</a>
-
- SETsecondt_(set, type)
- return second element of set as a type
-*/
-#define SETsecondt_(set, type) ((type*)((set)->e[1].p))
-
-/*-<a href="qh-set.htm#TOC"
- >---------------------------------------</a><a name="SETaddr_">-</a>
-
- SETaddr_(set, type)
- return address of set's elements
-*/
-#define SETaddr_(set,type) ((type **)(&((set)->e[0].p)))
-
-/*-<a href="qh-set.htm#TOC"
- >---------------------------------------</a><a name="SETreturnsize_">-</a>
-
- SETreturnsize_(set, size)
- return size of a set
-
- notes:
- set must be defined
- use qh_setsize(set) unless speed is critical
-*/
-#define SETreturnsize_(set, size) (((size)= ((set)->e[(set)->maxsize].i))?(--(size)):((size)= (set)->maxsize))
-
-/*-<a href="qh-set.htm#TOC"
- >---------------------------------------</a><a name="SETempty_">-</a>
-
- SETempty_(set)
- return true (1) if set is empty
-
- notes:
- set may be NULL
-*/
-#define SETempty_(set) (!set || (SETfirst_(set) ? 0:1))
-
-/*-<a href="qh-set.htm#TOC"
- >---------------------------------------</a><a name="SETtruncate_">-</a>
-
- SETtruncate_(set)
- return first element of set
-
- see:
- qh_settruncate()
-
-*/
-#define SETtruncate_(set, size) {set->e[set->maxsize].i= size+1; /* maybe overwritten */ \
- set->e[size].p= NULL;}
-
-/*======= prototypes in alphabetical order ============*/
-
-void qh_setaddsorted(setT** setp, void* elem);
-void qh_setaddnth(setT** setp, int nth, void* newelem);
-void qh_setappend(setT** setp, void* elem);
-void qh_setappend_set(setT** setp, setT* setA);
-void qh_setappend2ndlast(setT** setp, void* elem);
-void qh_setcheck(setT* set, char* tname, int id);
-void qh_setcompact(setT* set);
-setT* qh_setcopy(setT* set, int extra);
-void* qh_setdel(setT* set, void* elem);
-void* qh_setdellast(setT* set);
-void* qh_setdelnth(setT* set, int nth);
-void* qh_setdelnthsorted(setT* set, int nth);
-void* qh_setdelsorted(setT* set, void* newelem);
-setT* qh_setduplicate(setT* set, int elemsize);
-int qh_setequal(setT* setA, setT* setB);
-int qh_setequal_except(setT* setA, void* skipelemA, setT* setB, void* skipelemB);
-int qh_setequal_skip(setT* setA, int skipA, setT* setB, int skipB);
-void qh_setfree(setT** set);
-void qh_setfree2(setT** setp, int elemsize);
-void qh_setfreelong(setT** set);
-int qh_setin(setT* set, void* setelem);
-int qh_setindex(setT* set, void* setelem);
-void qh_setlarger(setT** setp);
-void* qh_setlast(setT* set);
-setT* qh_setnew(int size);
-setT* qh_setnew_delnthsorted(setT* set, int size, int nth, int prepend);
-void qh_setprint(FILE* fp, char* string, setT* set);
-void qh_setreplace(setT* set, void* oldelem, void* newelem);
-int qh_setsize(setT* set);
-setT* qh_settemp(int setsize);
-void qh_settempfree(setT** set);
-void qh_settempfree_all(void);
-setT* qh_settemppop(void);
-void qh_settemppush(setT* set);
-void qh_settruncate(setT* set, int size);
-int qh_setunique(setT** set, void* elem);
-void qh_setzero(setT* set, int index, int size);
-
-
-#endif /* qhDEFset */
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/stat.h b/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/stat.h
deleted file mode 100644
index 6e7b0fc60e59b0b60d74d338425efe5812a1b554..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/stat.h
+++ /dev/null
@@ -1,528 +0,0 @@
-/*<html><pre> -<a href="qh-stat.htm"
->-------------------------------</a><a name="TOP">-</a>
-
- stat.h
- contains all statistics that are collected for qhull
-
- see qh-stat.htm and stat.c
-
- copyright (c) 1993-2003, The Geometry Center
-
- recompile qhull if you change this file
-
- Integer statistics are Z* while real statistics are W*.
-
- define maydebugx to call a routine at every statistic event
-
-*/
-
-#ifndef qhDEFstat
-#define qhDEFstat 1
-
-
-/*-<a href="qh-stat.htm#TOC"
- >-------------------------------</a><a name="KEEPstatistics">-</a>
-
- qh_KEEPstatistics
- 0 turns off statistic gathering (except zzdef/zzinc/zzadd/zzval/wwval)
-*/
-#ifndef qh_KEEPstatistics
-#define qh_KEEPstatistics 1
-#endif
-
-/*-<a href="qh-stat.htm#TOC"
- >-------------------------------</a><a name="statistics">-</a>
-
- Zxxx for integers, Wxxx for reals
-
- notes:
- be sure that all statistics are defined in stat.c
- otherwise initialization may core dump
- can pick up all statistics by:
- grep '[zw].*_[(][ZW]' *.c >z.x
- remove trailers with query">-</a>
- remove leaders with query-replace-regexp [ ^I]+ (
-*/
-#if qh_KEEPstatistics
-enum statistics /* alphabetical after Z/W */
-{
- Zacoplanar,
- Wacoplanarmax,
- Wacoplanartot,
- Zangle,
- Wangle,
- Wanglemax,
- Wanglemin,
- Zangletests,
- Wareatot,
- Wareamax,
- Wareamin,
- Zavoidold,
- Wavoidoldmax,
- Wavoidoldtot,
- Zback0,
- Zbestcentrum,
- Zbestdist,
- Zbestlower,
- Zbestlowerv,
- Zcentrumtests,
- Zcheckpart,
- Zcomputefurthest,
- Zconcave,
- Wconcavemax,
- Wconcavetot,
- Zconcaveridges,
- Zconcaveridge,
- Zcoplanar,
- Wcoplanarmax,
- Wcoplanartot,
- Zcoplanarangle,
- Zcoplanarcentrum,
- Zcoplanarhorizon,
- Zcoplanarinside,
- Zcoplanarpart,
- Zcoplanarridges,
- Wcpu,
- Zcyclefacetmax,
- Zcyclefacettot,
- Zcyclehorizon,
- Zcyclevertex,
- Zdegen,
- Wdegenmax,
- Wdegentot,
- Zdegenvertex,
- Zdelfacetdup,
- Zdelridge,
- Zdelvertextot,
- Zdelvertexmax,
- Zdetsimplex,
- Zdistcheck,
- Zdistconvex,
- Zdistgood,
- Zdistio,
- Zdistplane,
- Zdiststat,
- Zdistvertex,
- Zdistzero,
- Zdoc1,
- Zdoc2,
- Zdoc3,
- Zdoc4,
- Zdoc5,
- Zdoc6,
- Zdoc7,
- Zdoc8,
- Zdoc9,
- Zdoc10,
- Zdoc11,
- Zdoc12,
- Zdropdegen,
- Zdropneighbor,
- Zdupflip,
- Zduplicate,
- Wduplicatemax,
- Wduplicatetot,
- Zdupridge,
- Zdupsame,
- Zflipped,
- Wflippedmax,
- Wflippedtot,
- Zflippedfacets,
- Zfindbest,
- Zfindbestmax,
- Zfindbesttot,
- Zfindcoplanar,
- Zfindfail,
- Zfindhorizon,
- Zfindhorizonmax,
- Zfindhorizontot,
- Zfindjump,
- Zfindnew,
- Zfindnewmax,
- Zfindnewtot,
- Zfindnewjump,
- Zfindnewsharp,
- Zgauss0,
- Zgoodfacet,
- Zhashlookup,
- Zhashridge,
- Zhashridgetest,
- Zhashtests,
- Zinsidevisible,
- Zintersect,
- Zintersectfail,
- Zintersectmax,
- Zintersectnum,
- Zintersecttot,
- Zmaxneighbors,
- Wmaxout,
- Wmaxoutside,
- Zmaxridges,
- Zmaxvertex,
- Zmaxvertices,
- Zmaxvneighbors,
- Zmemfacets,
- Zmempoints,
- Zmemridges,
- Zmemvertices,
- Zmergeflipdup,
- Zmergehorizon,
- Zmergeinittot,
- Zmergeinitmax,
- Zmergeinittot2,
- Zmergeintohorizon,
- Zmergenew,
- Zmergesettot,
- Zmergesetmax,
- Zmergesettot2,
- Zmergesimplex,
- Zmergevertex,
- Wmindenom,
- Wminvertex,
- Zminnorm,
- Zmultiridge,
- Znearlysingular,
- Zneighbor,
- Wnewbalance,
- Wnewbalance2,
- Znewfacettot,
- Znewfacetmax,
- Znewvertex,
- Wnewvertex,
- Wnewvertexmax,
- Znoarea,
- Znonsimplicial,
- Znowsimplicial,
- Znotgood,
- Znotgoodnew,
- Znotmax,
- Znumfacets,
- Znummergemax,
- Znummergetot,
- Znumneighbors,
- Znumridges,
- Znumvertices,
- Znumvisibility,
- Znumvneighbors,
- Zonehorizon,
- Zpartangle,
- Zpartcoplanar,
- Zpartflip,
- Zparthorizon,
- Zpartinside,
- Zpartition,
- Zpartitionall,
- Zpartnear,
- Zpbalance,
- Wpbalance,
- Wpbalance2,
- Zpostfacets,
- Zpremergetot,
- Zprocessed,
- Zremvertex,
- Zremvertexdel,
- Zrenameall,
- Zrenamepinch,
- Zrenameshare,
- Zretry,
- Wretrymax,
- Zridge,
- Wridge,
- Wridgemax,
- Zridge0,
- Wridge0,
- Wridge0max,
- Zridgemid,
- Wridgemid,
- Wridgemidmax,
- Zridgeok,
- Wridgeok,
- Wridgeokmax,
- Zsearchpoints,
- Zsetplane,
- Ztestvneighbor,
- Ztotcheck,
- Ztothorizon,
- Ztotmerge,
- Ztotpartcoplanar,
- Ztotpartition,
- Ztotridges,
- Ztotvertices,
- Ztotvisible,
- Ztricoplanar,
- Ztricoplanarmax,
- Ztricoplanartot,
- Ztridegen,
- Ztrimirror,
- Ztrinull,
- Wvertexmax,
- Wvertexmin,
- Zvertexridge,
- Zvertexridgetot,
- Zvertexridgemax,
- Zvertices,
- Zvisfacettot,
- Zvisfacetmax,
- Zvisvertextot,
- Zvisvertexmax,
- Zwidefacet,
- Zwidevertices,
- ZEND
-};
-
-/*-<a href="qh-stat.htm#TOC"
- >-------------------------------</a><a name="ZZstat">-</a>
-
- Zxxx/Wxxx statistics that remain defined if qh_KEEPstatistics=0
-
- notes:
- be sure to use zzdef, zzinc, etc. with these statistics (no double checking!)
-*/
-#else
-enum statistics /* for zzdef etc. macros */
-{
- Zback0,
- Zbestdist,
- Zcentrumtests,
- Zcheckpart,
- Zconcaveridges,
- Zcoplanarhorizon,
- Zcoplanarpart,
- Zcoplanarridges,
- Zcyclefacettot,
- Zcyclehorizon,
- Zdelvertextot,
- Zdistcheck,
- Zdistconvex,
- Zdistzero,
- Zdoc1,
- Zdoc2,
- Zdoc3,
- Zdoc11,
- Zflippedfacets,
- Zgauss0,
- Zminnorm,
- Zmultiridge,
- Znearlysingular,
- Wnewvertexmax,
- Znumvisibility,
- Zpartcoplanar,
- Zpartition,
- Zpartitionall,
- Zprocessed,
- Zretry,
- Zridge,
- Wridge,
- Wridgemax,
- Zridge0,
- Wridge0,
- Wridge0max,
- Zridgemid,
- Wridgemid,
- Wridgemidmax,
- Zridgeok,
- Wridgeok,
- Wridgeokmax,
- Zsetplane,
- Ztotmerge,
- ZEND
-};
-#endif
-
-/*-<a href="qh-stat.htm#TOC"
- >-------------------------------</a><a name="ztype">-</a>
-
- ztype
- the type of a statistic sets its initial value.
-
- notes:
- The type should be the same as the macro for collecting the statistic
-*/
-enum ztypes {zdoc, zinc, zadd, zmax, zmin, ZTYPEreal, wadd, wmax, wmin, ZTYPEend};
-
-/*========== macros and constants =============*/
-
-/*-<a href="qh-stat.htm#TOC"
- >--------------------------------</a><a name="MAYdebugx">-</a>
-
- MAYdebugx
- define as maydebug() to be called frequently for error trapping
-*/
-#define MAYdebugx
-
-/*-<a href="qh-stat.htm#TOC"
- >--------------------------------</a><a name="zdef_">-</a>
-
- zzdef_, zdef_( type, name, doc, -1)
- define a statistic (assumes 'qhstat.next= 0;')
-
- zdef_( type, name, doc, count)
- define an averaged statistic
- printed as name/count
-*/
-#define zzdef_(stype,name,string,cnt) qhstat id[qhstat next++]=name; \
- qhstat doc[name]= string; qhstat count[name]= cnt; qhstat type[name]= stype
-#if qh_KEEPstatistics
-#define zdef_(stype,name,string,cnt) qhstat id[qhstat next++]=name; \
- qhstat doc[name]= string; qhstat count[name]= cnt; qhstat type[name]= stype
-#else
-#define zdef_(type,name,doc,count)
-#endif
-
-/*-<a href="qh-stat.htm#TOC"
- >--------------------------------</a><a name="zinc_">-</a>
-
- zzinc_( name ), zinc_( name)
- increment an integer statistic
-*/
-#define zzinc_(id) {MAYdebugx; qhstat stats[id].i++;}
-#if qh_KEEPstatistics
-#define zinc_(id) {MAYdebugx; qhstat stats[id].i++;}
-#else
-#define zinc_(id) {}
-#endif
-
-/*-<a href="qh-stat.htm#TOC"
- >--------------------------------</a><a name="zadd_">-</a>
-
- zzadd_( name, value ), zadd_( name, value ), wadd_( name, value )
- add value to an integer or real statistic
-*/
-#define zzadd_(id, val) {MAYdebugx; qhstat stats[id].i += (val);}
-#define wwadd_(id, val) {MAYdebugx; qhstat stats[id].r += (val);}
-#if qh_KEEPstatistics
-#define zadd_(id, val) {MAYdebugx; qhstat stats[id].i += (val);}
-#define wadd_(id, val) {MAYdebugx; qhstat stats[id].r += (val);}
-#else
-#define zadd_(id, val) {}
-#define wadd_(id, val) {}
-#endif
-
-/*-<a href="qh-stat.htm#TOC"
- >--------------------------------</a><a name="zval_">-</a>
-
- zzval_( name ), zval_( name ), wwval_( name )
- set or return value of a statistic
-*/
-#define zzval_(id) ((qhstat stats[id]).i)
-#define wwval_(id) ((qhstat stats[id]).r)
-#if qh_KEEPstatistics
-#define zval_(id) ((qhstat stats[id]).i)
-#define wval_(id) ((qhstat stats[id]).r)
-#else
-#define zval_(id) qhstat tempi
-#define wval_(id) qhstat tempr
-#endif
-
-/*-<a href="qh-stat.htm#TOC"
- >--------------------------------</a><a name="zmax_">-</a>
-
- zmax_( id, val ), wmax_( id, value )
- maximize id with val
-*/
-#define wwmax_(id, val) {MAYdebugx; maximize_(qhstat stats[id].r,(val));}
-#if qh_KEEPstatistics
-#define zmax_(id, val) {MAYdebugx; maximize_(qhstat stats[id].i,(val));}
-#define wmax_(id, val) {MAYdebugx; maximize_(qhstat stats[id].r,(val));}
-#else
-#define zmax_(id, val) {}
-#define wmax_(id, val) {}
-#endif
-
-/*-<a href="qh-stat.htm#TOC"
- >--------------------------------</a><a name="zmin_">-</a>
-
- zmin_( id, val ), wmin_( id, value )
- minimize id with val
-*/
-#if qh_KEEPstatistics
-#define zmin_(id, val) {MAYdebugx; minimize_(qhstat stats[id].i,(val));}
-#define wmin_(id, val) {MAYdebugx; minimize_(qhstat stats[id].r,(val));}
-#else
-#define zmin_(id, val) {}
-#define wmin_(id, val) {}
-#endif
-
-/*================== stat.h types ==============*/
-
-
-/*-<a href="qh-stat.htm#TOC"
- >--------------------------------</a><a name="intrealT">-</a>
-
- intrealT
- union of integer and real, used for statistics
-*/
-typedef union intrealT intrealT; /* union of int and realT */
-union intrealT
-{
- int i;
- realT r;
-};
-
-/*-<a href="qh-stat.htm#TOC"
- >--------------------------------</a><a name="qhstat">-</a>
-
- qhstat
- global data structure for statistics
-
- notes:
- access to qh_qhstat is via the "qhstat" macro. There are two choices
- qh_QHpointer = 1 access globals via a pointer
- enables qh_saveqhull() and qh_restoreqhull()
- = 0 qh_qhstat is a static data structure
- only one instance of qhull() can be active at a time
- default value
- qh_QHpointer is defined in qhull.h
-
- allocated in stat.c
-*/
-typedef struct qhstatT qhstatT;
-#if qh_QHpointer
-#define qhstat qh_qhstat->
-extern qhstatT* qh_qhstat;
-#else
-#define qhstat qh_qhstat.
-extern qhstatT qh_qhstat;
-#endif
-struct qhstatT
-{
- intrealT stats[ZEND]; /* integer and real statistics */
- unsigned char id[ZEND + 10]; /* id's in print order */
- char* doc[ZEND]; /* array of documentation strings */
- short int count[ZEND]; /* -1 if none, else index of count to use */
- char type[ZEND]; /* type, see ztypes above */
- char printed[ZEND]; /* true, if statistic has been printed */
- intrealT init[ZTYPEend]; /* initial values by types, set initstatistics */
-
- int next; /* next index for zdef_ */
- int precision; /* index for precision problems */
- int vridges; /* index for Voronoi ridges */
- int tempi;
- realT tempr;
-};
-
-/*========== function prototypes ===========*/
-
-void qh_allstatA(void);
-void qh_allstatB(void);
-void qh_allstatC(void);
-void qh_allstatD(void);
-void qh_allstatE(void);
-void qh_allstatE2(void);
-void qh_allstatF(void);
-void qh_allstatG(void);
-void qh_allstatH(void);
-void qh_allstatI(void);
-void qh_allstatistics(void);
-void qh_collectstatistics(void);
-void qh_freestatistics(void);
-void qh_initstatistics(void);
-boolT qh_newstats(int index, int* nextindex);
-boolT qh_nostatistic(int i);
-void qh_printallstatistics(FILE* fp, char* string);
-void qh_printstatistics(FILE* fp, char* string);
-void qh_printstatlevel(FILE* fp, int id, int start);
-void qh_printstats(FILE* fp, int index, int* nextindex);
-realT qh_stddev(int num, realT tot, realT tot2, realT* ave);
-
-#endif /* qhDEFstat */
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/user.h b/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/user.h
deleted file mode 100644
index 63ee9e5b77500cba8fbbc5ed2f4769d24b38d663..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/include/qhull/user.h
+++ /dev/null
@@ -1,762 +0,0 @@
-/*<html><pre> -<a href="qh-user.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- user.h
- user redefinable constants
-
- see qh-user.htm. see COPYING for copyright information.
-
- before reading any code, review qhull.h for data structure definitions and
- the "qh" macro.
-*/
-
-#ifndef qhDEFuser
-#define qhDEFuser 1
-
-/*============= data types and configuration macros ==========*/
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="realT">-</a>
-
- realT
- set the size of floating point numbers
-
- qh_REALdigits
- maximimum number of significant digits
-
- qh_REAL_1, qh_REAL_2n, qh_REAL_3n
- format strings for printf
-
- qh_REALmax, qh_REALmin
- maximum and minimum (near zero) values
-
- qh_REALepsilon
- machine roundoff. Maximum roundoff error for addition and multiplication.
-
- notes:
- Select whether to store floating point numbers in single precision (float)
- or double precision (double).
-
- Use 'float' to save about 8% in time and 25% in space. This is particularly
- help if high-d where convex hulls are space limited. Using 'float' also
- reduces the printed size of Qhull's output since numbers have 8 digits of
- precision.
-
- Use 'double' when greater arithmetic precision is needed. This is needed
- for Delaunay triangulations and Voronoi diagrams when you are not merging
- facets.
-
- If 'double' gives insufficient precision, your data probably includes
- degeneracies. If so you should use facet merging (done by default)
- or exact arithmetic (see imprecision section of manual, qh-impre.htm).
- You may also use option 'Po' to force output despite precision errors.
-
- You may use 'long double', but many format statements need to be changed
- and you may need a 'long double' square root routine. S. Grundmann
- (sg@eeiwzb.et.tu-dresden.de) has done this. He reports that the code runs
- much slower with little gain in precision.
-
- WARNING: on some machines, int f(){realT a= REALmax;return (a == REALmax);}
- returns False. Use (a > REALmax/2) instead of (a == REALmax).
-
- REALfloat = 1 all numbers are 'float' type
- = 0 all numbers are 'double' type
-*/
-#define REALfloat 0
-
-#if (REALfloat == 1)
-#define realT float
-#define REALmax FLT_MAX
-#define REALmin FLT_MIN
-#define REALepsilon FLT_EPSILON
-#define qh_REALdigits 8 /* maximum number of significant digits */
-#define qh_REAL_1 "%6.8g "
-#define qh_REAL_2n "%6.8g %6.8g\n"
-#define qh_REAL_3n "%6.8g %6.8g %6.8g\n"
-
-#elif (REALfloat == 0)
-#define realT double
-#define REALmax DBL_MAX
-#define REALmin DBL_MIN
-#define REALepsilon DBL_EPSILON
-#define qh_REALdigits 16 /* maximum number of significant digits */
-#define qh_REAL_1 "%6.16g "
-#define qh_REAL_2n "%6.16g %6.16g\n"
-#define qh_REAL_3n "%6.16g %6.16g %6.16g\n"
-
-#else
-#error unknown float option
-#endif
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="CPUclock">-</a>
-
- qh_CPUclock
- define the clock() function for reporting the total time spent by Qhull
- returns CPU ticks as a 'long int'
- qh_CPUclock is only used for reporting the total time spent by Qhull
-
- qh_SECticks
- the number of clock ticks per second
-
- notes:
- looks for CLOCKS_PER_SEC, CLOCKS_PER_SECOND, or assumes microseconds
- to define a custom clock, set qh_CLOCKtype to 0
-
- if your system does not use clock() to return CPU ticks, replace
- qh_CPUclock with the corresponding function. It is converted
- to unsigned long to prevent wrap-around during long runs.
-
-
- Set qh_CLOCKtype to
-
- 1 for CLOCKS_PER_SEC, CLOCKS_PER_SECOND, or microsecond
- Note: may fail if more than 1 hour elapsed time
-
- 2 use qh_clock() with POSIX times() (see global.c)
-*/
-#define qh_CLOCKtype 1 /* change to the desired number */
-
-#if (qh_CLOCKtype == 1)
-
-#if defined (CLOCKS_PER_SECOND)
-#define qh_CPUclock ((unsigned long)clock()) /* return CPU clock */
-#define qh_SECticks CLOCKS_PER_SECOND
-
-#elif defined (CLOCKS_PER_SEC)
-#define qh_CPUclock ((unsigned long)clock()) /* return CPU clock */
-#define qh_SECticks CLOCKS_PER_SEC
-
-#elif defined (CLK_TCK)
-#define qh_CPUclock ((unsigned long)clock()) /* return CPU clock */
-#define qh_SECticks CLK_TCK
-
-#else
-#define qh_CPUclock ((unsigned long)clock()) /* return CPU clock */
-#define qh_SECticks 1E6
-#endif
-
-#elif (qh_CLOCKtype == 2)
-#define qh_CPUclock qh_clock() /* return CPU clock */
-#define qh_SECticks 100
-
-#else /* qh_CLOCKtype == ? */
-#error unknown clock option
-#endif
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="RANDOM">-</a>
-
- qh_RANDOMtype, qh_RANDOMmax, qh_RANDOMseed
- define random number generator
-
- qh_RANDOMint generates a random integer between 0 and qh_RANDOMmax.
- qh_RANDOMseed sets the random number seed for qh_RANDOMint
-
- Set qh_RANDOMtype (default 5) to:
- 1 for random() with 31 bits (UCB)
- 2 for rand() with RAND_MAX or 15 bits (system 5)
- 3 for rand() with 31 bits (Sun)
- 4 for lrand48() with 31 bits (Solaris)
- 5 for qh_rand() with 31 bits (included with Qhull)
-
- notes:
- Random numbers are used by rbox to generate point sets. Random
- numbers are used by Qhull to rotate the input ('QRn' option),
- simulate a randomized algorithm ('Qr' option), and to simulate
- roundoff errors ('Rn' option).
-
- Random number generators differ between systems. Most systems provide
- rand() but the period varies. The period of rand() is not critical
- since qhull does not normally use random numbers.
-
- The default generator is Park & Miller's minimal standard random
- number generator [CACM 31:1195 '88]. It is included with Qhull.
-
- If qh_RANDOMmax is wrong, qhull will report a warning and Geomview
- output will likely be invisible.
-*/
-#define qh_RANDOMtype 5 /* *** change to the desired number *** */
-
-#if (qh_RANDOMtype == 1)
-#define qh_RANDOMmax ((realT)0x7fffffffUL) /* 31 bits, random()/MAX */
-#define qh_RANDOMint random()
-#define qh_RANDOMseed_(seed) srandom(seed);
-
-#elif (qh_RANDOMtype == 2)
-#ifdef RAND_MAX
-#define qh_RANDOMmax ((realT)RAND_MAX)
-#else
-#define qh_RANDOMmax ((realT)32767) /* 15 bits (System 5) */
-#endif
-#define qh_RANDOMint rand()
-#define qh_RANDOMseed_(seed) srand((unsigned)seed);
-
-#elif (qh_RANDOMtype == 3)
-#define qh_RANDOMmax ((realT)0x7fffffffUL) /* 31 bits, Sun */
-#define qh_RANDOMint rand()
-#define qh_RANDOMseed_(seed) srand((unsigned)seed);
-
-#elif (qh_RANDOMtype == 4)
-#define qh_RANDOMmax ((realT)0x7fffffffUL) /* 31 bits, lrand38()/MAX */
-#define qh_RANDOMint lrand48()
-#define qh_RANDOMseed_(seed) srand48(seed);
-
-#elif (qh_RANDOMtype == 5)
-#define qh_RANDOMmax ((realT)2147483646UL) /* 31 bits, qh_rand/MAX */
-#define qh_RANDOMint qh_rand()
-#define qh_RANDOMseed_(seed) qh_srand(seed);
-/* unlike rand(), never returns 0 */
-
-#else
-#error: unknown random option
-#endif
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="ORIENTclock">-</a>
-
- qh_ORIENTclock
- 0 for inward pointing normals by Geomview convention
-*/
-#define qh_ORIENTclock 0
-
-
-/*========= performance related constants =========*/
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="HASHfactor">-</a>
-
- qh_HASHfactor
- total hash slots / used hash slots. Must be at least 1.1.
-
- notes:
- =2 for at worst 50% occupancy for qh hash_table and normally 25% occupancy
-*/
-#define qh_HASHfactor 2
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="VERIFYdirect">-</a>
-
- qh_VERIFYdirect
- with 'Tv' verify all points against all facets if op count is smaller
-
- notes:
- if greater, calls qh_check_bestdist() instead
-*/
-#define qh_VERIFYdirect 1000000
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="INITIALsearch">-</a>
-
- qh_INITIALsearch
- if qh_INITIALmax, search points up to this dimension
-*/
-#define qh_INITIALsearch 6
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="INITIALmax">-</a>
-
- qh_INITIALmax
- if dim >= qh_INITIALmax, use min/max coordinate points for initial simplex
-
- notes:
- from points with non-zero determinants
- use option 'Qs' to override (much slower)
-*/
-#define qh_INITIALmax 8
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="JOGGLEdefault">-</a>
-
- qh_JOGGLEdefault
- default qh.JOGGLEmax is qh.DISTround * qh_JOGGLEdefault
-
- notes:
- rbox s r 100 | qhull QJ1e-15 QR0 generates 90% faults at distround 7e-16
- rbox s r 100 | qhull QJ1e-14 QR0 generates 70% faults
- rbox s r 100 | qhull QJ1e-13 QR0 generates 35% faults
- rbox s r 100 | qhull QJ1e-12 QR0 generates 8% faults
- rbox s r 100 | qhull QJ1e-11 QR0 generates 1% faults
- rbox s r 100 | qhull QJ1e-10 QR0 generates 0% faults
- rbox 1000 W0 | qhull QJ1e-12 QR0 generates 86% faults
- rbox 1000 W0 | qhull QJ1e-11 QR0 generates 20% faults
- rbox 1000 W0 | qhull QJ1e-10 QR0 generates 2% faults
- the later have about 20 points per facet, each of which may interfere
-
- pick a value large enough to avoid retries on most inputs
-*/
-#define qh_JOGGLEdefault 30000.0
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="JOGGLEincrease">-</a>
-
- qh_JOGGLEincrease
- factor to increase qh.JOGGLEmax on qh_JOGGLEretry or qh_JOGGLEagain
-*/
-#define qh_JOGGLEincrease 10.0
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="JOGGLEretry">-</a>
-
- qh_JOGGLEretry
- if ZZretry = qh_JOGGLEretry, increase qh.JOGGLEmax
-
- notes:
- try twice at the original value in case of bad luck the first time
-*/
-#define qh_JOGGLEretry 2
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="JOGGLEagain">-</a>
-
- qh_JOGGLEagain
- every following qh_JOGGLEagain, increase qh.JOGGLEmax
-
- notes:
- 1 is OK since it's already failed qh_JOGGLEretry times
-*/
-#define qh_JOGGLEagain 1
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="JOGGLEmaxincrease">-</a>
-
- qh_JOGGLEmaxincrease
- maximum qh.JOGGLEmax due to qh_JOGGLEincrease
- relative to qh.MAXwidth
-
- notes:
- qh.joggleinput will retry at this value until qh_JOGGLEmaxretry
-*/
-#define qh_JOGGLEmaxincrease 1e-2
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="JOGGLEmaxretry">-</a>
-
- qh_JOGGLEmaxretry
- stop after qh_JOGGLEmaxretry attempts
-*/
-#define qh_JOGGLEmaxretry 100
-
-/*========= memory constants =========*/
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="MEMalign">-</a>
-
- qh_MEMalign
- memory alignment for qh_meminitbuffers() in global.c
-
- notes:
- to avoid bus errors, memory allocation must consider alignment requirements.
- malloc() automatically takes care of alignment. Since mem.c manages
- its own memory, we need to explicitly specify alignment in
- qh_meminitbuffers().
-
- A safe choice is sizeof(double). sizeof(float) may be used if doubles
- do not occur in data structures and pointers are the same size. Be careful
- of machines (e.g., DEC Alpha) with large pointers.
-
- If using gcc, best alignment is
- #define qh_MEMalign fmax_(__alignof__(realT),__alignof__(void *))
-*/
-#define qh_MEMalign fmax_(sizeof(realT), sizeof(void *))
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="MEMbufsize">-</a>
-
- qh_MEMbufsize
- size of additional memory buffers
-
- notes:
- used for qh_meminitbuffers() in global.c
-*/
-#define qh_MEMbufsize 0x10000 /* allocate 64K memory buffers */
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="MEMinitbuf">-</a>
-
- qh_MEMinitbuf
- size of initial memory buffer
-
- notes:
- use for qh_meminitbuffers() in global.c
-*/
-#define qh_MEMinitbuf 0x20000 /* initially allocate 128K buffer */
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="INFINITE">-</a>
-
- qh_INFINITE
- on output, indicates Voronoi center at infinity
-*/
-#define qh_INFINITE -10.101
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="DEFAULTbox">-</a>
-
- qh_DEFAULTbox
- default box size (Geomview expects 0.5)
-*/
-#define qh_DEFAULTbox 0.5
-
-/*======= conditional compilation ============================*/
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="compiler">-</a>
-
- __cplusplus
- defined by C++ compilers
-
- __MSC_VER
- defined by Microsoft Visual C++
-
- __MWERKS__ && __POWERPC__
- defined by Metrowerks when compiling for the Power Macintosh
-
- __STDC__
- defined for strict ANSI C
-*/
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="COMPUTEfurthest">-</a>
-
- qh_COMPUTEfurthest
- compute furthest distance to an outside point instead of storing it with the facet
- =1 to compute furthest
-
- notes:
- computing furthest saves memory but costs time
- about 40% more distance tests for partitioning
- removes facet->furthestdist
-*/
-#define qh_COMPUTEfurthest 0
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="KEEPstatistics">-</a>
-
- qh_KEEPstatistics
- =0 removes most of statistic gathering and reporting
-
- notes:
- if 0, code size is reduced by about 4%.
-*/
-#define qh_KEEPstatistics 1
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="MAXoutside">-</a>
-
- qh_MAXoutside
- record outer plane for each facet
- =1 to record facet->maxoutside
-
- notes:
- this takes a realT per facet and slightly slows down qhull
- it produces better outer planes for geomview output
-*/
-#define qh_MAXoutside 1
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="NOmerge">-</a>
-
- qh_NOmerge
- disables facet merging if defined
-
- notes:
- This saves about 10% space.
-
- Unless 'Q0'
- qh_NOmerge sets 'QJ' to avoid precision errors
-
- #define qh_NOmerge
-
- see:
- <a href="mem.h#NOmem">qh_NOmem</a> in mem.c
-
- see user.c/user_eg.c for removing io.o
-*/
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="NOtrace">-</a>
-
- qh_NOtrace
- no tracing if defined
-
- notes:
- This saves about 5% space.
-
- #define qh_NOtrace
-*/
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="QHpointer">-</a>
-
- qh_QHpointer
- access global data with pointer or static structure
-
- qh_QHpointer = 1 access globals via a pointer to allocated memory
- enables qh_saveqhull() and qh_restoreqhull()
- costs about 8% in time and 2% in space
-
- = 0 qh_qh and qh_qhstat are static data structures
- only one instance of qhull() can be active at a time
- default value
-
- notes:
- all global variables for qhull are in qh, qhmem, and qhstat
- qh is defined in qhull.h
- qhmem is defined in mem.h
- qhstat is defined in stat.h
-
- see:
- user_eg.c for an example
-*/
-#define qh_QHpointer 0
-#if 0 /* sample code */
-qhT* oldqhA, *oldqhB;
-
-exitcode = qh_new_qhull(dim, numpoints, points, ismalloc,
- flags, outfile, errfile);
-/* use results from first call to qh_new_qhull */
-oldqhA = qh_save_qhull();
-exitcode = qh_new_qhull(dimB, numpointsB, pointsB, ismalloc,
- flags, outfile, errfile);
-/* use results from second call to qh_new_qhull */
-oldqhB = qh_save_qhull();
-qh_restore_qhull(&oldqhA);
-/* use results from first call to qh_new_qhull */
-qh_freeqhull(qh_ALL); /* frees all memory used by first call */
-qh_restore_qhull(&oldqhB);
-/* use results from second call to qh_new_qhull */
-qh_freeqhull(!qh_ALL); /* frees long memory used by second call */
-qh_memfreeshort(&curlong, &totlong); /* frees short memory and memory allocator */
-#endif
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="QUICKhelp">-</a>
-
- qh_QUICKhelp
- =1 to use abbreviated help messages, e.g., for degenerate inputs
-*/
-#define qh_QUICKhelp 0
-
-/* ============ -merge constants- ====================
-
- These constants effect facet merging. You probably will not need
- to modify these. They effect the performance of facet merging.
-*/
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="DIMmergeVertex">-</a>
-
- qh_DIMmergeVertex
- max dimension for vertex merging (it is not effective in high-d)
-*/
-#define qh_DIMmergeVertex 6
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="DIMreduceBuild">-</a>
-
- qh_DIMreduceBuild
- max dimension for vertex reduction during build (slow in high-d)
-*/
-#define qh_DIMreduceBuild 5
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="BESTcentrum">-</a>
-
- qh_BESTcentrum
- if > 2*dim+n vertices, qh_findbestneighbor() tests centrums (faster)
- else, qh_findbestneighbor() tests all vertices (much better merges)
-
- qh_BESTcentrum2
- if qh_BESTcentrum2 * DIM3 + BESTcentrum < #vertices tests centrums
-*/
-#define qh_BESTcentrum 20
-#define qh_BESTcentrum2 2
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="BESTnonconvex">-</a>
-
- qh_BESTnonconvex
- if > dim+n neighbors, qh_findbestneighbor() tests nonconvex ridges.
-
- notes:
- It is needed because qh_findbestneighbor is slow for large facets
-*/
-#define qh_BESTnonconvex 15
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="MAXnewmerges">-</a>
-
- qh_MAXnewmerges
- if >n newmerges, qh_merge_nonconvex() calls qh_reducevertices_centrums.
-
- notes:
- It is needed because postmerge can merge many facets at once
-*/
-#define qh_MAXnewmerges 2
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="MAXnewcentrum">-</a>
-
- qh_MAXnewcentrum
- if <= dim+n vertices (n approximates the number of merges),
- reset the centrum in qh_updatetested() and qh_mergecycle_facets()
-
- notes:
- needed to reduce cost and because centrums may move too much if
- many vertices in high-d
-*/
-#define qh_MAXnewcentrum 5
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="COPLANARratio">-</a>
-
- qh_COPLANARratio
- for 3-d+ merging, qh.MINvisible is n*premerge_centrum
-
- notes:
- for non-merging, it's DISTround
-*/
-#define qh_COPLANARratio 3
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="DISToutside">-</a>
-
- qh_DISToutside
- When is a point clearly outside of a facet?
- Stops search in qh_findbestnew or qh_partitionall
- qh_findbest uses qh.MINoutside since since it is only called if no merges.
-
- notes:
- 'Qf' always searches for best facet
- if !qh.MERGING, same as qh.MINoutside.
- if qh_USEfindbestnew, increase value since neighboring facets may be ill-behaved
- [Note: Zdelvertextot occurs normally with interior points]
- RBOX 1000 s Z1 G1e-13 t1001188774 | QHULL Tv
- When there is a sharp edge, need to move points to a
- clearly good facet; otherwise may be lost in another partitioning.
- if too big then O(n^2) behavior for partitioning in cone
- if very small then important points not processed
- Needed in qh_partitionall for
- RBOX 1000 s Z1 G1e-13 t1001032651 | QHULL Tv
- Needed in qh_findbestnew for many instances of
- RBOX 1000 s Z1 G1e-13 t | QHULL Tv
-
- See:
- qh_DISToutside -- when is a point clearly outside of a facet
- qh_SEARCHdist -- when is facet coplanar with the best facet?
- qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
-*/
-#define qh_DISToutside ((qh_USEfindbestnew ? 2 : 1) * \
- fmax_((qh MERGING ? 2 : 1)*qh MINoutside, qh max_outside))
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="RATIOnearinside">-</a>
-
- qh_RATIOnearinside
- ratio of qh.NEARinside to qh.ONEmerge for retaining inside points for
- qh_check_maxout().
-
- notes:
- This is overkill since do not know the correct value.
- It effects whether 'Qc' reports all coplanar points
- Not used for 'd' since non-extreme points are coplanar
-*/
-#define qh_RATIOnearinside 5
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="SEARCHdist">-</a>
-
- qh_SEARCHdist
- When is a facet coplanar with the best facet?
- qh_findbesthorizon: all coplanar facets of the best facet need to be searched.
-
- See:
- qh_DISToutside -- when is a point clearly outside of a facet
- qh_SEARCHdist -- when is facet coplanar with the best facet?
- qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
-*/
-#define qh_SEARCHdist ((qh_USEfindbestnew ? 2 : 1) * \
- (qh max_outside + 2 * qh DISTround + fmax_( qh MINvisible, qh MAXcoplanar)));
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="USEfindbestnew">-</a>
-
- qh_USEfindbestnew
- Always use qh_findbestnew for qh_partitionpoint, otherwise use
- qh_findbestnew if merged new facet or sharpnewfacets.
-
- See:
- qh_DISToutside -- when is a point clearly outside of a facet
- qh_SEARCHdist -- when is facet coplanar with the best facet?
- qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
-*/
-#define qh_USEfindbestnew (zzval_(Ztotmerge) > 50)
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="WIDEcoplanar">-</a>
-
- qh_WIDEcoplanar
- n*MAXcoplanar or n*MINvisible for a WIDEfacet
-
- if vertex is further than qh.WIDEfacet from the hyperplane
- then its ridges are not counted in computing the area, and
- the facet's centrum is frozen.
-
- notes:
- qh.WIDEfacet= max(qh.MAXoutside,qh_WIDEcoplanar*qh.MAXcoplanar,
- qh_WIDEcoplanar * qh.MINvisible);
-*/
-#define qh_WIDEcoplanar 6
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="MAXnarrow">-</a>
-
- qh_MAXnarrow
- max. cosine in initial hull that sets qh.NARROWhull
-
- notes:
- If qh.NARROWhull, the initial partition does not make
- coplanar points. If narrow, a coplanar point can be
- coplanar to two facets of opposite orientations and
- distant from the exact convex hull.
-
- Conservative estimate. Don't actually see problems until it is -1.0
-*/
-#define qh_MAXnarrow -0.99999999
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="WARNnarrow">-</a>
-
- qh_WARNnarrow
- max. cosine in initial hull to warn about qh.NARROWhull
-
- notes:
- this is a conservative estimate.
- Don't actually see problems until it is -1.0. See qh-impre.htm
-*/
-#define qh_WARNnarrow -0.999999999999999
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="ZEROdelaunay">-</a>
-
- qh_ZEROdelaunay
- a zero Delaunay facet occurs for input sites coplanar with their convex hull
- the last normal coefficient of a zero Delaunay facet is within
- qh_ZEROdelaunay * qh.ANGLEround of 0
-
- notes:
- qh_ZEROdelaunay does not allow for joggled input ('QJ').
-
- You can avoid zero Delaunay facets by surrounding the input with a box.
-
- Use option 'PDk:-n' to explicitly define zero Delaunay facets
- k= dimension of input sites (e.g., 3 for 3-d Delaunay triangulation)
- n= the cutoff for zero Delaunay facets (e.g., 'PD3:-1e-12')
-*/
-#define qh_ZEROdelaunay 2
-
-#endif /* qh_DEFuser */
-
-
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/index.htm b/GraspPlanning/ExternalDependencies/qhull-2003.1/index.htm
deleted file mode 100644
index b00b715c793df145828d49a037b79cb2fd0283b0..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/index.htm
+++ /dev/null
@@ -1,246 +0,0 @@
-<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
-<html>
-
-<head>
-<title>Qhull for Convex Hull, Delaunay Triangulation, Voronoi Diagram, and Halfspace Intersection about a Point</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<b>URL:</b> <a href="http://www.qhull.org">http://www.qhull.org</a>
-<br><b>To:</b>
-<a href="http://www.qhull.org/news">News</a>
-• <a href="http://www.qhull.org/download">Download</a>
-• <a href="http://citeseer.nj.nec.com/83502.html">CiteSeer</a>
-• <a href=http://images.google.com/images?q=qhull&num=100>Images</a>
-• <a href="html/index.htm#TOC">Manual</a>
-• <a href="http://www.qhull.org/html/qh-faq.htm">FAQ</a>
-• <a href="html/qh-quick.htm#programs">Programs</a>
-• <a href="html/qh-quick.htm#options">Options</a>
-</p>
-
-<hr>
-<!-- Main text of document -->
-<table>
-<tr><td valign=top>
- <h1>Qhull</h1>
- <a
- href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html"><img
- src="html/qh--cone.gif" alt="[CONE]" align="middle" width="100"
- height="100"></a>
-</td><td>
-Qhull computes convex hulls, Delaunay triangulations,
-halfspace intersections about a point, Voronoi diagrams, furthest-site Delaunay
-triangulations, and furthest-site Voronoi diagrams. It runs in
-2-d, 3-d, 4-d, and higher dimensions. It implements the Quickhull
-algorithm for computing the convex hull. Qhull handles roundoff
-errors from floating point arithmetic. It computes volumes,
-surface areas, and approximations to the convex hull.</p>
-
-<!-- duplicated in index.htm and html/index.htm -->
-<p>Qhull does <i>not</i> support constrained Delaunay
-triangulations, triangulation of non-convex surfaces, mesh
-generation of non-convex objects, or medium-sized inputs in 9-D
-and higher. </p>
-</td></tr></table>
-
-<hr>
-<ul>
- <li><a href="http://www.qhull.org/news">News</a> about Qhull </li>
- <li><a href="http://www.qhull.org/download">Download</a>
- Qhull</li>
- <li><a
- href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/welcome.html">Examples
- </a>of Qhull output </li>
- <li><a href=http://savannah.gnu.org/projects/qhull/>Qhull development</a> at Savannah
- <p>
- <li><a href="http://www.qhull.org/news/qhull-news.html#use">How</a> is Qhull used?</li>
- <li><a href="http://citeseer.nj.nec.com/context/86585/83502">CiteSeer</a> references to Qhull
-</p>
- <li><a href=http://www.google.com/search?as_q=qhull&num=100>Google</a> Qhull,
- Qhull <a href=http://images.google.com/images?q=qhull&num=100>Images</a>,
- Qhull in <a href=http://groups.google.com/groups?as_q=qhull&num=100&as_scoring=d>Newsgroups</a>,
- and <a href=http://www.googlism.com/who_is/q/qhull/>Who is</a> Qhull?
-
- <p>
- <li><a href=http://www.mathworks.com/>MATLAB</a> uses Qhull for their computational geometry functions: <a href=http://www.mathworks.com/access/helpdesk/help/techdoc/ref/convhulln.shtml>convhulln</a>
- <a href=http://www.mathworks.com/access/helpdesk/help/techdoc/ref/delaunayn.shtml>delaunayn</a>
- <a href=http://www.mathworks.com/access/helpdesk/help/techdoc/ref/griddata3.shtml>griddata3</a>
- <a href=http://www.mathworks.com/access/helpdesk/help/techdoc/ref/griddatan.shtml>griddatan</a>
- <a href=http://www.mathworks.com/access/helpdesk/help/techdoc/ref/tsearch.shtml>tsearch</a>
- <a href=http://www.mathworks.com/access/helpdesk/help/techdoc/ref/tsearchn.shtml>tsearchn</a>
- <a href=http://www.mathworks.com/access/helpdesk/help/techdoc/ref/voronoin.shtml>voronoin</a>. MATLAB R14 will upgrade to
- Qhull 2003.1 and triangulated output ('Qt').
- </li>
- <li><a href=http://www.octave.org/>GNU Octave</a> uses Qhull for their
- <a href=http://octave.sourceforge.net/index/analysis.html#Geometry>computational geometry functions</a>. Octave has partially upgraded
- to Qhull 2002.1 and triangulated output ('Qt').
- <li><a href=http://www.wolfram.com/products/mathematica/>Mathematica</a>'s Delaunay interface: <a href=http://www.mathsource.com/Content/Enhancements/Geometry/0211-251>qh-math</a>
- <li><a href=http://www.geomview.org>Geomview</a> for 3-D and 4-D visualization of Qhull output
-</ul>
-
-<p><b>Introduction</b>
-<ul>
- <li><a
- href="http://www.ifor.math.ethz.ch/staff/fukuda/polyfaq/polyfaq.html">Fukuda's
- introduction</a> to convex hulls, Delaunay
- triangulations, Voronoi diagrams, and linear programming</li>
- <li><a
- href="http://www.cse.unsw.edu.au/~lambert/java/3d/hull.html">Lambert's
- Java</a> visualization of convex hull algorithms </li>
- <li><a
- href="http://www.cs.sunysb.edu/~algorith/major_section/1.6.shtml">Stony
- Brook</a> Algorithm Repository, computational geometry</li>
-</ul>
-
-<p><b>Qhull Documentation and Support</b>
-<ul>
- <li><a href="html/index.htm">Manual</a> for Qhull and rbox
- <ul>
- <li><a href="html/qconvex.htm">qconvex</a> -- convex hull
- <li><a href="html/qdelaun.htm">qdelaunay</a> -- Delaunay triangulation
- <li><a href="html/qvoronoi.htm">qvoronoi</a> -- Voronoi diagram
- <li><a href="html/qhalf.htm">qhalf</a> -- halfspace intersection about a point
- <li><a href="html/rbox.htm">rbox</a> -- generate point distributions
- <li><a href=src/index.htm>Qhull functions</a>, macros, and data structures with source
- </ul>
- <li><a href="http://www.qhull.org/html/qh-faq.htm">Frequently</a> asked
- questions about Qhull</li>
- <li>Send e-mail to <a href=mailto:qhull@qhull.org>qhull@qhull.org</a> </li>
- <li>Report bugs to <a
- href="mailto:qhull_bug@qhull.org">qhull_bug@qhull.org</a>
-</ul>
-
-<p><b>Related URLs</b>
-<ul>
- <li><a href="http://www.geom.uiuc.edu/software/cglist">Amenta's directory</a> of
- computational geometry software </li>
-
- <li><a href=http://www.boost.org/libs/graph/doc/table_of_contents.html>BGL</a>
- Boost Graph Library provides C++ classes for graph data structures
-and algorithms,
- <li><a
- href="http://netlib.bell-labs.com/netlib/voronoi/hull.html">Clarkson's
- hull </a>program with exact arithmetic for convex hulls, Delaunay triangulations,
- Voronoi volumes, and alpha shapes. </li>
- <li><a href="http://compgeom.cs.uiuc.edu/~jeffe/compgeom/compgeom.html">Erickson's
- Computational</a> Geometry Pages and
- <a href="http://compgeom.cs.uiuc.edu/~jeffe/compgeom/code.html">Software</a>
- <li><a
- href="http://www.cs.mcgill.ca/~fukuda/soft/cdd_home/cdd.html">Fukuda's
- cdd</a> program for halfspace intersection and convex hulls</li>
- <li><a href="http://www.inf.ethz.ch/personal/gaertner/miniball.html">Gartner's
- Miniball</a> for fast and robust smallest enclosing balls (up to 20-d)
-
- <li><a href=http://directory.google.com/Top/Science/Math/Geometry/Computational_Geometry/Software/>Google's directory</a> for
- Science > Math > Geometry > Computational Geometry > Software
- <li><a href=http://www.algorithmic-solutions.com/enleda.htm>Leda</a>
-and <a href=http://www.cgal.org/>CGAL</a> libraries for writing computational
-geometry programs and other combinatorial algorithms
- <li><a href=http://www.magic-software.com>Magic Software</a> source code for computer
- graphics, image analysis, and numerical methods
- <li><a href=http://www.mathtools.net/>Mathtools.net</a> of scientific and engineering
- software
- <li><a href="http://www.andrew.cmu.edu/user/sowen/mesh.html">Owen's Meshing</a> Research Corner
- <li><a
- href="http://www-users.informatik.rwth-aachen.de/~roberts/meshgeneration.html">Schneiders'
- Finite Element</a> Mesh Generation page</li>
- <li><a href="http://www.cs.cmu.edu/~quake/triangle.html">Shewchuk's
- triangle </a>program for 2-d Delaunay</li>
- <li><a href=ftp://ftp.zib.de/pub/Packages/mathprog/index.html>Skorobohatyj's Mathprog@ZIB</a> for
- mathematical software
- <li><a href=http://www.voronoi.com>Voronoi Web Site</a> for all things Voronoi
-</ul>
-
-<p><b>FAQs and Newsgroups</b>
-<ul>
- <li><a
- href="http://exaflop.org/docs/cgafaq/">FAQ</a>
- for computer graphics algorithms
- (<a href="http://exaflop.org/docs/cgafaq/cga6.html">geometric</a> structures)
- </li>
- <li><a
- href="http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html">FAQ
- </a>for linear programming </li>
- <li><a href="news:comp.graphics.algorithms">Newsgroup</a>:
- comp.graphics.algorithms </li>
- <li><a href="news:comp.soft-sys.matlab">Newsgroup</a>:
- comp.soft-sys.matlab</li>
- <li><a href="news:sci.math.num-analysis">Newsgroup</a>:
- sci.math.num-analysis </li>
- <li><a href="news:sci.op-research">Newsgroup</a>:
- sci.op-research </li>
-</ul>
-</blockquote>
-<hr>
-
-<p>The program includes options for input transformations,
-randomization, tracing, multiple output formats, and execution
-statistics. The program can be called from within your
-application. </p>
-
-<p>You can view the results in 2-d, 3-d and 4-d with <a
-href="http://www.geomview.org">Geomview</a>. An alternative
-is <a href=http://www.kitware.com/vtk.html>VTK</a>.</p>
-
-<p>For an article about Qhull, download from <a
-href="http://citeseer.nj.nec.com/83502.html">CiteSeer</a>:
-</p>
-
-<blockquote>
- <p>Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., "The
- Quickhull algorithm for convex hulls," <i>ACM Trans. on
- Mathematical Software</i>, Dec 1996. <a
- href="http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p469-barber/">http://www.acm.org</a>;
- </p>
-</blockquote>
-
-<p>Abstract: </p>
-
-<blockquote>
- <p>The convex hull of a set of points is the smallest convex
- set that contains the points. This article presents a
- practical convex hull algorithm that combines the
- two-dimensional Quickhull Algorithm with the general
- dimension Beneath-Beyond Algorithm. It is similar to the
- randomized, incremental algorithms for convex hull and
- Delaunay triangulation. We provide empirical evidence that
- the algorithm runs faster when the input contains non-extreme
- points, and that it uses less memory. </p>
- <p>Computational geometry algorithms have traditionally
- assumed that input sets are well behaved. When an algorithm
- is implemented with floating point arithmetic, this
- assumption can lead to serious errors. We briefly describe a
- solution to this problem when computing the convex hull in
- two, three, or four dimensions. The output is a set of
- "thick" facets that contain all possible exact convex hulls
- of the input. A variation is effective in five or more
- dimensions. </p>
-</blockquote>
-<!-- Navigation links -->
-<hr>
-
-<p><b>Up:</b> <a href="http://www.geom.uiuc.edu/software/past-projects.html"><i>Past Software
-Projects of the Geometry Center</i></a> <br>
-<b>URL:</b> <a href="http://www.qhull.org">http://www.qhull.org</a>
-<br><b>To:</b>
-<a href="http://www.qhull.org/news">News</a>
-• <a href="http://www.qhull.org/download">Download</a>
-• <a href="http://citeseer.nj.nec.com/83502.html">CiteSeer</a>
-• <a href=http://images.google.com/images?q=qhull&num=100>Images</a>
-• <a href="html/index.htm#TOC">Manual</a>
-• <a href="http://www.qhull.org/html/qh-faq.htm">FAQ</a>
-• <a href="html/qh-quick.htm#programs">Programs</a>
-• <a href="html/qh-quick.htm#options">Options</a>
-<!-- GC common information --></p>
-
-<hr>
-
-<p><a href="http://www.geom.uiuc.edu/"><img src="html/qh--geom.gif" alt="[HOME]"
-align="middle"></a> <i>The Geometry Center Home Page</i> </p>
-
-<p>Comments to: <a href="mailto:qhull@qhull.org">qhull@qhull.org</a>
-<br>
-Created: May 17 1995 --- <!-- hhmts start -->
-</body>
-</html>
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/Changes.txt b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/Changes.txt
deleted file mode 100644
index 626008a6068791b2cd340deb97977bcaf2741094..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/Changes.txt
+++ /dev/null
@@ -1,1063 +0,0 @@
-
-.............This file lists all changes to qhull and rbox.....................
-
-qhull 2003.1 2003/12/30
-
-New Features:
- - Add Maple output ('FM') for 2-d and 3-d convex hulls [T. Abraham]
-
-Bug Fixes and Code Changes:
- - Fixed qh_findbest() for upperdelaunay facets w/o better, lower neighbors
- - For library users and some qhull users [A. Cutti, E. Milloti, K. Sun]
- - Preserved qhmem.ferr in qh_memfreeshort() for library users
- - Removed 'static' from qh_compare... for io.h and merge.h [V. Brumberg]
-
-Documentation:
- - Add warning to findDelaunay() and qh_in.htm about tricoplanar facets
- - Noted Edelsbrunner's Geometry & Topology for Mesh Generation [qh-impre.htm]
- - Noted Gartner's Miniball algorithm [qh_impre.htm]
- - Noted Veron and Leon's shape preserving simplification [qh_impre.htm]
-
-qhull 2003.1 2003/12/19
-
-Bug Fixes:
- - Reversed coordinate order for qh.ATinfinity in qh_projectinput [V. Brumberg]
- - This effects:
- - Qhull library 'd' or 'v' users with 'Qz' and unequal coordinate ranges.
- - qdelaunay/qvoronoi users with 'Qbk:0Bk:0', 'Qz', and unequal coordinate ranges
-
-Changes to code:
- - Replaced qh_VERSION with qh_version in global.c [B. Pearlmutter]
- The previous techniques were either clumsy or caused compiler errors
- - Removed unused variables from qh_findbest and qh_findbestnew [B. Pearlmutter]
- - Note that qh.TESTpoints was added in 2002.1 for tsearch implementation
-
-Changes to distribution:
- - Added Unix distribution including Debian files [R. Laboissiere]
- The previous Unix distribution is now the source distribution
- - Added rpm distribution [L. Mazet]
- - Investigated generation of Win32 dll. Need to define a C++ interface.
-
-Changes to documentation:
- - Moved Qhull to www.qhull.org (geom.umn.edu is not available)
- - The Geometry Center is archived at http://www.geom.uiuc.edu
- - Reviewed introduction to each program
- Triangulated output ('Qt') is more accurate than joggled input ('QJ')
- qdelaunay is 'qhull d Qbb' [C. Ulbrich]
- qvoronoi is 'qhull v Qbb'
- Added example of non-simplicial intersection to halfspace intersections
- - Added warning about using the Qhull library.
- - Added qhull timings to When to use Qhull [C. Ulbrich]
- - Reorganized the home page index and the manual index
- - Moved qh-home.htm to index.htm
-
-Changes to examples
- - Fixed options for eg/eg.t23.voronoi.imprecise [B. Pearlmutter]
-
-
-qhull 2002.1 2002/8/20
-
-Changes to distribution:
- - Set up savannah.gnu.org/projects/qhull/ [R. Laboissiere]
- - Set up www.thesa.com as a backup
- - Added qh-get.htm, a local copy of the download page
- - Added Visual C++ interface to Qhull, qhull_interface.cpp [K. Erleben]
- - Use HTTP instead of FTP for downloading Qhull
- - Renamed qhull-1.0.sit.hqx
-
-Bug fixes:
- - Fixed sign of coefficients for cdd halfspaces ('FD','Fd') [T. Abraham]
-
-Changes to code:
- - Replace qh_version with qh_VERSION in qhull.h.
- Allows shared libraries and single point of definition
- - Added qh.TESTpoints for future implementation of tsearch
-
-Changes to build
- - Makefile.txt works under cygwin
- - Added Make-config.sh to create a Debian build [R. Laboissiere]
- - Added .exe to Makefile.txt#clean.
- - In README, use -fno-strict-aliasing with gcc-2.95.1 [Karas, Krishnaswami]
- - Fixed chmod in Makefile.txt [B. Karas]
-
-Documentation updates
- - Documented input options for each program [A. Montesinos]
- - FAQ: "How to get the radii of the empty spheres for Voronoi vertices"
-
-URL updates:
- - Changed official URL from locate/qhull to software/qhull
- - Changed URLs from relative to absolute in qh-home.htm and qh-get.htm
- - Added URL for Newsgroup: comp.soft-sys.matlab
- - Added URL for GNU Octave
- - Added URLs for Google and Google Groups
- - Replaced qhull_mail.html and qhull_bug.html with mailto links.
- - Removed URL for Computational Geometry Tribune
- - Changed URL for locate/cglist to software/cglist
- - Used site relative links for qh-home.htm
-
-qhull 3.1 2001/10/04
-
-New features
- - Added option 'Qt' to triangulate non-simplicial facets
- - Added option 'TI file' to input data from file
- - Added option 'Q10' to prevent special processing for narrow distributions
- e.g., RBOX 1000 L100000 s G1e-6 t1001803691 | QHULL Tv Q10
- - Tried to compute Voronoi volumes ('Pv'). Requires dual face graph--not easy
- See Clarkson's hull program for code.
-
-Changes to options
- - Added numtricoplanars to 'Fs'. Number of good, triangulated facets for 'Qt'
- - Added Zdelvertextot to 'Fs'. If non-zero and Delaunay, input is degenerate
- - Qhull command ('FQ') may be repeated.
- - If 'TPn' and 'TWn' defined, trace the addition of point 'n'
- otherwise continue tracing (previously it stopped in 4-d)
- - Removed 'Ft' from qdelaunay. Use 'Qt o' or 'qhull d QJ Qt' instead.
- For non-simplicial regions, 'Ft' does not satisify the Delaunay property.
- - If 'Po' or 'TVn', qhull checks outer planes. Use 'Q5' to turn off.
- - If 'T4', print facet lists and check polygon after adding each point
-
-Corrections to code
- - rbox: allow 'c' and 'd' with 's r', meshes, etc.
- - qh_findbest: redesigned as directed search. qh_findbesthorizon for coplanar
- qh_findbest is faster for many distributions
- - qh_findbestnew: redesigned to search horizon of coplanar best newfacets
- needed for distributions with a sharp edge,
- e.g., rbox 1000 s Z1 G1e-13 | qhull Tv
- - qh_findbest/qh_findbestnew: search neighbors of better horizon facets
- was needed for RBOX 1000 s Z1 G1e-13 t996564279 | qhull Tv
- and RBOX 1000 s W1e-13 P0 t996547055 | QHULL d Qbb Qc Tv
- - qh_findbest with noupper: could return an upperdelaunay facet if dist>qh.MINoutside.
- - qh_findbestnew: allow facet->upperdelaunay if dist > qh.MINoutside
- - qh_partitioncoplanar: call qh_partitionpoint if outside and perpendicular
- for distributions with a sharp edge
- - qh_partitionvisible: report precision error if all newfacets degenerate.
- was needed for RBOX 1000 s W1e-13 t995138628 | QHULL d
- - qh_createsimplex: clears qh.num_visible, may be non-zero with 'TRn QJ'
-
-Changes to prompts, warnings, and statistics
- - For Delaunay & Voronoi, 's' reports deleted vertices due to facet merging.
- They were incorrectly reported as nearly incident points.
- - Warn if recompute centrum after constructing hull
- - Simplified narrow hull warning and print all digits of cosine.
- A narrow hull may lead to a point outside of the hull.
- - Print total vertices deleted instead of ave. per iteration (Zdelvertextot)
- - Improved tracing for qh_partitionpoint and qh_partitioncoplanar
- - Added number of distance tests for checking outer planes (qh_check_maxout)
- - Simplified "qhull precision error: Only n facets remain."
- - Included 'TRn' in the causes of a premature exit
-
-Changes to documentation
- - README.txt: Added quickstart instructions for Visual C++
- - rbox: Added example of edge of narrow lens, rbox 1000 L100000 s G1e-6
- - Added cross references between options 'o' and 'p'.
- - qh-eg.html: added examples comparing 'Qt', 'QJ', and neither 'Qt' nor 'QJ'
- eg.15a.surface, eg.15b.triangle, eg.17a.delaunay.2, etc.
- - Reorganized and enhanced discussion of precision problems in qh_impre.htm
- - Fixed spelling errors [K. Briggs]
- - Fixed link errors, validated HTML, and spell checked [HomeSite]
- - Removed unnecessary #TOP links
- - Added source links to the qh-quick.htm's header and footer
- - qh-geom.htm, qh-poly.htm: add links to Voronoi functions in io.c
- - src/index.htm: Added how to search qhull.h for qhull options
- - qvoronoi.htm/qdelaun.htm: 'Fc' and 'FN' includes deleted vertices
-
-Changes to URLs
- - Added http://www.voronoi.com and http://www.magic-software.com
-
-Changes to code
- - qh_qhull: if 'TVn' or 'TCn' do not call qh_check_maxout and qh_nearcoplanar
- - reviewed time profile. Qhull is slower. Optimized qh_findbestnew()
- - qh_addpoint: Added warning note about avoiding a local minimum
- - qh_checkpolygon: report qh.facet_next error if NARROWhull & dist>MINoutside
- - qh_findbest: renamed "newfacets" parameter to "isnewfacets" since it is boolT
- - qh_findbest/qh_findbestnew: testhorizon even if !MERGING
- Otherwise qhull c D6 | qhull Q0 Tv assigns coplanar points
- - qh_resetlists: add qh_RESETvisible for qh_triangulate
- - qh_findbest: search better facets first. Rewritten.
- - qh_findbest: increased minminsearch, always check coplanar facets.
- See: RBOX 1000 s Z1 G1e-13 t996564279 | QHULL Tv
- - qh_findbestnew: report precision error for deleted cones [rare event]
- e.g.: RBOX 1000 s W1e-13 P0 t1001034076 | QHULL d Qbb Qc Tv
- - qh_findbesthorizon: search horizon of qh.coplanarset. New.
- - qh_findbestsharp: replaced with qh_sharpnewfacets followed by qh_findbestnew
- - qh_partitionpoint, Delaunay sites can not be inside. Otherwise points may
- be outside upperDelaunay facets yet not near-inside Delaunay facets
- See: RBOX s 1000 t993602376 | QHULL C-1e-3 d Qbb FA Tv
- - qh_partitioncoplanar: call qh_findbest/qh_findbestnew with qh DELAUNAY
- - qh_printlists: format long lines
- - qh_printvertex: format long lines
- - user.h: tightened qh_WARNnarrow and qh_MAXnarrow. Do not see problems
- until they are -1.0.
- - user.h: defined qh_DISToutside, qh_SEARCHdist, and qh_USEfindbestnew
- - qh_checkfacet: in 3-d, allow #ridges > #vertices. Can get a vertex twice
- in a ridge list, e.g, RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv
-
-Changes to FAQ
- - Recommended use of triangulated output ('Qt')
-
-Changes to distribution
- - Recompiled in Visual C++ 5.0 with optimization (as was version 2.6)
- - q_test: Added bad cases for Qhull and tests for new features
-
-Changes to Qhull library
- - Added qh_triangulate() to poly2.c. It triangulates the output.
- - Added option 'Q11' to copy normals and recompute centrums for tricoplanar facets
- 'FP' may not print the nearest vertex for coplanar points
- Use option 'Q11' when adding points after qh_triangulate()
-
-qhull 3.0 2001/02/11
-
-Changes to distribution
- - added qconvex, qdelaunay, qhalf, and qvoronoi
- - added qhull-interface.cpp on calling Qhull from C++ [K. Erleben]
- - renamed to qhull3.0/.
- - added eg/, html/, and src/ directories
-
-Changes to URLs
- - MathLab6 qhull: convhulln, delaunayn, griddatan, tsearchn, vororoin [Z. You]
- - Wolfram Research wrote a Mathematica interface for qdelaunay [Hinton]
- - Geomview moved from www.geom.umn.edu to www.geomview.org [M. Phillips}
- - added URLs for tcsh and cygwin to README.txt
-
-Changes to documentation
- - reorganized table of contents and renamed qh-man.htm to index.htm
- - wrote program documentation, dropped qh-opt.htm and qh-optv.htm
- - added quick reference, qh-quick.htm
- - reorganized qh-rbox.htm and renamed it to rbox.htm
- - split up qh-c.htm for quick navigation
-
-Corrections to code
- - fixed type of arg for error message in qh_initqhull_globals [N. Max]
- - fixed incorrect initialization of qh MINdenom_1 for scalepoints
- - fixed drop dim for 'H Qbk:0Bk:0'. Added qh.feasible_point to qh_projectinput
- - qh_WARNnarrow is angle between facet normals. Negate for warning message.
- - statistics for Wangle/etc. concerns facet normals. Reworded [E. Voth]
- - fixed error message for 'FC v'
- - report cospherical points if Delaunay and error in qh_scalelast()
-
-Changes to code
- - turn on Pg if (QVn or QGn) and not (Qg or PG)
- - turn on Qc if format option 'Fc', 'FP', or 'Gp' (removes warning)
- - removed last good facet unless ONLYgood ('Qg').
- - added count of non-simplicial or merged facets to 'FS'
- - added count of non-simplicial facets to 's' (OK if #vertices==dim)
- - added Znonsimplicial and Znowsimplicial to 'Ts'
- - allow Mathematica output of dual polytope for halfspace intersection
- - added qh_checkflags to globals.c for multiple front ends
- - qh_initqhull_globals sets qh.MERGING if qh.MERGEexact
- - removed hashentryT. It is no longer used.
-
-Changes to prompts and warnings
- - reorganized prompts
- - reorganized synopsis for rbox.c
- - print warning if 'Fc' or 'FP' with 'd QJ'. Coincident points are unlikely.
- - ignore warning if options 'v i Pp'. qvoronoi users may need Delaunay tri.
- - reworded warning if 'Pg' and 'QVn' is not a vertex.
- - reworded warning for 'Qx Tv', qh_check_points() in poly2.c
- - if 'Pp', turn off warning for 'Qbb' without 'd' or 'v'
- - in qh_printsummary() of Voronoi and Delaunay, distinguish QVn, QGn, Pdn, PDn
-
-Changes to FAQ
- - added FAQ item for nearly flat Delaunay triangles [Z. You]
- - added FAQ item for area and volume [R. Konatham]
- - added FAQ item for Voronoi diagram of a square [J. Yong]
- - edited FAQ item on point location in Delaunay triangles [Z. You]
- - added FAQ item on nearly flat Delaunay triangles [Dehghani]
- - added FAQ item about halfspace intersection [V. Tyberghein]
- - added FAQ item for missing ridges [M. Schmidt]
- - added FAQ item about qh_call_qhull [R. Snyder]
- - added FAQ item about memory statistics [Masi]
- - added FAQ item on meshing non-convex objects
- - added FAQ item on MATLAB and Mathematica interface
-
-qhull 2.6 1999/04/19
- - fixed memory overwrite (no effect) in qh_initstatistics() [K. Ford]
- - added zdoc11 to qh-stat.h#ZZdef for !qh_KEEPstatistics [K. Ford]
- - enhanced qh_initqhull_globals() test of qh_RANDOMint and qh_RANDOMmax
- - added debugging option to always return qh_RANDOMmax from qh_rand()
- - fixed option 'Qr', qh_initialvertices(), to allow a broken qh_rand()
- fixed option 'Qr', qh_nextfurthest(), to allow narrow hulls
- Option 'Qr' simulates the random incremental algorithm for convex hulls
- - added note that qh.num_outside includes coplanar points for narrow hulls
- - added FAQ items for triangles/ridges of 3-d Delaunay triangulation[P. Kumar]
- - added FAQ item about on-line processing with the Qhull library [O. Skare]
- - changed name of option 'Error-roundoff' to 'Distance-roundoff'
-
-qhull 2.6 1998/12/30
- - for the unbounded rays of the Voronoi diagram, use a large box [Schmidt]
- e.g., 'rbox P4,4,4 P4,2,4 P2,4,4 P4,4,2 10 | qhull v Fv' fails for point 0
- while 'rbox P4,4,4 P4,2,4 P2,4,4 P4,4,2 10 c G5 | qhull v Fv' is OK.
- - fixed qh_new_qhull() to use outfile/errfile instead of stdout/stderr [Ford]
- - clarified COPYING.txt for use in other programs [Archer]
- - improved qh_readpoints() error message for incorrect point count.
- - added FAQ item for closest triangle to a point [Sminchisescu & Heijting]
- - added FAQ item for is a point outside of a facet [Beardsley]
- - added FAQ item for visiting facets of the Delaunay triangulation [Heijting]
- - added link to Erickson's Computational Geometry Software
- - added link to Sharman's HTML version of the comp.graphics.algorithms FAQ
- - added link to Owen's Meshing Research Corner
- - added note to 'd' about quadratic size of 'rbox 100 l | qhull d' [Kumar]
- - added 'about a point' to mentions of halfspace intersection
- - added request to qh-in.htm to compute largest empty circle [Hase]
- - the DOS window in Windows NT is better than the DOS window in Windows 95
- - removed obsolete qh_findfacet() from qh-c.htm [Sminchisescu]
-
-qhull 2.6 1998/8/12
- new and modified features
- - rbox: added option Mn,m,r to generate a rotated lattice or mesh
- - rbox: report error if more than one of 'l', 'x', 'L', 's', or 'M'
-
- Qhull library changes
- - added qh_new_qhull() to user.c for calling qhull() from a program [D. Zwick]
- rewrote user_eg.c to use qh_new_qhull(). Added qh_QHpointer example.
- - added qh_CLOCKtype 2 in user.h to call times() for CPU time [B. Hemkemeier]
- - renamed set.c/set.h to avoid conflict with STL's set.h [G. van den Bergen]
- can also use '#include <qhull/qhull_a.h>' for Qhull library
-
- fixed errors
- - fixed qh_init_B() to call qh_initqhull_mem() once only [D. Zwick]
- This only effects Qhull library users of qh_QHpointer.
- - fixed qh_mergecycle_all() to check for redundant vertices [J. Nagle]
- e.g., 'rbox M3,4 64 | qhull Qc' should report 8 vertices & 48 coplanars
- - fixed gmcoord initialization in qh_setfacetplane() for qh.RANDOMdist
- - turn off qh.RANDOMdist during qh_printfacetheader()
- - fixed error messages for unknown option flags
-
- documentation changes
- - added note to FAQ on the Voronoi diagram of cospherical points [H. Hase]
- - added note to 'Qu' on furthest-site Delaunay triangulation via convex hull
- - added note to 'QJ' about coplanar points on the convex hull of the input
- - added note that 'o' and 'FN' list Voronoi regions in site id order [Arvind]
- - added links to Fukuda's introduction to convex hulls, etc. [H. Hase]
- - added .c and .h source files to web distribution and qh-c.htm [J. Sands]
- - documented qh_ZEROdelaunay. Delaunay and Voronoi diagrams do not include
- facets that are coplanar with the convex hull of the input sites.
-
- modified code
- - replaced computed minnorm in qh_sethyperplane_det with distance test
- - removed 'qh rand_seed' since random number generator is independent of qhull
- - dropt 'qhull-PPC.sit.bin' from the distribution (out-of-date) [M. Harris]
-
-qhull 2.5 1998/5/4
-
- fixed errors
- - removed zero-area Delaunay triangles and furthest-site triangles [I. Beichl]
- Zero-area triangles occur for points coplanar with the input's convex hull.
- - replaced qh.MINnorm with computed minnorm in qh_sethyperplane_det [J. Nagle]
- qh.MINnorm was incorrect for the convex hull of the "teapot" example.
- Qhull runs 0-20% slower in 3-d and 4-d.
- - allow 'Qg' with furthest-site Delaunay triangulation (may be faster)
- - removed extra space in definition of FOREACHmerge_() for Alpha cc [R. LeRoy]
- - fixed innerouter type in qh_printvdiagram2 [does not effect code, R. Adams]
-
- documentation changes
- - to browse qh-c.htm, set MIME type of .c and .h files to text/html
- - added example of 3-d Delaunay triangulation to q-faq.htm
- - added Delaunay and Voronoi examples to qh-optv.htm
-
-qhull 2.5 1998/2/4
- - added option 'v Fi' for separating hyperplanes of bounded Voronoi regions
- - added option 'v Fo' for separating hyperplanes of unbounded Voronoi regions
- - option 'Pp' turns off the warning, "initial hull is narrow"
- - fixed partial, 3-d Voronoi diagrams (i.e., 'v Fv QVn Tc')
- - fixed missing statistics in qh_allstat* [T. Johnson]
- - rearranged qh_printvdiagram. Use qh_eachvoronoi to iterate Voronoi ridges.
- - added qh_check_points to qh-math.c
-
-qhull 2.5 1998/1/28
- - added option 'Fv' to print the Voronoi diagram
- - added rbox option 'x' to generate random points in a simplex
- - added rbox option 'y' to generate a simplex and random points
- - added rbox option 'On' to offset the output
- - add unpacking instructions to README.txt
- - updated discussion of forced output, 'Po'
- - sorted the options alphabetically
- - removed __STDC__ check from qhull.h for VisualC++
- - moved qh_markvoronoi from qh_printvoronoi and cleared facet->seen flags
- - added facet->seen2 flag for 'Fv'
-
-qhull 2.5 1998/1/16
- - fixed initialization of qh.last_low on restart of 'd QJ'
- - renamed qh_JOGGLEmax to qh_JOGGLEmaxincrease
- - updated URL for Fukuda's cdd program
-
-qhull 2.5 1998/1/12
-
-New or modified features
- - added option 'Fx' to print vertices by point id [G. Harris, T. McClendon]
- in 2-d, the vertices are printed in counter-clockwise order
- for Delaunay triangl., 'Fx' lists the extreme points of the input sites
- - added option 'QJ' to randomly joggle input instead of merging facets
- - added option 'TO file' to output results to a file. Needed for Windows95.
- - added option 'TRn' to rerun Qhull n times. Use to collect joggle statistics
-
-Corrections
- - fixed 2-d facet orientation for 'i' and 'o' outputs
- - for Mathematica 2.2 ('m') changed %10.8g to %16.8f [A. Zhaxybayev]
- - fixed incorrect warning for 'QV0 Qg' in qh_initbuild [B. Wythoff]
- - fixed unaccessible statistic if !qh_KEEPstatistics for Wnewvertexmax
- - fixed overestimate of qh ONEmerge for point sets outside of
- first quadrant and far from the origin
- - fixed overestimate of 'Qbb' for point sets far from the origin
- - fixed potential overestimate of qh DISTround under 'Qbb'
- - fixed 'p' printing coplanar points of unselected facets
- - fixed 'Ft' printing centrums unnecessarily in 2-d
-
-Changes to documentation
- - wrote internal design documentation (qh-c.htm)
- - started frequently asked questions (qh-faq.htm)
- - added a section on joggled input to qh-impre.htm
- - added joggle example to qh-eg.htm (eg.15.joggle)
- - changed q_eg to use 'QJ' instead of 'Q0' were appropriate
- - added an example to each of the main options
- - added examples to rbox.htm
- - added examples to the synopsis
- - added a reference to Mucke, et al ['96], Fast randomized point location ...
- - added code for printing Delaunay triangles to qh-in.htm [A. Tsui]
- - options 'Pdk' and 'PDk' do not drop on equality
-
-Improvements to the code
- - reviewed warning messages for Qhull options in qh_initflags
- - added warning to 's' if premature exit from 'TCn' or 'TVn'
- - 's' prints max distance above/below only if qh.MERGING
- - reduced maxoutside in qh_check_bestdist/qh_check_points for 'Rn'
- - in post-merging, rebuild centrums of large facets that become small
- - lowered cutoff for coplanar facets for ischeckmax/qh_findbest
- - removed qh_check_maxout for 'Wn Q0'
- - reset tracing after 'TPn' adds point in 4-d and higher
-
-Changes for the Qhull library
- - changed qh_setdelaunay to call qh_scalelast if used with 'Qbb' or 'QJ'
- Delaunay callers to qh_findbestfacet, qh_addpoint, or qh_findfacet_all
- should always use qh_setdelaunay as in user_eg.c
- - defined qh.outside_err to check points against a given epsilon [E. Voth]
- - added header to user_eg.c to avoid its incorporation into qhull [C. Begnis]
- - added qh_nearcoplanar() calls to user_eg.c
- only needed if use 'QJ'
- - expanded __STDC__ warning message in qhull.h [C. Begnis]
- - renamed qh maxmaxcoord to qh MAXabs_coord
- - replaced qh MAXlowcoord with qh MAXabs_coord
- - random seed ('QR-n') is reset in qh_initqhull_globals after testing
- - replaced 'FO' options "_max-coord/_min-coord" with "_max-width"/qh.MAXwidth
-
-Other changes to Qhull functions
- - report error for !bestfacet in qh_findbest (it shouldn't happen) [H. Meuret]
- - set newbest in qh_findbest only if bestfacet updated
- - renamed facet parameter for qh_findbest
- - added maxdist argument to qh_checkpoint
- - moved 'FO' output after qh_partitionall
- - separated qh_initbuild from qh_qhull
- - reinitialize globals modified by qh_buildhull
- - moved initialization of qh.GOODvertexp & qh.GOODpointp to qh_initbuild
- - separated qh_nearcoplanar from qh_check_maxout
- - separated qh_geomplanes from qh_printfacet2geom, etc.
- - separated qh_freebuild from qh_freeqhull
- - separated qh_outerinner from io.c to return outer and inner planes
- - separated qh_distround and qh_detroundoff from qh_maxmin
-
-
-qhull 2.4 97/4/2
-
-New or modified features
- - made 'C-0' and 'Qx' default options. Use 'Q0' to not handle roundoff errors
- - removed point-at-infinity from Delaunay/Voronoi.
- you no longer need to use 'Qu PDk'
- - added 'Qz' to add a point-at-infinity to Delaunay and Voronoi constructions
- - added published version of qhull article in ACM Trans Math Software
- - ported qhull to Windows95 under Visual C++ and Borland C++
- - added 'Ft' for triangulation by adding the centrums of non-simplicial facets
- - added 'Gt' to display 3-d Delaunay triangulations with a transparent hull
- - changed definition of coplanar point in output to qh min_vertex (see 'Qc')
- it was qh MAXcoplanar ('Un') [could make vertices non-coplanar]
- - automatically set 'Qi' for options 'd Qc' and 'v Qc'.
- - reworded summary ('s') for Delaunay/Voronoi/halfspace.
- use 'Fs' and 'FS' for summary statistics.
- - for summary 's' of Delaunay/Voronoi, display number of coplanars for facets
- if none, display total number of coplanars (i.e., non-vertices)
- - input comment is first non-numeric text (previously limited to header)
- - added input warning if use 'Qbb' without 'd' or 'v'
- - 'Q3' can not be followed with a numeric option
-
-Corrections
- - fixed qh_partitioncoplanar() to not drop interior points if 'Qi' is used
- - fixed 'FP d' to report distance in point set instead of paraboloid
- - fixed qh_findbest() to search all coplanar facets for qh_check_maxout()
-
-Changes to documentation
- - added example eg.17f.delaunay.3 to show a triangulation of cospherical sites
- - split up qh-opt.htm into multiple pieces
- - split off qh-in.htm for Qhull internals
- - renamed .html files to .htm for Windows95
- - rewrote qh-optv.htm on Delaunay triangulation and Voronoi vertices
- - added 'man' pages qhull.txt and rbox.txt. These list all the options
- - removed 'txt' versions of html files
- - added note to 'PDk' about avoiding a 'd' option immediately after a float
- - under option 'd', display the triangulation with 'GrD3', not 'GnrD3'
-
-Changes to the Qhull library
- - added 'format' argument to qh_printfacetNvertex_nonsimplicial() in io.c
- - removed C++ type errors [J. Stern, S. Marino]
- - created SETelemt, SETfirstt, etc. for specifying data types.
- - use SETelem,etc. for assignments.
- - changed setT.maxsize to 'int' to prevent type conversion warnings
- - changed FOREACH.. to a comma expression for better code and less warning
- - changed qh.vertex_visit and .visit_id to unsigned int to prevent warnings
- - changed clock() to qh_CPUclock (user.h)
- - qh_init_B() and qh_readpoints() do not set qh.ATinfinity for Delaunay tri.
- - qh_setvoronoi_all() sets upper Delaunay facets if qh.UPPERdelaunay is set
- - qh_nearvertex() returns distance in dim-1 for qh.DELAUNAY
- - removed MSDOS path from qhull_command. Spaces in Win95 tripped qh_setflags
- - removed memory.h from qhull_a.h. memset,etc. should be in strings.h
- - split qh_prompt into pieces for Visual C++
- - added note to qh_addpoint that coordinates can not be deallocated
- - added Baker '89 to constrained Delaunay diagrams under Enhancements
- please let me know if you try this
- - added request for unbounded Voronoi rays to Enhancements
- please let me know if you try this
-
-qhull V2.3 96/6/5
- - fixed total area of Delaunay triangulation. [A. Enge]
- It should ignore facets on the upper-envelope.
- - if 'd Qu FA', the total area is summed over the upper-Delaunay triangles
- - fixed sign of area for Delaunay triangulations.
- - fixed cdd input format for Delaunay triangulation. [A. Enge]
- - for cdd input, allow feasible point for halfspaces.
- - warning if cdd output format for centrums, halfspace intersections, or OFF.
- - print '0' for area ('Fa') if area is not computed for a facet
- - option 'QR-n' sets random number seed to n without rotating input
- - fixed qh_findbest() to retest coplanar and flipped facets after a restart
- - for 'd Qu Ts' collects angle statistics for upper Delaunay facets
-
- Changes to the Qhull library
- - expanded user_eg.c for incremental constructions and Delaunay triangulation
- - added discussion of incremental construction to qh_man.html#library
- - WARNING: The default value of qh ATinfinity was changed from True to False.
- A new flag, qh UPPERdelaunay, was defined for 'Qu'.
- Please set qh ATinfinity if you explicitly add the point "at-infinity"
- Please set qh ATinfinity if you explicitly call qh_projectinput.
- Please set qh UPPERdelaunay if you explicitly cleared qh ATinfinity.
- Other users do not need to change their code.
- Now you can build a Delaunay triangulation without creating a point
- "at-infinity". This removes a potential, hard-to-understand error.
- qh_readpoints sets qh ATinfinity for options 'd' or 'v' without 'Qu'.
- qh_initB sets qh ATinfinity for qh PROJECTdelaunay w/o qh UPPERdelaunay.
- qh_projectinput adds a point "at-infinity" only if qh ATinfinity is set.
- - added qh_setdelaunay to geom2.c to project points to paraboloid
- - added qh_findbestfacet() to poly2.c to replace qh_findfacet()
- - removed procedure qh_findfacet(). It does not always work.
- - removed NULL option for facet in qh_addpoint(). It does not always work.
- - added noupper parameter to qh_findbest.
- - added search of upperdelaunay facets to qh_findbest()
- - allowed qh_findbest() to start with a flipped or upperdelaunay facet
- - removed qh_nonupper() -- it is no longer needed
- - allow space at end of options
- - fixed qh_projectinput for furthest-site Delaunay (qh PROJECTdelaunay 'd Qu')
- - added voids to procedure declarations with empty parameter lists
-
-qhull V2.3 96/3/25
- - fixed missing qh_check_maxout when coplanar points and no merged facets.
- - fixed qh_freeqhull/allmem (e.g., if qh_NOmem) [only custom code] [E. Voth]
- - fixed qh_freeqhull to free qh interior_point [E. Voth]
- - fixed main() to free all of memory if qh_NOmem. Include "mem.h" [E. Voth]
- - reset f.newcycle link in qh_mergecycle_all [E. Voth]
- - fixed false error if 'Tc', coplanar points, and a narrow hull
- - turn off 'Rn' when computing statistics, checking code, or tracing code
- - removed ={0} from global.c and stat.c to reduce compiler warnings
- - changed Makefile dependences to $(HFILES) for all but unix.o, set.o, mem.o
- - pulled out qh_printpointid and reordered qh_pointid [E. Voth]
- - removed some compiler warnings
- - moved 'FO' print of options to just before qh_buildhull
- - changed 'FO' to list difference from -1 for _narrow-hull
-
-qhull V2.2 96/2/15
- - detect narrow initial hulls (cosine of min angle < qh_MAXnarrow in user.h).
- Write warning if cosine < qh_WARNnarrow in user.h. If narrow (qh NARROWhull),
- partition coplanar points as outside points and delay coplanar test to end.
- Needed for RBOX 1000 L100000 s G1e-6 t995127886 | QHULL Tv
- See 'limitations' in qh-impre.html for further discussion.
- - corrected some confusions between 'FV' and 'Fv' in qh-opt.html
- - fixed initialization error for small Voronoi diagrams (e.g., [0,0], [1,0], [0,1]) [J. Velez]
- - fixed bad return from qh_mindiff in geom2.c
- - for initial hull, first process facet with furthest outside point (qh_furthestnext)
- - added facet->notfurthest flag for recomputing furthest point
- - added check for __STDC__ (needs ANSI C) [E. Voth]
- - reduced warning messages from [E. Voth]. e[1] in setT still reports a warning.
- - added a cube to the discussion of option 'v' (Voronoi) in qh-opt.html [J. Velez]
- - added notes about adjacent vertices to "Calling Qhull" in qh-man.html [R. Lewis & J. Velez]
- - added note about 'lines closer' when viewing 3-d Delaunay triangulations [P. Kallberg]
- - added option 'Q9' to always process furthest of furthest outside points.
- - removed option 'Pp' from q_eg and qh-eg.html.
-
-qhull V2.2 95/12/28
- - added option 'Qbb' to scale the last coordinate to [0,m] (max prev coord).
- This reduces roundoff errors for Delaunay triangulations with integer coordinates.
- - changed option 'Qu d' to print out the furthest-site Delaunay triangulation
- Use options 'Qu d PD2' to compute the normal 2-d Delaunay triangulation without
- the point at infinity.
- - added notes to the documentation of option 'd'
- - added notes to limitations of how Qhull handles imprecision
- - added warning if options 'FP', 'Fc', or 'Gp' without option 'Qc' or 'Qi'
- - added note to options 'PDk:n' and 'Pdk:n' that closest facet is returned if none match
- - added check that 'Qbk' and 'QBk' does not invert paraboloid for 'd'
- - added notes that qh_findfacet and qh_addpoint require lifted points for Delaunay triangulations
- - fixed 'rbox s 5000 W1e-13 D2 | qhull d Qcu C-0 Qbb'
- - fixed option 'QbB' (qh SCALEpoints was not set)
- - fixed minor confusion between 'Gc' (print centrums) and 'Gp' (print points)
- - rewrote qh_findbestnew for upper convex hull, Delaunay facets
- - changed option name for 'Gp' from 'Gcoplanar' to 'Gpoints'
- - changed "nearest" facet for 'Pdk' to threshold - normal
- - reworked qh GOODclosest for 'Qg'
- - added note that 'Qg' does not always work
- - recorded option 'C-0' as "_zero-merge" in option 'FO'
- - refined qh DISTround in qh_maxmin/geom2.c for Delaunay triangulations
-
-qhull V2.2 95/12/4
- - Version 2.2 fixes an important bug in computing Delaunay triangulations
- and convex hulls with edges sharper than ninety degrees. The problem
- occurs when processing a point at a sharp edge. A directed search can
- not be used for partitioning because one side may hide facets from the
- other side. The new lens-shaped distribution for rbox demonstrates the
- problem. For example, 'rbox 100 L3 G0.5 s | qhull Tv' fails for Version 2.1.
- O. Schramm found the bug when computing the Delaunay triangulation of points
- near an outside edge.
-
- I rewrote qh_findbest and related functions. Qh_findbest
- uses an exhaustive test for sharp edges (qh_findbest_sharp).
- Qh_findbest avoids the upper convex hull of Delaunay triangulations.
-
- Options 'd' and 'v' no longer assign coplanar points to the upper convex hull.
-
- Qh_check_maxout tests near-inside points. It ignores fully inside points.
- When done, it removes near-inside points from the coplanar sets.
-
- If you use qh_addpoint or qh_findbest, please review the function headers.
- They do not work for lens-shaped hulls for arbitrary facets. They do work for
- Delaunay triangulations.
-
- Changes to options for V2.2
- - added 'Qu' for computing the furthest-site Delaunay triangulation (upper hull)
- and furthest-site Voronoi vertices.
- - added 'FP' to print nearest vertex for coplanar points
- - added coplanar count to 'Fs' and 's'
- - added number of similar points to summary for Delaunay/Voronoi
- - Option 'Qc' is no longer necessary when merging.
- - 'o' format for Voronoi vertices ('v') generates "0" lines for similar points
- - 'QRn' for Delaunay ('d' or 'v') now rotates about the Z axis (see qh_init_B).
- Otherwise Qhull does not identify the upper hull
- - removed option 'Qa' for "all points outside". In V2.1 it was automatically
- set for 'd'. Even though it was a bad idea, it revealed the above bug.
- - for option list ('FO'), added version, values for one-merge, maxpos, maxneg,
- and near-inside, and flags for zero-centrum
- - optimized 'C-0' and 'Qx'. These options ("zero-centrum") test vertices
- instead of centrums for adjacent simplicial facets.
- - if 'Tv', report number of points that are not verified due to qh_findbest
- - Option 'Q8' ignores near-inside points.
-
- rbox 95/12/3
- - added lens distribution ('Ln') It may be used with 's', 'r', 'Wn', and 'Gn'
- - removed default point count except for the test case, 'Dn'
- - divided main() of rbox.c into sections
-
- Documentation changes for V2.2
- - added examples for lens distribution and furthest-site Delaunay triangulation
- and renumbered the examples for q_eg
- - described facet orientation in 'data structure' section [P. Soikkonen]
- - added notes to qh-man.html/"What to do if something goes wrong"
- - added note about using 'Tv' to verify the results [O. Schramm]
- - expanded definition of f_r in Performance section [S. Grundmann]
- - noted that Geomview display of a Voronoi diagram adds extra edges
- for unbounded Voronoi cells
- - rewrote error "convexity constraints may be too strong" [D. Newland]
- - added limitations section to "Imprecision in Qhull"
- - added note about zero-area facets to 'Imprecise convex hulls' in qh-impre.html
- - added note to 'Qi' that it does not retain coplanar points
- - added note that option 'Q5' may be used if outer planes are not needed
- - added note to README.txt about Irix 5.1 [C. Goudeseune]
- - added code fragment for visiting Voronoi vertices to "Calling Qhull" [M. Downes]
- - added note about qh_addpoint() to "Calling Qhull" [M. Downes]
-
- Errors fixed for V2.2
- - use qh_sethyperplane_gauss if 3-d or 4-d norm is less than qh MINnorm
- - count Zcentrumtests if qh_NOstat
- - reversed sign convention for qh_sethyperplane_gauss
- it was opposite to qh_sethyperplane_det
- this effects qh_determinant and qh_detsimplex
- - fixed error in qh_findgood_all with multiple restrictions, e.g., 'QVn Pdk'
- - fixed call to qh_clearcenters for qh_produce_output
- - in qh_errexit, report p0 if last furthest point
-
- Changes for users of the Qhull library
- - user code needs to define qh_version (see user_eg.c)
- - merged initialization code into qh_init_A and qh_init_B [M. Mazzario]
- old code works as before.
- qh_initflags also sets qh qhull_command for qh_initthresholds
- redid initialization for user_eg.c
- - simplified user_eg.c. It computes the convex hull of a cube.
- - added qh_setvoronoi_all in poly2.c to compute Voronoi centers
- added related note to call_qhull
- - added qh_findfacet to use in place of qh_findbest
- - added qh_nearvertex to return nearest vertex in facet to point
- - redid notes on multiple, concurrent calls in call_qhull/user.c
- - changed BoolT to unsigned int (prevent implicit enum conversion warnings)
- - added upperdelaunay to facetT. It indicates a facet of the upper convex hull.
- - converted qhull-PPC.sit for CodeWarrior 7
-
- Code changes for V2.2
- - simplified calls to setjmp() for Cray J916 [Salazar & Velez]
- - replaced fprintf(fp,string) with fputs in io.c
- - 'qh num_coplanar' removed (too expensive and not used).
- - added numcoplanars to qh_countfacets()
- - added min norm to qh_normalize2(). qh_normalize() wasn't changed
- - removed type casts from qh_point and qh_pointid [Salazar & Velez]
- - account for roundoff error in detecting upper convex hull (qh ANGLEround).
- - post merging uses qh_findbestnew for partitioning
- - qh_findbestnew for qh_partitioncoplanar goes to best facet
- - 'Qm' always processes points above the upper hull of a Delaunay triangulation
- - GOODvertex initialized with qh_findbestnew instead of qh_findbest
- - for 'v', qh_facetcenter returns furthest-neighbor vertex if 'Qu'
- - added test for qh feasible_point if use 'Fp' and qh_sethalfspace_all
- - reviewed Sugihara's algorithm for topologically robust beneath-beyond
- - on error, report if qhull in post-merging or has completed
- - if tracing, option 'FO' and qhull command always printed
- - added current furthest point ("during p%d") to 'T-1' events
- - added 'TWn' tracing for vertices of new facets (qh_setfacetplane)
- - added 'TWn' tracing for vertices in an output facet (qh_check_maxout)
- - reorganized split between poly/poly2.c and geom/geom2.c
- - reordered object files in Makefile
-
-qhull V2.1 95/9/25
- - converted qhull.man to html format, many edits
- - referenced Shewchuk's triangle program and Schneiders' Mesh Generation page
- - added option 'Qa' to force all points outside
- automatically set for "precise" Delaunay or Voronoi [Salazar & Velez]
- it is turned off by merging, 'Wn', 'Qc' or 'Qi'
- - added coplanar points to option 'FN'
- - moved option 'FO' to include default precision options
- - changed default random number generator to qh_rand in geom2.c (user.h)
-
- other code changes
- - fixed option comment Pdrop-facets-dim-less, Qbound-dim-low, QbBound-unit-box
- - defined ptr_intT for converting 64-bit ptrs to 'unsigned long' [D. Bremner]
- - defined setelemT to distinguish actual size from pointers [D. Bremner]
- use either e[...].p or e[...].i (user-level code should use set.h macros)
- - changed %x to %p in format statements for pointers [D. Bremner]
- - added test of REALmax,etc. to qh_maxmin [H. Poulard]
- - added type parameter to qh_memalloc_() macro for type conversion
- - added type conversion to qh_memalloc() calls where missing
- - added type conversion to calls into set.c that return void*
-
- other documentation changes:
- - new URLs for graphics images
- - fixed comment for facetT.neighbors in qhull.h [P. Soikkonen]
- - changed recommendations for precision errors in qh_printhelp_degenerate()
- - added recommendation for 'V0' (facet is visible if distance >= 0)
- - added note about 'long double' to user.h [S. Grundmann]
- - added note about zero area Delaunay triangles for the 'v' option
- - added note about locating Delaunay triangles to option 'd' [A. Curtis]
- - added note that coplanar vertices correspond to duplicate points for 'd'
- - added note about option 'd' automatically setting 'PDk' (lower convex hull)
- - added note about precision errors to option 'd' [many users]
- - added note about qh_findbest() to the Qhull library section [L. Lai]
- - 'make install' renames qhull.man to qhull.1 for Unix [M. Phillips]
- - renamed README, etc. to *.txt to match WWW conventions [D. Cervone]
-
-qhull V2.1 7/10/95
- - in 2-d, 'v o' lists the vertex at infinity in order [R. Critchlow]
- - it used to always list the vertex at infinity ("0") first
- - rewrote description of 'v' option (Voronoi vertices and 2-d diagrams)
- - added 'PFn' for printing facets whose area is at least 'n' [D. Holland]
- - prefixed 'Q',etc. to the 'Q',etc. options in the long help prompt
- - fixed references to 'Fv' and 'FV' options under option 'Hn,n,n'
- - updated reference to cdd, <ftp://ifor13.ethz.ch/pub/fukuda/cdd/>
- - in set.c, added some missing type coercions for qhmem.tempstack
-
-qhull V2.1 6/12/95
- - replaced qhull.ps with qhull-2.ps (paper submitted to ACM TOMS)
- - use BUFSIZ for setvbuf for Power Macintosh
- - number of good facets printed if QVn, QGn, Pd, or PD
- - added Makefile for Borland C++ 4.02 with Win32 [D. Zwick]
- - added note to Enhancements section of qhull.1 about constrained
- Delaunay triangulations [T. Rasanen]
-
-qhull V2.1 6/7/95
- - fixed qh_facetarea_simplex() for non-simplicial facets [L. Schramm]
- - fixed cast in qh_point and qh_pointid for 64-bit architectures
- - fixed URL for Amenta's list of computational geometry software
- - fixed cast in qh_meminitbuffers for qhmem.freelists
- - added test for !qh half_space in qh readpoints
- - clarified options for qh_printhelp_singular()
- - discussed non-simplicial facet area under option 'Fa' in qhull.1
-
-qhull V2.1 6/3/95
- - home page for Qhull and new descriptions for the Qhull examples
- http://www.qhull.org
- - changed SIOUX buffering for Power Macintosh. It runs fast now.
- added a project file for Metrowerk's C
- - note in README about compiling qhull on the PC
-
-qhull V2.1 beta 5/15/95
-
- ======= main changes ========
- - added halfspace intersection ('Hn,n,n')
- - facet merging is better, especially for high dimensions
- - added 'Qx' for exact merges of coplanar points and precision faults
- - facet merging is faster, especially for high dimensions.
- e.g., convex hull of the 8-d hypercube is seven times faster
- - added 'F' output formats for printing each aspect of the convex hull
- - format 'Fa' computes facet areas, total area, and total volume
- - format 'FO' writes a descriptive list of selected options to stderr
- - moved all customization options to user.h
- - changed the default precision to 'double' since it's needed for Delaunay.
- using 'float' is faster and takes less space (REALfloat in user.h)
- - option 'Qm' is no longer important for facet merging
- - removed need for 'Qs' by selecting initial simplex with pos. determinants
- - renamed 'Qv' to 'Q7' since virtual memory does not work well for qhull
- - Qhull is available for the Power Mac (no graphical output)
-
- ====== other new and modified options ===========
- - changed default MINvisible ('Vn') to a multiple of premerge_centrum ('C-n')
- - added 'Un' option to set width of facet for coplanar points.
- This replaces the previous rules for determining coplanar points.
- - changed default MINoutside ('Wn') to twice MINvisible ('Vn')
- - Geomview output adjusts point radii for MINvisible 'Vn'
- - the input format allows the number of points to precede the dimension
- - options 'v' 'd' 'FAn' and 'FMn' record good facets ('Pg')
- - added 'Fd' and 'FD' options for homogeneous coordinates in cdd format
- - in rbox, added 'h' flag to generate homogeneous coordinates in cdd format
- - option 'PAn' prints out the n facets with the largest area
- - option 'PMn' prints out the n facets with the most merges
- - option 'Po' under tracing ('Tn') no longer tries to write erroneous facets
- - option 'TCn' only prints the old 'visible' facets for 'f'
- - 'TFn' reports intermediate results when post-merging
- - option 'Ts' with option 'TFn' prints intermediate statistics
- - the message for 'Tv' reports if it is checking outer planes
- - 'Tz' sends stderr output to stdout
- - added 'Q1' to ignore angle when sorting merges (merges are worse)
- - added 'Q2' to not perform merges in independent sets (merges are worse)
- - added 'Q3' to not remove redundant vertices (faster)
- - added 'Q4' to avoid merges of old facets into new facets (does worse)
- - added 'Q5' to skip qh_check_maxout (faster, but less accurate)
- - added 'Q6' to skip pre-merge of concave and coplanar facets
- - added 'Qv' for testing vertex neighbors for convexity (needs merge option)
- - added warning if mix Geomview output with other outputs ('Po' turns off)
- - options 'o v' for 3-d and higher sort the Voronoi vertices by index
-
- ======= documentation =======
- - rewrote the introduction and precision sections
- - added a section on performance
- - added an example on halfspace intersection
- - installed examples of Qhull in
- <http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/>
-
- ======= Makefile, user.h, and messages =======
- - Makefile calls ./qhull, ./rbox, and prints short prompt for qhull
- - added new statistics, e.g., for buildhull
- - changed default qh_RANDOMtype to RAND_MAX with rand()
- - added comment about numeric overflow to printhelp_singular
- - reorganized the code to improve locality of reference
- - option in mem.h (qh_NOmem) to turn off memory management in qhull
- - option in user.h (qh_NOtrace) to turn off tracing in qhull
- - option in user.h (qh_NOmerge) to turn off merging in qhull.
- - use this instead of redefining qh_merge_nonconvex in user.c
- - simplified user_eg.c. See qh_call_qhull() in user.c for the full version
-
- ======== bug fixes ============
- - fixed error in number of points for 'rbox 100 r' (odd distribution)
- - fixed performance error in qh_degen_redundant_neighbors
- - qh_partitionpoint now sets facet->maxoutside for first outside point
- - fixed performance error in partitioning when merging a large, regular cone
- - removed memory leak in qh_appendmergeset
- - removed double free of qh line under errors in qh_readinput()
- - forcing output on error ('Po') fixed for options 'n' 'o' 'i' 's'
- - fixed optimization error on HP machines [fprintf(... *p++)]
-
- ======== changes to qhull.h for user code =======
- - qh_collectstatistics and qh_printstatistics removed from qhull.h.
- should use qh_printallstatistics instead
- - qh_findbest uses boolT for newfacets
- - added qh_findbestnew for non-simplicial facets. qh_findbest is
- too slow in this case since it needs to look at many nearly coplanar
- facets.
- - renamed qh_voronoi/qh_centrum to qh_ASvoronoi, qh_AScentrum
- - changed facet->id to 32-bits, added new flags for merging
- - added facet->f for facet pointers while merging and for facet area
- - added dfacet/dvertex for printing facets/vertices while debugging
- - added qh_produce_output and qh_printsummary
-
- ======== changes to code ==========
- - moved qh_setfacetplane from qh_makenewfacets to qh_makenewplanes
- - added qh_setfree2, qh_setcompact, and qh_setduplicate to set.c
- - qh_findgooddist returns list of visible facets instead of setting global
- - in qh_check_maxout, inside points may be added to coplanar list.
- - qh_findbestnew used for qh_partitionall. It is faster.
- - in qh_findbest, changed searchdist to MINvisible+max_outside+DISTround.
- MINvisible is the default MAXcoplanar.
- - cleaned up list management via qh_resetlists
- - uses facet->dupridge to indicate duplicated ridges instead of ->seen
- - qh_buildtracing records CPU time relative to qh hulltime instead of 0
-
- ========== changes to merging =======
- - many performance improvements, especially in high-d.
- - when merging, qh_findbest and qh_findbestnew stops search at qh_DISToutside
- - vertex neighbors delayed until first merge
- - post merges reported every TFn/2 merges
- - vertex merging turned off in 7-d and higher (lots of work, no benefit).
- vertex merging moved to qh_qhull_postmerging in 6-d.
- - replaced qh min_vertex with MAXcoplanar for determining coplanarity
- - pick closest facets to merge in duplicate ridge instead of flip/flip
- (see qh_matchduplicates in poly2.c)
- - optimize merge of simplex into a facet
- - optimize merge of a "samecycle" of facets into a coplanar horizon facet
- - cleaned up qh_forcedmerges/qh_flippedmerges and removed facet->newmerge
- - rewrote qh_merge_degenredundant with separate queue
- - qh_facetdegen replaced by facet->degenredun
- - flipped neighbors no longer merged in preference to flip/non-flip pairs
- - removed angle argument from qh_merge_degenredundant and qh_mergefacet
- only used for tracing
- - getmergeset_initial had extra test of neighbor->simplicial
- - ridge->nonconvex is now set on only one ridge between non-convex facets
- - moved centrum deletion to qh_updatetested
- - qh_isnewmerge(facet) changed to facet->newmerge (removed NEWmerges)
- - qh_findbestneighbor reports correct distance even if testcentrum
- - added hull_dim factor to qh_BESTcentrum
- - removed horizon preference in qh_merge_nonconvex (qh AVOIDold)
- - facet->keepcentrum if qh WIDEfacet or qh_MAXnewcentrum extra vertices
-
-qhull V2.02 1/25/95
- - rbox 'z' prints integer coordinates, use 'Bn' to change range
- - fixed rare bug in qh_check_maxout when qh_bestfacet returns NULL
- - fixed performance bug in findbestneighbor, should be + BESTnonconvex
- - renamed 'notgood' flag in 'f' option to 'notG' flag (caused confusion)
- - changed qh.hulltime to (unsigned) to prevent negative CPU times
- - added random perturbations to qh_getangle under the 'Rn' option
- - reviewed the documentation and enhancement list
- - added discussion of how to intersect halfspaces using qhull
- - replaced expression that caused incorrect code under an old version of gcc
- - added buffer after qh.errexit in case 'jmp_buf' has the wrong size
- - rewrote qh_printhelp_singular for lower-dimensional inputs
- - rewrote qh_printhelp_degenerate
- - added options for qh_RANDOMint in qhull_a.h
- - changed time format for 'TFn' to %02d
-
-qhull V2.01 6/20/94
- - fixed bug in qh_matchnewfacets that occured when memory alignment makes
- facet->neighbors larger than necessary.
- - fixed bug in computing worst-case simplicial merge of angle coplanar
- facets (ONEmerge). This decreases (...x) in printsummary.
-
-qhull V2.01 6/17/94
- - added recommendation for 'Qcm' to documentation and help prompts
- - added an input warning to qh_check_points ('Tv') if coplanars and no 'Qc'
- - qh_partitionpoint: always counts coplanar partitions (Zcoplanarpart)
- - rewrote qh_printhelp_degenerate to emphasize option 'C-0'
- - For Geomview output, roundoff is not needed when printing the inner and
- outer planes. This improves Geomview output for the 'Rn' option.
- - For Geomview output without coplanar points or vertices, qh_GEOMepislon
- is not needed. This removes the edge gap when displaying a Voronoi cell.
- - For Geomview output 'Gp', direct vertices to the interior point
- instead of the arithmetic center of the displayed vertices.
-
-qhull V2.01 6/11/94
- - if pre-merge, 'Qf' is automatically set. Otherwise an outside point may
- be dropt by qh_findbest(). This slows down partitioning.
- - always use 'Qc' if merging and all facet->maxoutside's must be right.
- Otherwise distributions with many coplanar points may occassionally
- miss a coplanar point for a facet. This is because qh_findbest, when
- called by qh_check_maxout, can become stuck at a local maximum if
- the search is started at an arbitrary facet. With 'Qc', the search
- is started from a coplanar facet. For example,
- rbox 1000 W8e-6 t | qhull C-0 Tv
- will (rarely) report that a facet->minoutside is incorrect
- - option 'Pp' turns off "Verifying" message for 'Tv'
- - added qh_copynonconvex to qh_renameridgevertex (fixes rare error)
- - 'rbox tn' sets random seed to n
- - 'rbox t' reports random seed in comment line
- - qh_errexit reports rbox_command | qhull_command and 'QR' random seed
- - added additional tracing to bestdist and setfacetplane
- - in qh_checkconvex, need to test coplanar against 0 instead of -DISTround
- - in qh_checkconvex, always test centrums if merging. The opposite
- vertex of a simplicial facet may be coplanar since a vertex of
- a simplicial facet may be above the facet's hyperplane.
- - fixed error handling in qh_checkconvex when merging
- - in qh_printsummary, one merge ratio not printed if less than 'Wn'
- - documented that 'Tv' verifies all facet->maxoutside
-
-qhull V2.01 6/2/94
- - 's' prints summary to stderr
- - multiple output formats printed in order to stdout
- - added statistic for worst-case distance for merging simplicial facets
- can not hope for a better "max distance above/below facet"
- print factor for "max distance.."/"merge simplicial" in printsummary
- - fixed error in scaling input with min/max reversed ('Qb0:1B0:-1')
- - fixed error in scaling if project & Delaunay & scale ('d Qb0:0B1:0b2:0')
- - user_eg.c: qh_delpoint removed since it does not always work
- - user_eg.c now works for either convex hull or Delaunay triangulation
- - added PROJECTdelaunay for Delaunay triangulations and Voronoi diagrams
- with libqhull.a and user_eg.c
- - user_eg.c: if project or scale input, need to copy points
- - user_eg.c: default just defines main, added fprintf's for qh_errprint etc.
- - qh_gausselim: a 0 pivot no longer zeros the rest of the array,
- need the remaining elements for area computation
- - qh_qhull: restore cos_max, centrum_radius at end of POSTmerging
- - qh_checkflipped with !allerror is >=0.0 instead of >0.0
- - removed -Wall from gcc due to unnecesssary "warning: implicit declaration"
- - renamed 'new' variables and fields to allow compilation by g++
- - added README notes on C++, and "size isn't known"
- - updated manual on 'Qg' with coplanar facets and no merging ('rbox c D7')
- 'Qg Pg' and 'Pg' produce different results because of precision problems
-
-Converting from qhull 1.01 to qhull 2.00
- - 'qhull An' is now 'qhull Wn'
- option 'Wn Po' is faster but it doesn't check coplanars
- - 'qhull g' is now 'qhull G', and the output formats are different
- - 'qhull c' is now 'qhull Tc'
- - 'qhull f' is now 'qhull Qf'
- - 'qhull o' is now 'qhull Po'
- - 'qhull b' is now always done
- - qhull and rbox now use floats, change REALfloat in qhull.h for doubles
- - qhull 2.00 fixes several initialization errors and performanace errors
- e.g., "singular input" on data with lots of 0 coordinates
- - 'rbox b' is now 'rbox c G0.48'
- - all rbox distributions are now scaled to a 0.5 box (use 'Bn' to change)
- - rbox now adds a comment line. This may be removed by 'rbox n'
- - 'rbox r s Z G' no longer includes the positive pole
- - no changes to the Macintosh version
-
-qhull V2.00 5/23/94
- - if force output ('Po'), facet->maxoutside= 'Wn' since coplanars not updated
- convexity checked if precision problems or verify ('Tv')
- - if merging, new facets always checked for flipped orientation
- - a facet is visible (findhorizon) under 'Qm' if distance > max_vertex
- - if using 'Qm' then min. outside is max_vertex instead of max_outside
- - default is random()/srandom() in qhull_a.h, checked in initqhull_globals
- - created internal strtod since strtod may skip spacing after number
- - removed lower bound (1.0) for qh maxmaxcoord
- - divzero needs to handle 0/0 and large/small
- - decreased size of precise vertices
- - need to initialize qh MINdenom_1 for scalepoints
- - added factor of qh maxmaxcoord into DISTround (needed for offset)
- - 'Rn' perturbs distance computations by random +/-n
- - check_points needs an extra DISTround to get from precise point to computed
- - rewrote some of the IMPRECISION section in qhull.man
- - added the input format to the qhull prompt
- - moved include files to qhull_a.h since some compilers do not use float.h
- - added qhull.1 and rbox.1 since SGI does not ship nroff
- - reduced cutoff for printpointvect
- - use time for qhull random seed only if QR0 or QR-1
- - radius of vertices and coplanar points determined by pre-merge values
-
-qhull V2.00 5/12/94
- - facet2point (io.c) used vertex0 instead of vertex1
- - can't print visible facets after cone is attached
- - shouldn't check output after STOPcone (TCn)
- - statistic 'Wminvertex' and 'Wmaxoutside' only if MERGING or APPROXhull
- - 'make doc' uses lineprinter format for paging
- - warning if Gpv in 4-d
-
-qhull V2.b05 5/9/94
- - decreased size of precise vertices
- - precise facets in 2-d print hyperplanes
- - accounted for GOODpoint in printsummary
- - added IMPRECISION section to qhull.man
- - 'Qg' does work in 7-d unless there's many coplanar facets
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/Make-config.sh b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/Make-config.sh
deleted file mode 100755
index cc247865257de3b26f6c1665b9f85d243812c62a..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/Make-config.sh
+++ /dev/null
@@ -1,285 +0,0 @@
-#!/bin/sh -e
-#
-# Make-config.sh
-#
-# Setup for Debian build
-#
-# Writes configure.in and Makefile.am files
-# and runs automake and autoconfig
-#
-# Use 'make dist' to build Unix distribution.
-# Use 'configure; make' to build Qhull
-#
-#note:
-# 'configure; make' does not work under cygwin.
-# src/unix.c:354: variable 'qh_qh' can't be auto-imported.
-# Please read the documentation for ld's --enable-auto-import for details.
-
-###################################################
-########### ../configure.in ######################
-###################################################
-
-echo Create ../configure.in
-cat >../configure.in <<\HERE-CONFIGURE
-dnl configure.in for the qhull package
-dnl Author: Rafael Laboissiere <rafael@debian.org>
-dnl Created: Mon Dec 3 21:36:21 CET 2001
-
-AC_INIT(src/qhull.c)
-AM_INIT_AUTOMAKE(qhull, 2002.1)
-
-AC_PROG_CC
-AC_PROG_LIBTOOL
-
-AC_OUTPUT([Makefile src/Makefile html/Makefile eg/Makefile])
-
-HERE-CONFIGURE
-
-###################################################
-########### ../Makefile.am #######################
-###################################################
-
-echo Create ../Makefile.am
-cat >../Makefile.am <<\HERE-TOP
-### Makefile.am for the qhull package (main)
-### Author: Rafael Laboissiere <rafael@debian.org>
-### Created: Mon Dec 3 21:36:21 CET 2001
-
-### Documentation files
-
-# to:
-docdir = $(prefix)/share/doc/$(PACKAGE)
-
-# which:
-doc_DATA = \
- index.htm \
- Announce.txt \
- COPYING.txt \
- README.txt \
- REGISTER.txt
-
-### Extra files to be included in the tarball
-
-EXTRA_DIST = \
- $(doc_DATA) \
- File_id.diz \
- QHULL-GO.pif
-
-### Subdirectories for Automaking
-
-SUBDIRS = src html eg
-
-HERE-TOP
-
-###################################################
-########### ../eg/Makefile.am ####################
-###################################################
-
-echo Create ../eg/Makefile.am
-cat >../eg/Makefile.am <<\HERE-AM
-### Makefile.am for the qhull package (eg)
-### Author: Rafael Laboissiere <rafael@debian.org>
-### Created: Mon Dec 3 21:36:21 CET 2001
-
-### Documentation files
-
-# to:
-docdir = $(prefix)/share/doc/$(PACKAGE)
-examplesdir = $(docdir)/examples
-
-# which:
-examples_DATA = \
- q_eg \
- q_egtest \
- q_test \
- Qhull-go.bat \
- q_test.bat
-
-### Extra files to be included in the tarball
-
-EXTRA_DIST = $(examples_DATA)
-
-HERE-AM
-
-###################################################
-########### ../html/Makefile.am ##################
-###################################################
-
-echo Create ../html/Makefile.am
-cat >../html/Makefile.am <<\HERE-HTML
-### Makefile.am for the qhull package (html)
-### Author: Rafael Laboissiere <rafael@debian.org>
-### Created: Mon Dec 3 21:36:21 CET 2001
-
-### Man pages (trick to get around .man extension)
-
-%.1: %.man
- cp $< $@
-CLEANFILES = *.1
-man_MANS = rbox.1 qhull.1
-
-### Documentation files
-
-# to:
-docdir = $(prefix)/share/doc/$(PACKAGE)
-htmldir = $(docdir)/html
-
-# which:
-html_DATA = \
- index.htm \
- qconvex.htm \
- qdelau_f.htm \
- qdelaun.htm \
- qh--4d.gif \
- qh--cone.gif \
- qh--dt.gif \
- qh--geom.gif \
- qh--half.gif \
- qh--rand.gif \
- qh-eg.htm \
- qh-faq.htm \
- qh-get.htm \
- qh-impre.htm \
- qh-in.htm \
- qh-optc.htm \
- qh-optf.htm \
- qh-optg.htm \
- qh-opto.htm \
- qh-optp.htm \
- qh-optq.htm \
- qh-optt.htm \
- qh-quick.htm \
- qhalf.htm \
- qhull.htm \
- qvoron_f.htm \
- qvoronoi.htm \
- rbox.htm
-
-### Extra files to be included in the tarball
-
-EXTRA_DIST = \
- $(html_DATA) \
- qhull.man \
- qhull.txt \
- rbox.man \
- rbox.txt
-
-HERE-HTML
-
-###################################################
-########### ../src/Makefile.am ###################
-###################################################
-
-echo Create ../src/Makefile.am
-cat >../src/Makefile.am <<\HERE-SRC
-### Makefile.am for the qhull package (src)
-### Author: Rafael Laboissiere <rafael@debian.org>
-### Created: Mon Dec 3 21:36:21 CET 2001
-
-### Shared Library
-
-# to:
-lib_LTLIBRARIES = libqhull.la
-
-# from:
-libqhull_la_SOURCES = \
- user.c \
- global.c \
- stat.c \
- io.c \
- geom2.c \
- poly2.c \
- merge.c \
- qhull.c \
- geom.c \
- poly.c \
- qset.c \
- mem.c
-
-# how:
-libqhull_la_LDFLAGS = -version-info 0:0:0 -lm
-
-### Utility programs
-
-# to:
-bin_PROGRAMS = qhull rbox qconvex qdelaunay qvoronoi qhalf
-
-# from:
-qhull_SOURCES = unix.c
-rbox_SOURCES = rbox.c
-qconvex_SOURCES = qconvex.c
-qdelaunay_SOURCES = qdelaun.c
-qvoronoi_SOURCES = qvoronoi.c
-qhalf_SOURCES = qhalf.c
-
-# how:
-qhull_LDADD = libqhull.la
-rbox_LDADD = libqhull.la
-qconvex_LDADD = libqhull.la
-qdelaunay_LDADD = libqhull.la
-qvoronoi_LDADD = libqhull.la
-qhalf_LDADD = libqhull.la
-
-### Include files
-
-pkginclude_HEADERS = \
- geom.h \
- mem.h \
- poly.h \
- qhull_a.h \
- stat.h \
- io.h \
- merge.h \
- qhull.h \
- qset.h \
- user.h
-
-
-### Example programs
-
-# to:
-docdir = $(prefix)/share/doc/$(PACKAGE)
-examplesdir = $(docdir)/examples
-
-# which:
-examples_DATA = \
- user_eg.c \
- user_eg2.c \
- qhull_interface.cpp \
- Makefile.txt \
- Make-config.sh \
- MBorland
-
-doc_DATA = Changes.txt \
- index.htm \
- qh-geom.htm \
- qh-globa.htm \
- qh-io.htm \
- qh-mem.htm \
- qh-merge.htm \
- qh-poly.htm \
- qh-qhull.htm \
- qh-set.htm \
- qh-stat.htm \
- qh-user.htm
-
-
-### Extra files to be included in the tarball
-
-EXTRA_DIST = \
- $(doc_DATA) \
- $(examples_DATA)
-
-HERE-SRC
-
-###################################################
-########### run automake autoconf ################
-###################################################
-
-
-echo Run automake, libtoolize, and autoconf
-cd ..; aclocal &&\
- automake --foreign --add-missing --force-missing && \
- libtoolize --force && \
- autoconf
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/Makefile b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/Makefile
deleted file mode 100644
index 498ffbade83e2a1bccff32d82cc9521d10ce3c3c..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/Makefile
+++ /dev/null
@@ -1,193 +0,0 @@
-# Unix Makefile for qhull and rbox
-#
-# see README.txt
-# the Unix distribution contains a configure Makefile
-#
-# make to produce qhull qconvex qdelaunay qhalf qvoronoi rbox
-# make qvoronoi to produce qvoronoi (etc.)
-# make qhullx to produce qhull qconvex etc. w/o using libqhull.so
-# make doc to print documentation
-# make install to copy qhull, rbox, qhull.1, rbox.1 to BINDIR, MANDIR
-# make new to rebuild qhull and rbox from source
-#
-# make printall to print all files
-# make user_eg to produce user_eg
-# make user_eg2 to produce user_eg2
-# make clean to remove object files and core
-# make cleanall to remove all generated files
-#
-# PRINTMAN -- command for printing manual pages
-# PRINTC -- command for printing C files
-# BINDIR -- directory where to copy executables
-# MANDIR -- directory where to copy manual pages
-# CC -- ANSI C or C++ compiler
-# CCOPTS1 - options used to compile .c files
-# CCOPTS2 -- options used to link .o files
-#
-# CFILES -- .c files for printing
-# HFILES -- .h files for printing
-# DFILES -- documentation files
-# MFILES -- man pages and html files
-# TFILES -- .txt versions of html html files
-# FILES -- all other files
-# OBJS -- specifies the object files of libqhull.so
-#
-BINDIR = /usr/local/bin
-MANDIR = /usr/local/man/man1
-
-# if you do not have enscript, try a2ps or just use lpr. The files are text.
-PRINTMAN = enscript -2rl
-PRINTC = enscript -2r
-# PRINTMAN = lpr
-# PRINTC = lpr
-
-#for Gnu's gcc compiler -O2 for optimization, -g for debugging, -Wall for check
-#
-CC = gcc
-CCOPTS1 = -O1 -ansi
-
-# for Sun's cc compiler, -fast or O2 for optimization, -g for debugging, -Xc for ANSI
-#CC = cc
-#CCOPTS1 = -Xc -v -fast
-
-# for Silicon Graphics cc compiler, -O2 for optimization, -g for debugging
-#CC = cc
-#CCOPTS1 = -ansi -O2
-
-# for Next cc compiler with fat executable
-#CC = cc
-#CCOPTS1 = -ansi -O2 -arch m68k -arch i386 -arch hppa
-
-# for loader, ld
-CCOPTS2 = $(CCOPTS1)
-
-# OBJS in execution frequency order. CFILES after qhull.c are alphabetical
-OBJS = user.o global.o stat.o io.o geom2.o poly2.o \
- merge.o qhull.o geom.o poly.o qset.o mem.o
-
-CFILES= unix.c qhull.c geom.c geom2.c global.c io.c mem.c merge.c poly.c \
- poly2.c qset.c stat.c user.c qconvex.c qdelaun.c qhalf.c qvoronoi.c
-HFILES= user.h qhull.h qhull_a.h geom.h io.h mem.h merge.h poly.h qset.h stat.h
-TXTFILES= ../Announce.txt ../REGISTER.txt ../COPYING.txt ../README.txt Changes.txt
-DOCFILES= ../html/rbox.txt ../html/qhull.txt
-FILES= Makefile rbox.c user_eg.c ../eg/q_test ../eg/q_egtest ../eg/q_eg
-HTMFILES= qhull.man rbox.man qh-in.htm qh-optg.htm qh-optt.htm qh-optp.htm \
- index.htm qh-quick.htm qh-impre.htm qh-eg.htm \
- qh-optc.htm qh-opto.htm qh-optf.htm qh-optq.htm \
- qh-c.htm qh-faq.htm qhull.htm qconvex.htm qdelaun.htm \
- qh-geom.htm qh-globa.htm qh-io.htm qh-mem.htm qh-merge.htm \
- qh-poly.htm qh-qhull.htm qh-set.htm qh-stat.htm qh-user.htm \
- qdelau_f.htm qhalf.htm qvoronoi.htm qvoron_f.htm rbox.htm
-
-all: rbox qconvex qdelaunay qhalf qvoronoi qhull
-
-unix.o: qhull.h user.h mem.h
-qconvex.o: qhull.h user.h mem.h
-qdelaun.o: qhull.h user.h mem.h
-qhalf.o: qhull.h user.h mem.h
-qvoronoi.o: qhull.h user.h mem.h
-qhull.o: $(HFILES)
-geom.o: $(HFILES)
-geom2.o: $(HFILES)
-global.o: $(HFILES)
-io.o: $(HFILES)
-mem.o: mem.h
-merge.o: $(HFILES)
-poly.o: $(HFILES)
-poly2.o: $(HFILES)
-qset.o: qset.h mem.h
-stat.o: $(HFILES)
-user.o: $(HFILES)
-
-.c.o:
- $(CC) -c $(CCOPTS1) $<
-
-clean:
- rm -f *.o ../core qconvex qdelaunay qhalf qvoronoi qhull libqhull.so ../lib/linux/libqhull.so ../../../lib/linux/libqhull.so
-
-cleanall: clean
- rm -f *~ ../rbox ../qhull ../qhalf ../qconvex ../qdelaunay ../qhalf\
- ../qvoronoi ../user_eg ../user_eg2 ../*.exe >/dev/null
-
-doc:
- $(PRINTMAN) $(TXTFILES) $(DOCFILES)
-
-install: all
- cp ../qconvex $(BINDIR)/qconvex
- cp ../qdelaunay $(BINDIR)/qdelaunay
- cp ../qhalf $(BINDIR)/qhalf
- cp ../qhull $(BINDIR)/qhull
- cp ../qvoronoi $(BINDIR)/qvoronoi
- cp ../rbox $(BINDIR)/rbox
- cp ../html/qhull.man $(MANDIR)/qhull.1
- cp ../html/rbox.man $(MANDIR)/rbox.1
-
-new: cleanall all
-
-printall: doc printh printc printf
-
-printh:
- $(PRINTC) $(HFILES)
-
-printc:
- $(PRINTC) $(CFILES)
-
-printf:
- $(PRINTC) $(FILES)
-
-libqhull.so: $(OBJS)
- ${CC} ${CCOPTS1} -shared -Wl,-soname,libqhull.so -o $@ $(OBJS)
- cp libqhull.so ../lib/linux
- cp libqhull.so ../../../lib/linux
- #@echo if 'ar' or 'ranlib' fails, try 'make qhullx'
- #ar rv libqhull.so $(OBJS)
- #@echo the next line may need to be removed.
- # -test -x /bin/ranlib -o -x /usr/bin/ranlib && ranlib libqhull.so
-
-# don't use ../qconvex. Does not work on Red Hat Linux
-qconvex: qconvex.o libqhull.so
- $(CC) -o qconvex $(CCOPTS2) qconvex.o -L. -lqhull -lm
- cp qconvex ..
-
-qdelaunay: qdelaun.o libqhull.so
- $(CC) -o qdelaunay $(CCOPTS2) qdelaun.o -L. -lqhull -lm
- cp qdelaunay ..
-
-qhalf: qhalf.o libqhull.so
- $(CC) -o qhalf $(CCOPTS2) qhalf.o -L. -lqhull -lm
- cp qhalf ..
-
-qvoronoi: qvoronoi.o libqhull.so
- $(CC) -o qvoronoi $(CCOPTS2) qvoronoi.o -L. -lqhull -lm
- cp qvoronoi ..
-
-qhull: unix.o libqhull.so
- $(CC) -o qhull $(CCOPTS2) unix.o -L. -lqhull -lm
- cp qhull ..
- -chmod +x ../eg/q_test ../eg/q_eg ../eg/q_egtest
-#-cd ..; ./rbox D4 | ./qhull
-
-# compile qhull without using libqhull.so
-qhullx: qconvex.o qdelaun.o qhalf.o qvoronoi.o unix.o $(OBJS)
- $(CC) -o qconvex $(CCOPTS2) qconvex.o $(OBJS) -lm
- $(CC) -o qdelaunay $(CCOPTS2) qdelaun.o $(OBJS) -lm
- $(CC) -o qhalf $(CCOPTS2) qhalf.o $(OBJS) -lm
- $(CC) -o qvoronoi $(CCOPTS2) qvoronoi.o $(OBJS) -lm
- $(CC) -o qhull $(CCOPTS2) unix.o $(OBJS) -lm
- cp qconvex qdelaunay qhalf qvoronoi qhull ..
- -chmod +x ../eg/q_test ../eg/q_eg ../eg/q_egtest
-#-cd ..; ./rbox D4 | ./qhull
-
-rbox: rbox.o
- $(CC) -o rbox rbox.o $(CCOPTS2) -lm
- cp rbox ..
-
-user_eg: user_eg.o libqhull.so
- $(CC) -o user_eg $(CCOPTS2) user_eg.o -L. -lqhull -lm
- cp user_eg ..
-
-user_eg2: user_eg2.o libqhull.so
- $(CC) -o user_eg2 $(CCOPTS2) user_eg2.o -L. -lqhull -lm
- cp user_eg2 ..
-
-# end of Makefile
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/Mborland b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/Mborland
deleted file mode 100644
index 103c49e7a916d707485d03b8e81710953e09ba71..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/Mborland
+++ /dev/null
@@ -1,186 +0,0 @@
-#########################################################################
-# Borland C++ 4.02 for Win32 and DOS Power Pack #
-# Makefile for qhull and rbox #
-# #
-# make -fMborland all to produce qconvex, qhull, and rbox #
-# make -fMborland user_eg to produce user_eg #
-# make -fMborland user_eg2 to produce user_eg2 #
-# make -fMborland new to rebuild qhull and rbox from source #
-# make -fMborland clean to remove object files #
-# make -fMborland cleanall to remove all generated files #
-# make -fMborland test to test rbox and qhull #
-# #
-# Author: D. Zwick of Germany, C.B. Barber #
-#########################################################################
-
-CC = bcc32 # 32 bit compiler for DOS
- # bcc32i - Intel's compiler
-LINKER = $(CC) # bcc calls tlink32 with needed options
-CFLAGS = -w- -A -O2
- # -w- no warnings, bcc doesn't handle assigns in conditions
- # -A Ansi standard
- # -X no auto-dependency outputs
- # -v debugging, use CCOPTS for both
- # -O2 optimization
-!if $d(_DPMI)
-LFLAGS = -WX -w- # -WX loads DPMI library
-!else
-LFLAGS = -lap -lx -lc
- # -lap 32-bit console application
- # -lx no map file
- # -lc case is significant
-!endif
-
-EXERB = rbox
-EXEQH = qhull
-EXEQC = qconvex
-EXEQD = qdelaunay
-EXEQV = qvoronoi
-EXEQF = qhalf
-EXEEG = user_eg
-EXEEG2 = user_eg2
-
-TMPFILE = BCC32tmp.cfg
-
-OBJS1 = global.obj stat.obj geom2.obj poly2.obj io.obj
-OBJS2 = merge.obj qhull.obj mem.obj qset.obj poly.obj geom.obj
-
-HFILES1 = qhull.h stat.h qhull_a.h user.h
-
-
-# General rules
-
-.c.obj:
- $(CC) -c $(CFLAGS) $<
-
-# Default
-
-all: $(EXERB) $(EXEQH) $(EXEQC) $(EXEQD) $(EXEQV) $(EXEQF) test
-
-help:
- @echo USAGE:
- @echo "make all to produce qhull, rbox, qconvex, qdelaun, qvoronoi, qhalf"
- @echo "make user_eg to produce user_eg"
- @echo "make user_eg2 to produce user_eg2"
- @echo "make new to rebuild qhull and rbox from source"
- @echo "make clean to remove object files"
- @echo "make cleanall to remove all generated file"
- @echo "make test to test rbox and qhull"
- @echo OPTIONS (default is 32-bit console app):
- @echo "-D_DPMI for C++ 4.01 and DOS Power Pack"
-
-# Executables
-
-$(EXEQH): ..\$(EXEQH).exe
- @echo Made ..\$(EXEQH).exe
-
-..\$(EXEQH).exe: unix.obj user.obj $(OBJS1) $(OBJS2)
- @echo unix.obj user.obj > $(TMPFILE)
- @echo $(OBJS1) >> $(TMPFILE)
- @echo $(OBJS2) >> $(TMPFILE)
- $(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)
-
-$(EXEQC): ..\$(EXEQC).exe
- @echo Made ..\$(EXEQC).exe
-
-..\$(EXEQC).exe: qconvex.obj user.obj $(OBJS1) $(OBJS2)
- @echo qconvex.obj user.obj > $(TMPFILE)
- @echo $(OBJS1) >> $(TMPFILE)
- @echo $(OBJS2) >> $(TMPFILE)
- $(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)
-
-$(EXEQD): ..\$(EXEQD).exe
- @echo Made ..\$(EXEQD).exe
-
-..\$(EXEQD).exe: qdelaun.obj user.obj $(OBJS1) $(OBJS2)
- @echo qdelaun.obj user.obj > $(TMPFILE)
- @echo $(OBJS1) >> $(TMPFILE)
- @echo $(OBJS2) >> $(TMPFILE)
- $(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)
-
-$(EXEQV): ..\$(EXEQV).exe
- @echo Made ..\$(EXEQV).exe
-
-..\$(EXEQV).exe: qvoronoi.obj user.obj $(OBJS1) $(OBJS2)
- @echo qvoronoi.obj user.obj > $(TMPFILE)
- @echo $(OBJS1) >> $(TMPFILE)
- @echo $(OBJS2) >> $(TMPFILE)
- $(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)
-
-$(EXEQF): ..\$(EXEQF).exe
- @echo Made ..\$(EXEQF).exe
-
-..\$(EXEQF).exe: qhalf.obj user.obj $(OBJS1) $(OBJS2)
- @echo qhalf.obj user.obj > $(TMPFILE)
- @echo $(OBJS1) >> $(TMPFILE)
- @echo $(OBJS2) >> $(TMPFILE)
- $(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)
-
-$(EXEEG): ..\$(EXEEG).exe
- @echo Made ..\$(EXEEG).exe
-
-..\$(EXEEG).exe: user_eg.obj $(OBJS1) $(OBJS2)
- @echo user_eg.obj user.obj > $(TMPFILE)
- @echo $(OBJS1) >> $(TMPFILE)
- @echo $(OBJS2) >> $(TMPFILE)
- $(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)
-
-$(EXEEG2): ..\$(EXEEG2).exe
- @echo Made ..\$(EXEEG2).exe
-
-..\$(EXEEG2).exe: user_eg2.obj $(OBJS1) $(OBJS2)
- @echo user_eg2.obj > $(TMPFILE)
- @echo $(OBJS1) >> $(TMPFILE)
- @echo $(OBJS2) >> $(TMPFILE)
- $(LINKER) -e$@ $(CFLAGS) $(LFLAGS) @$(TMPFILE)
-
-$(EXERB): ..\$(EXERB).exe
- @echo Made ..\$(EXERB).exe
-
-..\$(EXERB).exe: rbox.obj
- $(LINKER) -e$@ $(CFLAGS) $(LFLAGS) rbox.obj
-
-# Test rbox and qhull
-
-test:
- @..\rbox D4 > test.x
- @..\qhull <test.x
- @del test.x
-
-# Clean up
-
-clean:
- @del *.obj
- @del $(TMPFILE)
-
-cleanall: clean
- @del ..\$(EXERB).exe
- @del ..\$(EXEQC).exe
- @del ..\$(EXEQD).exe
- @del ..\$(EXEQF).exe
- @del ..\$(EXEQH).exe
- @del ..\$(EXEQV).exe
- @del ..\$(EXEEG).exe
- @del ..\$(EXEEG2).exe
- @del ..\q_test.x
- @del ..\q_test.log.1
-
-# Clean up and rebuild all
-
-new: cleanall all
-
-# Header file dependencies
-
-qhull.obj stat.obj user.obj global.obj: $(HFILES1)
-geom.obj geom2.obj: $(HFILES1) geom.h
-poly.obj poly2.obj: $(HFILES1) poly.h
-io.obj: $(HFILES1) io.h
-merge.obj: $(HFILES1) merge.h
-mem.obj: mem.h
-qset.obj: qset.h mem.h
-unix.obj: qhull.h user.h
-qconvex.obj: qhull.h user.h
-qdelaun.obj: qhull.h user.h
-qhalf.obj: qhull.h user.h
-qvoronoi.obj: qhull.h user.h
-rbox.obj: user.h
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/geom.c b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/geom.c
deleted file mode 100644
index af633eeafc2710e7b354e7c76b36b5d131d8126f..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/geom.c
+++ /dev/null
@@ -1,1229 +0,0 @@
-/*<html><pre> -<a href="qh-geom.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- geom.c
- geometric routines of qhull
-
- see qh-geom.htm and geom.h
-
- copyright (c) 1993-2003 The Geometry Center
-
- infrequent code goes into geom2.c
-*/
-
-#include "qhull_a.h"
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="distplane">-</a>
-
- qh_distplane( point, facet, dist )
- return distance from point to facet
-
- returns:
- dist
- if qh.RANDOMdist, joggles result
-
- notes:
- dist > 0 if point is above facet (i.e., outside)
- does not error (for sortfacets)
-
- see:
- qh_distnorm in geom2.c
-*/
-void qh_distplane (pointT *point, facetT *facet, realT *dist) {
- coordT *normal= facet->normal, *coordp, randr;
- int k;
-
- switch(qh hull_dim){
- case 2:
- *dist= facet->offset + point[0] * normal[0] + point[1] * normal[1];
- break;
- case 3:
- *dist= facet->offset + point[0] * normal[0] + point[1] * normal[1] + point[2] * normal[2];
- break;
- case 4:
- *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3];
- break;
- case 5:
- *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4];
- break;
- case 6:
- *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5];
- break;
- case 7:
- *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6];
- break;
- case 8:
- *dist= facet->offset+point[0]*normal[0]+point[1]*normal[1]+point[2]*normal[2]+point[3]*normal[3]+point[4]*normal[4]+point[5]*normal[5]+point[6]*normal[6]+point[7]*normal[7];
- break;
- default:
- *dist= facet->offset;
- coordp= point;
- for (k= qh hull_dim; k--; )
- *dist += *coordp++ * *normal++;
- break;
- }
- zinc_(Zdistplane);
- if (!qh RANDOMdist && qh IStracing < 4)
- return;
- if (qh RANDOMdist) {
- randr= qh_RANDOMint;
- *dist += (2.0 * randr / qh_RANDOMmax - 1.0) *
- qh RANDOMfactor * qh MAXabs_coord;
- }
- if (qh IStracing >= 4) {
- fprintf (qh ferr, "qh_distplane: ");
- fprintf (qh ferr, qh_REAL_1, *dist);
- fprintf (qh ferr, "from p%d to f%d\n", qh_pointid(point), facet->id);
- }
- return;
-} /* distplane */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="findbest">-</a>
-
- qh_findbest( point, startfacet, bestoutside, qh_ISnewfacets, qh_NOupper, dist, isoutside, numpart )
- find facet that is furthest below a point
- for upperDelaunay facets
- returns facet only if !qh_NOupper and clearly above
-
- input:
- starts search at 'startfacet' (can not be flipped)
- if !bestoutside (qh_ALL), stops at qh.MINoutside
-
- returns:
- best facet (reports error if NULL)
- early out if isoutside defined and bestdist > qh.MINoutside
- dist is distance to facet
- isoutside is true if point is outside of facet
- numpart counts the number of distance tests
-
- see also:
- qh_findbestnew()
-
- notes:
- If merging (testhorizon), searches horizon facets of coplanar best facets because
- after qh_distplane, this and qh_partitionpoint are the most expensive in 3-d
- avoid calls to distplane, function calls, and real number operations.
- caller traces result
- Optimized for outside points. Tried recording a search set for qh_findhorizon.
- Made code more complicated.
-
- when called by qh_partitionvisible():
- indicated by qh_ISnewfacets
- qh.newfacet_list is list of simplicial, new facets
- qh_findbestnew set if qh_sharpnewfacets returns True (to use qh_findbestnew)
- qh.bestfacet_notsharp set if qh_sharpnewfacets returns False
-
- when called by qh_findfacet(), qh_partitionpoint(), qh_partitioncoplanar(),
- qh_check_bestdist(), qh_addpoint()
- indicated by !qh_ISnewfacets
- returns best facet in neighborhood of given facet
- this is best facet overall if dist > - qh.MAXcoplanar
- or hull has at least a "spherical" curvature
-
- design:
- initialize and test for early exit
- repeat while there are better facets
- for each neighbor of facet
- exit if outside facet found
- test for better facet
- if point is inside and partitioning
- test for new facets with a "sharp" intersection
- if so, future calls go to qh_findbestnew()
- test horizon facets
-*/
-facetT *qh_findbest (pointT *point, facetT *startfacet,
- boolT bestoutside, boolT isnewfacets, boolT noupper,
- realT *dist, boolT *isoutside, int *numpart) {
- realT bestdist= -REALmax/2 /* avoid underflow */;
- facetT *facet, *neighbor, **neighborp;
- facetT *bestfacet= NULL, *lastfacet= NULL;
- int oldtrace= qh IStracing;
- unsigned int visitid= ++qh visit_id;
- int numpartnew=0;
- boolT testhorizon = True; /* needed if precise, e.g., rbox c D6 | qhull Q0 Tv */
-
- zinc_(Zfindbest);
- if (qh IStracing >= 3 || (qh TRACElevel && qh TRACEpoint >= 0 && qh TRACEpoint == qh_pointid (point))) {
- if (qh TRACElevel > qh IStracing)
- qh IStracing= qh TRACElevel;
- fprintf (qh ferr, "qh_findbest: point p%d starting at f%d isnewfacets? %d, unless %d exit if > %2.2g\n",
- qh_pointid(point), startfacet->id, isnewfacets, bestoutside, qh MINoutside);
- fprintf(qh ferr, " testhorizon? %d noupper? %d", testhorizon, noupper);
- fprintf (qh ferr, " Last point added was p%d.", qh furthest_id);
- fprintf(qh ferr, " Last merge was #%d. max_outside %2.2g\n", zzval_(Ztotmerge), qh max_outside);
- }
- if (isoutside)
- *isoutside= True;
- if (!startfacet->flipped) { /* test startfacet */
- *numpart= 1;
- qh_distplane (point, startfacet, dist); /* this code is duplicated below */
- if (!bestoutside && *dist >= qh MINoutside
- && (!startfacet->upperdelaunay || !noupper)) {
- bestfacet= startfacet;
- goto LABELreturn_best;
- }
- bestdist= *dist;
- if (!startfacet->upperdelaunay) {
- bestfacet= startfacet;
- }
- }else
- *numpart= 0;
- startfacet->visitid= visitid;
- facet= startfacet;
- while (facet) {
- trace4((qh ferr, "qh_findbest: neighbors of f%d, bestdist %2.2g f%d\n",
- facet->id, bestdist, getid_(bestfacet)));
- lastfacet= facet;
- FOREACHneighbor_(facet) {
- if (!neighbor->newfacet && isnewfacets)
- continue;
- if (neighbor->visitid == visitid)
- continue;
- neighbor->visitid= visitid;
- if (!neighbor->flipped) { /* code duplicated above */
- (*numpart)++;
- qh_distplane (point, neighbor, dist);
- if (*dist > bestdist) {
- if (!bestoutside && *dist >= qh MINoutside
- && (!neighbor->upperdelaunay || !noupper)) {
- bestfacet= neighbor;
- goto LABELreturn_best;
- }
- if (!neighbor->upperdelaunay) {
- bestfacet= neighbor;
- bestdist= *dist;
- break; /* switch to neighbor */
- }else if (!bestfacet) {
- bestdist= *dist;
- break; /* switch to neighbor */
- }
- } /* end of *dist>bestdist */
- } /* end of !flipped */
- } /* end of FOREACHneighbor */
- facet= neighbor; /* non-NULL only if *dist>bestdist */
- } /* end of while facet (directed search) */
- if (isnewfacets) {
- if (!bestfacet) {
- bestdist= -REALmax/2;
- bestfacet= qh_findbestnew (point, startfacet->next, &bestdist, bestoutside, isoutside, &numpartnew);
- testhorizon= False; /* qh_findbestnew calls qh_findbesthorizon */
- }else if (!qh findbest_notsharp && bestdist < - qh DISTround) {
- if (qh_sharpnewfacets()) {
- /* seldom used, qh_findbestnew will retest all facets */
- zinc_(Zfindnewsharp);
- bestfacet= qh_findbestnew (point, bestfacet, &bestdist, bestoutside, isoutside, &numpartnew);
- testhorizon= False; /* qh_findbestnew calls qh_findbesthorizon */
- qh findbestnew= True;
- }else
- qh findbest_notsharp= True;
- }
- }
- if (!bestfacet)
- bestfacet= qh_findbestlower (lastfacet, point, &bestdist, numpart);
- if (testhorizon)
- bestfacet= qh_findbesthorizon (!qh_IScheckmax, point, bestfacet, noupper, &bestdist, &numpartnew);
- *dist= bestdist;
- if (isoutside && bestdist < qh MINoutside)
- *isoutside= False;
-LABELreturn_best:
- zadd_(Zfindbesttot, *numpart);
- zmax_(Zfindbestmax, *numpart);
- (*numpart) += numpartnew;
- qh IStracing= oldtrace;
- return bestfacet;
-} /* findbest */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="findbesthorizon">-</a>
-
- qh_findbesthorizon( qh_IScheckmax, point, startfacet, qh_NOupper, &bestdist, &numpart )
- search coplanar and better horizon facets from startfacet/bestdist
- ischeckmax turns off statistics and minsearch update
- all arguments must be initialized
- returns (ischeckmax):
- best facet
- returns (!ischeckmax):
- best facet that is not upperdelaunay
- allows upperdelaunay that is clearly outside
- returns:
- bestdist is distance to bestfacet
- numpart -- updates number of distance tests
-
- notes:
- no early out -- use qh_findbest() or qh_findbestnew()
- Searches coplanar or better horizon facets
-
- when called by qh_check_maxout() (qh_IScheckmax)
- startfacet must be closest to the point
- Otherwise, if point is beyond and below startfacet, startfacet may be a local minimum
- even though other facets are below the point.
- updates facet->maxoutside for good, visited facets
- may return NULL
-
- searchdist is qh.max_outside + 2 * DISTround
- + max( MINvisible('Vn'), MAXcoplanar('Un'));
- This setting is a guess. It must be at least max_outside + 2*DISTround
- because a facet may have a geometric neighbor across a vertex
-
- design:
- for each horizon facet of coplanar best facets
- continue if clearly inside
- unless upperdelaunay or clearly outside
- update best facet
-*/
-facetT *qh_findbesthorizon (boolT ischeckmax, pointT* point, facetT *startfacet, boolT noupper, realT *bestdist, int *numpart) {
- facetT *bestfacet= startfacet;
- realT dist;
- facetT *neighbor, **neighborp, *facet;
- facetT *nextfacet= NULL; /* optimize last facet of coplanarset */
- int numpartinit= *numpart, coplanarset_size;
- unsigned int visitid= ++qh visit_id;
- boolT newbest= False; /* for tracing */
- realT minsearch, searchdist; /* skip facets that are too far from point */
-
- if (!ischeckmax) {
- zinc_(Zfindhorizon);
- }else {
-#if qh_MAXoutside
- if ((!qh ONLYgood || startfacet->good) && *bestdist > startfacet->maxoutside)
- startfacet->maxoutside= *bestdist;
-#endif
- }
- searchdist= qh_SEARCHdist; /* multiple of qh.max_outside and precision constants */
- minsearch= *bestdist - searchdist;
- if (ischeckmax) {
- /* Always check coplanar facets. Needed for RBOX 1000 s Z1 G1e-13 t996564279 | QHULL Tv */
- minimize_(minsearch, -searchdist);
- }
- coplanarset_size= 0;
- facet= startfacet;
- while (True) {
- trace4((qh ferr, "qh_findbesthorizon: neighbors of f%d bestdist %2.2g f%d ischeckmax? %d noupper? %d minsearch %2.2g searchdist %2.2g\n",
- facet->id, *bestdist, getid_(bestfacet), ischeckmax, noupper,
- minsearch, searchdist));
- FOREACHneighbor_(facet) {
- if (neighbor->visitid == visitid)
- continue;
- neighbor->visitid= visitid;
- if (!neighbor->flipped) {
- qh_distplane (point, neighbor, &dist);
- (*numpart)++;
- if (dist > *bestdist) {
- if (!neighbor->upperdelaunay || ischeckmax || (!noupper && dist >= qh MINoutside)) {
- bestfacet= neighbor;
- *bestdist= dist;
- newbest= True;
- if (!ischeckmax) {
- minsearch= dist - searchdist;
- if (dist > *bestdist + searchdist) {
- zinc_(Zfindjump); /* everything in qh.coplanarset at least searchdist below */
- coplanarset_size= 0;
- }
- }
- }
- }else if (dist < minsearch)
- continue; /* if ischeckmax, dist can't be positive */
-#if qh_MAXoutside
- if (ischeckmax && dist > neighbor->maxoutside)
- neighbor->maxoutside= dist;
-#endif
- } /* end of !flipped */
- if (nextfacet) {
- if (!coplanarset_size++) {
- SETfirst_(qh coplanarset)= nextfacet;
- SETtruncate_(qh coplanarset, 1);
- }else
- qh_setappend (&qh coplanarset, nextfacet); /* Was needed for RBOX 1000 s W1e-13 P0 t996547055 | QHULL d Qbb Qc Tv
- and RBOX 1000 s Z1 G1e-13 t996564279 | qhull Tv */
- }
- nextfacet= neighbor;
- } /* end of EACHneighbor */
- facet= nextfacet;
- if (facet)
- nextfacet= NULL;
- else if (!coplanarset_size)
- break;
- else if (!--coplanarset_size) {
- facet= SETfirst_(qh coplanarset);
- SETtruncate_(qh coplanarset, 0);
- }else
- facet= (facetT*)qh_setdellast (qh coplanarset);
- } /* while True, for each facet in qh.coplanarset */
- if (!ischeckmax) {
- zadd_(Zfindhorizontot, *numpart - numpartinit);
- zmax_(Zfindhorizonmax, *numpart - numpartinit);
- if (newbest)
- zinc_(Zparthorizon);
- }
- trace4((qh ferr, "qh_findbesthorizon: newbest? %d bestfacet f%d bestdist %2.2g\n", newbest, getid_(bestfacet), *bestdist));
- return bestfacet;
-} /* findbesthorizon */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="findbestnew">-</a>
-
- qh_findbestnew( point, startfacet, dist, isoutside, numpart )
- find best newfacet for point
- searches all of qh.newfacet_list starting at startfacet
- searches horizon facets of coplanar best newfacets
- searches all facets if startfacet == qh.facet_list
- returns:
- best new or horizon facet that is not upperdelaunay
- early out if isoutside and not 'Qf'
- dist is distance to facet
- isoutside is true if point is outside of facet
- numpart is number of distance tests
-
- notes:
- Always used for merged new facets (see qh_USEfindbestnew)
- Avoids upperdelaunay facet unless (isoutside and outside)
-
- Uses qh.visit_id, qh.coplanarset.
- If share visit_id with qh_findbest, coplanarset is incorrect.
-
- If merging (testhorizon), searches horizon facets of coplanar best facets because
- a point maybe coplanar to the bestfacet, below its horizon facet,
- and above a horizon facet of a coplanar newfacet. For example,
- rbox 1000 s Z1 G1e-13 | qhull
- rbox 1000 s W1e-13 P0 t992110337 | QHULL d Qbb Qc
-
- qh_findbestnew() used if
- qh_sharpnewfacets -- newfacets contains a sharp angle
- if many merges, qh_premerge found a merge, or 'Qf' (qh.findbestnew)
-
- see also:
- qh_partitionall() and qh_findbest()
-
- design:
- for each new facet starting from startfacet
- test distance from point to facet
- return facet if clearly outside
- unless upperdelaunay and a lowerdelaunay exists
- update best facet
- test horizon facets
-*/
-facetT *qh_findbestnew (pointT *point, facetT *startfacet,
- realT *dist, boolT bestoutside, boolT *isoutside, int *numpart) {
- realT bestdist= -REALmax/2;
- facetT *bestfacet= NULL, *facet;
- int oldtrace= qh IStracing, i;
- unsigned int visitid= ++qh visit_id;
- realT distoutside= 0.0;
- boolT isdistoutside; /* True if distoutside is defined */
- boolT testhorizon = True; /* needed if precise, e.g., rbox c D6 | qhull Q0 Tv */
-
- if (!startfacet) {
- if (qh MERGING)
- fprintf(qh ferr, "qhull precision error (qh_findbestnew): merging has formed and deleted a cone of new facets. Can not continue.\n");
- else
- fprintf(qh ferr, "qhull internal error (qh_findbestnew): no new facets for point p%d\n",
- qh furthest_id);
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- zinc_(Zfindnew);
- if (qh BESToutside || bestoutside)
- isdistoutside= False;
- else {
- isdistoutside= True;
- distoutside= qh_DISToutside; /* multiple of qh.MINoutside & qh.max_outside, see user.h */
- }
- if (isoutside)
- *isoutside= True;
- *numpart= 0;
- if (qh IStracing >= 3 || (qh TRACElevel && qh TRACEpoint >= 0 && qh TRACEpoint == qh_pointid (point))) {
- if (qh TRACElevel > qh IStracing)
- qh IStracing= qh TRACElevel;
- fprintf(qh ferr, "qh_findbestnew: point p%d facet f%d. Stop? %d if dist > %2.2g\n",
- qh_pointid(point), startfacet->id, isdistoutside, distoutside);
- fprintf(qh ferr, " Last point added p%d visitid %d.", qh furthest_id, visitid);
- fprintf(qh ferr, " Last merge was #%d.\n", zzval_(Ztotmerge));
- }
- /* visit all new facets starting with startfacet, maybe qh facet_list */
- for (i= 0, facet= startfacet; i < 2; i++, facet= qh newfacet_list) {
- FORALLfacet_(facet) {
- if (facet == startfacet && i)
- break;
- facet->visitid= visitid;
- if (!facet->flipped) {
- qh_distplane (point, facet, dist);
- (*numpart)++;
- if (*dist > bestdist) {
- if (!facet->upperdelaunay || *dist >= qh MINoutside) {
- bestfacet= facet;
- if (isdistoutside && *dist >= distoutside)
- goto LABELreturn_bestnew;
- bestdist= *dist;
- }
- }
- } /* end of !flipped */
- } /* FORALLfacet from startfacet or qh newfacet_list */
- }
- if (testhorizon || !bestfacet)
- bestfacet= qh_findbesthorizon (!qh_IScheckmax, point, bestfacet ? bestfacet : startfacet,
- !qh_NOupper, &bestdist, numpart);
- *dist= bestdist;
- if (isoutside && *dist < qh MINoutside)
- *isoutside= False;
-LABELreturn_bestnew:
- zadd_(Zfindnewtot, *numpart);
- zmax_(Zfindnewmax, *numpart);
- trace4((qh ferr, "qh_findbestnew: bestfacet f%d bestdist %2.2g\n", getid_(bestfacet), *dist));
- qh IStracing= oldtrace;
- return bestfacet;
-} /* findbestnew */
-
-/* ============ hyperplane functions -- keep code together [?] ============ */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="backnormal">-</a>
-
- qh_backnormal( rows, numrow, numcol, sign, normal, nearzero )
- given an upper-triangular rows array and a sign,
- solve for normal equation x using back substitution over rows U
-
- returns:
- normal= x
-
- if will not be able to divzero() when normalized (qh.MINdenom_2 and qh.MINdenom_1_2),
- if fails on last row
- this means that the hyperplane intersects [0,..,1]
- sets last coordinate of normal to sign
- otherwise
- sets tail of normal to [...,sign,0,...], i.e., solves for b= [0...0]
- sets nearzero
-
- notes:
- assumes numrow == numcol-1
-
- see Golub & van Loan 4.4-9 for back substitution
-
- solves Ux=b where Ax=b and PA=LU
- b= [0,...,0,sign or 0] (sign is either -1 or +1)
- last row of A= [0,...,0,1]
-
- 1) Ly=Pb == y=b since P only permutes the 0's of b
-
- design:
- for each row from end
- perform back substitution
- if near zero
- use qh_divzero for division
- if zero divide and not last row
- set tail of normal to 0
-*/
-void qh_backnormal (realT **rows, int numrow, int numcol, boolT sign,
- coordT *normal, boolT *nearzero) {
- int i, j;
- coordT *normalp, *normal_tail, *ai, *ak;
- realT diagonal;
- boolT waszero;
- int zerocol= -1;
-
- normalp= normal + numcol - 1;
- *normalp--= (sign ? -1.0 : 1.0);
- for(i= numrow; i--; ) {
- *normalp= 0.0;
- ai= rows[i] + i + 1;
- ak= normalp+1;
- for(j= i+1; j < numcol; j++)
- *normalp -= *ai++ * *ak++;
- diagonal= (rows[i])[i];
- if (fabs_(diagonal) > qh MINdenom_2)
- *(normalp--) /= diagonal;
- else {
- waszero= False;
- *normalp= qh_divzero (*normalp, diagonal, qh MINdenom_1_2, &waszero);
- if (waszero) {
- zerocol= i;
- *(normalp--)= (sign ? -1.0 : 1.0);
- for (normal_tail= normalp+2; normal_tail < normal + numcol; normal_tail++)
- *normal_tail= 0.0;
- }else
- normalp--;
- }
- }
- if (zerocol != -1) {
- zzinc_(Zback0);
- *nearzero= True;
- trace4((qh ferr, "qh_backnormal: zero diagonal at column %d.\n", i));
- qh_precision ("zero diagonal on back substitution");
- }
-} /* backnormal */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="gausselim">-</a>
-
- qh_gausselim( rows, numrow, numcol, sign )
- Gaussian elimination with partial pivoting
-
- returns:
- rows is upper triangular (includes row exchanges)
- flips sign for each row exchange
- sets nearzero if pivot[k] < qh.NEARzero[k], else clears it
-
- notes:
- if nearzero, the determinant's sign may be incorrect.
- assumes numrow <= numcol
-
- design:
- for each row
- determine pivot and exchange rows if necessary
- test for near zero
- perform gaussian elimination step
-*/
-void qh_gausselim(realT **rows, int numrow, int numcol, boolT *sign, boolT *nearzero) {
- realT *ai, *ak, *rowp, *pivotrow;
- realT n, pivot, pivot_abs= 0.0, temp;
- int i, j, k, pivoti, flip=0;
-
- *nearzero= False;
- for(k= 0; k < numrow; k++) {
- pivot_abs= fabs_((rows[k])[k]);
- pivoti= k;
- for(i= k+1; i < numrow; i++) {
- if ((temp= fabs_((rows[i])[k])) > pivot_abs) {
- pivot_abs= temp;
- pivoti= i;
- }
- }
- if (pivoti != k) {
- rowp= rows[pivoti];
- rows[pivoti]= rows[k];
- rows[k]= rowp;
- *sign ^= 1;
- flip ^= 1;
- }
- if (pivot_abs <= qh NEARzero[k]) {
- *nearzero= True;
- if (pivot_abs == 0.0) { /* remainder of column == 0 */
- if (qh IStracing >= 4) {
- fprintf (qh ferr, "qh_gausselim: 0 pivot at column %d. (%2.2g < %2.2g)\n", k, pivot_abs, qh DISTround);
- qh_printmatrix (qh ferr, "Matrix:", rows, numrow, numcol);
- }
- zzinc_(Zgauss0);
- qh_precision ("zero pivot for Gaussian elimination");
- goto LABELnextcol;
- }
- }
- pivotrow= rows[k] + k;
- pivot= *pivotrow++; /* signed value of pivot, and remainder of row */
- for(i= k+1; i < numrow; i++) {
- ai= rows[i] + k;
- ak= pivotrow;
- n= (*ai++)/pivot; /* divzero() not needed since |pivot| >= |*ai| */
- for(j= numcol - (k+1); j--; )
- *ai++ -= n * *ak++;
- }
- LABELnextcol:
- ;
- }
- wmin_(Wmindenom, pivot_abs); /* last pivot element */
- if (qh IStracing >= 5)
- qh_printmatrix (qh ferr, "qh_gausselem: result", rows, numrow, numcol);
-} /* gausselim */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="getangle">-</a>
-
- qh_getangle( vect1, vect2 )
- returns the dot product of two vectors
- if qh.RANDOMdist, joggles result
-
- notes:
- the angle may be > 1.0 or < -1.0 because of roundoff errors
-
-*/
-realT qh_getangle(pointT *vect1, pointT *vect2) {
- realT angle= 0, randr;
- int k;
-
- for(k= qh hull_dim; k--; )
- angle += *vect1++ * *vect2++;
- if (qh RANDOMdist) {
- randr= qh_RANDOMint;
- angle += (2.0 * randr / qh_RANDOMmax - 1.0) *
- qh RANDOMfactor;
- }
- trace4((qh ferr, "qh_getangle: %2.2g\n", angle));
- return(angle);
-} /* getangle */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="getcenter">-</a>
-
- qh_getcenter( vertices )
- returns arithmetic center of a set of vertices as a new point
-
- notes:
- allocates point array for center
-*/
-pointT *qh_getcenter(setT *vertices) {
- int k;
- pointT *center, *coord;
- vertexT *vertex, **vertexp;
- int count= qh_setsize(vertices);
-
- if (count < 2) {
- fprintf (qh ferr, "qhull internal error (qh_getcenter): not defined for %d points\n", count);
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- center= (pointT *)qh_memalloc(qh normal_size);
- for (k=0; k < qh hull_dim; k++) {
- coord= center+k;
- *coord= 0.0;
- FOREACHvertex_(vertices)
- *coord += vertex->point[k];
- *coord /= count;
- }
- return(center);
-} /* getcenter */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="getcentrum">-</a>
-
- qh_getcentrum( facet )
- returns the centrum for a facet as a new point
-
- notes:
- allocates the centrum
-*/
-pointT *qh_getcentrum(facetT *facet) {
- realT dist;
- pointT *centrum, *point;
-
- point= qh_getcenter(facet->vertices);
- zzinc_(Zcentrumtests);
- qh_distplane (point, facet, &dist);
- centrum= qh_projectpoint(point, facet, dist);
- qh_memfree(point, qh normal_size);
- trace4((qh ferr, "qh_getcentrum: for f%d, %d vertices dist= %2.2g\n",
- facet->id, qh_setsize(facet->vertices), dist));
- return centrum;
-} /* getcentrum */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="getdistance">-</a>
-
- qh_getdistance( facet, neighbor, mindist, maxdist )
- returns the maxdist and mindist distance of any vertex from neighbor
-
- returns:
- the max absolute value
-
- design:
- for each vertex of facet that is not in neighbor
- test the distance from vertex to neighbor
-*/
-realT qh_getdistance(facetT *facet, facetT *neighbor, realT *mindist, realT *maxdist) {
- vertexT *vertex, **vertexp;
- realT dist, maxd, mind;
-
- FOREACHvertex_(facet->vertices)
- vertex->seen= False;
- FOREACHvertex_(neighbor->vertices)
- vertex->seen= True;
- mind= 0.0;
- maxd= 0.0;
- FOREACHvertex_(facet->vertices) {
- if (!vertex->seen) {
- zzinc_(Zbestdist);
- qh_distplane(vertex->point, neighbor, &dist);
- if (dist < mind)
- mind= dist;
- else if (dist > maxd)
- maxd= dist;
- }
- }
- *mindist= mind;
- *maxdist= maxd;
- mind= -mind;
- if (maxd > mind)
- return maxd;
- else
- return mind;
-} /* getdistance */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="normalize">-</a>
-
- qh_normalize( normal, dim, toporient )
- normalize a vector and report if too small
- does not use min norm
-
- see:
- qh_normalize2
-*/
-void qh_normalize (coordT *normal, int dim, boolT toporient) {
- qh_normalize2( normal, dim, toporient, NULL, NULL);
-} /* normalize */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="normalize2">-</a>
-
- qh_normalize2( normal, dim, toporient, minnorm, ismin )
- normalize a vector and report if too small
- qh.MINdenom/MINdenom1 are the upper limits for divide overflow
-
- returns:
- normalized vector
- flips sign if !toporient
- if minnorm non-NULL,
- sets ismin if normal < minnorm
-
- notes:
- if zero norm
- sets all elements to sqrt(1.0/dim)
- if divide by zero (divzero ())
- sets largest element to +/-1
- bumps Znearlysingular
-
- design:
- computes norm
- test for minnorm
- if not near zero
- normalizes normal
- else if zero norm
- sets normal to standard value
- else
- uses qh_divzero to normalize
- if nearzero
- sets norm to direction of maximum value
-*/
-void qh_normalize2 (coordT *normal, int dim, boolT toporient,
- realT *minnorm, boolT *ismin) {
- int k;
- realT *colp, *maxp, norm= 0, temp, *norm1, *norm2, *norm3;
- boolT zerodiv;
-
- norm1= normal+1;
- norm2= normal+2;
- norm3= normal+3;
- if (dim == 2)
- norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1));
- else if (dim == 3)
- norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2));
- else if (dim == 4) {
- norm= sqrt((*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2)
- + (*norm3)*(*norm3));
- }else if (dim > 4) {
- norm= (*normal)*(*normal) + (*norm1)*(*norm1) + (*norm2)*(*norm2)
- + (*norm3)*(*norm3);
- for (k= dim-4, colp= normal+4; k--; colp++)
- norm += (*colp) * (*colp);
- norm= sqrt(norm);
- }
- if (minnorm) {
- if (norm < *minnorm)
- *ismin= True;
- else
- *ismin= False;
- }
- wmin_(Wmindenom, norm);
- if (norm > qh MINdenom) {
- if (!toporient)
- norm= -norm;
- *normal /= norm;
- *norm1 /= norm;
- if (dim == 2)
- ; /* all done */
- else if (dim == 3)
- *norm2 /= norm;
- else if (dim == 4) {
- *norm2 /= norm;
- *norm3 /= norm;
- }else if (dim >4) {
- *norm2 /= norm;
- *norm3 /= norm;
- for (k= dim-4, colp= normal+4; k--; )
- *colp++ /= norm;
- }
- }else if (norm == 0.0) {
- temp= sqrt (1.0/dim);
- for (k= dim, colp= normal; k--; )
- *colp++ = temp;
- }else {
- if (!toporient)
- norm= -norm;
- for (k= dim, colp= normal; k--; colp++) { /* k used below */
- temp= qh_divzero (*colp, norm, qh MINdenom_1, &zerodiv);
- if (!zerodiv)
- *colp= temp;
- else {
- maxp= qh_maxabsval(normal, dim);
- temp= ((*maxp * norm >= 0.0) ? 1.0 : -1.0);
- for (k= dim, colp= normal; k--; colp++)
- *colp= 0.0;
- *maxp= temp;
- zzinc_(Znearlysingular);
- trace0((qh ferr, "qh_normalize: norm=%2.2g too small during p%d\n",
- norm, qh furthest_id));
- return;
- }
- }
- }
-} /* normalize */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="projectpoint">-</a>
-
- qh_projectpoint( point, facet, dist )
- project point onto a facet by dist
-
- returns:
- returns a new point
-
- notes:
- if dist= distplane(point,facet)
- this projects point to hyperplane
- assumes qh_memfree_() is valid for normal_size
-*/
-pointT *qh_projectpoint(pointT *point, facetT *facet, realT dist) {
- pointT *newpoint, *np, *normal;
- int normsize= qh normal_size,k;
- void **freelistp; /* used !qh_NOmem */
-
- qh_memalloc_(normsize, freelistp, newpoint, pointT);
- np= newpoint;
- normal= facet->normal;
- for(k= qh hull_dim; k--; )
- *(np++)= *point++ - dist * *normal++;
- return(newpoint);
-} /* projectpoint */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="setfacetplane">-</a>
-
- qh_setfacetplane( facet )
- sets the hyperplane for a facet
- if qh.RANDOMdist, joggles hyperplane
-
- notes:
- uses global buffers qh.gm_matrix and qh.gm_row
- overwrites facet->normal if already defined
- updates Wnewvertex if PRINTstatistics
- sets facet->upperdelaunay if upper envelope of Delaunay triangulation
-
- design:
- copy vertex coordinates to qh.gm_matrix/gm_row
- compute determinate
- if nearzero
- recompute determinate with gaussian elimination
- if nearzero
- force outside orientation by testing interior point
-*/
-void qh_setfacetplane(facetT *facet) {
- pointT *point;
- vertexT *vertex, **vertexp;
- int k,i, normsize= qh normal_size, oldtrace= 0;
- realT dist;
- void **freelistp; /* used !qh_NOmem */
- coordT *coord, *gmcoord;
- pointT *point0= SETfirstt_(facet->vertices, vertexT)->point;
- boolT nearzero= False;
-
- zzinc_(Zsetplane);
- if (!facet->normal)
- qh_memalloc_(normsize, freelistp, facet->normal, coordT);
- if (facet == qh tracefacet) {
- oldtrace= qh IStracing;
- qh IStracing= 5;
- fprintf (qh ferr, "qh_setfacetplane: facet f%d created.\n", facet->id);
- fprintf (qh ferr, " Last point added to hull was p%d.", qh furthest_id);
- if (zzval_(Ztotmerge))
- fprintf(qh ferr, " Last merge was #%d.", zzval_(Ztotmerge));
- fprintf (qh ferr, "\n\nCurrent summary is:\n");
- qh_printsummary (qh ferr);
- }
- if (qh hull_dim <= 4) {
- i= 0;
- if (qh RANDOMdist) {
- gmcoord= qh gm_matrix;
- FOREACHvertex_(facet->vertices) {
- qh gm_row[i++]= gmcoord;
- coord= vertex->point;
- for (k= qh hull_dim; k--; )
- *(gmcoord++)= *coord++ * qh_randomfactor();
- }
- }else {
- FOREACHvertex_(facet->vertices)
- qh gm_row[i++]= vertex->point;
- }
- qh_sethyperplane_det(qh hull_dim, qh gm_row, point0, facet->toporient,
- facet->normal, &facet->offset, &nearzero);
- }
- if (qh hull_dim > 4 || nearzero) {
- i= 0;
- gmcoord= qh gm_matrix;
- FOREACHvertex_(facet->vertices) {
- if (vertex->point != point0) {
- qh gm_row[i++]= gmcoord;
- coord= vertex->point;
- point= point0;
- for(k= qh hull_dim; k--; )
- *(gmcoord++)= *coord++ - *point++;
- }
- }
- qh gm_row[i]= gmcoord; /* for areasimplex */
- if (qh RANDOMdist) {
- gmcoord= qh gm_matrix;
- for (i= qh hull_dim-1; i--; ) {
- for (k= qh hull_dim; k--; )
- *(gmcoord++) *= qh_randomfactor();
- }
- }
- qh_sethyperplane_gauss(qh hull_dim, qh gm_row, point0, facet->toporient,
- facet->normal, &facet->offset, &nearzero);
- if (nearzero) {
- if (qh_orientoutside (facet)) {
- trace0((qh ferr, "qh_setfacetplane: flipped orientation after testing interior_point during p%d\n", qh furthest_id));
- /* this is part of using Gaussian Elimination. For example in 5-d
- 1 1 1 1 0
- 1 1 1 1 1
- 0 0 0 1 0
- 0 1 0 0 0
- 1 0 0 0 0
- norm= 0.38 0.38 -0.76 0.38 0
- has a determinate of 1, but g.e. after subtracting pt. 0 has
- 0's in the diagonal, even with full pivoting. It does work
- if you subtract pt. 4 instead. */
- }
- }
- }
- facet->upperdelaunay= False;
- if (qh DELAUNAY) {
- if (qh UPPERdelaunay) { /* matches qh_triangulate_facet and qh.lower_threshold in qh_initbuild */
- if (facet->normal[qh hull_dim -1] >= qh ANGLEround * qh_ZEROdelaunay)
- facet->upperdelaunay= True;
- }else {
- if (facet->normal[qh hull_dim -1] > -qh ANGLEround * qh_ZEROdelaunay)
- facet->upperdelaunay= True;
- }
- }
- if (qh PRINTstatistics || qh IStracing || qh TRACElevel || qh JOGGLEmax < REALmax) {
- qh old_randomdist= qh RANDOMdist;
- qh RANDOMdist= False;
- FOREACHvertex_(facet->vertices) {
- if (vertex->point != point0) {
- boolT istrace= False;
- zinc_(Zdiststat);
- qh_distplane(vertex->point, facet, &dist);
- dist= fabs_(dist);
- zinc_(Znewvertex);
- wadd_(Wnewvertex, dist);
- if (dist > wwval_(Wnewvertexmax)) {
- wwval_(Wnewvertexmax)= dist;
- if (dist > qh max_outside) {
- qh max_outside= dist; /* used by qh_maxouter() */
- if (dist > qh TRACEdist)
- istrace= True;
- }
- }else if (-dist > qh TRACEdist)
- istrace= True;
- if (istrace) {
- fprintf (qh ferr, "qh_setfacetplane: ====== vertex p%d (v%d) increases max_outside to %2.2g for new facet f%d last p%d\n",
- qh_pointid(vertex->point), vertex->id, dist, facet->id, qh furthest_id);
- qh_errprint ("DISTANT", facet, NULL, NULL, NULL);
- }
- }
- }
- qh RANDOMdist= qh old_randomdist;
- }
- if (qh IStracing >= 3) {
- fprintf (qh ferr, "qh_setfacetplane: f%d offset %2.2g normal: ",
- facet->id, facet->offset);
- for (k=0; k < qh hull_dim; k++)
- fprintf (qh ferr, "%2.2g ", facet->normal[k]);
- fprintf (qh ferr, "\n");
- }
- if (facet == qh tracefacet)
- qh IStracing= oldtrace;
-} /* setfacetplane */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="sethyperplane_det">-</a>
-
- qh_sethyperplane_det( dim, rows, point0, toporient, normal, offset, nearzero )
- given dim X dim array indexed by rows[], one row per point,
- toporient (flips all signs),
- and point0 (any row)
- set normalized hyperplane equation from oriented simplex
-
- returns:
- normal (normalized)
- offset (places point0 on the hyperplane)
- sets nearzero if hyperplane not through points
-
- notes:
- only defined for dim == 2..4
- rows[] is not modified
- solves det(P-V_0, V_n-V_0, ..., V_1-V_0)=0, i.e. every point is on hyperplane
- see Bower & Woodworth, A programmer's geometry, Butterworths 1983.
-
- derivation of 3-d minnorm
- Goal: all vertices V_i within qh.one_merge of hyperplane
- Plan: exactly translate the facet so that V_0 is the origin
- exactly rotate the facet so that V_1 is on the x-axis and y_2=0.
- exactly rotate the effective perturbation to only effect n_0
- this introduces a factor of sqrt(3)
- n_0 = ((y_2-y_0)*(z_1-z_0) - (z_2-z_0)*(y_1-y_0)) / norm
- Let M_d be the max coordinate difference
- Let M_a be the greater of M_d and the max abs. coordinate
- Let u be machine roundoff and distround be max error for distance computation
- The max error for n_0 is sqrt(3) u M_a M_d / norm. n_1 is approx. 1 and n_2 is approx. 0
- The max error for distance of V_1 is sqrt(3) u M_a M_d M_d / norm. Offset=0 at origin
- Then minnorm = 1.8 u M_a M_d M_d / qh.ONEmerge
- Note that qh.one_merge is approx. 45.5 u M_a and norm is usually about M_d M_d
-
- derivation of 4-d minnorm
- same as above except rotate the facet so that V_1 on x-axis and w_2, y_3, w_3=0
- [if two vertices fixed on x-axis, can rotate the other two in yzw.]
- n_0 = det3_(...) = y_2 det2_(z_1, w_1, z_3, w_3) = - y_2 w_1 z_3
- [all other terms contain at least two factors nearly zero.]
- The max error for n_0 is sqrt(4) u M_a M_d M_d / norm
- Then minnorm = 2 u M_a M_d M_d M_d / qh.ONEmerge
- Note that qh.one_merge is approx. 82 u M_a and norm is usually about M_d M_d M_d
-*/
-void qh_sethyperplane_det (int dim, coordT **rows, coordT *point0,
- boolT toporient, coordT *normal, realT *offset, boolT *nearzero) {
- realT maxround, dist;
- int i;
- pointT *point;
-
-
- if (dim == 2) {
- normal[0]= dY(1,0);
- normal[1]= dX(0,1);
- qh_normalize2 (normal, dim, toporient, NULL, NULL);
- *offset= -(point0[0]*normal[0]+point0[1]*normal[1]);
- *nearzero= False; /* since nearzero norm => incident points */
- }else if (dim == 3) {
- normal[0]= det2_(dY(2,0), dZ(2,0),
- dY(1,0), dZ(1,0));
- normal[1]= det2_(dX(1,0), dZ(1,0),
- dX(2,0), dZ(2,0));
- normal[2]= det2_(dX(2,0), dY(2,0),
- dX(1,0), dY(1,0));
- qh_normalize2 (normal, dim, toporient, NULL, NULL);
- *offset= -(point0[0]*normal[0] + point0[1]*normal[1]
- + point0[2]*normal[2]);
- maxround= qh DISTround;
- for (i=dim; i--; ) {
- point= rows[i];
- if (point != point0) {
- dist= *offset + (point[0]*normal[0] + point[1]*normal[1]
- + point[2]*normal[2]);
- if (dist > maxround || dist < -maxround) {
- *nearzero= True;
- break;
- }
- }
- }
- }else if (dim == 4) {
- normal[0]= - det3_(dY(2,0), dZ(2,0), dW(2,0),
- dY(1,0), dZ(1,0), dW(1,0),
- dY(3,0), dZ(3,0), dW(3,0));
- normal[1]= det3_(dX(2,0), dZ(2,0), dW(2,0),
- dX(1,0), dZ(1,0), dW(1,0),
- dX(3,0), dZ(3,0), dW(3,0));
- normal[2]= - det3_(dX(2,0), dY(2,0), dW(2,0),
- dX(1,0), dY(1,0), dW(1,0),
- dX(3,0), dY(3,0), dW(3,0));
- normal[3]= det3_(dX(2,0), dY(2,0), dZ(2,0),
- dX(1,0), dY(1,0), dZ(1,0),
- dX(3,0), dY(3,0), dZ(3,0));
- qh_normalize2 (normal, dim, toporient, NULL, NULL);
- *offset= -(point0[0]*normal[0] + point0[1]*normal[1]
- + point0[2]*normal[2] + point0[3]*normal[3]);
- maxround= qh DISTround;
- for (i=dim; i--; ) {
- point= rows[i];
- if (point != point0) {
- dist= *offset + (point[0]*normal[0] + point[1]*normal[1]
- + point[2]*normal[2] + point[3]*normal[3]);
- if (dist > maxround || dist < -maxround) {
- *nearzero= True;
- break;
- }
- }
- }
- }
- if (*nearzero) {
- zzinc_(Zminnorm);
- trace0((qh ferr, "qh_sethyperplane_det: degenerate norm during p%d.\n", qh furthest_id));
- zzinc_(Znearlysingular);
- }
-} /* sethyperplane_det */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="sethyperplane_gauss">-</a>
-
- qh_sethyperplane_gauss( dim, rows, point0, toporient, normal, offset, nearzero )
- given (dim-1) X dim array of rows[i]= V_{i+1} - V_0 (point0)
- set normalized hyperplane equation from oriented simplex
-
- returns:
- normal (normalized)
- offset (places point0 on the hyperplane)
-
- notes:
- if nearzero
- orientation may be incorrect because of incorrect sign flips in gausselim
- solves [V_n-V_0,...,V_1-V_0, 0 .. 0 1] * N == [0 .. 0 1]
- or [V_n-V_0,...,V_1-V_0, 0 .. 0 1] * N == [0]
- i.e., N is normal to the hyperplane, and the unnormalized
- distance to [0 .. 1] is either 1 or 0
-
- design:
- perform gaussian elimination
- flip sign for negative values
- perform back substitution
- normalize result
- compute offset
-*/
-void qh_sethyperplane_gauss (int dim, coordT **rows, pointT *point0,
- boolT toporient, coordT *normal, coordT *offset, boolT *nearzero) {
- coordT *pointcoord, *normalcoef;
- int k;
- boolT sign= toporient, nearzero2= False;
-
- qh_gausselim(rows, dim-1, dim, &sign, nearzero);
- for(k= dim-1; k--; ) {
- if ((rows[k])[k] < 0)
- sign ^= 1;
- }
- if (*nearzero) {
- zzinc_(Znearlysingular);
- trace0((qh ferr, "qh_sethyperplane_gauss: nearly singular or axis parallel hyperplane during p%d.\n", qh furthest_id));
- qh_backnormal(rows, dim-1, dim, sign, normal, &nearzero2);
- }else {
- qh_backnormal(rows, dim-1, dim, sign, normal, &nearzero2);
- if (nearzero2) {
- zzinc_(Znearlysingular);
- trace0((qh ferr, "qh_sethyperplane_gauss: singular or axis parallel hyperplane at normalization during p%d.\n", qh furthest_id));
- }
- }
- if (nearzero2)
- *nearzero= True;
- qh_normalize2(normal, dim, True, NULL, NULL);
- pointcoord= point0;
- normalcoef= normal;
- *offset= -(*pointcoord++ * *normalcoef++);
- for(k= dim-1; k--; )
- *offset -= *pointcoord++ * *normalcoef++;
-} /* sethyperplane_gauss */
-
-
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/geom.h b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/geom.h
deleted file mode 100644
index 6b37268941f66df7a774ca3cdbb0fb22d89611b3..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/geom.h
+++ /dev/null
@@ -1,177 +0,0 @@
-/*<html><pre> -<a href="qh-geom.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- geom.h
- header file for geometric routines
-
- see qh-geom.htm and geom.c
-
- copyright (c) 1993-2003 The Geometry Center
-*/
-
-#ifndef qhDEFgeom
-#define qhDEFgeom 1
-
-/* ============ -macros- ======================== */
-
-/*-<a href="qh-geom.htm#TOC"
- >--------------------------------</a><a name="fabs_">-</a>
-
- fabs_(a)
- returns the absolute value of a
-*/
-#define fabs_( a ) ((( a ) < 0 ) ? -( a ):( a ))
-
-/*-<a href="qh-geom.htm#TOC"
- >--------------------------------</a><a name="fmax_">-</a>
-
- fmax_(a,b)
- returns the maximum value of a and b
-*/
-#define fmax_( a,b ) ( ( a ) < ( b ) ? ( b ) : ( a ) )
-
-/*-<a href="qh-geom.htm#TOC"
- >--------------------------------</a><a name="fmin_">-</a>
-
- fmin_(a,b)
- returns the minimum value of a and b
-*/
-#define fmin_( a,b ) ( ( a ) > ( b ) ? ( b ) : ( a ) )
-
-/*-<a href="qh-geom.htm#TOC"
- >--------------------------------</a><a name="maximize_">-</a>
-
- maximize_(maxval, val)
- set maxval to val if val is greater than maxval
-*/
-#define maximize_( maxval, val ) {if (( maxval ) < ( val )) ( maxval )= ( val );}
-
-/*-<a href="qh-geom.htm#TOC"
- >--------------------------------</a><a name="minimize_">-</a>
-
- minimize_(minval, val)
- set minval to val if val is less than minval
-*/
-#define minimize_( minval, val ) {if (( minval ) > ( val )) ( minval )= ( val );}
-
-/*-<a href="qh-geom.htm#TOC"
- >--------------------------------</a><a name="det2_">-</a>
-
- det2_(a1, a2,
- b1, b2)
-
- compute a 2-d determinate
-*/
-#define det2_( a1,a2,b1,b2 ) (( a1 )*( b2 ) - ( a2 )*( b1 ))
-
-/*-<a href="qh-geom.htm#TOC"
- >--------------------------------</a><a name="det3_">-</a>
-
- det3_(a1, a2, a3,
- b1, b2, b3,
- c1, c2, c3)
-
- compute a 3-d determinate
-*/
-#define det3_( a1,a2,a3,b1,b2,b3,c1,c2,c3 ) ( ( a1 )*det2_( b2,b3,c2,c3 ) \
- - ( b1 )*det2_( a2,a3,c2,c3 ) + ( c1 )*det2_( a2,a3,b2,b3 ) )
-
-/*-<a href="qh-geom.htm#TOC"
- >--------------------------------</a><a name="dX">-</a>
-
- dX( p1, p2 )
- dY( p1, p2 )
- dZ( p1, p2 )
-
- given two indices into rows[],
-
- compute the difference between X, Y, or Z coordinates
-*/
-#define dX( p1,p2 ) ( *( rows[p1] ) - *( rows[p2] ))
-#define dY( p1,p2 ) ( *( rows[p1]+1 ) - *( rows[p2]+1 ))
-#define dZ( p1,p2 ) ( *( rows[p1]+2 ) - *( rows[p2]+2 ))
-#define dW( p1,p2 ) ( *( rows[p1]+3 ) - *( rows[p2]+3 ))
-
-/*============= prototypes in alphabetical order, infrequent at end ======= */
-
-void qh_backnormal(realT** rows, int numrow, int numcol, boolT sign, coordT* normal, boolT* nearzero);
-void qh_distplane(pointT* point, facetT* facet, realT* dist);
-facetT* qh_findbest(pointT* point, facetT* startfacet,
- boolT bestoutside, boolT isnewfacets, boolT noupper,
- realT* dist, boolT* isoutside, int* numpart);
-facetT* qh_findbesthorizon(boolT ischeckmax, pointT* point,
- facetT* startfacet, boolT noupper, realT* bestdist, int* numpart);
-facetT* qh_findbestnew(pointT* point, facetT* startfacet, realT* dist,
- boolT bestoutside, boolT* isoutside, int* numpart);
-void qh_gausselim(realT** rows, int numrow, int numcol, boolT* sign, boolT* nearzero);
-realT qh_getangle(pointT* vect1, pointT* vect2);
-pointT* qh_getcenter(setT* vertices);
-pointT* qh_getcentrum(facetT* facet);
-realT qh_getdistance(facetT* facet, facetT* neighbor, realT* mindist, realT* maxdist);
-void qh_normalize(coordT* normal, int dim, boolT toporient);
-void qh_normalize2(coordT* normal, int dim, boolT toporient,
- realT* minnorm, boolT* ismin);
-pointT* qh_projectpoint(pointT* point, facetT* facet, realT dist);
-
-void qh_setfacetplane(facetT* newfacets);
-void qh_sethyperplane_det(int dim, coordT** rows, coordT* point0,
- boolT toporient, coordT* normal, realT* offset, boolT* nearzero);
-void qh_sethyperplane_gauss(int dim, coordT** rows, pointT* point0,
- boolT toporient, coordT* normal, coordT* offset, boolT* nearzero);
-boolT qh_sharpnewfacets(void);
-
-/*========= infrequently used code in geom2.c =============*/
-
-
-coordT* qh_copypoints(coordT* points, int numpoints, int dimension);
-void qh_crossproduct(int dim, realT vecA[3], realT vecB[3], realT vecC[3]);
-realT qh_determinant(realT** rows, int dim, boolT* nearzero);
-realT qh_detjoggle(pointT* points, int numpoints, int dimension);
-void qh_detroundoff(void);
-realT qh_detsimplex(pointT* apex, setT* points, int dim, boolT* nearzero);
-realT qh_distnorm(int dim, pointT* point, pointT* normal, realT* offsetp);
-realT qh_distround(int dimension, realT maxabs, realT maxsumabs);
-realT qh_divzero(realT numer, realT denom, realT mindenom1, boolT* zerodiv);
-realT qh_facetarea(facetT* facet);
-realT qh_facetarea_simplex(int dim, coordT* apex, setT* vertices,
- vertexT* notvertex, boolT toporient, coordT* normal, realT* offset);
-pointT* qh_facetcenter(setT* vertices);
-facetT* qh_findgooddist(pointT* point, facetT* facetA, realT* distp, facetT** facetlist);
-void qh_getarea(facetT* facetlist);
-boolT qh_gram_schmidt(int dim, realT** rows);
-boolT qh_inthresholds(coordT* normal, realT* angle);
-void qh_joggleinput(void);
-realT* qh_maxabsval(realT* normal, int dim);
-setT* qh_maxmin(pointT* points, int numpoints, int dimension);
-realT qh_maxouter(void);
-void qh_maxsimplex(int dim, setT* maxpoints, pointT* points, int numpoints, setT** simplex);
-realT qh_minabsval(realT* normal, int dim);
-int qh_mindiff(realT* vecA, realT* vecB, int dim);
-boolT qh_orientoutside(facetT* facet);
-void qh_outerinner(facetT* facet, realT* outerplane, realT* innerplane);
-coordT qh_pointdist(pointT* point1, pointT* point2, int dim);
-void qh_printmatrix(FILE* fp, char* string, realT** rows, int numrow, int numcol);
-void qh_printpoints(FILE* fp, char* string, setT* points);
-void qh_projectinput(void);
-void qh_projectpoints(signed char* project, int n, realT* points,
- int numpoints, int dim, realT* newpoints, int newdim);
-int qh_rand(void);
-void qh_srand(int seed);
-realT qh_randomfactor(void);
-void qh_randommatrix(realT* buffer, int dim, realT** row);
-void qh_rotateinput(realT** rows);
-void qh_rotatepoints(realT* points, int numpoints, int dim, realT** rows);
-void qh_scaleinput(void);
-void qh_scalelast(coordT* points, int numpoints, int dim, coordT low,
- coordT high, coordT newhigh);
-void qh_scalepoints(pointT* points, int numpoints, int dim,
- realT* newlows, realT* newhighs);
-boolT qh_sethalfspace(int dim, coordT* coords, coordT** nextp,
- coordT* normal, coordT* offset, coordT* feasible);
-coordT* qh_sethalfspace_all(int dim, int count, coordT* halfspaces, pointT* feasible);
-pointT* qh_voronoi_center(int dim, setT* points);
-
-#endif /* qhDEFgeom */
-
-
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/geom2.c b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/geom2.c
deleted file mode 100644
index 55b6d80832e49d0fd6842e04a26bab0fd7bb268f..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/geom2.c
+++ /dev/null
@@ -1,2160 +0,0 @@
-/*<html><pre> -<a href="qh-geom.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
-
- geom2.c
- infrequently used geometric routines of qhull
-
- see qh-geom.htm and geom.h
-
- copyright (c) 1993-2003 The Geometry Center
-
- frequently used code goes into geom.c
-*/
-
-#include "qhull_a.h"
-
-/*================== functions in alphabetic order ============*/
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="copypoints">-</a>
-
- qh_copypoints( points, numpoints, dimension)
- return malloc'd copy of points
-*/
-coordT *qh_copypoints (coordT *points, int numpoints, int dimension) {
- int size;
- coordT *newpoints;
-
- size= numpoints * dimension * sizeof(coordT);
- if (!(newpoints=(coordT*)malloc(size))) {
- fprintf(qh ferr, "qhull error: insufficient memory to copy %d points\n",
- numpoints);
- qh_errexit(qh_ERRmem, NULL, NULL);
- }
- memcpy ((char *)newpoints, (char *)points, size);
- return newpoints;
-} /* copypoints */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="crossproduct">-</a>
-
- qh_crossproduct( dim, vecA, vecB, vecC )
- crossproduct of 2 dim vectors
- C= A x B
-
- notes:
- from Glasner, Graphics Gems I, p. 639
- only defined for dim==3
-*/
-void qh_crossproduct (int dim, realT vecA[3], realT vecB[3], realT vecC[3]){
-
- if (dim == 3) {
- vecC[0]= det2_(vecA[1], vecA[2],
- vecB[1], vecB[2]);
- vecC[1]= - det2_(vecA[0], vecA[2],
- vecB[0], vecB[2]);
- vecC[2]= det2_(vecA[0], vecA[1],
- vecB[0], vecB[1]);
- }
-} /* vcross */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="determinant">-</a>
-
- qh_determinant( rows, dim, nearzero )
- compute signed determinant of a square matrix
- uses qh.NEARzero to test for degenerate matrices
-
- returns:
- determinant
- overwrites rows and the matrix
- if dim == 2 or 3
- nearzero iff determinant < qh NEARzero[dim-1]
- (not quite correct, not critical)
- if dim >= 4
- nearzero iff diagonal[k] < qh NEARzero[k]
-*/
-realT qh_determinant (realT **rows, int dim, boolT *nearzero) {
- realT det=0;
- int i;
- boolT sign= False;
-
- *nearzero= False;
- if (dim < 2) {
- fprintf (qh ferr, "qhull internal error (qh_determinate): only implemented for dimension >= 2\n");
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }else if (dim == 2) {
- det= det2_(rows[0][0], rows[0][1],
- rows[1][0], rows[1][1]);
- if (fabs_(det) < qh NEARzero[1]) /* not really correct, what should this be? */
- *nearzero= True;
- }else if (dim == 3) {
- det= det3_(rows[0][0], rows[0][1], rows[0][2],
- rows[1][0], rows[1][1], rows[1][2],
- rows[2][0], rows[2][1], rows[2][2]);
- if (fabs_(det) < qh NEARzero[2]) /* not really correct, what should this be? */
- *nearzero= True;
- }else {
- qh_gausselim(rows, dim, dim, &sign, nearzero); /* if nearzero, diagonal still ok*/
- det= 1.0;
- for (i= dim; i--; )
- det *= (rows[i])[i];
- if (sign)
- det= -det;
- }
- return det;
-} /* determinant */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="detjoggle">-</a>
-
- qh_detjoggle( points, numpoints, dimension )
- determine default max joggle for point array
- as qh_distround * qh_JOGGLEdefault
-
- returns:
- initial value for JOGGLEmax from points and REALepsilon
-
- notes:
- computes DISTround since qh_maxmin not called yet
- if qh SCALElast, last dimension will be scaled later to MAXwidth
-
- loop duplicated from qh_maxmin
-*/
-realT qh_detjoggle (pointT *points, int numpoints, int dimension) {
- realT abscoord, distround, joggle, maxcoord, mincoord;
- pointT *point, *pointtemp;
- realT maxabs= -REALmax;
- realT sumabs= 0;
- realT maxwidth= 0;
- int k;
-
- for (k= 0; k < dimension; k++) {
- if (qh SCALElast && k == dimension-1)
- abscoord= maxwidth;
- else if (qh DELAUNAY && k == dimension-1) /* will qh_setdelaunay() */
- abscoord= 2 * maxabs * maxabs; /* may be low by qh hull_dim/2 */
- else {
- maxcoord= -REALmax;
- mincoord= REALmax;
- FORALLpoint_(points, numpoints) {
- maximize_(maxcoord, point[k]);
- minimize_(mincoord, point[k]);
- }
- maximize_(maxwidth, maxcoord-mincoord);
- abscoord= fmax_(maxcoord, -mincoord);
- }
- sumabs += abscoord;
- maximize_(maxabs, abscoord);
- } /* for k */
- distround= qh_distround (qh hull_dim, maxabs, sumabs);
- joggle= distround * qh_JOGGLEdefault;
- maximize_(joggle, REALepsilon * qh_JOGGLEdefault);
- trace2((qh ferr, "qh_detjoggle: joggle=%2.2g maxwidth=%2.2g\n", joggle, maxwidth));
- return joggle;
-} /* detjoggle */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="detroundoff">-</a>
-
- qh_detroundoff()
- determine maximum roundoff errors from
- REALepsilon, REALmax, REALmin, qh.hull_dim, qh.MAXabs_coord,
- qh.MAXsumcoord, qh.MAXwidth, qh.MINdenom_1
-
- accounts for qh.SETroundoff, qh.RANDOMdist, qh MERGEexact
- qh.premerge_cos, qh.postmerge_cos, qh.premerge_centrum,
- qh.postmerge_centrum, qh.MINoutside,
- qh_RATIOnearinside, qh_COPLANARratio, qh_WIDEcoplanar
-
- returns:
- sets qh.DISTround, etc. (see below)
- appends precision constants to qh.qhull_options
-
- see:
- qh_maxmin() for qh.NEARzero
-
- design:
- determine qh.DISTround for distance computations
- determine minimum denominators for qh_divzero
- determine qh.ANGLEround for angle computations
- adjust qh.premerge_cos,... for roundoff error
- determine qh.ONEmerge for maximum error due to a single merge
- determine qh.NEARinside, qh.MAXcoplanar, qh.MINvisible,
- qh.MINoutside, qh.WIDEfacet
- initialize qh.max_vertex and qh.minvertex
-*/
-void qh_detroundoff (void) {
-
- qh_option ("_max-width", NULL, &qh MAXwidth);
- if (!qh SETroundoff) {
- qh DISTround= qh_distround (qh hull_dim, qh MAXabs_coord, qh MAXsumcoord);
- if (qh RANDOMdist)
- qh DISTround += qh RANDOMfactor * qh MAXabs_coord;
- qh_option ("Error-roundoff", NULL, &qh DISTround);
- }
- qh MINdenom= qh MINdenom_1 * qh MAXabs_coord;
- qh MINdenom_1_2= sqrt (qh MINdenom_1 * qh hull_dim) ; /* if will be normalized */
- qh MINdenom_2= qh MINdenom_1_2 * qh MAXabs_coord;
- /* for inner product */
- qh ANGLEround= 1.01 * qh hull_dim * REALepsilon;
- if (qh RANDOMdist)
- qh ANGLEround += qh RANDOMfactor;
- if (qh premerge_cos < REALmax/2) {
- qh premerge_cos -= qh ANGLEround;
- if (qh RANDOMdist)
- qh_option ("Angle-premerge-with-random", NULL, &qh premerge_cos);
- }
- if (qh postmerge_cos < REALmax/2) {
- qh postmerge_cos -= qh ANGLEround;
- if (qh RANDOMdist)
- qh_option ("Angle-postmerge-with-random", NULL, &qh postmerge_cos);
- }
- qh premerge_centrum += 2 * qh DISTround; /*2 for centrum and distplane()*/
- qh postmerge_centrum += 2 * qh DISTround;
- if (qh RANDOMdist && (qh MERGEexact || qh PREmerge))
- qh_option ("Centrum-premerge-with-random", NULL, &qh premerge_centrum);
- if (qh RANDOMdist && qh POSTmerge)
- qh_option ("Centrum-postmerge-with-random", NULL, &qh postmerge_centrum);
- { /* compute ONEmerge, max vertex offset for merging simplicial facets */
- realT maxangle= 1.0, maxrho;
-
- minimize_(maxangle, qh premerge_cos);
- minimize_(maxangle, qh postmerge_cos);
- /* max diameter * sin theta + DISTround for vertex to its hyperplane */
- qh ONEmerge= sqrt (qh hull_dim) * qh MAXwidth *
- sqrt (1.0 - maxangle * maxangle) + qh DISTround;
- maxrho= qh hull_dim * qh premerge_centrum + qh DISTround;
- maximize_(qh ONEmerge, maxrho);
- maxrho= qh hull_dim * qh postmerge_centrum + qh DISTround;
- maximize_(qh ONEmerge, maxrho);
- if (qh MERGING)
- qh_option ("_one-merge", NULL, &qh ONEmerge);
- }
- qh NEARinside= qh ONEmerge * qh_RATIOnearinside; /* only used if qh KEEPnearinside */
- if (qh JOGGLEmax < REALmax/2 && (qh KEEPcoplanar || qh KEEPinside)) {
- realT maxdist; /* adjust qh.NEARinside for joggle */
- qh KEEPnearinside= True;
- maxdist= sqrt (qh hull_dim) * qh JOGGLEmax + qh DISTround;
- maxdist= 2*maxdist; /* vertex and coplanar point can joggle in opposite directions */
- maximize_(qh NEARinside, maxdist); /* must agree with qh_nearcoplanar() */
- }
- if (qh KEEPnearinside)
- qh_option ("_near-inside", NULL, &qh NEARinside);
- if (qh JOGGLEmax < qh DISTround) {
- fprintf (qh ferr, "qhull error: the joggle for 'QJn', %.2g, is below roundoff for distance computations, %.2g\n",
- qh JOGGLEmax, qh DISTround);
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- if (qh MINvisible > REALmax/2) {
- if (!qh MERGING)
- qh MINvisible= qh DISTround;
- else if (qh hull_dim <= 3)
- qh MINvisible= qh premerge_centrum;
- else
- qh MINvisible= qh_COPLANARratio * qh premerge_centrum;
- if (qh APPROXhull && qh MINvisible > qh MINoutside)
- qh MINvisible= qh MINoutside;
- qh_option ("Visible-distance", NULL, &qh MINvisible);
- }
- if (qh MAXcoplanar > REALmax/2) {
- qh MAXcoplanar= qh MINvisible;
- qh_option ("U-coplanar-distance", NULL, &qh MAXcoplanar);
- }
- if (!qh APPROXhull) { /* user may specify qh MINoutside */
- qh MINoutside= 2 * qh MINvisible;
- if (qh premerge_cos < REALmax/2)
- maximize_(qh MINoutside, (1- qh premerge_cos) * qh MAXabs_coord);
- qh_option ("Width-outside", NULL, &qh MINoutside);
- }
- qh WIDEfacet= qh MINoutside;
- maximize_(qh WIDEfacet, qh_WIDEcoplanar * qh MAXcoplanar);
- maximize_(qh WIDEfacet, qh_WIDEcoplanar * qh MINvisible);
- qh_option ("_wide-facet", NULL, &qh WIDEfacet);
- if (qh MINvisible > qh MINoutside + 3 * REALepsilon
- && !qh BESToutside && !qh FORCEoutput)
- fprintf (qh ferr, "qhull input warning: minimum visibility V%.2g is greater than \nminimum outside W%.2g. Flipped facets are likely.\n",
- qh MINvisible, qh MINoutside);
- qh max_vertex= qh DISTround;
- qh min_vertex= -qh DISTround;
- /* numeric constants reported in printsummary */
-} /* detroundoff */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="detsimplex">-</a>
-
- qh_detsimplex( apex, points, dim, nearzero )
- compute determinant of a simplex with point apex and base points
-
- returns:
- signed determinant and nearzero from qh_determinant
-
- notes:
- uses qh.gm_matrix/qh.gm_row (assumes they're big enough)
-
- design:
- construct qm_matrix by subtracting apex from points
- compute determinate
-*/
-realT qh_detsimplex(pointT *apex, setT *points, int dim, boolT *nearzero) {
- pointT *coorda, *coordp, *gmcoord, *point, **pointp;
- coordT **rows;
- int k, i=0;
- realT det;
-
- zinc_(Zdetsimplex);
- gmcoord= qh gm_matrix;
- rows= qh gm_row;
- FOREACHpoint_(points) {
- if (i == dim)
- break;
- rows[i++]= gmcoord;
- coordp= point;
- coorda= apex;
- for (k= dim; k--; )
- *(gmcoord++)= *coordp++ - *coorda++;
- }
- if (i < dim) {
- fprintf (qh ferr, "qhull internal error (qh_detsimplex): #points %d < dimension %d\n",
- i, dim);
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- det= qh_determinant (rows, dim, nearzero);
- trace2((qh ferr, "qh_detsimplex: det=%2.2g for point p%d, dim %d, nearzero? %d\n",
- det, qh_pointid(apex), dim, *nearzero));
- return det;
-} /* detsimplex */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="distnorm">-</a>
-
- qh_distnorm( dim, point, normal, offset )
- return distance from point to hyperplane at normal/offset
-
- returns:
- dist
-
- notes:
- dist > 0 if point is outside of hyperplane
-
- see:
- qh_distplane in geom.c
-*/
-realT qh_distnorm (int dim, pointT *point, pointT *normal, realT *offsetp) {
- coordT *normalp= normal, *coordp= point;
- realT dist;
- int k;
-
- dist= *offsetp;
- for (k= dim; k--; )
- dist += *(coordp++) * *(normalp++);
- return dist;
-} /* distnorm */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="distround">-</a>
-
- qh_distround ( dimension, maxabs, maxsumabs )
- compute maximum round-off error for a distance computation
- to a normalized hyperplane
- maxabs is the maximum absolute value of a coordinate
- maxsumabs is the maximum possible sum of absolute coordinate values
-
- returns:
- max dist round for REALepsilon
-
- notes:
- calculate roundoff error according to
- Lemma 3.2-1 of Golub and van Loan "Matrix Computation"
- use sqrt(dim) since one vector is normalized
- or use maxsumabs since one vector is < 1
-*/
-realT qh_distround (int dimension, realT maxabs, realT maxsumabs) {
- realT maxdistsum, maxround;
-
- maxdistsum= sqrt (dimension) * maxabs;
- minimize_( maxdistsum, maxsumabs);
- maxround= REALepsilon * (dimension * maxdistsum * 1.01 + maxabs);
- /* adds maxabs for offset */
- trace4((qh ferr, "qh_distround: %2.2g maxabs %2.2g maxsumabs %2.2g maxdistsum %2.2g\n",
- maxround, maxabs, maxsumabs, maxdistsum));
- return maxround;
-} /* distround */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="divzero">-</a>
-
- qh_divzero( numer, denom, mindenom1, zerodiv )
- divide by a number that's nearly zero
- mindenom1= minimum denominator for dividing into 1.0
-
- returns:
- quotient
- sets zerodiv and returns 0.0 if it would overflow
-
- design:
- if numer is nearly zero and abs(numer) < abs(denom)
- return numer/denom
- else if numer is nearly zero
- return 0 and zerodiv
- else if denom/numer non-zero
- return numer/denom
- else
- return 0 and zerodiv
-*/
-realT qh_divzero (realT numer, realT denom, realT mindenom1, boolT *zerodiv) {
- realT temp, numerx, denomx;
-
-
- if (numer < mindenom1 && numer > -mindenom1) {
- numerx= fabs_(numer);
- denomx= fabs_(denom);
- if (numerx < denomx) {
- *zerodiv= False;
- return numer/denom;
- }else {
- *zerodiv= True;
- return 0.0;
- }
- }
- temp= denom/numer;
- if (temp > mindenom1 || temp < -mindenom1) {
- *zerodiv= False;
- return numer/denom;
- }else {
- *zerodiv= True;
- return 0.0;
- }
-} /* divzero */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="facetarea">-</a>
-
- qh_facetarea( facet )
- return area for a facet
-
- notes:
- if non-simplicial,
- uses centrum to triangulate facet and sums the projected areas.
- if (qh DELAUNAY),
- computes projected area instead for last coordinate
- assumes facet->normal exists
- projecting tricoplanar facets to the hyperplane does not appear to make a difference
-
- design:
- if simplicial
- compute area
- else
- for each ridge
- compute area from centrum to ridge
- negate area if upper Delaunay facet
-*/
-realT qh_facetarea (facetT *facet) {
- vertexT *apex;
- pointT *centrum;
- realT area= 0.0;
- ridgeT *ridge, **ridgep;
-
- if (facet->simplicial) {
- apex= SETfirstt_(facet->vertices, vertexT);
- area= qh_facetarea_simplex (qh hull_dim, apex->point, facet->vertices,
- apex, facet->toporient, facet->normal, &facet->offset);
- }else {
- if (qh CENTERtype == qh_AScentrum)
- centrum= facet->center;
- else
- centrum= qh_getcentrum (facet);
- FOREACHridge_(facet->ridges)
- area += qh_facetarea_simplex (qh hull_dim, centrum, ridge->vertices,
- NULL, (ridge->top == facet), facet->normal, &facet->offset);
- if (qh CENTERtype != qh_AScentrum)
- qh_memfree (centrum, qh normal_size);
- }
- if (facet->upperdelaunay && qh DELAUNAY)
- area= -area; /* the normal should be [0,...,1] */
- trace4((qh ferr, "qh_facetarea: f%d area %2.2g\n", facet->id, area));
- return area;
-} /* facetarea */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="facetarea_simplex">-</a>
-
- qh_facetarea_simplex( dim, apex, vertices, notvertex, toporient, normal, offset )
- return area for a simplex defined by
- an apex, a base of vertices, an orientation, and a unit normal
- if simplicial or tricoplanar facet,
- notvertex is defined and it is skipped in vertices
-
- returns:
- computes area of simplex projected to plane [normal,offset]
- returns 0 if vertex too far below plane (qh WIDEfacet)
- vertex can't be apex of tricoplanar facet
-
- notes:
- if (qh DELAUNAY),
- computes projected area instead for last coordinate
- uses qh gm_matrix/gm_row and qh hull_dim
- helper function for qh_facetarea
-
- design:
- if Notvertex
- translate simplex to apex
- else
- project simplex to normal/offset
- translate simplex to apex
- if Delaunay
- set last row/column to 0 with -1 on diagonal
- else
- set last row to Normal
- compute determinate
- scale and flip sign for area
-*/
-realT qh_facetarea_simplex (int dim, coordT *apex, setT *vertices,
- vertexT *notvertex, boolT toporient, coordT *normal, realT *offset) {
- pointT *coorda, *coordp, *gmcoord;
- coordT **rows, *normalp;
- int k, i=0;
- realT area, dist;
- vertexT *vertex, **vertexp;
- boolT nearzero;
-
- gmcoord= qh gm_matrix;
- rows= qh gm_row;
- FOREACHvertex_(vertices) {
- if (vertex == notvertex)
- continue;
- rows[i++]= gmcoord;
- coorda= apex;
- coordp= vertex->point;
- normalp= normal;
- if (notvertex) {
- for (k= dim; k--; )
- *(gmcoord++)= *coordp++ - *coorda++;
- }else {
- dist= *offset;
- for (k= dim; k--; )
- dist += *coordp++ * *normalp++;
- if (dist < -qh WIDEfacet) {
- zinc_(Znoarea);
- return 0.0;
- }
- coordp= vertex->point;
- normalp= normal;
- for (k= dim; k--; )
- *(gmcoord++)= (*coordp++ - dist * *normalp++) - *coorda++;
- }
- }
- if (i != dim-1) {
- fprintf (qh ferr, "qhull internal error (qh_facetarea_simplex): #points %d != dim %d -1\n",
- i, dim);
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- rows[i]= gmcoord;
- if (qh DELAUNAY) {
- for (i= 0; i < dim-1; i++)
- rows[i][dim-1]= 0.0;
- for (k= dim; k--; )
- *(gmcoord++)= 0.0;
- rows[dim-1][dim-1]= -1.0;
- }else {
- normalp= normal;
- for (k= dim; k--; )
- *(gmcoord++)= *normalp++;
- }
- zinc_(Zdetsimplex);
- area= qh_determinant (rows, dim, &nearzero);
- if (toporient)
- area= -area;
- area *= qh AREAfactor;
- trace4((qh ferr, "qh_facetarea_simplex: area=%2.2g for point p%d, toporient %d, nearzero? %d\n",
- area, qh_pointid(apex), toporient, nearzero));
- return area;
-} /* facetarea_simplex */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="facetcenter">-</a>
-
- qh_facetcenter( vertices )
- return Voronoi center (Voronoi vertex) for a facet's vertices
-
- returns:
- return temporary point equal to the center
-
- see:
- qh_voronoi_center()
-*/
-pointT *qh_facetcenter (setT *vertices) {
- setT *points= qh_settemp (qh_setsize (vertices));
- vertexT *vertex, **vertexp;
- pointT *center;
-
- FOREACHvertex_(vertices)
- qh_setappend (&points, vertex->point);
- center= qh_voronoi_center (qh hull_dim-1, points);
- qh_settempfree (&points);
- return center;
-} /* facetcenter */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="findgooddist">-</a>
-
- qh_findgooddist( point, facetA, dist, facetlist )
- find best good facet visible for point from facetA
- assumes facetA is visible from point
-
- returns:
- best facet, i.e., good facet that is furthest from point
- distance to best facet
- NULL if none
-
- moves good, visible facets (and some other visible facets)
- to end of qh facet_list
-
- notes:
- uses qh visit_id
-
- design:
- initialize bestfacet if facetA is good
- move facetA to end of facetlist
- for each facet on facetlist
- for each unvisited neighbor of facet
- move visible neighbors to end of facetlist
- update best good neighbor
- if no good neighbors, update best facet
-*/
-facetT *qh_findgooddist (pointT *point, facetT *facetA, realT *distp,
- facetT **facetlist) {
- realT bestdist= -REALmax, dist;
- facetT *neighbor, **neighborp, *bestfacet=NULL, *facet;
- boolT goodseen= False;
-
- if (facetA->good) {
- zinc_(Zcheckpart); /* calls from check_bestdist occur after print stats */
- qh_distplane (point, facetA, &bestdist);
- bestfacet= facetA;
- goodseen= True;
- }
- qh_removefacet (facetA);
- qh_appendfacet (facetA);
- *facetlist= facetA;
- facetA->visitid= ++qh visit_id;
- FORALLfacet_(*facetlist) {
- FOREACHneighbor_(facet) {
- if (neighbor->visitid == qh visit_id)
- continue;
- neighbor->visitid= qh visit_id;
- if (goodseen && !neighbor->good)
- continue;
- zinc_(Zcheckpart);
- qh_distplane (point, neighbor, &dist);
- if (dist > 0) {
- qh_removefacet (neighbor);
- qh_appendfacet (neighbor);
- if (neighbor->good) {
- goodseen= True;
- if (dist > bestdist) {
- bestdist= dist;
- bestfacet= neighbor;
- }
- }
- }
- }
- }
- if (bestfacet) {
- *distp= bestdist;
- trace2((qh ferr, "qh_findgooddist: p%d is %2.2g above good facet f%d\n",
- qh_pointid(point), bestdist, bestfacet->id));
- return bestfacet;
- }
- trace4((qh ferr, "qh_findgooddist: no good facet for p%d above f%d\n",
- qh_pointid(point), facetA->id));
- return NULL;
-} /* findgooddist */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="getarea">-</a>
-
- qh_getarea( facetlist )
- set area of all facets in facetlist
- collect statistics
-
- returns:
- sets qh totarea/totvol to total area and volume of convex hull
- for Delaunay triangulation, computes projected area of the lower or upper hull
- ignores upper hull if qh ATinfinity
-
- notes:
- could compute outer volume by expanding facet area by rays from interior
- the following attempt at perpendicular projection underestimated badly:
- qh.totoutvol += (-dist + facet->maxoutside + qh DISTround)
- * area/ qh hull_dim;
- design:
- for each facet on facetlist
- compute facet->area
- update qh.totarea and qh.totvol
-*/
-void qh_getarea (facetT *facetlist) {
- realT area;
- realT dist;
- facetT *facet;
-
- if (qh REPORTfreq)
- fprintf (qh ferr, "computing area of each facet and volume of the convex hull\n");
- else
- trace1((qh ferr, "qh_getarea: computing volume and area for each facet\n"));
- qh totarea= qh totvol= 0.0;
- FORALLfacet_(facetlist) {
- if (!facet->normal)
- continue;
- if (facet->upperdelaunay && qh ATinfinity)
- continue;
- facet->f.area= area= qh_facetarea (facet);
- facet->isarea= True;
- if (qh DELAUNAY) {
- if (facet->upperdelaunay == qh UPPERdelaunay)
- qh totarea += area;
- }else {
- qh totarea += area;
- qh_distplane (qh interior_point, facet, &dist);
- qh totvol += -dist * area/ qh hull_dim;
- }
- if (qh PRINTstatistics) {
- wadd_(Wareatot, area);
- wmax_(Wareamax, area);
- wmin_(Wareamin, area);
- }
- }
-} /* getarea */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="gram_schmidt">-</a>
-
- qh_gram_schmidt( dim, row )
- implements Gram-Schmidt orthogonalization by rows
-
- returns:
- false if zero norm
- overwrites rows[dim][dim]
-
- notes:
- see Golub & van Loan Algorithm 6.2-2
- overflow due to small divisors not handled
-
- design:
- for each row
- compute norm for row
- if non-zero, normalize row
- for each remaining rowA
- compute inner product of row and rowA
- reduce rowA by row * inner product
-*/
-boolT qh_gram_schmidt(int dim, realT **row) {
- realT *rowi, *rowj, norm;
- int i, j, k;
-
- for(i=0; i < dim; i++) {
- rowi= row[i];
- for (norm= 0.0, k= dim; k--; rowi++)
- norm += *rowi * *rowi;
- norm= sqrt(norm);
- wmin_(Wmindenom, norm);
- if (norm == 0.0) /* either 0 or overflow due to sqrt */
- return False;
- for(k= dim; k--; )
- *(--rowi) /= norm;
- for(j= i+1; j < dim; j++) {
- rowj= row[j];
- for(norm= 0.0, k=dim; k--; )
- norm += *rowi++ * *rowj++;
- for(k=dim; k--; )
- *(--rowj) -= *(--rowi) * norm;
- }
- }
- return True;
-} /* gram_schmidt */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="inthresholds">-</a>
-
- qh_inthresholds( normal, angle )
- return True if normal within qh.lower_/upper_threshold
-
- returns:
- estimate of angle by summing of threshold diffs
- angle may be NULL
- smaller "angle" is better
-
- notes:
- invalid if qh.SPLITthresholds
-
- see:
- qh.lower_threshold in qh_initbuild()
- qh_initthresholds()
-
- design:
- for each dimension
- test threshold
-*/
-boolT qh_inthresholds (coordT *normal, realT *angle) {
- boolT within= True;
- int k;
- realT threshold;
-
- if (angle)
- *angle= 0.0;
- for(k= 0; k < qh hull_dim; k++) {
- threshold= qh lower_threshold[k];
- if (threshold > -REALmax/2) {
- if (normal[k] < threshold)
- within= False;
- if (angle) {
- threshold -= normal[k];
- *angle += fabs_(threshold);
- }
- }
- if (qh upper_threshold[k] < REALmax/2) {
- threshold= qh upper_threshold[k];
- if (normal[k] > threshold)
- within= False;
- if (angle) {
- threshold -= normal[k];
- *angle += fabs_(threshold);
- }
- }
- }
- return within;
-} /* inthresholds */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="joggleinput">-</a>
-
- qh_joggleinput()
- randomly joggle input to Qhull by qh.JOGGLEmax
- initial input is qh.first_point/qh.num_points of qh.hull_dim
- repeated calls use qh.input_points/qh.num_points
-
- returns:
- joggles points at qh.first_point/qh.num_points
- copies data to qh.input_points/qh.input_malloc if first time
- determines qh.JOGGLEmax if it was zero
- if qh.DELAUNAY
- computes the Delaunay projection of the joggled points
-
- notes:
- if qh.DELAUNAY, unnecessarily joggles the last coordinate
- the initial 'QJn' may be set larger than qh_JOGGLEmaxincrease
-
- design:
- if qh.DELAUNAY
- set qh.SCALElast for reduced precision errors
- if first call
- initialize qh.input_points to the original input points
- if qh.JOGGLEmax == 0
- determine default qh.JOGGLEmax
- else
- increase qh.JOGGLEmax according to qh.build_cnt
- joggle the input by adding a random number in [-qh.JOGGLEmax,qh.JOGGLEmax]
- if qh.DELAUNAY
- sets the Delaunay projection
-*/
-void qh_joggleinput (void) {
- int size, i, seed;
- coordT *coordp, *inputp;
- realT randr, randa, randb;
-
- if (!qh input_points) { /* first call */
- qh input_points= qh first_point;
- qh input_malloc= qh POINTSmalloc;
- size= qh num_points * qh hull_dim * sizeof(coordT);
- if (!(qh first_point=(coordT*)malloc(size))) {
- fprintf(qh ferr, "qhull error: insufficient memory to joggle %d points\n",
- qh num_points);
- qh_errexit(qh_ERRmem, NULL, NULL);
- }
- qh POINTSmalloc= True;
- if (qh JOGGLEmax == 0.0) {
- qh JOGGLEmax= qh_detjoggle (qh input_points, qh num_points, qh hull_dim);
- qh_option ("QJoggle", NULL, &qh JOGGLEmax);
- }
- }else { /* repeated call */
- if (!qh RERUN && qh build_cnt > qh_JOGGLEretry) {
- if (((qh build_cnt-qh_JOGGLEretry-1) % qh_JOGGLEagain) == 0) {
- realT maxjoggle= qh MAXwidth * qh_JOGGLEmaxincrease;
- if (qh JOGGLEmax < maxjoggle) {
- qh JOGGLEmax *= qh_JOGGLEincrease;
- minimize_(qh JOGGLEmax, maxjoggle);
- }
- }
- }
- qh_option ("QJoggle", NULL, &qh JOGGLEmax);
- }
- if (qh build_cnt > 1 && qh JOGGLEmax > fmax_(qh MAXwidth/4, 0.1)) {
- fprintf (qh ferr, "qhull error: the current joggle for 'QJn', %.2g, is too large for the width\nof the input. If possible, recompile Qhull with higher-precision reals.\n",
- qh JOGGLEmax);
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- /* for some reason, using qh ROTATErandom and qh_RANDOMseed does not repeat the run. Use 'TRn' instead */
- seed= qh_RANDOMint;
- qh_option ("_joggle-seed", &seed, NULL);
- trace0((qh ferr, "qh_joggleinput: joggle input by %2.2g with seed %d\n",
- qh JOGGLEmax, seed));
- inputp= qh input_points;
- coordp= qh first_point;
- randa= 2.0 * qh JOGGLEmax/qh_RANDOMmax;
- randb= -qh JOGGLEmax;
- size= qh num_points * qh hull_dim;
- for (i= size; i--; ) {
- randr= qh_RANDOMint;
- *(coordp++)= *(inputp++) + (randr * randa + randb);
- }
- if (qh DELAUNAY) {
- qh last_low= qh last_high= qh last_newhigh= REALmax;
- qh_setdelaunay (qh hull_dim, qh num_points, qh first_point);
- }
-} /* joggleinput */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="maxabsval">-</a>
-
- qh_maxabsval( normal, dim )
- return pointer to maximum absolute value of a dim vector
- returns NULL if dim=0
-*/
-realT *qh_maxabsval (realT *normal, int dim) {
- realT maxval= -REALmax;
- realT *maxp= NULL, *colp, absval;
- int k;
-
- for (k= dim, colp= normal; k--; colp++) {
- absval= fabs_(*colp);
- if (absval > maxval) {
- maxval= absval;
- maxp= colp;
- }
- }
- return maxp;
-} /* maxabsval */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="maxmin">-</a>
-
- qh_maxmin( points, numpoints, dimension )
- return max/min points for each dimension
- determine max and min coordinates
-
- returns:
- returns a temporary set of max and min points
- may include duplicate points. Does not include qh.GOODpoint
- sets qh.NEARzero, qh.MAXabs_coord, qh.MAXsumcoord, qh.MAXwidth
- qh.MAXlastcoord, qh.MINlastcoord
- initializes qh.max_outside, qh.min_vertex, qh.WAScoplanar, qh.ZEROall_ok
-
- notes:
- loop duplicated in qh_detjoggle()
-
- design:
- initialize global precision variables
- checks definition of REAL...
- for each dimension
- for each point
- collect maximum and minimum point
- collect maximum of maximums and minimum of minimums
- determine qh.NEARzero for Gaussian Elimination
-*/
-setT *qh_maxmin(pointT *points, int numpoints, int dimension) {
- int k;
- realT maxcoord, temp;
- pointT *minimum, *maximum, *point, *pointtemp;
- setT *set;
-
- qh max_outside= 0.0;
- qh MAXabs_coord= 0.0;
- qh MAXwidth= -REALmax;
- qh MAXsumcoord= 0.0;
- qh min_vertex= 0.0;
- qh WAScoplanar= False;
- if (qh ZEROcentrum)
- qh ZEROall_ok= True;
- if (REALmin < REALepsilon && REALmin < REALmax && REALmin > -REALmax
- && REALmax > 0.0 && -REALmax < 0.0)
- ; /* all ok */
- else {
- fprintf (qh ferr, "qhull error: floating point constants in user.h are wrong\n\
-REALepsilon %g REALmin %g REALmax %g -REALmax %g\n",
- REALepsilon, REALmin, REALmax, -REALmax);
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- set= qh_settemp(2*dimension);
- for(k= 0; k < dimension; k++) {
- if (points == qh GOODpointp)
- minimum= maximum= points + dimension;
- else
- minimum= maximum= points;
- FORALLpoint_(points, numpoints) {
- if (point == qh GOODpointp)
- continue;
- if (maximum[k] < point[k])
- maximum= point;
- else if (minimum[k] > point[k])
- minimum= point;
- }
- if (k == dimension-1) {
- qh MINlastcoord= minimum[k];
- qh MAXlastcoord= maximum[k];
- }
- if (qh SCALElast && k == dimension-1)
- maxcoord= qh MAXwidth;
- else {
- maxcoord= fmax_(maximum[k], -minimum[k]);
- if (qh GOODpointp) {
- temp= fmax_(qh GOODpointp[k], -qh GOODpointp[k]);
- maximize_(maxcoord, temp);
- }
- temp= maximum[k] - minimum[k];
- maximize_(qh MAXwidth, temp);
- }
- maximize_(qh MAXabs_coord, maxcoord);
- qh MAXsumcoord += maxcoord;
- qh_setappend (&set, maximum);
- qh_setappend (&set, minimum);
- /* calculation of qh NEARzero is based on error formula 4.4-13 of
- Golub & van Loan, authors say n^3 can be ignored and 10 be used in
- place of rho */
- qh NEARzero[k]= 80 * qh MAXsumcoord * REALepsilon;
- }
- if (qh IStracing >=1)
- qh_printpoints (qh ferr, "qh_maxmin: found the max and min points (by dim):", set);
- return(set);
-} /* maxmin */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="maxouter">-</a>
-
- qh_maxouter()
- return maximum distance from facet to outer plane
- normally this is qh.max_outside+qh.DISTround
- does not include qh.JOGGLEmax
-
- see:
- qh_outerinner()
-
- notes:
- need to add another qh.DISTround if testing actual point with computation
-
- for joggle:
- qh_setfacetplane() updated qh.max_outer for Wnewvertexmax (max distance to vertex)
- need to use Wnewvertexmax since could have a coplanar point for a high
- facet that is replaced by a low facet
- need to add qh.JOGGLEmax if testing input points
-*/
-realT qh_maxouter (void) {
- realT dist;
-
- dist= fmax_(qh max_outside, qh DISTround);
- dist += qh DISTround;
- trace4((qh ferr, "qh_maxouter: max distance from facet to outer plane is %2.2g max_outside is %2.2g\n", dist, qh max_outside));
- return dist;
-} /* maxouter */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="maxsimplex">-</a>
-
- qh_maxsimplex( dim, maxpoints, points, numpoints, simplex )
- determines maximum simplex for a set of points
- starts from points already in simplex
- skips qh.GOODpointp (assumes that it isn't in maxpoints)
-
- returns:
- simplex with dim+1 points
-
- notes:
- assumes at least pointsneeded points in points
- maximizes determinate for x,y,z,w, etc.
- uses maxpoints as long as determinate is clearly non-zero
-
- design:
- initialize simplex with at least two points
- (find points with max or min x coordinate)
- for each remaining dimension
- add point that maximizes the determinate
- (use points from maxpoints first)
-*/
-void qh_maxsimplex (int dim, setT *maxpoints, pointT *points, int numpoints, setT **simplex) {
- pointT *point, **pointp, *pointtemp, *maxpoint, *minx=NULL, *maxx=NULL;
- boolT nearzero, maxnearzero= False;
- int k, sizinit;
- realT maxdet= -REALmax, det, mincoord= REALmax, maxcoord= -REALmax;
-
- sizinit= qh_setsize (*simplex);
- if (sizinit < 2) {
- if (qh_setsize (maxpoints) >= 2) {
- FOREACHpoint_(maxpoints) {
- if (maxcoord < point[0]) {
- maxcoord= point[0];
- maxx= point;
- }
- if (mincoord > point[0]) {
- mincoord= point[0];
- minx= point;
- }
- }
- }else {
- FORALLpoint_(points, numpoints) {
- if (point == qh GOODpointp)
- continue;
- if (maxcoord < point[0]) {
- maxcoord= point[0];
- maxx= point;
- }
- if (mincoord > point[0]) {
- mincoord= point[0];
- minx= point;
- }
- }
- }
- qh_setunique (simplex, minx);
- if (qh_setsize (*simplex) < 2)
- qh_setunique (simplex, maxx);
- sizinit= qh_setsize (*simplex);
- if (sizinit < 2) {
- qh_precision ("input has same x coordinate");
- if (zzval_(Zsetplane) > qh hull_dim+1) {
- fprintf (qh ferr, "qhull precision error (qh_maxsimplex for voronoi_center):\n%d points with the same x coordinate.\n",
- qh_setsize(maxpoints)+numpoints);
- qh_errexit (qh_ERRprec, NULL, NULL);
- }else {
- fprintf (qh ferr, "qhull input error: input is less than %d-dimensional since it has the same x coordinate\n", qh hull_dim);
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- }
- }
- for(k= sizinit; k < dim+1; k++) {
- maxpoint= NULL;
- maxdet= -REALmax;
- FOREACHpoint_(maxpoints) {
- if (!qh_setin (*simplex, point)) {
- det= qh_detsimplex(point, *simplex, k, &nearzero);
- if ((det= fabs_(det)) > maxdet) {
- maxdet= det;
- maxpoint= point;
- maxnearzero= nearzero;
- }
- }
- }
- if (!maxpoint || maxnearzero) {
- zinc_(Zsearchpoints);
- if (!maxpoint) {
- trace0((qh ferr, "qh_maxsimplex: searching all points for %d-th initial vertex.\n", k+1));
- }else {
- trace0((qh ferr, "qh_maxsimplex: searching all points for %d-th initial vertex, better than p%d det %2.2g\n",
- k+1, qh_pointid(maxpoint), maxdet));
- }
- FORALLpoint_(points, numpoints) {
- if (point == qh GOODpointp)
- continue;
- if (!qh_setin (*simplex, point)) {
- det= qh_detsimplex(point, *simplex, k, &nearzero);
- if ((det= fabs_(det)) > maxdet) {
- maxdet= det;
- maxpoint= point;
- maxnearzero= nearzero;
- }
- }
- }
- } /* !maxpoint */
- if (!maxpoint) {
- fprintf (qh ferr, "qhull internal error (qh_maxsimplex): not enough points available\n");
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- qh_setappend(simplex, maxpoint);
- trace1((qh ferr, "qh_maxsimplex: selected point p%d for %d`th initial vertex, det=%2.2g\n",
- qh_pointid(maxpoint), k+1, maxdet));
- } /* k */
-} /* maxsimplex */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="minabsval">-</a>
-
- qh_minabsval( normal, dim )
- return minimum absolute value of a dim vector
-*/
-realT qh_minabsval (realT *normal, int dim) {
- realT minval= 0;
- realT maxval= 0;
- realT *colp;
- int k;
-
- for (k= dim, colp= normal; k--; colp++) {
- maximize_(maxval, *colp);
- minimize_(minval, *colp);
- }
- return fmax_(maxval, -minval);
-} /* minabsval */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="mindiff">-</a>
-
- qh_mindif( vecA, vecB, dim )
- return index of min abs. difference of two vectors
-*/
-int qh_mindiff (realT *vecA, realT *vecB, int dim) {
- realT mindiff= REALmax, diff;
- realT *vecAp= vecA, *vecBp= vecB;
- int k, mink= 0;
-
- for (k= 0; k < dim; k++) {
- diff= *vecAp++ - *vecBp++;
- diff= fabs_(diff);
- if (diff < mindiff) {
- mindiff= diff;
- mink= k;
- }
- }
- return mink;
-} /* mindiff */
-
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="orientoutside">-</a>
-
- qh_orientoutside( facet )
- make facet outside oriented via qh.interior_point
-
- returns:
- True if facet reversed orientation.
-*/
-boolT qh_orientoutside (facetT *facet) {
- int k;
- realT dist;
-
- qh_distplane (qh interior_point, facet, &dist);
- if (dist > 0) {
- for (k= qh hull_dim; k--; )
- facet->normal[k]= -facet->normal[k];
- facet->offset= -facet->offset;
- return True;
- }
- return False;
-} /* orientoutside */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="outerinner">-</a>
-
- qh_outerinner( facet, outerplane, innerplane )
- if facet and qh.maxoutdone (i.e., qh_check_maxout)
- returns outer and inner plane for facet
- else
- returns maximum outer and inner plane
- accounts for qh.JOGGLEmax
-
- see:
- qh_maxouter(), qh_check_bestdist(), qh_check_points()
-
- notes:
- outerplaner or innerplane may be NULL
-
- includes qh.DISTround for actual points
- adds another qh.DISTround if testing with floating point arithmetic
-*/
-void qh_outerinner (facetT *facet, realT *outerplane, realT *innerplane) {
- realT dist, mindist;
- vertexT *vertex, **vertexp;
-
- if (outerplane) {
- if (!qh_MAXoutside || !facet || !qh maxoutdone) {
- *outerplane= qh_maxouter(); /* includes qh.DISTround */
- }else { /* qh_MAXoutside ... */
-#if qh_MAXoutside
- *outerplane= facet->maxoutside + qh DISTround;
-#endif
-
- }
- if (qh JOGGLEmax < REALmax/2)
- *outerplane += qh JOGGLEmax * sqrt (qh hull_dim);
- }
- if (innerplane) {
- if (facet) {
- mindist= REALmax;
- FOREACHvertex_(facet->vertices) {
- zinc_(Zdistio);
- qh_distplane (vertex->point, facet, &dist);
- minimize_(mindist, dist);
- }
- *innerplane= mindist - qh DISTround;
- }else
- *innerplane= qh min_vertex - qh DISTround;
- if (qh JOGGLEmax < REALmax/2)
- *innerplane -= qh JOGGLEmax * sqrt (qh hull_dim);
- }
-} /* outerinner */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="pointdist">-</a>
-
- qh_pointdist( point1, point2, dim )
- return distance between two points
-
- notes:
- returns distance squared if 'dim' is negative
-*/
-coordT qh_pointdist(pointT *point1, pointT *point2, int dim) {
- coordT dist, diff;
- int k;
-
- dist= 0.0;
- for (k= (dim > 0 ? dim : -dim); k--; ) {
- diff= *point1++ - *point2++;
- dist += diff * diff;
- }
- if (dim > 0)
- return(sqrt(dist));
- return dist;
-} /* pointdist */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="printmatrix">-</a>
-
- qh_printmatrix( fp, string, rows, numrow, numcol )
- print matrix to fp given by row vectors
- print string as header
-
- notes:
- print a vector by qh_printmatrix(fp, "", &vect, 1, len)
-*/
-void qh_printmatrix (FILE *fp, char *string, realT **rows, int numrow, int numcol) {
- realT *rowp;
- realT r; /*bug fix*/
- int i,k;
-
- fprintf (fp, "%s\n", string);
- for (i= 0; i < numrow; i++) {
- rowp= rows[i];
- for (k= 0; k < numcol; k++) {
- r= *rowp++;
- fprintf (fp, "%6.3g ", r);
- }
- fprintf (fp, "\n");
- }
-} /* printmatrix */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="printpoints">-</a>
-
- qh_printpoints( fp, string, points )
- print pointids to fp for a set of points
- if string, prints string and 'p' point ids
-*/
-void qh_printpoints (FILE *fp, char *string, setT *points) {
- pointT *point, **pointp;
-
- if (string) {
- fprintf (fp, "%s", string);
- FOREACHpoint_(points)
- fprintf (fp, " p%d", qh_pointid(point));
- fprintf (fp, "\n");
- }else {
- FOREACHpoint_(points)
- fprintf (fp, " %d", qh_pointid(point));
- fprintf (fp, "\n");
- }
-} /* printpoints */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="projectinput">-</a>
-
- qh_projectinput()
- project input points using qh.lower_bound/upper_bound and qh DELAUNAY
- if qh.lower_bound[k]=qh.upper_bound[k]= 0,
- removes dimension k
- if halfspace intersection
- removes dimension k from qh.feasible_point
- input points in qh first_point, num_points, input_dim
-
- returns:
- new point array in qh first_point of qh hull_dim coordinates
- sets qh POINTSmalloc
- if qh DELAUNAY
- projects points to paraboloid
- lowbound/highbound is also projected
- if qh ATinfinity
- adds point "at-infinity"
- if qh POINTSmalloc
- frees old point array
-
- notes:
- checks that qh.hull_dim agrees with qh.input_dim, PROJECTinput, and DELAUNAY
-
-
- design:
- sets project[k] to -1 (delete), 0 (keep), 1 (add for Delaunay)
- determines newdim and newnum for qh hull_dim and qh num_points
- projects points to newpoints
- projects qh.lower_bound to itself
- projects qh.upper_bound to itself
- if qh DELAUNAY
- if qh ATINFINITY
- projects points to paraboloid
- computes "infinity" point as vertex average and 10% above all points
- else
- uses qh_setdelaunay to project points to paraboloid
-*/
-void qh_projectinput (void) {
- int k,i;
- int newdim= qh input_dim, newnum= qh num_points;
- signed char *project;
- int size= (qh input_dim+1)*sizeof(*project);
- pointT *newpoints, *coord, *infinity;
- realT paraboloid, maxboloid= 0;
-
- project= (signed char*)qh_memalloc (size);
- memset ((char*)project, 0, size);
- for (k= 0; k < qh input_dim; k++) { /* skip Delaunay bound */
- if (qh lower_bound[k] == 0 && qh upper_bound[k] == 0) {
- project[k]= -1;
- newdim--;
- }
- }
- if (qh DELAUNAY) {
- project[k]= 1;
- newdim++;
- if (qh ATinfinity)
- newnum++;
- }
- if (newdim != qh hull_dim) {
- fprintf(qh ferr, "qhull internal error (qh_projectinput): dimension after projection %d != hull_dim %d\n", newdim, qh hull_dim);
- qh_errexit(qh_ERRqhull, NULL, NULL);
- }
- if (!(newpoints=(coordT*)malloc(newnum*newdim*sizeof(coordT)))){
- fprintf(qh ferr, "qhull error: insufficient memory to project %d points\n",
- qh num_points);
- qh_errexit(qh_ERRmem, NULL, NULL);
- }
- qh_projectpoints (project, qh input_dim+1, qh first_point,
- qh num_points, qh input_dim, newpoints, newdim);
- trace1((qh ferr, "qh_projectinput: updating lower and upper_bound\n"));
- qh_projectpoints (project, qh input_dim+1, qh lower_bound,
- 1, qh input_dim+1, qh lower_bound, newdim+1);
- qh_projectpoints (project, qh input_dim+1, qh upper_bound,
- 1, qh input_dim+1, qh upper_bound, newdim+1);
- if (qh HALFspace) {
- if (!qh feasible_point) {
- fprintf(qh ferr, "qhull internal error (qh_projectinput): HALFspace defined without qh.feasible_point\n");
- qh_errexit(qh_ERRqhull, NULL, NULL);
- }
- qh_projectpoints (project, qh input_dim, qh feasible_point,
- 1, qh input_dim, qh feasible_point, newdim);
- }
- qh_memfree(project, ((qh input_dim+1)*sizeof(*project)));
- if (qh POINTSmalloc)
- free (qh first_point);
- qh first_point= newpoints;
- qh POINTSmalloc= True;
- if (qh DELAUNAY && qh ATinfinity) {
- coord= qh first_point;
- infinity= qh first_point + qh hull_dim * qh num_points;
- for (k=qh hull_dim-1; k--; )
- infinity[k]= 0.0;
- for (i=qh num_points; i--; ) {
- paraboloid= 0.0;
- for (k=0; k < qh hull_dim-1; k++) {
- paraboloid += *coord * *coord;
- infinity[k] += *coord;
- coord++;
- }
- *(coord++)= paraboloid;
- maximize_(maxboloid, paraboloid);
- }
- /* coord == infinity */
- for (k=qh hull_dim-1; k--; )
- *(coord++) /= qh num_points;
- *(coord++)= maxboloid * 1.1;
- qh num_points++;
- trace0((qh ferr, "qh_projectinput: projected points to paraboloid for Delaunay\n"));
- }else if (qh DELAUNAY) /* !qh ATinfinity */
- qh_setdelaunay( qh hull_dim, qh num_points, qh first_point);
-} /* projectinput */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="projectpoints">-</a>
-
- qh_projectpoints( project, n, points, numpoints, dim, newpoints, newdim )
- project points/numpoints/dim to newpoints/newdim
- if project[k] == -1
- delete dimension k
- if project[k] == 1
- add dimension k by duplicating previous column
- n is size of project
-
- notes:
- newpoints may be points if only adding dimension at end
-
- design:
- check that 'project' and 'newdim' agree
- for each dimension
- if project == -1
- skip dimension
- else
- determine start of column in newpoints
- determine start of column in points
- if project == +1, duplicate previous column
- copy dimension (column) from points to newpoints
-*/
-void qh_projectpoints (signed char *project, int n, realT *points,
- int numpoints, int dim, realT *newpoints, int newdim) {
- int testdim= dim, oldk=0, newk=0, i,j=0,k;
- realT *newp, *oldp;
-
- for (k= 0; k < n; k++)
- testdim += project[k];
- if (testdim != newdim) {
- fprintf (qh ferr, "qhull internal error (qh_projectpoints): newdim %d should be %d after projection\n",
- newdim, testdim);
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- for (j= 0; j<n; j++) {
- if (project[j] == -1)
- oldk++;
- else {
- newp= newpoints+newk++;
- if (project[j] == +1) {
- if (oldk >= dim)
- continue;
- oldp= points+oldk;
- }else
- oldp= points+oldk++;
- for (i=numpoints; i--; ) {
- *newp= *oldp;
- newp += newdim;
- oldp += dim;
- }
- }
- if (oldk >= dim)
- break;
- }
- trace1((qh ferr, "qh_projectpoints: projected %d points from dim %d to dim %d\n",
- numpoints, dim, newdim));
-} /* projectpoints */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="rand">-</a>
-
- qh_rand()
- qh_srand( seed )
- generate pseudo-random number between 1 and 2^31 -2
-
- notes:
- from Park & Miller's minimimal standard random number generator
- Communications of the ACM, 31:1192-1201, 1988.
- does not use 0 or 2^31 -1
- this is silently enforced by qh_srand()
- can make 'Rn' much faster by moving qh_rand to qh_distplane
-*/
-int qh_rand_seed= 1; /* define as global variable instead of using qh */
-
-int qh_rand( void) {
-#define qh_rand_a 16807
-#define qh_rand_m 2147483647
-#define qh_rand_q 127773 /* m div a */
-#define qh_rand_r 2836 /* m mod a */
- int lo, hi, test;
- int seed = qh_rand_seed;
-
- hi = seed / qh_rand_q; /* seed div q */
- lo = seed % qh_rand_q; /* seed mod q */
- test = qh_rand_a * lo - qh_rand_r * hi;
- if (test > 0)
- seed= test;
- else
- seed= test + qh_rand_m;
- qh_rand_seed= seed;
- /* seed = seed < qh_RANDOMmax/2 ? 0 : qh_RANDOMmax; for testing */
- /* seed = qh_RANDOMmax; for testing */
- return seed;
-} /* rand */
-
-void qh_srand( int seed) {
- if (seed < 1)
- qh_rand_seed= 1;
- else if (seed >= qh_rand_m)
- qh_rand_seed= qh_rand_m - 1;
- else
- qh_rand_seed= seed;
-} /* qh_srand */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="randomfactor">-</a>
-
- qh_randomfactor()
- return a random factor within qh.RANDOMmax of 1.0
-
- notes:
- qh.RANDOMa/b are defined in global.c
-*/
-realT qh_randomfactor (void) {
- realT randr;
-
- randr= qh_RANDOMint;
- return randr * qh RANDOMa + qh RANDOMb;
-} /* randomfactor */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="randommatrix">-</a>
-
- qh_randommatrix( buffer, dim, rows )
- generate a random dim X dim matrix in range [-1,1]
- assumes buffer is [dim+1, dim]
-
- returns:
- sets buffer to random numbers
- sets rows to rows of buffer
- sets row[dim] as scratch row
-*/
-void qh_randommatrix (realT *buffer, int dim, realT **rows) {
- int i, k;
- realT **rowi, *coord, realr;
-
- coord= buffer;
- rowi= rows;
- for (i=0; i < dim; i++) {
- *(rowi++)= coord;
- for (k=0; k < dim; k++) {
- realr= qh_RANDOMint;
- *(coord++)= 2.0 * realr/(qh_RANDOMmax+1) - 1.0;
- }
- }
- *rowi= coord;
-} /* randommatrix */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="rotateinput">-</a>
-
- qh_rotateinput( rows )
- rotate input using row matrix
- input points given by qh first_point, num_points, hull_dim
- assumes rows[dim] is a scratch buffer
- if qh POINTSmalloc, overwrites input points, else mallocs a new array
-
- returns:
- rotated input
- sets qh POINTSmalloc
-
- design:
- see qh_rotatepoints
-*/
-void qh_rotateinput (realT **rows) {
-
- if (!qh POINTSmalloc) {
- qh first_point= qh_copypoints (qh first_point, qh num_points, qh hull_dim);
- qh POINTSmalloc= True;
- }
- qh_rotatepoints (qh first_point, qh num_points, qh hull_dim, rows);
-} /* rotateinput */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="rotatepoints">-</a>
-
- qh_rotatepoints( points, numpoints, dim, row )
- rotate numpoints points by a d-dim row matrix
- assumes rows[dim] is a scratch buffer
-
- returns:
- rotated points in place
-
- design:
- for each point
- for each coordinate
- use row[dim] to compute partial inner product
- for each coordinate
- rotate by partial inner product
-*/
-void qh_rotatepoints (realT *points, int numpoints, int dim, realT **row) {
- realT *point, *rowi, *coord= NULL, sum, *newval;
- int i,j,k;
-
- if (qh IStracing >= 1)
- qh_printmatrix (qh ferr, "qh_rotatepoints: rotate points by", row, dim, dim);
- for (point= points, j= numpoints; j--; point += dim) {
- newval= row[dim];
- for (i= 0; i < dim; i++) {
- rowi= row[i];
- coord= point;
- for (sum= 0.0, k= dim; k--; )
- sum += *rowi++ * *coord++;
- *(newval++)= sum;
- }
- for (k= dim; k--; )
- *(--coord)= *(--newval);
- }
-} /* rotatepoints */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="scaleinput">-</a>
-
- qh_scaleinput()
- scale input points using qh low_bound/high_bound
- input points given by qh first_point, num_points, hull_dim
- if qh POINTSmalloc, overwrites input points, else mallocs a new array
-
- returns:
- scales coordinates of points to low_bound[k], high_bound[k]
- sets qh POINTSmalloc
-
- design:
- see qh_scalepoints
-*/
-void qh_scaleinput (void) {
-
- if (!qh POINTSmalloc) {
- qh first_point= qh_copypoints (qh first_point, qh num_points, qh hull_dim);
- qh POINTSmalloc= True;
- }
- qh_scalepoints (qh first_point, qh num_points, qh hull_dim,
- qh lower_bound, qh upper_bound);
-} /* scaleinput */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="scalelast">-</a>
-
- qh_scalelast( points, numpoints, dim, low, high, newhigh )
- scale last coordinate to [0,m] for Delaunay triangulations
- input points given by points, numpoints, dim
-
- returns:
- changes scale of last coordinate from [low, high] to [0, newhigh]
- overwrites last coordinate of each point
- saves low/high/newhigh in qh.last_low, etc. for qh_setdelaunay()
-
- notes:
- when called by qh_setdelaunay, low/high may not match actual data
-
- design:
- compute scale and shift factors
- apply to last coordinate of each point
-*/
-void qh_scalelast (coordT *points, int numpoints, int dim, coordT low,
- coordT high, coordT newhigh) {
- realT scale, shift;
- coordT *coord;
- int i;
- boolT nearzero= False;
-
- trace4((qh ferr, "qh_scalelast: scale last coordinate from [%2.2g, %2.2g] to [0,%2.2g]\n",
- low, high, newhigh));
- qh last_low= low;
- qh last_high= high;
- qh last_newhigh= newhigh;
- scale= qh_divzero (newhigh, high - low,
- qh MINdenom_1, &nearzero);
- if (nearzero) {
- if (qh DELAUNAY)
- fprintf (qh ferr, "qhull input error: can not scale last coordinate. Input is cocircular\n or cospherical. Use option 'Qz' to add a point at infinity.\n");
- else
- fprintf (qh ferr, "qhull input error: can not scale last coordinate. New bounds [0, %2.2g] are too wide for\nexisting bounds [%2.2g, %2.2g] (width %2.2g)\n",
- newhigh, low, high, high-low);
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- shift= - low * newhigh / (high-low);
- coord= points + dim - 1;
- for (i= numpoints; i--; coord += dim)
- *coord= *coord * scale + shift;
-} /* scalelast */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="scalepoints">-</a>
-
- qh_scalepoints( points, numpoints, dim, newlows, newhighs )
- scale points to new lowbound and highbound
- retains old bound when newlow= -REALmax or newhigh= +REALmax
-
- returns:
- scaled points
- overwrites old points
-
- design:
- for each coordinate
- compute current low and high bound
- compute scale and shift factors
- scale all points
- enforce new low and high bound for all points
-*/
-void qh_scalepoints (pointT *points, int numpoints, int dim,
- realT *newlows, realT *newhighs) {
- int i,k;
- realT shift, scale, *coord, low, high, newlow, newhigh, mincoord, maxcoord;
- boolT nearzero= False;
-
- for (k= 0; k < dim; k++) {
- newhigh= newhighs[k];
- newlow= newlows[k];
- if (newhigh > REALmax/2 && newlow < -REALmax/2)
- continue;
- low= REALmax;
- high= -REALmax;
- for (i= numpoints, coord= points+k; i--; coord += dim) {
- minimize_(low, *coord);
- maximize_(high, *coord);
- }
- if (newhigh > REALmax/2)
- newhigh= high;
- if (newlow < -REALmax/2)
- newlow= low;
- if (qh DELAUNAY && k == dim-1 && newhigh < newlow) {
- fprintf (qh ferr, "qhull input error: 'Qb%d' or 'QB%d' inverts paraboloid since high bound %.2g < low bound %.2g\n",
- k, k, newhigh, newlow);
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- scale= qh_divzero (newhigh - newlow, high - low,
- qh MINdenom_1, &nearzero);
- if (nearzero) {
- fprintf (qh ferr, "qhull input error: %d'th dimension's new bounds [%2.2g, %2.2g] too wide for\nexisting bounds [%2.2g, %2.2g]\n",
- k, newlow, newhigh, low, high);
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- shift= (newlow * high - low * newhigh)/(high-low);
- coord= points+k;
- for (i= numpoints; i--; coord += dim)
- *coord= *coord * scale + shift;
- coord= points+k;
- if (newlow < newhigh) {
- mincoord= newlow;
- maxcoord= newhigh;
- }else {
- mincoord= newhigh;
- maxcoord= newlow;
- }
- for (i= numpoints; i--; coord += dim) {
- minimize_(*coord, maxcoord); /* because of roundoff error */
- maximize_(*coord, mincoord);
- }
- trace0((qh ferr, "qh_scalepoints: scaled %d'th coordinate [%2.2g, %2.2g] to [%.2g, %.2g] for %d points by %2.2g and shifted %2.2g\n",
- k, low, high, newlow, newhigh, numpoints, scale, shift));
- }
-} /* scalepoints */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="setdelaunay">-</a>
-
- qh_setdelaunay( dim, count, points )
- project count points to dim-d paraboloid for Delaunay triangulation
-
- dim is one more than the dimension of the input set
- assumes dim is at least 3 (i.e., at least a 2-d Delaunay triangulation)
-
- points is a dim*count realT array. The first dim-1 coordinates
- are the coordinates of the first input point. array[dim] is
- the first coordinate of the second input point. array[2*dim] is
- the first coordinate of the third input point.
-
- if qh.last_low defined (i.e., 'Qbb' called qh_scalelast)
- calls qh_scalelast to scale the last coordinate the same as the other points
-
- returns:
- for each point
- sets point[dim-1] to sum of squares of coordinates
- scale points to 'Qbb' if needed
-
- notes:
- to project one point, use
- qh_setdelaunay (qh hull_dim, 1, point)
-
- Do not use options 'Qbk', 'QBk', or 'QbB' since they scale
- the coordinates after the original projection.
-
-*/
-void qh_setdelaunay (int dim, int count, pointT *points) {
- int i, k;
- coordT *coordp, coord;
- realT paraboloid;
-
- trace0((qh ferr, "qh_setdelaunay: project %d points to paraboloid for Delaunay triangulation\n", count));
- coordp= points;
- for (i= 0; i < count; i++) {
- coord= *coordp++;
- paraboloid= coord*coord;
- for (k= dim-2; k--; ) {
- coord= *coordp++;
- paraboloid += coord*coord;
- }
- *coordp++ = paraboloid;
- }
- if (qh last_low < REALmax/2)
- qh_scalelast (points, count, dim, qh last_low, qh last_high, qh last_newhigh);
-} /* setdelaunay */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="sethalfspace">-</a>
-
- qh_sethalfspace( dim, coords, nextp, normal, offset, feasible )
- set point to dual of halfspace relative to feasible point
- halfspace is normal coefficients and offset.
-
- returns:
- false if feasible point is outside of hull (error message already reported)
- overwrites coordinates for point at dim coords
- nextp= next point (coords)
-
- design:
- compute distance from feasible point to halfspace
- divide each normal coefficient by -dist
-*/
-boolT qh_sethalfspace (int dim, coordT *coords, coordT **nextp,
- coordT *normal, coordT *offset, coordT *feasible) {
- coordT *normp= normal, *feasiblep= feasible, *coordp= coords;
- realT dist;
- realT r; /*bug fix*/
- int k;
- boolT zerodiv;
-
- dist= *offset;
- for (k= dim; k--; )
- dist += *(normp++) * *(feasiblep++);
- if (dist > 0)
- goto LABELerroroutside;
- normp= normal;
- if (dist < -qh MINdenom) {
- for (k= dim; k--; )
- *(coordp++)= *(normp++) / -dist;
- }else {
- for (k= dim; k--; ) {
- *(coordp++)= qh_divzero (*(normp++), -dist, qh MINdenom_1, &zerodiv);
- if (zerodiv)
- goto LABELerroroutside;
- }
- }
- *nextp= coordp;
- if (qh IStracing >= 4) {
- fprintf (qh ferr, "qh_sethalfspace: halfspace at offset %6.2g to point: ", *offset);
- for (k= dim, coordp= coords; k--; ) {
- r= *coordp++;
- fprintf (qh ferr, " %6.2g", r);
- }
- fprintf (qh ferr, "\n");
- }
- return True;
-LABELerroroutside:
- feasiblep= feasible;
- normp= normal;
- fprintf(qh ferr, "qhull input error: feasible point is not clearly inside halfspace\nfeasible point: ");
- for (k= dim; k--; )
- fprintf (qh ferr, qh_REAL_1, r=*(feasiblep++));
- fprintf (qh ferr, "\n halfspace: ");
- for (k= dim; k--; )
- fprintf (qh ferr, qh_REAL_1, r=*(normp++));
- fprintf (qh ferr, "\n at offset: ");
- fprintf (qh ferr, qh_REAL_1, *offset);
- fprintf (qh ferr, " and distance: ");
- fprintf (qh ferr, qh_REAL_1, dist);
- fprintf (qh ferr, "\n");
- return False;
-} /* sethalfspace */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="sethalfspace_all">-</a>
-
- qh_sethalfspace_all( dim, count, halfspaces, feasible )
- generate dual for halfspace intersection with feasible point
- array of count halfspaces
- each halfspace is normal coefficients followed by offset
- the origin is inside the halfspace if the offset is negative
-
- returns:
- malloc'd array of count X dim-1 points
-
- notes:
- call before qh_init_B or qh_initqhull_globals
- unused/untested code: please email bradb@shore.net if this works ok for you
- If using option 'Fp', also set qh feasible_point. It is a malloc'd array
- that is freed by qh_freebuffers.
-
- design:
- see qh_sethalfspace
-*/
-coordT *qh_sethalfspace_all (int dim, int count, coordT *halfspaces, pointT *feasible) {
- int i, newdim;
- pointT *newpoints;
- coordT *coordp, *normalp, *offsetp;
-
- trace0((qh ferr, "qh_sethalfspace_all: compute dual for halfspace intersection\n"));
- newdim= dim - 1;
- if (!(newpoints=(coordT*)malloc(count*newdim*sizeof(coordT)))){
- fprintf(qh ferr, "qhull error: insufficient memory to compute dual of %d halfspaces\n",
- count);
- qh_errexit(qh_ERRmem, NULL, NULL);
- }
- coordp= newpoints;
- normalp= halfspaces;
- for (i= 0; i < count; i++) {
- offsetp= normalp + newdim;
- if (!qh_sethalfspace (newdim, coordp, &coordp, normalp, offsetp, feasible)) {
- fprintf (qh ferr, "The halfspace was at index %d\n", i);
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- normalp= offsetp + 1;
- }
- return newpoints;
-} /* sethalfspace_all */
-
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="sharpnewfacets">-</a>
-
- qh_sharpnewfacets()
-
- returns:
- true if could be an acute angle (facets in different quadrants)
-
- notes:
- for qh_findbest
-
- design:
- for all facets on qh.newfacet_list
- if two facets are in different quadrants
- set issharp
-*/
-boolT qh_sharpnewfacets () {
- facetT *facet;
- boolT issharp = False;
- int *quadrant, k;
-
- quadrant= (int*)qh_memalloc (qh hull_dim * sizeof(int));
- FORALLfacet_(qh newfacet_list) {
- if (facet == qh newfacet_list) {
- for (k= qh hull_dim; k--; )
- quadrant[ k]= (facet->normal[ k] > 0);
- }else {
- for (k= qh hull_dim; k--; ) {
- if (quadrant[ k] != (facet->normal[ k] > 0)) {
- issharp= True;
- break;
- }
- }
- }
- if (issharp)
- break;
- }
- qh_memfree( quadrant, qh hull_dim * sizeof(int));
- trace3((qh ferr, "qh_sharpnewfacets: %d\n", issharp));
- return issharp;
-} /* sharpnewfacets */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="voronoi_center">-</a>
-
- qh_voronoi_center( dim, points )
- return Voronoi center for a set of points
- dim is the orginal dimension of the points
- gh.gm_matrix/qh.gm_row are scratch buffers
-
- returns:
- center as a temporary point
- if non-simplicial,
- returns center for max simplex of points
-
- notes:
- from Bowyer & Woodwark, A Programmer's Geometry, 1983, p. 65
-
- design:
- if non-simplicial
- determine max simplex for points
- translate point0 of simplex to origin
- compute sum of squares of diagonal
- compute determinate
- compute Voronoi center (see Bowyer & Woodwark)
-*/
-pointT *qh_voronoi_center (int dim, setT *points) {
- pointT *point, **pointp, *point0;
- pointT *center= (pointT*)qh_memalloc (qh center_size);
- setT *simplex;
- int i, j, k, size= qh_setsize(points);
- coordT *gmcoord;
- realT *diffp, sum2, *sum2row, *sum2p, det, factor;
- boolT nearzero, infinite;
-
- if (size == dim+1)
- simplex= points;
- else if (size < dim+1) {
- fprintf (qh ferr, "qhull internal error (qh_voronoi_center):\n need at least %d points to construct a Voronoi center\n",
- dim+1);
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }else {
- simplex= qh_settemp (dim+1);
- qh_maxsimplex (dim, points, NULL, 0, &simplex);
- }
- point0= SETfirstt_(simplex, pointT);
- gmcoord= qh gm_matrix;
- for (k=0; k < dim; k++) {
- qh gm_row[k]= gmcoord;
- FOREACHpoint_(simplex) {
- if (point != point0)
- *(gmcoord++)= point[k] - point0[k];
- }
- }
- sum2row= gmcoord;
- for (i=0; i < dim; i++) {
- sum2= 0.0;
- for (k= 0; k < dim; k++) {
- diffp= qh gm_row[k] + i;
- sum2 += *diffp * *diffp;
- }
- *(gmcoord++)= sum2;
- }
- det= qh_determinant (qh gm_row, dim, &nearzero);
- factor= qh_divzero (0.5, det, qh MINdenom, &infinite);
- if (infinite) {
- for (k=dim; k--; )
- center[k]= qh_INFINITE;
- if (qh IStracing)
- qh_printpoints (qh ferr, "qh_voronoi_center: at infinity for ", simplex);
- }else {
- for (i=0; i < dim; i++) {
- gmcoord= qh gm_matrix;
- sum2p= sum2row;
- for (k=0; k < dim; k++) {
- qh gm_row[k]= gmcoord;
- if (k == i) {
- for (j= dim; j--; )
- *(gmcoord++)= *sum2p++;
- }else {
- FOREACHpoint_(simplex) {
- if (point != point0)
- *(gmcoord++)= point[k] - point0[k];
- }
- }
- }
- center[i]= qh_determinant (qh gm_row, dim, &nearzero)*factor + point0[i];
- }
-#ifndef qh_NOtrace
- if (qh IStracing >= 3) {
- fprintf (qh ferr, "qh_voronoi_center: det %2.2g factor %2.2g ", det, factor);
- qh_printmatrix (qh ferr, "center:", ¢er, 1, dim);
- if (qh IStracing >= 5) {
- qh_printpoints (qh ferr, "points", simplex);
- FOREACHpoint_(simplex)
- fprintf (qh ferr, "p%d dist %.2g, ", qh_pointid (point),
- qh_pointdist (point, center, dim));
- fprintf (qh ferr, "\n");
- }
- }
-#endif
- }
- if (simplex != points)
- qh_settempfree (&simplex);
- return center;
-} /* voronoi_center */
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/global.c b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/global.c
deleted file mode 100644
index ff0cafb5eb339f21fdda7f6b908e1f82b0044b62..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/global.c
+++ /dev/null
@@ -1,2041 +0,0 @@
-/*<html><pre> -<a href="qh-globa.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- global.c
- initializes all the globals of the qhull application
-
- see README
-
- see qhull.h for qh.globals and function prototypes
-
- see qhull_a.h for internal functions
-
- copyright (c) 1993-2003, The Geometry Center
- */
-
-#include "qhull_a.h"
-
-/*========= qh definition (see qhull.h) =======================*/
-
-#if qh_QHpointer
-qhT *qh_qh= NULL; /* pointer to all global variables */
-#else
-qhT qh_qh; /* all global variables.
- Add "= {0}" if this causes a compiler error.
- Also qh_qhstat in stat.c and qhmem in mem.c. */
-#endif
-
-/*-<a href ="qh-globa.htm#TOC"
- >--------------------------------</a><a name="qh_version">-</a>
-
- qh_version
- version string by year and date
-
- the revision increases on code changes only
-
- notes:
- change date: Changes.txt, Announce.txt, README.txt,
- qhull.man, qhull.txt, qhull-news.html, Eudora signatures,
- change version: README.txt, qh-get.htm, File_id.diz, Makefile.txt
- change year: Copying.txt
- check download size
- recompile user_eg.c, rbox.c, qhull.c, qconvex.c, qdelaun.c qvoronoi.c, qhalf.c
-*/
-
-char *qh_version = "2003.1 2003/12/30";
-
-/*-<a href="qh-globa.htm#TOC"
- >-------------------------------</a><a name="appendprint">-</a>
-
- qh_appendprint( printFormat )
- append printFormat to qh.PRINTout unless already defined
-*/
-void qh_appendprint (qh_PRINT format) {
- int i;
-
- for (i=0; i < qh_PRINTEND; i++) {
- if (qh PRINTout[i] == format && format != qh_PRINTqhull)
- break;
- if (!qh PRINTout[i]) {
- qh PRINTout[i]= format;
- break;
- }
- }
-} /* appendprint */
-
-/*-<a href="qh-globa.htm#TOC"
- >-------------------------------</a><a name="checkflags">-</a>
-
- qh_checkflags( commandStr, hiddenFlags )
- errors if commandStr contains hiddenFlags
- hiddenFlags starts and ends with a space and is space deliminated (checked)
-
- notes:
- ignores first word (e.g., "qconvex i")
- use qh_strtol/strtod since strtol/strtod may or may not skip trailing spaces
-
- see:
- qh_initflags() initializes Qhull according to commandStr
-*/
-void qh_checkflags(char *command, char *hiddenflags) {
- char *s= command, *t, *chkerr, key, opt, prevopt;
- char chkkey[]= " ";
- char chkopt[]= " ";
- char chkopt2[]= " ";
-
- if (*hiddenflags != ' ' || hiddenflags[strlen(hiddenflags)-1] != ' ') {
- fprintf(qh ferr, "qhull error (qh_checkflags): hiddenflags must start and end with a space: \"%s\"", hiddenflags);
- qh_errexit(qh_ERRinput, NULL, NULL);
- }
- if (strpbrk(hiddenflags, ",\n\r\t")) {
- fprintf(qh ferr, "qhull error (qh_checkflags): hiddenflags contains commas, newlines, or tabs: \"%s\"", hiddenflags);
- qh_errexit(qh_ERRinput, NULL, NULL);
- }
- while (*s && !isspace(*s)) /* skip program name */
- s++;
- while (*s) {
- while (*s && isspace(*s))
- s++;
- if (*s == '-')
- s++;
- if (!*s)
- break;
- key = *s++;
- chkerr = NULL;
- if (key == '\'') { /* TO 'file name' */
- t= strchr(s, '\'');
- if (!t) {
- fprintf(qh ferr, "qhull error (qh_checkflags): missing the 2nd single-quote for:\n%s\n", s-1);
- qh_errexit(qh_ERRinput, NULL, NULL);
- }
- s= t+1;
- continue;
- }
- chkkey[1]= key;
- if (strstr(hiddenflags, chkkey)) {
- chkerr= chkkey;
- }else if (isupper(key)) {
- opt= ' ';
- prevopt= ' ';
- chkopt[1]= key;
- chkopt2[1]= key;
- while (!chkerr && *s && !isspace(*s)) {
- opt= *s++;
- if (isalpha(opt)) {
- chkopt[2]= opt;
- if (strstr(hiddenflags, chkopt))
- chkerr= chkopt;
- if (prevopt != ' ') {
- chkopt2[2]= prevopt;
- chkopt2[3]= opt;
- if (strstr(hiddenflags, chkopt2))
- chkerr= chkopt2;
- }
- }else if (key == 'Q' && isdigit(opt) && prevopt != 'b'
- && (prevopt == ' ' || islower(prevopt))) {
- chkopt[2]= opt;
- if (strstr(hiddenflags, chkopt))
- chkerr= chkopt;
- }else {
- qh_strtod (s-1, &t);
- if (s < t)
- s= t;
- }
- prevopt= opt;
- }
- }
- if (chkerr) {
- *chkerr= '\'';
- chkerr[strlen(chkerr)-1]= '\'';
- fprintf(qh ferr, "qhull error: option %s is not used with this program.\n It may be used with qhull.\n", chkerr);
- qh_errexit(qh_ERRinput, NULL, NULL);
- }
- }
-} /* checkflags */
-
-/*-<a href="qh-globa.htm#TOC"
- >-------------------------------</a><a name="clock">-</a>
-
- qh_clock()
- return user CPU time in 100ths (qh_SECtick)
- only defined for qh_CLOCKtype == 2
-
- notes:
- use first value to determine time 0
- from Stevens '92 8.15
-*/
-unsigned long qh_clock (void) {
-
-#if (qh_CLOCKtype == 2)
- struct tms time;
- static long clktck; /* initialized first call */
- double ratio, cpu;
- unsigned long ticks;
-
- if (!clktck) {
- if ((clktck= sysconf (_SC_CLK_TCK)) < 0) {
- fprintf (qh ferr, "qhull internal error (qh_clock): sysconf() failed. Use qh_CLOCKtype 1 in user.h\n");
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- }
- if (times (&time) == -1) {
- fprintf (qh ferr, "qhull internal error (qh_clock): times() failed. Use qh_CLOCKtype 1 in user.h\n");
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- ratio= qh_SECticks / (double)clktck;
- ticks= time.tms_utime * ratio;
- return ticks;
-#else
- fprintf (qh ferr, "qhull internal error (qh_clock): use qh_CLOCKtype 2 in user.h\n");
- qh_errexit (qh_ERRqhull, NULL, NULL); /* never returns */
- return 0;
-#endif
-} /* clock */
-
-/*-<a href="qh-globa.htm#TOC"
- >-------------------------------</a><a name="freebuffers">-</a>
-
- qh_freebuffers()
- free up global memory buffers
-
- notes:
- must match qh_initbuffers()
-*/
-void qh_freebuffers (void) {
-
- trace5((qh ferr, "qh_freebuffers: freeing up global memory buffers\n"));
- /* allocated by qh_initqhull_buffers */
- qh_memfree (qh NEARzero, qh hull_dim * sizeof(realT));
- qh_memfree (qh lower_threshold, (qh input_dim+1) * sizeof(realT));
- qh_memfree (qh upper_threshold, (qh input_dim+1) * sizeof(realT));
- qh_memfree (qh lower_bound, (qh input_dim+1) * sizeof(realT));
- qh_memfree (qh upper_bound, (qh input_dim+1) * sizeof(realT));
- qh_memfree (qh gm_matrix, (qh hull_dim+1) * qh hull_dim * sizeof(coordT));
- qh_memfree (qh gm_row, (qh hull_dim+1) * sizeof(coordT *));
- qh NEARzero= qh lower_threshold= qh upper_threshold= NULL;
- qh lower_bound= qh upper_bound= NULL;
- qh gm_matrix= NULL;
- qh gm_row= NULL;
- qh_setfree (&qh other_points);
- qh_setfree (&qh del_vertices);
- qh_setfree (&qh coplanarset);
- if (qh line) /* allocated by qh_readinput, freed if no error */
- free (qh line);
- if (qh half_space)
- free (qh half_space);
- if (qh temp_malloc)
- free (qh temp_malloc);
- if (qh feasible_point) /* allocated by qh_readfeasible */
- free (qh feasible_point);
- if (qh feasible_string) /* allocated by qh_initflags */
- free (qh feasible_string);
- qh line= qh feasible_string= NULL;
- qh half_space= qh feasible_point= qh temp_malloc= NULL;
- /* usually allocated by qh_readinput */
- if (qh first_point && qh POINTSmalloc) {
- free(qh first_point);
- qh first_point= NULL;
- }
- if (qh input_points && qh input_malloc) { /* set by qh_joggleinput */
- free (qh input_points);
- qh input_points= NULL;
- }
- trace5((qh ferr, "qh_freebuffers: finished\n"));
-} /* freebuffers */
-
-
-/*-<a href="qh-globa.htm#TOC"
- >-------------------------------</a><a name="freebuild">-</a>
-
- qh_freebuild( allmem )
- free global memory used by qh_initbuild and qh_buildhull
- if !allmem,
- does not free short memory (freed by qh_memfreeshort)
-
- design:
- free centrums
- free each vertex
- mark unattached ridges
- for each facet
- free ridges
- free outside set, coplanar set, neighbor set, ridge set, vertex set
- free facet
- free hash table
- free interior point
- free merge set
- free temporary sets
-*/
-void qh_freebuild (boolT allmem) {
- facetT *facet;
- vertexT *vertex;
- ridgeT *ridge, **ridgep;
- mergeT *merge, **mergep;
-
- trace1((qh ferr, "qh_freebuild: free memory from qh_inithull and qh_buildhull\n"));
- if (qh del_vertices)
- qh_settruncate (qh del_vertices, 0);
- if (allmem) {
- qh_clearcenters (qh_ASnone);
- while ((vertex= qh vertex_list)) {
- if (vertex->next)
- qh_delvertex (vertex);
- else {
- qh_memfree (vertex, sizeof(vertexT));
- qh newvertex_list= qh vertex_list= NULL;
- }
- }
- }else if (qh VERTEXneighbors) {
- FORALLvertices
- qh_setfreelong (&(vertex->neighbors));
- }
- qh VERTEXneighbors= False;
- qh GOODclosest= NULL;
- if (allmem) {
- FORALLfacets {
- FOREACHridge_(facet->ridges)
- ridge->seen= False;
- }
- FORALLfacets {
- if (facet->visible) {
- FOREACHridge_(facet->ridges) {
- if (!otherfacet_(ridge, facet)->visible)
- ridge->seen= True; /* an unattached ridge */
- }
- }
- }
- while ((facet= qh facet_list)) {
- FOREACHridge_(facet->ridges) {
- if (ridge->seen) {
- qh_setfree(&(ridge->vertices));
- qh_memfree(ridge, sizeof(ridgeT));
- }else
- ridge->seen= True;
- }
- qh_setfree (&(facet->outsideset));
- qh_setfree (&(facet->coplanarset));
- qh_setfree (&(facet->neighbors));
- qh_setfree (&(facet->ridges));
- qh_setfree (&(facet->vertices));
- if (facet->next)
- qh_delfacet (facet);
- else {
- qh_memfree (facet, sizeof(facetT));
- qh visible_list= qh newfacet_list= qh facet_list= NULL;
- }
- }
- }else {
- FORALLfacets {
- qh_setfreelong (&(facet->outsideset));
- qh_setfreelong (&(facet->coplanarset));
- if (!facet->simplicial) {
- qh_setfreelong (&(facet->neighbors));
- qh_setfreelong (&(facet->ridges));
- qh_setfreelong (&(facet->vertices));
- }
- }
- }
- qh_setfree (&(qh hash_table));
- qh_memfree (qh interior_point, qh normal_size);
- qh interior_point= NULL;
- FOREACHmerge_(qh facet_mergeset) /* usually empty */
- qh_memfree (merge, sizeof(mergeT));
- qh facet_mergeset= NULL; /* temp set */
- qh degen_mergeset= NULL; /* temp set */
- qh_settempfree_all();
-} /* freebuild */
-
-/*-<a href="qh-globa.htm#TOC"
- >-------------------------------</a><a name="freeqhull">-</a>
-
- qh_freeqhull( allmem )
- free global memory
- if !allmem,
- does not free short memory (freed by qh_memfreeshort)
-
- notes:
- sets qh.NOerrexit in case caller forgets to
-
- design:
- free global and temporary memory from qh_initbuild and qh_buildhull
- free buffers
- free statistics
-*/
-void qh_freeqhull (boolT allmem) {
-
- trace1((qh ferr, "qh_freeqhull: free global memory\n"));
- qh NOerrexit= True; /* no more setjmp since called at exit */
- qh_freebuild (allmem);
- qh_freebuffers();
- qh_freestatistics();
-#if qh_QHpointer
- free (qh_qh);
- qh_qh= NULL;
-#else
- memset((char *)&qh_qh, 0, sizeof(qhT));
- qh NOerrexit= True;
-#endif
-} /* freeqhull */
-
-/*-<a href="qh-globa.htm#TOC"
- >-------------------------------</a><a name="init_A">-</a>
-
- qh_init_A( infile, outfile, errfile, argc, argv )
- initialize memory and stdio files
- convert input options to option string (qh.qhull_command)
-
- notes:
- infile may be NULL if qh_readpoints() is not called
-
- errfile should always be defined. It is used for reporting
- errors. outfile is used for output and format options.
-
- argc/argv may be 0/NULL
-
- called before error handling initialized
- qh_errexit() may not be used
-*/
-void qh_init_A (FILE *infile, FILE *outfile, FILE *errfile, int argc, char *argv[]) {
- qh_meminit (errfile);
- qh_initqhull_start (infile, outfile, errfile);
- qh_init_qhull_command (argc, argv);
-} /* init_A */
-
-/*-<a href="qh-globa.htm#TOC"
- >-------------------------------</a><a name="init_B">-</a>
-
- qh_init_B( points, numpoints, dim, ismalloc )
- initialize globals for points array
-
- points has numpoints dim-dimensional points
- points[0] is the first coordinate of the first point
- points[1] is the second coordinate of the first point
- points[dim] is the first coordinate of the second point
-
- ismalloc=True
- Qhull will call free(points) on exit or input transformation
- ismalloc=False
- Qhull will allocate a new point array if needed for input transformation
-
- qh.qhull_command
- is the option string.
- It is defined by qh_init_B(), qh_qhull_command(), or qh_initflags
-
- returns:
- if qh.PROJECTinput or (qh.DELAUNAY and qh.PROJECTdelaunay)
- projects the input to a new point array
-
- if qh.DELAUNAY,
- qh.hull_dim is increased by one
- if qh.ATinfinity,
- qh_projectinput adds point-at-infinity for Delaunay tri.
-
- if qh.SCALEinput
- changes the upper and lower bounds of the input, see qh_scaleinput()
-
- if qh.ROTATEinput
- rotates the input by a random rotation, see qh_rotateinput()
- if qh.DELAUNAY
- rotates about the last coordinate
-
- notes:
- called after points are defined
- qh_errexit() may be used
-*/
-void qh_init_B (coordT *points, int numpoints, int dim, boolT ismalloc) {
- qh_initqhull_globals (points, numpoints, dim, ismalloc);
- if (qhmem.LASTsize == 0)
- qh_initqhull_mem();
- /* mem.c and qset.c are initialized */
- qh_initqhull_buffers();
- qh_initthresholds (qh qhull_command);
- if (qh PROJECTinput || (qh DELAUNAY && qh PROJECTdelaunay))
- qh_projectinput();
- if (qh SCALEinput)
- qh_scaleinput();
- if (qh ROTATErandom >= 0) {
- qh_randommatrix (qh gm_matrix, qh hull_dim, qh gm_row);
- if (qh DELAUNAY) {
- int k, lastk= qh hull_dim-1;
- for (k= 0; k < lastk; k++) {
- qh gm_row[k][lastk]= 0.0;
- qh gm_row[lastk][k]= 0.0;
- }
- qh gm_row[lastk][lastk]= 1.0;
- }
- qh_gram_schmidt (qh hull_dim, qh gm_row);
- qh_rotateinput (qh gm_row);
- }
-} /* init_B */
-
-/*-<a href="qh-globa.htm#TOC"
- >-------------------------------</a><a name="init_qhull_command">-</a>
-
- qh_init_qhull_command( argc, argv )
- build qh.qhull_command from argc/argv
-
- returns:
- a space-deliminated string of options (just as typed)
-
- notes:
- makes option string easy to input and output
-
- argc/argv may be 0/NULL
-*/
-void qh_init_qhull_command(int argc, char *argv[]) {
- int i;
- char *s;
-
- if (argc) {
- if ((s= strrchr( argv[0], '\\'))) /* Borland gives full path */
- strcpy (qh qhull_command, s+1);
- else
- strcpy (qh qhull_command, argv[0]);
- if ((s= strstr (qh qhull_command, ".EXE"))
- || (s= strstr (qh qhull_command, ".exe")))
- *s= '\0';
- }
- for (i=1; i < argc; i++) {
- if (strlen (qh qhull_command) + strlen(argv[i]) + 1 < sizeof(qh qhull_command)) {
- strcat (qh qhull_command, " ");
- strcat (qh qhull_command, argv[i]);
- }else {
- fprintf (qh ferr, "qhull input error: more than %d characters in command line\n",
- (int)sizeof(qh qhull_command));
- exit (1); /* can not use qh_errexit */
- }
- }
-} /* init_qhull_command */
-
-/*-<a href="qh-globa.htm#TOC"
- >-------------------------------</a><a name="initflags">-</a>
-
- qh_initflags( commandStr )
- set flags and initialized constants from commandStr
-
- returns:
- sets qh.qhull_command to command if needed
-
- notes:
- ignores first word (e.g., "qhull d")
- use qh_strtol/strtod since strtol/strtod may or may not skip trailing spaces
-
- see:
- qh_initthresholds() continues processing of 'Pdn' and 'PDn'
- 'prompt' in unix.c for documentation
-
- design:
- for each space-deliminated option group
- if top-level option
- check syntax
- append approriate option to option string
- set appropriate global variable or append printFormat to print options
- else
- for each sub-option
- check syntax
- append approriate option to option string
- set appropriate global variable or append printFormat to print options
-
-
-*/
-void qh_initflags(char *command) {
- int k, i, lastproject;
- char *s= command, *t, *prev_s, *start, key;
- boolT isgeom= False, wasproject;
- realT r;
-
- if (command != &qh qhull_command[0]) {
- *qh qhull_command= '\0';
- strncat( qh qhull_command, command, sizeof( qh qhull_command));
- }
- while (*s && !isspace(*s)) /* skip program name */
- s++;
- while (*s) {
- while (*s && isspace(*s))
- s++;
- if (*s == '-')
- s++;
- if (!*s)
- break;
- prev_s= s;
- switch (*s++) {
- case 'd':
- qh_option ("delaunay", NULL, NULL);
- qh DELAUNAY= True;
- break;
- case 'f':
- qh_option ("facets", NULL, NULL);
- qh_appendprint (qh_PRINTfacets);
- break;
- case 'i':
- qh_option ("incidence", NULL, NULL);
- qh_appendprint (qh_PRINTincidences);
- break;
- case 'm':
- qh_option ("mathematica", NULL, NULL);
- qh_appendprint (qh_PRINTmathematica);
- break;
- case 'n':
- qh_option ("normals", NULL, NULL);
- qh_appendprint (qh_PRINTnormals);
- break;
- case 'o':
- qh_option ("offFile", NULL, NULL);
- qh_appendprint (qh_PRINToff);
- break;
- case 'p':
- qh_option ("points", NULL, NULL);
- qh_appendprint (qh_PRINTpoints);
- break;
- case 's':
- qh_option ("summary", NULL, NULL);
- qh PRINTsummary= True;
- break;
- case 'v':
- qh_option ("voronoi", NULL, NULL);
- qh VORONOI= True;
- qh DELAUNAY= True;
- break;
- case 'A':
- if (!isdigit(*s) && *s != '.' && *s != '-')
- fprintf(qh ferr, "qhull warning: no maximum cosine angle given for option 'An'. Ignored.\n");
- else {
- if (*s == '-') {
- qh premerge_cos= -qh_strtod (s, &s);
- qh_option ("Angle-premerge-", NULL, &qh premerge_cos);
- qh PREmerge= True;
- }else {
- qh postmerge_cos= qh_strtod (s, &s);
- qh_option ("Angle-postmerge", NULL, &qh postmerge_cos);
- qh POSTmerge= True;
- }
- qh MERGING= True;
- }
- break;
- case 'C':
- if (!isdigit(*s) && *s != '.' && *s != '-')
- fprintf(qh ferr, "qhull warning: no centrum radius given for option 'Cn'. Ignored.\n");
- else {
- if (*s == '-') {
- qh premerge_centrum= -qh_strtod (s, &s);
- qh_option ("Centrum-premerge-", NULL, &qh premerge_centrum);
- qh PREmerge= True;
- }else {
- qh postmerge_centrum= qh_strtod (s, &s);
- qh_option ("Centrum-postmerge", NULL, &qh postmerge_centrum);
- qh POSTmerge= True;
- }
- qh MERGING= True;
- }
- break;
- case 'E':
- if (*s == '-')
- fprintf(qh ferr, "qhull warning: negative maximum roundoff given for option 'An'. Ignored.\n");
- else if (!isdigit(*s))
- fprintf(qh ferr, "qhull warning: no maximum roundoff given for option 'En'. Ignored.\n");
- else {
- qh DISTround= qh_strtod (s, &s);
- qh_option ("Distance-roundoff", NULL, &qh DISTround);
- qh SETroundoff= True;
- }
- break;
- case 'H':
- start= s;
- qh HALFspace= True;
- qh_strtod (s, &t);
- while (t > s) {
- if (*t && !isspace (*t)) {
- if (*t == ',')
- t++;
- else
- fprintf (qh ferr, "qhull warning: origin for Halfspace intersection should be 'Hn,n,n,...'\n");
- }
- s= t;
- qh_strtod (s, &t);
- }
- if (start < t) {
- if (!(qh feasible_string= (char*)calloc (t-start+1, 1))) {
- fprintf(qh ferr, "qhull error: insufficient memory for 'Hn,n,n'\n");
- qh_errexit(qh_ERRmem, NULL, NULL);
- }
- strncpy (qh feasible_string, start, t-start);
- qh_option ("Halfspace-about", NULL, NULL);
- qh_option (qh feasible_string, NULL, NULL);
- }else
- qh_option ("Halfspace", NULL, NULL);
- break;
- case 'R':
- if (!isdigit(*s))
- fprintf(qh ferr, "qhull warning: missing random perturbation for option 'Rn'. Ignored\n");
- else {
- qh RANDOMfactor= qh_strtod (s, &s);
- qh_option ("Random_perturb", NULL, &qh RANDOMfactor);
- qh RANDOMdist= True;
- }
- break;
- case 'V':
- if (!isdigit(*s) && *s != '-')
- fprintf(qh ferr, "qhull warning: missing visible distance for option 'Vn'. Ignored\n");
- else {
- qh MINvisible= qh_strtod (s, &s);
- qh_option ("Visible", NULL, &qh MINvisible);
- }
- break;
- case 'U':
- if (!isdigit(*s) && *s != '-')
- fprintf(qh ferr, "qhull warning: missing coplanar distance for option 'Un'. Ignored\n");
- else {
- qh MAXcoplanar= qh_strtod (s, &s);
- qh_option ("U-coplanar", NULL, &qh MAXcoplanar);
- }
- break;
- case 'W':
- if (*s == '-')
- fprintf(qh ferr, "qhull warning: negative outside width for option 'Wn'. Ignored.\n");
- else if (!isdigit(*s))
- fprintf(qh ferr, "qhull warning: missing outside width for option 'Wn'. Ignored\n");
- else {
- qh MINoutside= qh_strtod (s, &s);
- qh_option ("W-outside", NULL, &qh MINoutside);
- qh APPROXhull= True;
- }
- break;
- /************ sub menus ***************/
- case 'F':
- while (*s && !isspace(*s)) {
- switch(*s++) {
- case 'a':
- qh_option ("Farea", NULL, NULL);
- qh_appendprint (qh_PRINTarea);
- qh GETarea= True;
- break;
- case 'A':
- qh_option ("FArea-total", NULL, NULL);
- qh GETarea= True;
- break;
- case 'c':
- qh_option ("Fcoplanars", NULL, NULL);
- qh_appendprint (qh_PRINTcoplanars);
- break;
- case 'C':
- qh_option ("FCentrums", NULL, NULL);
- qh_appendprint (qh_PRINTcentrums);
- break;
- case 'd':
- qh_option ("Fd-cdd-in", NULL, NULL);
- qh CDDinput= True;
- break;
- case 'D':
- qh_option ("FD-cdd-out", NULL, NULL);
- qh CDDoutput= True;
- break;
- case 'F':
- qh_option ("FFacets-xridge", NULL, NULL);
- qh_appendprint (qh_PRINTfacets_xridge);
- break;
- case 'i':
- qh_option ("Finner", NULL, NULL);
- qh_appendprint (qh_PRINTinner);
- break;
- case 'I':
- qh_option ("FIDs", NULL, NULL);
- qh_appendprint (qh_PRINTids);
- break;
- case 'm':
- qh_option ("Fmerges", NULL, NULL);
- qh_appendprint (qh_PRINTmerges);
- break;
- case 'M':
- qh_option ("FMaple", NULL, NULL);
- qh_appendprint (qh_PRINTmaple);
- break;
- case 'n':
- qh_option ("Fneighbors", NULL, NULL);
- qh_appendprint (qh_PRINTneighbors);
- break;
- case 'N':
- qh_option ("FNeighbors-vertex", NULL, NULL);
- qh_appendprint (qh_PRINTvneighbors);
- break;
- case 'o':
- qh_option ("Fouter", NULL, NULL);
- qh_appendprint (qh_PRINTouter);
- break;
- case 'O':
- if (qh PRINToptions1st) {
- qh_option ("FOptions", NULL, NULL);
- qh_appendprint (qh_PRINToptions);
- }else
- qh PRINToptions1st= True;
- break;
- case 'p':
- qh_option ("Fpoint-intersect", NULL, NULL);
- qh_appendprint (qh_PRINTpointintersect);
- break;
- case 'P':
- qh_option ("FPoint-nearest", NULL, NULL);
- qh_appendprint (qh_PRINTpointnearest);
- break;
- case 'Q':
- qh_option ("FQhull", NULL, NULL);
- qh_appendprint (qh_PRINTqhull);
- break;
- case 's':
- qh_option ("Fsummary", NULL, NULL);
- qh_appendprint (qh_PRINTsummary);
- break;
- case 'S':
- qh_option ("FSize", NULL, NULL);
- qh_appendprint (qh_PRINTsize);
- qh GETarea= True;
- break;
- case 't':
- qh_option ("Ftriangles", NULL, NULL);
- qh_appendprint (qh_PRINTtriangles);
- break;
- case 'v':
- /* option set in qh_initqhull_globals */
- qh_appendprint (qh_PRINTvertices);
- break;
- case 'V':
- qh_option ("FVertex-average", NULL, NULL);
- qh_appendprint (qh_PRINTaverage);
- break;
- case 'x':
- qh_option ("Fxtremes", NULL, NULL);
- qh_appendprint (qh_PRINTextremes);
- break;
- default:
- s--;
- fprintf (qh ferr, "qhull warning: unknown 'F' output option %c, rest ignored\n", (int)s[0]);
- while (*++s && !isspace(*s));
- break;
- }
- }
- break;
- case 'G':
- isgeom= True;
- qh_appendprint (qh_PRINTgeom);
- while (*s && !isspace(*s)) {
- switch(*s++) {
- case 'a':
- qh_option ("Gall-points", NULL, NULL);
- qh PRINTdots= True;
- break;
- case 'c':
- qh_option ("Gcentrums", NULL, NULL);
- qh PRINTcentrums= True;
- break;
- case 'h':
- qh_option ("Gintersections", NULL, NULL);
- qh DOintersections= True;
- break;
- case 'i':
- qh_option ("Ginner", NULL, NULL);
- qh PRINTinner= True;
- break;
- case 'n':
- qh_option ("Gno-planes", NULL, NULL);
- qh PRINTnoplanes= True;
- break;
- case 'o':
- qh_option ("Gouter", NULL, NULL);
- qh PRINTouter= True;
- break;
- case 'p':
- qh_option ("Gpoints", NULL, NULL);
- qh PRINTcoplanar= True;
- break;
- case 'r':
- qh_option ("Gridges", NULL, NULL);
- qh PRINTridges= True;
- break;
- case 't':
- qh_option ("Gtransparent", NULL, NULL);
- qh PRINTtransparent= True;
- break;
- case 'v':
- qh_option ("Gvertices", NULL, NULL);
- qh PRINTspheres= True;
- break;
- case 'D':
- if (!isdigit (*s))
- fprintf (qh ferr, "qhull input error: missing dimension for option 'GDn'\n");
- else {
- if (qh DROPdim >= 0)
- fprintf (qh ferr, "qhull warning: can only drop one dimension. Previous 'GD%d' ignored\n",
- qh DROPdim);
- qh DROPdim= qh_strtol (s, &s);
- qh_option ("GDrop-dim", &qh DROPdim, NULL);
- }
- break;
- default:
- s--;
- fprintf (qh ferr, "qhull warning: unknown 'G' print option %c, rest ignored\n", (int)s[0]);
- while (*++s && !isspace(*s));
- break;
- }
- }
- break;
- case 'P':
- while (*s && !isspace(*s)) {
- switch(*s++) {
- case 'd': case 'D': /* see qh_initthresholds() */
- key= s[-1];
- i= qh_strtol (s, &s);
- r= 0;
- if (*s == ':') {
- s++;
- r= qh_strtod (s, &s);
- }
- if (key == 'd')
- qh_option ("Pdrop-facets-dim-less", &i, &r);
- else
- qh_option ("PDrop-facets-dim-more", &i, &r);
- break;
- case 'g':
- qh_option ("Pgood-facets", NULL, NULL);
- qh PRINTgood= True;
- break;
- case 'G':
- qh_option ("PGood-facet-neighbors", NULL, NULL);
- qh PRINTneighbors= True;
- break;
- case 'o':
- qh_option ("Poutput-forced", NULL, NULL);
- qh FORCEoutput= True;
- break;
- case 'p':
- qh_option ("Pprecision-ignore", NULL, NULL);
- qh PRINTprecision= False;
- break;
- case 'A':
- if (!isdigit (*s))
- fprintf (qh ferr, "qhull input error: missing facet count for keep area option 'PAn'\n");
- else {
- qh KEEParea= qh_strtol (s, &s);
- qh_option ("PArea-keep", &qh KEEParea, NULL);
- qh GETarea= True;
- }
- break;
- case 'F':
- if (!isdigit (*s))
- fprintf (qh ferr, "qhull input error: missing facet area for option 'PFn'\n");
- else {
- qh KEEPminArea= qh_strtod (s, &s);
- qh_option ("PFacet-area-keep", NULL, &qh KEEPminArea);
- qh GETarea= True;
- }
- break;
- case 'M':
- if (!isdigit (*s))
- fprintf (qh ferr, "qhull input error: missing merge count for option 'PMn'\n");
- else {
- qh KEEPmerge= qh_strtol (s, &s);
- qh_option ("PMerge-keep", &qh KEEPmerge, NULL);
- }
- break;
- default:
- s--;
- fprintf (qh ferr, "qhull warning: unknown 'P' print option %c, rest ignored\n", (int)s[0]);
- while (*++s && !isspace(*s));
- break;
- }
- }
- break;
- case 'Q':
- lastproject= -1;
- while (*s && !isspace(*s)) {
- switch(*s++) {
- case 'b': case 'B': /* handled by qh_initthresholds */
- key= s[-1];
- if (key == 'b' && *s == 'B') {
- s++;
- r= qh_DEFAULTbox;
- qh SCALEinput= True;
- qh_option ("QbBound-unit-box", NULL, &r);
- break;
- }
- if (key == 'b' && *s == 'b') {
- s++;
- qh SCALElast= True;
- qh_option ("Qbbound-last", NULL, NULL);
- break;
- }
- k= qh_strtol (s, &s);
- r= 0.0;
- wasproject= False;
- if (*s == ':') {
- s++;
- if ((r= qh_strtod(s, &s)) == 0.0) {
- t= s; /* need true dimension for memory allocation */
- while (*t && !isspace(*t)) {
- if (toupper(*t++) == 'B'
- && k == qh_strtol (t, &t)
- && *t++ == ':'
- && qh_strtod(t, &t) == 0.0) {
- qh PROJECTinput++;
- trace2((qh ferr, "qh_initflags: project dimension %d\n", k));
- qh_option ("Qb-project-dim", &k, NULL);
- wasproject= True;
- lastproject= k;
- break;
- }
- }
- }
- }
- if (!wasproject) {
- if (lastproject == k && r == 0.0)
- lastproject= -1; /* doesn't catch all possible sequences */
- else if (key == 'b') {
- qh SCALEinput= True;
- if (r == 0.0)
- r= -qh_DEFAULTbox;
- qh_option ("Qbound-dim-low", &k, &r);
- }else {
- qh SCALEinput= True;
- if (r == 0.0)
- r= qh_DEFAULTbox;
- qh_option ("QBound-dim-high", &k, &r);
- }
- }
- break;
- case 'c':
- qh_option ("Qcoplanar-keep", NULL, NULL);
- qh KEEPcoplanar= True;
- break;
- case 'f':
- qh_option ("Qfurthest-outside", NULL, NULL);
- qh BESToutside= True;
- break;
- case 'g':
- qh_option ("Qgood-facets-only", NULL, NULL);
- qh ONLYgood= True;
- break;
- case 'i':
- qh_option ("Qinterior-keep", NULL, NULL);
- qh KEEPinside= True;
- break;
- case 'm':
- qh_option ("Qmax-outside-only", NULL, NULL);
- qh ONLYmax= True;
- break;
- case 'r':
- qh_option ("Qrandom-outside", NULL, NULL);
- qh RANDOMoutside= True;
- break;
- case 's':
- qh_option ("Qsearch-initial-simplex", NULL, NULL);
- qh ALLpoints= True;
- break;
- case 't':
- qh_option ("Qtriangulate", NULL, NULL);
- qh TRIangulate= True;
- break;
- case 'T':
- qh_option ("QTestPoints", NULL, NULL);
- if (!isdigit (*s))
- fprintf (qh ferr, "qhull input error: missing number of test points for option 'QTn'\n");
- else {
- qh TESTpoints= qh_strtol (s, &s);
- qh_option ("QTestPoints", &qh TESTpoints, NULL);
- }
- break;
- case 'u':
- qh_option ("QupperDelaunay", NULL, NULL);
- qh UPPERdelaunay= True;
- break;
- case 'v':
- qh_option ("Qvertex-neighbors-convex", NULL, NULL);
- qh TESTvneighbors= True;
- break;
- case 'x':
- qh_option ("Qxact-merge", NULL, NULL);
- qh MERGEexact= True;
- break;
- case 'z':
- qh_option ("Qz-infinity-point", NULL, NULL);
- qh ATinfinity= True;
- break;
- case '0':
- qh_option ("Q0-no-premerge", NULL, NULL);
- qh NOpremerge= True;
- break;
- case '1':
- if (!isdigit(*s)) {
- qh_option ("Q1-no-angle-sort", NULL, NULL);
- qh ANGLEmerge= False;
- break;
- }
- switch(*s++) {
- case '0':
- qh_option ("Q10-no-narrow", NULL, NULL);
- qh NOnarrow= True;
- break;
- case '1':
- qh_option ("Q11-trinormals Qtriangulate", NULL, NULL);
- qh TRInormals= True;
- qh TRIangulate= True;
- break;
- default:
- s--;
- fprintf (qh ferr, "qhull warning: unknown 'Q' qhull option 1%c, rest ignored\n", (int)s[0]);
- while (*++s && !isspace(*s));
- break;
- }
- break;
- case '2':
- qh_option ("Q2-no-merge-independent", NULL, NULL);
- qh MERGEindependent= False;
- goto LABELcheckdigit;
- break; /* no warnings */
- case '3':
- qh_option ("Q3-no-merge-vertices", NULL, NULL);
- qh MERGEvertices= False;
- LABELcheckdigit:
- if (isdigit(*s))
- fprintf (qh ferr, "qhull warning: can not follow '1', '2', or '3' with a digit. '%c' skipped.\n",
- *s++);
- break;
- case '4':
- qh_option ("Q4-avoid-old-into-new", NULL, NULL);
- qh AVOIDold= True;
- break;
- case '5':
- qh_option ("Q5-no-check-outer", NULL, NULL);
- qh SKIPcheckmax= True;
- break;
- case '6':
- qh_option ("Q6-no-concave-merge", NULL, NULL);
- qh SKIPconvex= True;
- break;
- case '7':
- qh_option ("Q7-no-breadth-first", NULL, NULL);
- qh VIRTUALmemory= True;
- break;
- case '8':
- qh_option ("Q8-no-near-inside", NULL, NULL);
- qh NOnearinside= True;
- break;
- case '9':
- qh_option ("Q9-pick-furthest", NULL, NULL);
- qh PICKfurthest= True;
- break;
- case 'G':
- i= qh_strtol (s, &t);
- if (qh GOODpoint)
- fprintf (qh ferr, "qhull warning: good point already defined for option 'QGn'. Ignored\n");
- else if (s == t)
- fprintf (qh ferr, "qhull warning: missing good point id for option 'QGn'. Ignored\n");
- else if (i < 0 || *s == '-') {
- qh GOODpoint= i-1;
- qh_option ("QGood-if-dont-see-point", &i, NULL);
- }else {
- qh GOODpoint= i+1;
- qh_option ("QGood-if-see-point", &i, NULL);
- }
- s= t;
- break;
- case 'J':
- if (!isdigit(*s) && *s != '-')
- qh JOGGLEmax= 0.0;
- else {
- qh JOGGLEmax= (realT) qh_strtod (s, &s);
- qh_option ("QJoggle", NULL, &qh JOGGLEmax);
- }
- break;
- case 'R':
- if (!isdigit(*s) && *s != '-')
- fprintf (qh ferr, "qhull warning: missing random seed for option 'QRn'. Ignored\n");
- else {
- qh ROTATErandom= i= qh_strtol(s, &s);
- if (i > 0)
- qh_option ("QRotate-id", &i, NULL );
- else if (i < -1)
- qh_option ("QRandom-seed", &i, NULL );
- }
- break;
- case 'V':
- i= qh_strtol (s, &t);
- if (qh GOODvertex)
- fprintf (qh ferr, "qhull warning: good vertex already defined for option 'QVn'. Ignored\n");
- else if (s == t)
- fprintf (qh ferr, "qhull warning: no good point id given for option 'QVn'. Ignored\n");
- else if (i < 0) {
- qh GOODvertex= i - 1;
- qh_option ("QV-good-facets-not-point", &i, NULL);
- }else {
- qh_option ("QV-good-facets-point", &i, NULL);
- qh GOODvertex= i + 1;
- }
- s= t;
- break;
- default:
- s--;
- fprintf (qh ferr, "qhull warning: unknown 'Q' qhull option %c, rest ignored\n", (int)s[0]);
- while (*++s && !isspace(*s));
- break;
- }
- }
- break;
- case 'T':
- while (*s && !isspace(*s)) {
- if (isdigit(*s) || *s == '-')
- qh IStracing= qh_strtol(s, &s);
- else switch(*s++) {
- case 'c':
- qh_option ("Tcheck-frequently", NULL, NULL);
- qh CHECKfrequently= True;
- break;
- case 's':
- qh_option ("Tstatistics", NULL, NULL);
- qh PRINTstatistics= True;
- break;
- case 'v':
- qh_option ("Tverify", NULL, NULL);
- qh VERIFYoutput= True;
- break;
- case 'z':
- if (!qh fout)
- fprintf (qh ferr, "qhull warning: output file undefined (stdout). Option 'Tz' ignored.\n");
- else {
- qh_option ("Tz-stdout", NULL, NULL);
- qh ferr= qh fout;
- qhmem.ferr= qh fout;
- }
- break;
- case 'C':
- if (!isdigit(*s))
- fprintf (qh ferr, "qhull warning: missing point id for cone for trace option 'TCn'. Ignored\n");
- else {
- i= qh_strtol (s, &s);
- qh_option ("TCone-stop", &i, NULL);
- qh STOPcone= i + 1;
- }
- break;
- case 'F':
- if (!isdigit(*s))
- fprintf (qh ferr, "qhull warning: missing frequency count for trace option 'TFn'. Ignored\n");
- else {
- qh REPORTfreq= qh_strtol (s, &s);
- qh_option ("TFacet-log", &qh REPORTfreq, NULL);
- qh REPORTfreq2= qh REPORTfreq/2; /* for tracemerging() */
- }
- break;
- case 'I':
- if (s[0] != ' ' || s[1] == '\"' || s[1] == '\'' ||isspace (s[1])) {
- s++;
- fprintf (qh ferr, "qhull warning: option 'TI' mistyped.\nUse 'TI', one space, file name, and space or end-of-line.\nDo not use quotes. Option 'FI' ignored.\n");
- }else { /* not a procedure because of qh_option (filename, NULL, NULL); */
- char filename[500], *t= filename;
-
- s++;
- while (*s) {
- if (t - filename >= sizeof (filename)-2) {
- fprintf (qh ferr, "qhull error: filename for 'TI' too long.\n");
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- if (isspace (*s))
- break;
- *(t++)= *s++;
- }
- *t= '\0';
- if (!freopen (filename, "r", stdin)) {
- fprintf (qh ferr, "qhull error: could not open file \"%s\".", filename);
- qh_errexit (qh_ERRinput, NULL, NULL);
- }else {
- qh_option ("TInput-file", NULL, NULL);
- qh_option (filename, NULL, NULL);
- }
- }
- break;
- case 'O':
- if (s[0] != ' ' || s[1] == '\"' || isspace (s[1])) {
- s++;
- fprintf (qh ferr, "qhull warning: option 'TO' mistyped.\nUse 'TO', one space, file name, and space or end-of-line.\nThe file name may be enclosed in single quotes.\nDo not use double quotes. Option 'FO' ignored.\n");
- }else { /* not a procedure because of qh_option (filename, NULL, NULL); */
- char filename[500], *t= filename;
- boolT isquote= False;
-
- s++;
- if (*s == '\'') {
- isquote= True;
- s++;
- }
- while (*s) {
- if (t - filename >= sizeof (filename)-2) {
- fprintf (qh ferr, "qhull error: filename for 'TO' too long.\n");
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- if (isquote) {
- if (*s == '\'') {
- s++;
- isquote= False;
- break;
- }
- }else if (isspace (*s))
- break;
- *(t++)= *s++;
- }
- *t= '\0';
- if (isquote)
- fprintf (qh ferr, "qhull error: missing end quote for option 'TO'. Rest of line ignored.\n");
- else if (!freopen (filename, "w", stdout)) {
- fprintf (qh ferr, "qhull error: could not open file \"%s\".", filename);
- qh_errexit (qh_ERRinput, NULL, NULL);
- }else {
- qh_option ("TOutput-file", NULL, NULL);
- qh_option (filename, NULL, NULL);
- }
- }
- break;
- case 'P':
- if (!isdigit(*s))
- fprintf (qh ferr, "qhull warning: missing point id for trace option 'TPn'. Ignored\n");
- else {
- qh TRACEpoint= qh_strtol (s, &s);
- qh_option ("Trace-point", &qh TRACEpoint, NULL);
- }
- break;
- case 'M':
- if (!isdigit(*s))
- fprintf (qh ferr, "qhull warning: missing merge id for trace option 'TMn'. Ignored\n");
- else {
- qh TRACEmerge= qh_strtol (s, &s);
- qh_option ("Trace-merge", &qh TRACEmerge, NULL);
- }
- break;
- case 'R':
- if (!isdigit(*s))
- fprintf (qh ferr, "qhull warning: missing rerun count for trace option 'TRn'. Ignored\n");
- else {
- qh RERUN= qh_strtol (s, &s);
- qh_option ("TRerun", &qh RERUN, NULL);
- }
- break;
- case 'V':
- i= qh_strtol (s, &t);
- if (s == t)
- fprintf (qh ferr, "qhull warning: missing furthest point id for trace option 'TVn'. Ignored\n");
- else if (i < 0) {
- qh STOPpoint= i - 1;
- qh_option ("TV-stop-before-point", &i, NULL);
- }else {
- qh STOPpoint= i + 1;
- qh_option ("TV-stop-after-point", &i, NULL);
- }
- s= t;
- break;
- case 'W':
- if (!isdigit(*s))
- fprintf (qh ferr, "qhull warning: missing max width for trace option 'TWn'. Ignored\n");
- else {
- qh TRACEdist= (realT) qh_strtod (s, &s);
- qh_option ("TWide-trace", NULL, &qh TRACEdist);
- }
- break;
- default:
- s--;
- fprintf (qh ferr, "qhull warning: unknown 'T' trace option %c, rest ignored\n", (int)s[0]);
- while (*++s && !isspace(*s));
- break;
- }
- }
- break;
- default:
- fprintf (qh ferr, "qhull warning: unknown flag %c (%x)\n", (int)s[-1],
- (int)s[-1]);
- break;
- }
- if (s-1 == prev_s && *s && !isspace(*s)) {
- fprintf (qh ferr, "qhull warning: missing space after flag %c (%x); reserved for menu. Skipped.\n",
- (int)*prev_s, (int)*prev_s);
- while (*s && !isspace(*s))
- s++;
- }
- }
- if (isgeom && !qh FORCEoutput && qh PRINTout[1])
- fprintf (qh ferr, "qhull warning: additional output formats are not compatible with Geomview\n");
- /* set derived values in qh_initqhull_globals */
-} /* initflags */
-
-
-/*-<a href="qh-globa.htm#TOC"
- >-------------------------------</a><a name="initqhull_buffers">-</a>
-
- qh_initqhull_buffers()
- initialize global memory buffers
-
- notes:
- must match qh_freebuffers()
-*/
-void qh_initqhull_buffers (void) {
- int k;
-
- qh TEMPsize= (qhmem.LASTsize - sizeof (setT))/SETelemsize;
- if (qh TEMPsize <= 0 || qh TEMPsize > qhmem.LASTsize)
- qh TEMPsize= 8; /* e.g., if qh_NOmem */
- qh other_points= qh_setnew (qh TEMPsize);
- qh del_vertices= qh_setnew (qh TEMPsize);
- qh coplanarset= qh_setnew (qh TEMPsize);
- qh NEARzero= (realT *)qh_memalloc(qh hull_dim * sizeof(realT));
- qh lower_threshold= (realT *)qh_memalloc((qh input_dim+1) * sizeof(realT));
- qh upper_threshold= (realT *)qh_memalloc((qh input_dim+1) * sizeof(realT));
- qh lower_bound= (realT *)qh_memalloc((qh input_dim+1) * sizeof(realT));
- qh upper_bound= (realT *)qh_memalloc((qh input_dim+1) * sizeof(realT));
- for(k= qh input_dim+1; k--; ) {
- qh lower_threshold[k]= -REALmax;
- qh upper_threshold[k]= REALmax;
- qh lower_bound[k]= -REALmax;
- qh upper_bound[k]= REALmax;
- }
- qh gm_matrix= (coordT *)qh_memalloc((qh hull_dim+1) * qh hull_dim * sizeof(coordT));
- qh gm_row= (coordT **)qh_memalloc((qh hull_dim+1) * sizeof(coordT *));
-} /* initqhull_buffers */
-
-/*-<a href="qh-globa.htm#TOC"
- >-------------------------------</a><a name="initqhull_globals">-</a>
-
- qh_initqhull_globals( points, numpoints, dim, ismalloc )
- initialize globals
- if ismalloc
- points were malloc'd and qhull should free at end
-
- returns:
- sets qh.first_point, num_points, input_dim, hull_dim and others
- seeds random number generator (seed=1 if tracing)
- modifies qh.hull_dim if ((qh.DELAUNAY and qh.PROJECTdelaunay) or qh.PROJECTinput)
- adjust user flags as needed
- also checks DIM3 dependencies and constants
-
- notes:
- do not use qh_point() since an input transformation may move them elsewhere
-
- see:
- qh_initqhull_start() sets default values for non-zero globals
-
- design:
- initialize points array from input arguments
- test for qh.ZEROcentrum
- (i.e., use opposite vertex instead of cetrum for convexity testing)
- test for qh.PRINTgood (i.e., only print 'good' facets)
- initialize qh.CENTERtype, qh.normal_size,
- qh.center_size, qh.TRACEpoint/level,
- initialize and test random numbers
- check for conflicting print output options
-*/
-void qh_initqhull_globals (coordT *points, int numpoints, int dim, boolT ismalloc) {
- int seed, pointsneeded, extra= 0, i, randi, k;
- boolT printgeom= False, printmath= False, printcoplanar= False;
- realT randr;
- realT factorial;
-
- time_t timedata;
-
- trace0((qh ferr, "qh_initqhull_globals: for %s | %s\n", qh rbox_command,
- qh qhull_command));
- qh POINTSmalloc= ismalloc;
- qh first_point= points;
- qh num_points= numpoints;
- qh hull_dim= qh input_dim= dim;
- if (!qh NOpremerge && !qh MERGEexact && !qh PREmerge && qh JOGGLEmax > REALmax/2) {
- qh MERGING= True;
- if (qh hull_dim <= 4) {
- qh PREmerge= True;
- qh_option ("_pre-merge", NULL, NULL);
- }else {
- qh MERGEexact= True;
- qh_option ("Qxact_merge", NULL, NULL);
- }
- }else if (qh MERGEexact)
- qh MERGING= True;
- if (!qh NOpremerge && qh JOGGLEmax > REALmax/2) {
-#ifdef qh_NOmerge
- qh JOGGLEmax= 0.0;
-#endif
- }
- if (qh TRIangulate && qh JOGGLEmax < REALmax/2 && qh PRINTprecision)
- fprintf(qh ferr, "qhull warning: joggle ('QJ') always produces simplicial output. Triangulated output ('Qt') does nothing.\n");
- if (qh JOGGLEmax < REALmax/2 && qh DELAUNAY && !qh SCALEinput && !qh SCALElast) {
- qh SCALElast= True;
- qh_option ("Qbbound-last-qj", NULL, NULL);
- }
- if (qh MERGING && !qh POSTmerge && qh premerge_cos > REALmax/2
- && qh premerge_centrum == 0) {
- qh ZEROcentrum= True;
- qh ZEROall_ok= True;
- qh_option ("_zero-centrum", NULL, NULL);
- }
- if (qh JOGGLEmax < REALmax/2 && REALepsilon > 2e-8 && qh PRINTprecision)
- fprintf(qh ferr, "qhull warning: real epsilon, %2.2g, is probably too large for joggle ('QJn')\nRecompile with double precision reals (see user.h).\n",
- REALepsilon);
-#ifdef qh_NOmerge
- if (qh MERGING) {
- fprintf (qh ferr, "qhull input error: merging not installed (qh_NOmerge + 'Qx', 'Cn' or 'An')\n");
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
-#endif
- if (!(qh PRINTgood || qh PRINTneighbors)) {
- if (qh KEEParea || qh KEEPminArea < REALmax/2 || qh KEEPmerge || qh DELAUNAY
- || (!qh ONLYgood && (qh GOODvertex || qh GOODpoint))) {
- qh PRINTgood= True;
- qh_option ("Pgood", NULL, NULL);
- }
- }
- if (qh DELAUNAY && qh KEEPcoplanar && !qh KEEPinside) {
- qh KEEPinside= True;
- qh_option ("Qinterior-keep", NULL, NULL);
- }
- if (qh DELAUNAY && qh HALFspace) {
- fprintf (qh ferr, "qhull input error: can not use Delaunay ('d') or Voronoi ('v') with halfspace intersection ('H')\n");
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- if (!qh DELAUNAY && (qh UPPERdelaunay || qh ATinfinity)) {
- fprintf (qh ferr, "qhull input error: use upper-Delaunay ('Qu') or infinity-point ('Qz') with Delaunay ('d') or Voronoi ('v')\n");
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- if (qh UPPERdelaunay && qh ATinfinity) {
- fprintf (qh ferr, "qhull input error: can not use infinity-point ('Qz') with upper-Delaunay ('Qu')\n");
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- if (qh SCALElast && !qh DELAUNAY && qh PRINTprecision)
- fprintf (qh ferr, "qhull input warning: option 'Qbb' (scale-last-coordinate) is normally used with 'd' or 'v'\n");
- qh DOcheckmax= (!qh SKIPcheckmax && qh MERGING );
- qh KEEPnearinside= (qh DOcheckmax && !(qh KEEPinside && qh KEEPcoplanar)
- && !qh NOnearinside);
- if (qh MERGING)
- qh CENTERtype= qh_AScentrum;
- else if (qh VORONOI)
- qh CENTERtype= qh_ASvoronoi;
- if (qh TESTvneighbors && !qh MERGING) {
- fprintf(qh ferr, "qhull input error: test vertex neighbors ('Qv') needs a merge option\n");
- qh_errexit (qh_ERRinput, NULL ,NULL);
- }
- if (qh PROJECTinput || (qh DELAUNAY && qh PROJECTdelaunay)) {
- qh hull_dim -= qh PROJECTinput;
- if (qh DELAUNAY) {
- qh hull_dim++;
- extra= 1;
- }
- }
- if (qh hull_dim <= 1) {
- fprintf(qh ferr, "qhull error: dimension %d must be > 1\n", qh hull_dim);
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- for (k= 2, factorial=1.0; k < qh hull_dim; k++)
- factorial *= k;
- qh AREAfactor= 1.0 / factorial;
- trace2((qh ferr, "qh_initqhull_globals: initialize globals. dim %d numpoints %d malloc? %d projected %d to hull_dim %d\n",
- dim, numpoints, ismalloc, qh PROJECTinput, qh hull_dim));
- qh normal_size= qh hull_dim * sizeof(coordT);
- qh center_size= qh normal_size - sizeof(coordT);
- pointsneeded= qh hull_dim+1;
- if (qh hull_dim > qh_DIMmergeVertex) {
- qh MERGEvertices= False;
- qh_option ("Q3-no-merge-vertices-dim-high", NULL, NULL);
- }
- if (qh GOODpoint)
- pointsneeded++;
-#ifdef qh_NOtrace
- if (qh IStracing) {
- fprintf (qh ferr, "qhull input error: tracing is not installed (qh_NOtrace in user.h)");
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
-#endif
- if (qh RERUN > 1) {
- qh TRACElastrun= qh IStracing; /* qh_build_withrestart duplicates next conditional */
- if (qh IStracing != -1)
- qh IStracing= 0;
- }else if (qh TRACEpoint != -1 || qh TRACEdist < REALmax/2 || qh TRACEmerge) {
- qh TRACElevel= (qh IStracing? qh IStracing : 3);
- qh IStracing= 0;
- }
- if (qh ROTATErandom == 0 || qh ROTATErandom == -1) {
- seed= time (&timedata);
- if (qh ROTATErandom == -1) {
- seed= -seed;
- qh_option ("QRandom-seed", &seed, NULL );
- }else
- qh_option ("QRotate-random", &seed, NULL);
- qh ROTATErandom= seed;
- }
- seed= qh ROTATErandom;
- if (seed == INT_MIN) /* default value */
- seed= 1;
- else if (seed < 0)
- seed= -seed;
- qh_RANDOMseed_(seed);
- randr= 0.0;
- for (i= 1000; i--; ) {
- randi= qh_RANDOMint;
- randr += randi;
- if (randi > qh_RANDOMmax) {
- fprintf (qh ferr, "\
-qhull configuration error (qh_RANDOMmax in user.h):\n\
- random integer %d > qh_RANDOMmax (%.8g)\n",
- randi, qh_RANDOMmax);
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- }
- qh_RANDOMseed_(seed);
- randr = randr/1000;
- if (randr < qh_RANDOMmax/10
- || randr > qh_RANDOMmax * 5)
- fprintf (qh ferr, "\
-qhull configuration warning (qh_RANDOMmax in user.h):\n\
- average of 1000 random integers (%.2g) is much different than expected (%.2g).\n\
- Is qh_RANDOMmax (%.2g) wrong?\n",
- randr, qh_RANDOMmax/2.0, qh_RANDOMmax);
- qh RANDOMa= 2.0 * qh RANDOMfactor/qh_RANDOMmax;
- qh RANDOMb= 1.0 - qh RANDOMfactor;
- if (qh_HASHfactor < 1.1) {
- fprintf(qh ferr, "qhull internal error (qh_initqhull_globals): qh_HASHfactor %d must be at least 1.1. Qhull uses linear hash probing\n",
- qh_HASHfactor);
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- if (numpoints+extra < pointsneeded) {
- fprintf(qh ferr,"qhull input error: not enough points (%d) to construct initial simplex (need %d)\n",
- numpoints, pointsneeded);
- qh_errexit(qh_ERRinput, NULL, NULL);
- }
- if (qh PRINTtransparent) {
- if (qh hull_dim != 4 || !qh DELAUNAY || qh VORONOI || qh DROPdim >= 0) {
- fprintf(qh ferr,"qhull input error: transparent Delaunay ('Gt') needs 3-d Delaunay ('d') w/o 'GDn'\n");
- qh_errexit(qh_ERRinput, NULL, NULL);
- }
- qh DROPdim = 3;
- qh PRINTridges = True;
- }
- for (i= qh_PRINTEND; i--; ) {
- if (qh PRINTout[i] == qh_PRINTgeom)
- printgeom= True;
- else if (qh PRINTout[i] == qh_PRINTmathematica || qh PRINTout[i] == qh_PRINTmaple)
- printmath= True;
- else if (qh PRINTout[i] == qh_PRINTcoplanars)
- printcoplanar= True;
- else if (qh PRINTout[i] == qh_PRINTpointnearest)
- printcoplanar= True;
- else if (qh PRINTout[i] == qh_PRINTpointintersect && !qh HALFspace) {
- fprintf (qh ferr, "qhull input error: option 'Fp' is only used for \nhalfspace intersection ('Hn,n,n').\n");
- qh_errexit (qh_ERRinput, NULL, NULL);
- }else if (qh PRINTout[i] == qh_PRINTtriangles && (qh HALFspace || qh VORONOI)) {
- fprintf (qh ferr, "qhull input error: option 'Ft' is not available for Voronoi vertices or halfspace intersection\n");
- qh_errexit (qh_ERRinput, NULL, NULL);
- }else if (qh PRINTout[i] == qh_PRINTcentrums && qh VORONOI) {
- fprintf (qh ferr, "qhull input error: option 'FC' is not available for Voronoi vertices ('v')\n");
- qh_errexit (qh_ERRinput, NULL, NULL);
- }else if (qh PRINTout[i] == qh_PRINTvertices) {
- if (qh VORONOI)
- qh_option ("Fvoronoi", NULL, NULL);
- else
- qh_option ("Fvertices", NULL, NULL);
- }
- }
- if (printcoplanar && qh DELAUNAY && qh JOGGLEmax < REALmax/2) {
- if (qh PRINTprecision)
- fprintf (qh ferr, "qhull input warning: 'QJ' (joggle) will usually prevent coincident input sites for options 'Fc' and 'FP'\n");
- }
- if (!qh KEEPcoplanar && !qh KEEPinside && !qh ONLYgood) {
- if ((qh PRINTcoplanar && qh PRINTspheres) || printcoplanar) {
- qh KEEPcoplanar = True;
- qh_option ("Qcoplanar", NULL, NULL);
- }
- }
- if (printmath && (qh hull_dim > 3 || qh VORONOI)) {
- fprintf (qh ferr, "qhull input error: Mathematica and Maple output is only available for 2-d and 3-d convex hulls and 2-d Delaunay triangulations\n");
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- if (printgeom) {
- if (qh hull_dim > 4) {
- fprintf (qh ferr, "qhull input error: Geomview output is only available for 2-d, 3-d and 4-d\n");
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- if (qh PRINTnoplanes && !(qh PRINTcoplanar + qh PRINTcentrums
- + qh PRINTdots + qh PRINTspheres + qh DOintersections + qh PRINTridges)) {
- fprintf (qh ferr, "qhull input error: no output specified for Geomview\n");
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- if (qh VORONOI && (qh hull_dim > 3 || qh DROPdim >= 0)) {
- fprintf (qh ferr, "qhull input error: Geomview output for Voronoi diagrams only for 2-d\n");
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- /* can not warn about furthest-site Geomview output: no lower_threshold */
- if (qh hull_dim == 4 && qh DROPdim == -1 &&
- (qh PRINTcoplanar || qh PRINTspheres || qh PRINTcentrums)) {
- fprintf (qh ferr, "qhull input warning: coplanars, vertices, and centrums output not\n\
-available for 4-d output (ignored). Could use 'GDn' instead.\n");
- qh PRINTcoplanar= qh PRINTspheres= qh PRINTcentrums= False;
- }
- }
- qh PRINTdim= qh hull_dim;
- if (qh DROPdim >=0) { /* after Geomview checks */
- if (qh DROPdim < qh hull_dim) {
- qh PRINTdim--;
- if (!printgeom || qh hull_dim < 3)
- fprintf (qh ferr, "qhull input warning: drop dimension 'GD%d' is only available for 3-d/4-d Geomview\n", qh DROPdim);
- }else
- qh DROPdim= -1;
- }else if (qh VORONOI) {
- qh DROPdim= qh hull_dim-1;
- qh PRINTdim= qh hull_dim-1;
- }
-} /* initqhull_globals */
-
-/*-<a href="qh-globa.htm#TOC"
- >-------------------------------</a><a name="initqhull_mem">-</a>
-
- qh_initqhull_mem( )
- initialize mem.c for qhull
- qh.hull_dim and qh.normal_size determine some of the allocation sizes
- if qh.MERGING,
- includes ridgeT
- calls qh_user_memsizes() to add up to 10 additional sizes for quick allocation
- (see numsizes below)
-
- returns:
- mem.c already for qh_memalloc/qh_memfree (errors if called beforehand)
-
- notes:
- qh_produceoutput() prints memsizes
-
-*/
-void qh_initqhull_mem (void) {
- int numsizes;
- int i;
-
- numsizes= 8+10;
- qh_meminitbuffers (qh IStracing, qh_MEMalign, numsizes,
- qh_MEMbufsize,qh_MEMinitbuf);
- qh_memsize(sizeof(vertexT));
- if (qh MERGING) {
- qh_memsize(sizeof(ridgeT));
- qh_memsize(sizeof(mergeT));
- }
- qh_memsize(sizeof(facetT));
- i= sizeof(setT) + (qh hull_dim - 1) * SETelemsize; /* ridge.vertices */
- qh_memsize(i);
- qh_memsize(qh normal_size); /* normal */
- i += SETelemsize; /* facet.vertices, .ridges, .neighbors */
- qh_memsize(i);
- qh_user_memsizes();
- qh_memsetup();
-} /* initqhull_mem */
-
-/*-<a href="qh-globa.htm#TOC"
- >-------------------------------</a><a name="initqhull_start">-</a>
-
- qh_initqhull_start( infile, outfile, errfile )
- start initialization of qhull
- initialize statistics, stdio, default values for global variables
-
- see:
- qh_maxmin() determines the precision constants
-*/
-void qh_initqhull_start (FILE *infile, FILE *outfile, FILE *errfile) {
-
- qh_CPUclock; /* start the clock */
-#if qh_QHpointer
- if (!(qh_qh= (qhT *)malloc (sizeof(qhT)))) {
- fprintf (errfile, "qhull error (qh_initqhull_globals): insufficient memory\n");
- exit (qh_ERRmem); /* no error handler */
- }
- memset((char *)qh_qh, 0, sizeof(qhT)); /* every field is 0, FALSE, NULL */
-#else
- memset((char *)&qh_qh, 0, sizeof(qhT));
-#endif
- strcat (qh qhull, "qhull");
- qh_initstatistics();
- qh ANGLEmerge= True;
- qh DROPdim= -1;
- qh ferr= errfile;
- qh fin= infile;
- qh fout= outfile;
- qh furthest_id= -1;
- qh JOGGLEmax= REALmax;
- qh KEEPminArea = REALmax;
- qh last_low= REALmax;
- qh last_high= REALmax;
- qh last_newhigh= REALmax;
- qh max_outside= 0.0;
- qh max_vertex= 0.0;
- qh MAXabs_coord= 0.0;
- qh MAXsumcoord= 0.0;
- qh MAXwidth= -REALmax;
- qh MERGEindependent= True;
- qh MINdenom_1= fmax_(1.0/REALmax, REALmin); /* used by qh_scalepoints */
- qh MINoutside= 0.0;
- qh MINvisible= REALmax;
- qh MAXcoplanar= REALmax;
- qh outside_err= REALmax;
- qh premerge_centrum= 0.0;
- qh premerge_cos= REALmax;
- qh PRINTprecision= True;
- qh PRINTradius= 0.0;
- qh postmerge_cos= REALmax;
- qh postmerge_centrum= 0.0;
- qh ROTATErandom= INT_MIN;
- qh MERGEvertices= True;
- qh totarea= 0.0;
- qh totvol= 0.0;
- qh TRACEdist= REALmax;
- qh TRACEpoint= -1; /* recompile or use 'TPn' */
- qh tracefacet_id= UINT_MAX; /* recompile to trace a facet */
- qh tracevertex_id= UINT_MAX; /* recompile to trace a vertex */
- qh_RANDOMseed_(1);
-} /* initqhull_start */
-
-/*-<a href="qh-globa.htm#TOC"
- >-------------------------------</a><a name="initthresholds">-</a>
-
- qh_initthresholds( commandString )
- set thresholds for printing and scaling from commandString
-
- returns:
- sets qh.GOODthreshold or qh.SPLITthreshold if 'Pd0D1' used
-
- see:
- qh_initflags(), 'Qbk' 'QBk' 'Pdk' and 'PDk'
- qh_inthresholds()
-
- design:
- for each 'Pdn' or 'PDn' option
- check syntax
- set qh.lower_threshold or qh.upper_threshold
- set qh.GOODthreshold if an unbounded threshold is used
- set qh.SPLITthreshold if a bounded threshold is used
-*/
-void qh_initthresholds(char *command) {
- realT value;
- int index, maxdim, k;
- char *s= command;
- char key;
-
- maxdim= qh input_dim;
- if (qh DELAUNAY && (qh PROJECTdelaunay || qh PROJECTinput))
- maxdim++;
- while (*s) {
- if (*s == '-')
- s++;
- if (*s == 'P') {
- s++;
- while (*s && !isspace(key= *s++)) {
- if (key == 'd' || key == 'D') {
- if (!isdigit(*s)) {
- fprintf(qh ferr, "qhull warning: no dimension given for Print option '%c' at: %s. Ignored\n",
- key, s-1);
- continue;
- }
- index= qh_strtol (s, &s);
- if (index >= qh hull_dim) {
- fprintf(qh ferr, "qhull warning: dimension %d for Print option '%c' is >= %d. Ignored\n",
- index, key, qh hull_dim);
- continue;
- }
- if (*s == ':') {
- s++;
- value= qh_strtod(s, &s);
- if (fabs((double)value) > 1.0) {
- fprintf(qh ferr, "qhull warning: value %2.4g for Print option %c is > +1 or < -1. Ignored\n",
- value, key);
- continue;
- }
- }else
- value= 0.0;
- if (key == 'd')
- qh lower_threshold[index]= value;
- else
- qh upper_threshold[index]= value;
- }
- }
- }else if (*s == 'Q') {
- s++;
- while (*s && !isspace(key= *s++)) {
- if (key == 'b' && *s == 'B') {
- s++;
- for (k=maxdim; k--; ) {
- qh lower_bound[k]= -qh_DEFAULTbox;
- qh upper_bound[k]= qh_DEFAULTbox;
- }
- }else if (key == 'b' && *s == 'b')
- s++;
- else if (key == 'b' || key == 'B') {
- if (!isdigit(*s)) {
- fprintf(qh ferr, "qhull warning: no dimension given for Qhull option %c. Ignored\n",
- key);
- continue;
- }
- index= qh_strtol (s, &s);
- if (index >= maxdim) {
- fprintf(qh ferr, "qhull warning: dimension %d for Qhull option %c is >= %d. Ignored\n",
- index, key, maxdim);
- continue;
- }
- if (*s == ':') {
- s++;
- value= qh_strtod(s, &s);
- }else if (key == 'b')
- value= -qh_DEFAULTbox;
- else
- value= qh_DEFAULTbox;
- if (key == 'b')
- qh lower_bound[index]= value;
- else
- qh upper_bound[index]= value;
- }
- }
- }else {
- while (*s && !isspace (*s))
- s++;
- }
- while (isspace (*s))
- s++;
- }
- for (k= qh hull_dim; k--; ) {
- if (qh lower_threshold[k] > -REALmax/2) {
- qh GOODthreshold= True;
- if (qh upper_threshold[k] < REALmax/2) {
- qh SPLITthresholds= True;
- qh GOODthreshold= False;
- break;
- }
- }else if (qh upper_threshold[k] < REALmax/2)
- qh GOODthreshold= True;
- }
-} /* initthresholds */
-
-/*-<a href="qh-globa.htm#TOC"
- >-------------------------------</a><a name="option">-</a>
-
- qh_option( option, intVal, realVal )
- add an option description to qh.qhull_options
-
- notes:
- will be printed with statistics ('Ts') and errors
- strlen(option) < 40
-*/
-void qh_option (char *option, int *i, realT *r) {
- char buf[200];
- int len, maxlen;
-
- sprintf (buf, " %s", option);
- if (i)
- sprintf (buf+strlen(buf), " %d", *i);
- if (r)
- sprintf (buf+strlen(buf), " %2.2g", *r);
- len= strlen(buf);
- qh qhull_optionlen += len;
- maxlen= sizeof (qh qhull_options) - len -1;
- maximize_(maxlen, 0);
- if (qh qhull_optionlen >= 80 && maxlen > 0) {
- qh qhull_optionlen= len;
- strncat (qh qhull_options, "\n", maxlen--);
- }
- strncat (qh qhull_options, buf, maxlen);
-} /* option */
-
-#if qh_QHpointer
-/*-<a href="qh-globa.htm#TOC"
- >-------------------------------</a><a name="restore_qhull">-</a>
-
- qh_restore_qhull( oldqh )
- restores a previously saved qhull
- also restores qh_qhstat and qhmem.tempstack
-
- notes:
- errors if current qhull hasn't been saved or freed
- uses qhmem for error reporting
-
- NOTE 1998/5/11:
- Freeing memory after qh_save_qhull and qh_restore_qhull
- is complicated. The procedures will be redesigned.
-
- see:
- qh_save_qhull()
-*/
-void qh_restore_qhull (qhT **oldqh) {
-
- if (*oldqh && strcmp ((*oldqh)->qhull, "qhull")) {
- fprintf (qhmem.ferr, "qhull internal error (qh_restore_qhull): %p is not a qhull data structure\n",
- *oldqh);
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- if (qh_qh) {
- fprintf (qhmem.ferr, "qhull internal error (qh_restore_qhull): did not save or free existing qhull\n");
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- if (!*oldqh || !(*oldqh)->old_qhstat) {
- fprintf (qhmem.ferr, "qhull internal error (qh_restore_qhull): did not previously save qhull %p\n",
- *oldqh);
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- qh_qh= *oldqh;
- *oldqh= NULL;
- qh_qhstat= qh old_qhstat;
- qhmem.tempstack= qh old_tempstack;
- trace1((qh ferr, "qh_restore_qhull: restored qhull from %p\n", *oldqh));
-} /* restore_qhull */
-
-/*-<a href="qh-globa.htm#TOC"
- >-------------------------------</a><a name="save_qhull">-</a>
-
- qh_save_qhull( )
- saves qhull for a later qh_restore_qhull
- also saves qh_qhstat and qhmem.tempstack
-
- returns:
- qh_qh=NULL
-
- notes:
- need to initialize qhull or call qh_restore_qhull before continuing
-
- NOTE 1998/5/11:
- Freeing memory after qh_save_qhull and qh_restore_qhull
- is complicated. The procedures will be redesigned.
-
- see:
- qh_restore_qhull()
-*/
-qhT *qh_save_qhull (void) {
- qhT *oldqh;
-
- trace1((qhmem.ferr, "qh_save_qhull: save qhull %p\n", qh_qh));
- if (!qh_qh) {
- fprintf (qhmem.ferr, "qhull internal error (qh_save_qhull): qhull not initialized\n");
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- qh old_qhstat= qh_qhstat;
- qh_qhstat= NULL;
- qh old_tempstack= qhmem.tempstack;
- qhmem.tempstack= NULL;
- oldqh= qh_qh;
- qh_qh= NULL;
- return oldqh;
-} /* save_qhull */
-
-#endif
-
-/*-<a href="qh-globa.htm#TOC"
- >-------------------------------</a><a name="strtol">-</a>
-
- qh_strtol( s, endp) qh_strtod( s, endp)
- internal versions of strtol() and strtod()
- does not skip trailing spaces
- notes:
- some implementations of strtol()/strtod() skip trailing spaces
-*/
-double qh_strtod (const char *s, char **endp) {
- double result;
-
- result= strtod (s, endp);
- if (s < (*endp) && (*endp)[-1] == ' ')
- (*endp)--;
- return result;
-} /* strtod */
-
-int qh_strtol (const char *s, char **endp) {
- int result;
-
- result= (int) strtol (s, endp, 10);
- if (s< (*endp) && (*endp)[-1] == ' ')
- (*endp)--;
- return result;
-} /* strtol */
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/index.htm b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/index.htm
deleted file mode 100644
index cdd0c63f60b044ae0041fbf0067ee92ffdfacdb3..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/index.htm
+++ /dev/null
@@ -1,239 +0,0 @@
-<!-- Do not edit with Front Page, it adds too many spaces -->
-<html>
-<head>
-<meta http-equiv="Content-Type"
-content="text/html; charset=iso-8859-1">
-<title>Qhull functions, macros, and data structures</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<p><a name="TOP"><b>Up:</b></a> <a
-href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
-<b>Up:</b> <a href="../html/qh-quick.htm#programs">Programs</a>
-• <a href="../html/qh-quick.htm#options">Options</a>
-• <a href="../html/qh-opto.htm#output">Output</a>
-• <a href="../html/qh-optf.htm#format">Formats</a>
-• <a href="../html/qh-optg.htm#geomview">Geomview</a>
-• <a href="../html/qh-optp.htm#print">Print</a>
-• <a href="../html/qh-optq.htm#qhull">Qhull</a>
-• <a href="../html/qh-optc.htm#prec">Precision</a>
-• <a href="../html/qh-optt.htm#trace">Trace</a><br>
-<b>Up:</b> <a href="../html/qh-in.htm#TOC">Qhull internals</a><br>
-<b>To:</b> <a href="#TOC">Qhull files</a><br>
-<b>To:</b> <a href="qh-geom.htm">Geom</a> • <a href="qh-globa.htm">Global</a>
-• <a href="qh-io.htm">Io</a> • <a href="qh-mem.htm">Mem</a>
-• <a href="qh-merge.htm">Merge</a> • <a href="qh-poly.htm">Poly</a>
-• <a href="qh-qhull.htm">Qhull</a> • <a href="qh-set.htm">Set</a>
-• <a href="qh-stat.htm">Stat</a> • <a href="qh-user.htm">User</a>
-
-<hr>
-<!-- Main text of document. -->
-
-<h1>Qhull functions, macros, and data structures</h1>
-<blockquote>
-<p>The following sections provide an overview and index to
-Qhull's functions, macros, and data structures. Each
-section starts with an introduction. Also see <a href=../html/qh-in.htm#library>Calling
-Qhull from your program</a>.</p>
-
-<p>Qhull uses the following conventions:</p>
-<blockquote>
-
-<ul>
-<li>in code, global variables start with "qh "
-<li>in documentation, global variables start with 'qh.'
-<li>constants start with an upper case word
-<li>important globals include an '_'
-<li>functions, macros, and constants start with "qh_"</li>
-<li>data types end in "T"</li>
-<li>macros with arguments end in "_"</li>
-<li>iterators are macros that use local variables</li>
-<li>iterators for sets start with "FOREACH"</li>
-<li>iterators for lists start with "FORALL"</li>
-<li>qhull options are in single quotes (e.g., 'Pdn')</li>
-<li>lists are sorted alphabetically</li>
-<li>preprocessor directives on left margin for older compilers</li>
-</ul>
-</blockquote>
-<p>
-When reading the code, please note that the
-global data structure, 'qh', is a macro. It
-either expands to "qh_qh." or to
-"qh_qh->". The later is used for
-applications which run concurrent calls to qh_qhull().
-<p>
-When reading code with an editor, a search for
-<i>"procedure</i>
-will locate the header of <i>qh_procedure</i>. A search for <i>* procedure</i>
-will locate the tail of <i>qh_procedure</i>.
-
-<p>A useful starting point is <a href="qhull.h">qhull.h</a>. It defines most
-of Qhull data structures and top-level functions. Search for <i>'PFn'</i> to
-determine the corresponding constant in Qhull. Search for <i>'Fp'</i> to
-determine the corresponding <a href="qhull.h#qh_PRINT">qh_PRINT...</a> constant.
-Search <a href="io.c">io.c</a> to learn how the print function is implemented.</p>
-
-<p>If your web browser loads .c and .h files with an external application,
-change the MIME type of .c and .h files to "text/html".
-Opera does not always work since it treats '<' characters as HTML tags.
-<p>
-Please report documentation and link errors
-to <a href="mailto:qhull-bug@qhull.org">qhull-bug@qhull.org</a>.
-<p>
-<i>Brad Barber, Cambridge MA, June 1, 2002</i>
-</p>
-</blockquote>
-
-<p><b>Copyright © 1997-2003 The Geometry Center, Minneapolis MN</b></p>
-
-<hr>
-
-<h2><a href="#TOP">»</a><a name="TOC">Qhull files</a> </h2>
-<blockquote>
-
-<p>This sections lists the .c and .h files for Qhull. Please
-refer to these files for detailed information.</p>
-<blockquote>
-
-<dl>
-<dt><a href="qhull.h"><b>qhull.h</b></a> </dt>
-<dd>Include file for the Qhull library, <tt>qhull.a</tt>.
-Data structures are documented under <a href="qh-poly.htm">Poly</a>.
-Global variables are documented under <a href="qh-globa.htm">Global</a>.
-Other data structures and variables are documented under
-<a href="qh-qhull.htm#TOC">Qhull</a> or <a href="qh-geom.htm"><b>Geom</b></a><b>.</b></dd>
-
-<dt> </dt>
-<dt><a href="qh-geom.htm"><b>Geom</b></a><b>, </b>
-<a href="geom.h"><b>geom.h</b></a><b>, </b>
-<a href="geom.c"><b>geom.c</b></a><b>, </b>
-<a href="geom2.c"><b>geom2.c</b></a> </dt>
-<dd>Geometric routines. These routines implement mathematical
-functions such as Gaussian elimination and geometric
-routines needed for Qhull. Frequently used routines are
-in <tt>geom.c</tt> while infrequent ones are in <tt>geom2.c</tt>.
-</dd>
-
-<dt> </dt>
-<dt><a href="qh-globa.htm"><b>Global</b></a><b>, </b>
-<a href="global.c"><b>global.c</b></a><b>, </b>
-<a href="qhull.h"><b>qhull.h</b></a> </dt>
-<dd>Global routines. Qhull uses a global data structure, <tt>qh</tt>,
-to store globally defined constants, lists, sets, and
-variables.
-<tt>global.c</tt> initializes and frees these
-structures. </dd>
-
-<dt> </dt>
-<dt><a href="qh-io.htm"><b>Io</b></a><b>, </b><a href="io.h"><b>io.h</b></a><b>,
-</b><a href="io.c"><b>io.c</b></a> </dt>
-<dd>Input and output routines. Qhull provides a wide range of
-input and output options.</dd>
-
-<dt> </dt>
-<dt><a href="qh-mem.htm"><b>Mem</b></a><b>, </b>
-<a href="mem.h"><b>mem.h</b></a><b>, </b>
-<a href="mem.c"><b>mem.c</b></a> </dt>
-<dd>Memory routines. Qhull provides memory allocation and
-deallocation. It uses quick-fit allocation.</dd>
-
-<dt> </dt>
-<dt><a href="qh-merge.htm"><b>Merge</b></a><b>, </b>
-<a href="merge.h"><b>merge.h</b></a><b>, </b>
-<a href="merge.c"><b>merge.c</b></a> </dt>
-<dd>Merge routines. Qhull handles precision problems by
-merged facets or joggled input. These routines merge simplicial facets,
-merge non-simplicial facets, merge cycles of facets, and
-rename redundant vertices.</dd>
-
-<dt> </dt>
-<dt><a href="qh-poly.htm"><b>Poly</b></a><b>, </b>
-<a href="poly.h"><b>poly.h</b></a><b>, </b>
-<a href="poly.c"><b>poly.c</b></a><b>, </b>
-<a href="poly2.c"><b>poly2.c</b></a><b>, </b>
-<a href="qhull.h"><b>qhull.h</b></a> </dt>
-<dd>Polyhedral routines. Qhull produces a polyhedron as a
-list of facets with vertices, neighbors, ridges, and
-geometric information. <tt>Qhull.h</tt> defines the main
-data structures. Frequently used routines are in <tt>poly.c</tt>
-while infrequent ones are in <tt>poly2.c</tt>.</dd>
-
-<dt> </dt>
-<dt><a href="qh-qhull.htm#TOC"><b>Qhull</b></a><b>, </b>
-<a href="qhull.c"><b>qhull.c</b></a><b>, </b>
-<a href="qhull.h"><b>qhull.h</b></a><b>, </b>
-<a href="qhull_a.h"><b>qhull_a.h</b></a><b>, </b>
-<a href="unix.c"><b>unix.c</b></a> <b>, </b>
-<a href="qconvex.c"><b>qconvex.c</b></a> <b>, </b>
-<a href="qdelaun.c"><b>qdelaun.c</b></a> <b>, </b>
-<a href="qhalf.c"><b>qhalf.c</b></a> <b>, </b>
-<a href="qvoronoi.c"><b>qvoronoi.c</b></a> </dt>
-<dd>Top-level routines. The Quickhull algorithm is
-implemented by <tt>qhull.c</tt>. <tt>qhull_a.h</tt>
-includes all header files. </dd>
-
-<dt> </dt>
-<dt><a href="qh-set.htm"><b>Set</b></a><b>, </b>
-<a href="qset.h"><b>qset.h</b></a><b>, </b>
-<a href="qset.c"><b>qset.c</b></a> </dt>
-<dd>Set routines. Qhull implements its data structures as
-sets. A set is an array of pointers that is expanded as
-needed. This is a separate package that may be used in
-other applications. </dd>
-
-<dt> </dt>
-<dt><a href="qh-stat.htm"><b>Stat</b></a><b>, </b>
-<a href="stat.h"><b>stat.h</b></a><b>, </b>
-<a href="stat.c"><b>stat.c</b></a> </dt>
-<dd>Statistical routines. Qhull maintains statistics about
-its implementation. </dd>
-
-<dt> </dt>
-<dt><a href="qh-user.htm"><b>User</b></a><b>, </b>
-<a href="user.h"><b>user.h</b></a><b>, </b>
-<a href="user.c"><b>user.c</b></a><b>, </b>
-<a href="user_eg.c"><b>user_eg.c</b></a><b>, </b>
-<a href="qhull_interface.cpp#TOP"><b>qhull_interface.cpp</b></a></dt>
-<dd>User-defined routines. Qhull allows the user to configure
-the code with defined constants and specialized routines.
-</dd>
-</dl>
-</blockquote>
-
-</blockquote>
-<p><!-- Navigation links --> </p>
-<hr>
-<p><b>Up:</b>
-<a href="http://www.qhull.org">Home page for
-Qhull</a> <br>
-<b>Up:</b> <a href="../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
-<b>Up:</b> <a href="../html/qh-quick.htm#programs">Programs</a>
-• <a href="../html/qh-quick.htm#options">Options</a>
-• <a href="../html/qh-opto.htm#output">Output</a>
-• <a href="../html/qh-optf.htm#format">Formats</a>
-• <a href="../html/qh-optg.htm#geomview">Geomview</a>
-• <a href="../html/qh-optp.htm#print">Print</a>
-• <a href="../html/qh-optq.htm#qhull">Qhull</a>
-• <a href="../html/qh-optc.htm#prec">Precision</a>
-• <a href="../html/qh-optt.htm#trace">Trace</a><br>
-<b>Up:</b> <a href="../html/qh-in.htm#TOC">Qhull internals: Table of Contents</a> <br>
-<b>To:</b> <a href="#TOC">Qhull files</a><br>
-<b>To:</b> <a href="qh-geom.htm">Geom</a> •
-<a href="qh-globa.htm">Global</a> • <a href="qh-io.htm">Io</a>
-• <a href="qh-mem.htm">Mem</a> • <a href="qh-merge.htm">Merge</a>
-• <a href="qh-poly.htm">Poly</a> • <a href="qh-qhull.htm#TOC">Qhull</a>
-• <a href="qh-set.htm">Set</a> • <a href="qh-stat.htm">Stat</a>
-• <a href="qh-user.htm">User</a><br>
-
-<p><!-- GC common information --> </p>
-<hr>
-<p><a href="http://www.geom.uiuc.edu/"><img
-src="../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
-Geometry Center Home Page </i></p>
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/io.c b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/io.c
deleted file mode 100644
index ebb6528cf80d69df6f036180b4f4f1d41bd5b457..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/io.c
+++ /dev/null
@@ -1,4108 +0,0 @@
-/*<html><pre> -<a href="qh-io.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- io.c
- Input/Output routines of qhull application
-
- see qh-io.htm and io.h
-
- see user.c for qh_errprint and qh_printfacetlist
-
- unix.c calls qh_readpoints and qh_produce_output
-
- unix.c and user.c are the only callers of io.c functions
- This allows the user to avoid loading io.o from qhull.a
-
- copyright (c) 1993-2003 The Geometry Center
-*/
-
-#include "qhull_a.h"
-
-/*========= -functions in alphabetical order after qh_produce_output() =====*/
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="produce_output">-</a>
-
- qh_produce_output()
- prints out the result of qhull in desired format
- if qh.GETarea
- computes and prints area and volume
- qh.PRINTout[] is an array of output formats
-
- notes:
- prints output in qh.PRINTout order
-*/
-void qh_produce_output(void) {
- int i, tempsize= qh_setsize ((setT*)qhmem.tempstack), d_1;
-
- if (qh VORONOI) {
- qh_clearcenters (qh_ASvoronoi);
- qh_vertexneighbors();
- }
- if (qh TRIangulate) {
- qh_triangulate();
- if (qh VERIFYoutput && !qh CHECKfrequently)
- qh_checkpolygon (qh facet_list);
- }
- qh_findgood_all (qh facet_list);
- if (qh GETarea)
- qh_getarea(qh facet_list);
- if (qh KEEParea || qh KEEPmerge || qh KEEPminArea < REALmax/2)
- qh_markkeep (qh facet_list);
- if (qh PRINTsummary)
- qh_printsummary(qh ferr);
- else if (qh PRINTout[0] == qh_PRINTnone)
- qh_printsummary(qh fout);
- for (i= 0; i < qh_PRINTEND; i++)
- qh_printfacets (qh fout, qh PRINTout[i], qh facet_list, NULL, !qh_ALL);
- qh_allstatistics();
- if (qh PRINTprecision && !qh MERGING && (qh JOGGLEmax > REALmax/2 || qh RERUN))
- qh_printstats (qh ferr, qhstat precision, NULL);
- if (qh VERIFYoutput && (zzval_(Zridge) > 0 || zzval_(Zridgemid) > 0))
- qh_printstats (qh ferr, qhstat vridges, NULL);
- if (qh PRINTstatistics) {
- qh_collectstatistics();
- qh_printstatistics(qh ferr, "");
- qh_memstatistics (qh ferr);
- d_1= sizeof(setT) + (qh hull_dim - 1) * SETelemsize;
- fprintf(qh ferr, "\
- size in bytes: merge %lu ridge %lu vertex %lu facet %lu\n\
- normal %d ridge vertices %d facet vertices or neighbors %lu\n",
- sizeof(mergeT), sizeof(ridgeT),
- sizeof(vertexT), sizeof(facetT),
- qh normal_size, d_1, d_1 + SETelemsize);
- }
- if (qh_setsize ((setT*)qhmem.tempstack) != tempsize) {
- fprintf (qh ferr, "qhull internal error (qh_produce_output): temporary sets not empty (%d)\n",
- qh_setsize ((setT*)qhmem.tempstack));
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
-} /* produce_output */
-
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="dfacet">-</a>
-
- dfacet( id )
- print facet by id, for debugging
-
-*/
-void dfacet (unsigned id) {
- facetT *facet;
-
- FORALLfacets {
- if (facet->id == id) {
- qh_printfacet (qh fout, facet);
- break;
- }
- }
-} /* dfacet */
-
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="dvertex">-</a>
-
- dvertex( id )
- print vertex by id, for debugging
-*/
-void dvertex (unsigned id) {
- vertexT *vertex;
-
- FORALLvertices {
- if (vertex->id == id) {
- qh_printvertex (qh fout, vertex);
- break;
- }
- }
-} /* dvertex */
-
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="compare_vertexpoint">-</a>
-
- qh_compare_vertexpoint( p1, p2 )
- used by qsort() to order vertices by point id
-*/
-int qh_compare_vertexpoint(const void *p1, const void *p2) {
- vertexT *a= *((vertexT **)p1), *b= *((vertexT **)p2);
-
- return ((qh_pointid(a->point) > qh_pointid(b->point)?1:-1));
-} /* compare_vertexpoint */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="compare_facetarea">-</a>
-
- qh_compare_facetarea( p1, p2 )
- used by qsort() to order facets by area
-*/
-int qh_compare_facetarea(const void *p1, const void *p2) {
- facetT *a= *((facetT **)p1), *b= *((facetT **)p2);
-
- if (!a->isarea)
- return -1;
- if (!b->isarea)
- return 1;
- if (a->f.area > b->f.area)
- return 1;
- else if (a->f.area == b->f.area)
- return 0;
- return -1;
-} /* compare_facetarea */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="compare_facetmerge">-</a>
-
- qh_compare_facetmerge( p1, p2 )
- used by qsort() to order facets by number of merges
-*/
-int qh_compare_facetmerge(const void *p1, const void *p2) {
- facetT *a= *((facetT **)p1), *b= *((facetT **)p2);
-
- return (a->nummerge - b->nummerge);
-} /* compare_facetvisit */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="compare_facetvisit">-</a>
-
- qh_compare_facetvisit( p1, p2 )
- used by qsort() to order facets by visit id or id
-*/
-int qh_compare_facetvisit(const void *p1, const void *p2) {
- facetT *a= *((facetT **)p1), *b= *((facetT **)p2);
- int i,j;
-
- if (!(i= a->visitid))
- i= - a->id; /* do not convert to int */
- if (!(j= b->visitid))
- j= - b->id;
- return (i - j);
-} /* compare_facetvisit */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="countfacets">-</a>
-
- qh_countfacets( facetlist, facets, printall,
- numfacets, numsimplicial, totneighbors, numridges, numcoplanar, numtricoplanars )
- count good facets for printing and set visitid
- if allfacets, ignores qh_skipfacet()
-
- notes:
- qh_printsummary and qh_countfacets must match counts
-
- returns:
- numfacets, numsimplicial, total neighbors, numridges, coplanars
- each facet with ->visitid indicating 1-relative position
- ->visitid==0 indicates not good
-
- notes
- numfacets >= numsimplicial
- if qh.NEWfacets,
- does not count visible facets (matches qh_printafacet)
-
- design:
- for all facets on facetlist and in facets set
- unless facet is skipped or visible (i.e., will be deleted)
- mark facet->visitid
- update counts
-*/
-void qh_countfacets (facetT *facetlist, setT *facets, boolT printall,
- int *numfacetsp, int *numsimplicialp, int *totneighborsp, int *numridgesp, int *numcoplanarsp, int *numtricoplanarsp) {
- facetT *facet, **facetp;
- int numfacets= 0, numsimplicial= 0, numridges= 0, totneighbors= 0, numcoplanars= 0, numtricoplanars= 0;
-
- FORALLfacet_(facetlist) {
- if ((facet->visible && qh NEWfacets)
- || (!printall && qh_skipfacet(facet)))
- facet->visitid= 0;
- else {
- facet->visitid= ++numfacets;
- totneighbors += qh_setsize (facet->neighbors);
- if (facet->simplicial) {
- numsimplicial++;
- if (facet->keepcentrum && facet->tricoplanar)
- numtricoplanars++;
- }else
- numridges += qh_setsize (facet->ridges);
- if (facet->coplanarset)
- numcoplanars += qh_setsize (facet->coplanarset);
- }
- }
- FOREACHfacet_(facets) {
- if ((facet->visible && qh NEWfacets)
- || (!printall && qh_skipfacet(facet)))
- facet->visitid= 0;
- else {
- facet->visitid= ++numfacets;
- totneighbors += qh_setsize (facet->neighbors);
- if (facet->simplicial){
- numsimplicial++;
- if (facet->keepcentrum && facet->tricoplanar)
- numtricoplanars++;
- }else
- numridges += qh_setsize (facet->ridges);
- if (facet->coplanarset)
- numcoplanars += qh_setsize (facet->coplanarset);
- }
- }
- qh visit_id += numfacets+1;
- *numfacetsp= numfacets;
- *numsimplicialp= numsimplicial;
- *totneighborsp= totneighbors;
- *numridgesp= numridges;
- *numcoplanarsp= numcoplanars;
- *numtricoplanarsp= numtricoplanars;
-} /* countfacets */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="detvnorm">-</a>
-
- qh_detvnorm( vertex, vertexA, centers, offset )
- compute separating plane of the Voronoi diagram for a pair of input sites
- centers= set of facets (i.e., Voronoi vertices)
- facet->visitid= 0 iff vertex-at-infinity (i.e., unbounded)
-
- assumes:
- qh_ASvoronoi and qh_vertexneighbors() already set
-
- returns:
- norm
- a pointer into qh.gm_matrix to qh.hull_dim-1 reals
- copy the data before reusing qh.gm_matrix
- offset
- if 'QVn'
- sign adjusted so that qh.GOODvertexp is inside
- else
- sign adjusted so that vertex is inside
-
- qh.gm_matrix= simplex of points from centers relative to first center
-
- notes:
- in io.c so that code for 'v Tv' can be removed by removing io.c
- returns pointer into qh.gm_matrix to avoid tracking of temporary memory
-
- design:
- determine midpoint of input sites
- build points as the set of Voronoi vertices
- select a simplex from points (if necessary)
- include midpoint if the Voronoi region is unbounded
- relocate the first vertex of the simplex to the origin
- compute the normalized hyperplane through the simplex
- orient the hyperplane toward 'QVn' or 'vertex'
- if 'Tv' or 'Ts'
- if bounded
- test that hyperplane is the perpendicular bisector of the input sites
- test that Voronoi vertices not in the simplex are still on the hyperplane
- free up temporary memory
-*/
-pointT *qh_detvnorm (vertexT *vertex, vertexT *vertexA, setT *centers, realT *offsetp) {
- facetT *facet, **facetp;
- int i, k, pointid, pointidA, point_i, point_n;
- setT *simplex= NULL;
- pointT *point, **pointp, *point0, *midpoint, *normal, *inpoint;
- coordT *coord, *gmcoord, *normalp;
- setT *points= qh_settemp (qh TEMPsize);
- boolT nearzero= False;
- boolT unbounded= False;
- int numcenters= 0;
- int dim= qh hull_dim - 1;
- realT dist, offset, angle, zero= 0.0;
-
- midpoint= qh gm_matrix + qh hull_dim * qh hull_dim; /* last row */
- for (k= 0; k < dim; k++)
- midpoint[k]= (vertex->point[k] + vertexA->point[k])/2;
- FOREACHfacet_(centers) {
- numcenters++;
- if (!facet->visitid)
- unbounded= True;
- else {
- if (!facet->center)
- facet->center= qh_facetcenter (facet->vertices);
- qh_setappend (&points, facet->center);
- }
- }
- if (numcenters > dim) {
- simplex= qh_settemp (qh TEMPsize);
- qh_setappend (&simplex, vertex->point);
- if (unbounded)
- qh_setappend (&simplex, midpoint);
- qh_maxsimplex (dim, points, NULL, 0, &simplex);
- qh_setdelnth (simplex, 0);
- }else if (numcenters == dim) {
- if (unbounded)
- qh_setappend (&points, midpoint);
- simplex= points;
- }else {
- fprintf(qh ferr, "qh_detvnorm: too few points (%d) to compute separating plane\n", numcenters);
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- i= 0;
- gmcoord= qh gm_matrix;
- point0= SETfirstt_(simplex, pointT);
- FOREACHpoint_(simplex) {
- if (qh IStracing >= 4)
- qh_printmatrix(qh ferr, "qh_detvnorm: Voronoi vertex or midpoint",
- &point, 1, dim);
- if (point != point0) {
- qh gm_row[i++]= gmcoord;
- coord= point0;
- for (k= dim; k--; )
- *(gmcoord++)= *point++ - *coord++;
- }
- }
- qh gm_row[i]= gmcoord; /* does not overlap midpoint, may be used later for qh_areasimplex */
- normal= gmcoord;
- qh_sethyperplane_gauss (dim, qh gm_row, point0, True,
- normal, &offset, &nearzero);
- if (qh GOODvertexp == vertexA->point)
- inpoint= vertexA->point;
- else
- inpoint= vertex->point;
- zinc_(Zdistio);
- dist= qh_distnorm (dim, inpoint, normal, &offset);
- if (dist > 0) {
- offset= -offset;
- normalp= normal;
- for (k= dim; k--; ) {
- *normalp= -(*normalp);
- normalp++;
- }
- }
- if (qh VERIFYoutput || qh PRINTstatistics) {
- pointid= qh_pointid (vertex->point);
- pointidA= qh_pointid (vertexA->point);
- if (!unbounded) {
- zinc_(Zdiststat);
- dist= qh_distnorm (dim, midpoint, normal, &offset);
- if (dist < 0)
- dist= -dist;
- zzinc_(Zridgemid);
- wwmax_(Wridgemidmax, dist);
- wwadd_(Wridgemid, dist);
- trace4((qh ferr, "qh_detvnorm: points %d %d midpoint dist %2.2g\n",
- pointid, pointidA, dist));
- for (k= 0; k < dim; k++)
- midpoint[k]= vertexA->point[k] - vertex->point[k]; /* overwrites midpoint! */
- qh_normalize (midpoint, dim, False);
- angle= qh_distnorm (dim, midpoint, normal, &zero); /* qh_detangle uses dim+1 */
- if (angle < 0.0)
- angle= angle + 1.0;
- else
- angle= angle - 1.0;
- if (angle < 0.0)
- angle -= angle;
- trace4((qh ferr, "qh_detvnorm: points %d %d angle %2.2g nearzero %d\n",
- pointid, pointidA, angle, nearzero));
- if (nearzero) {
- zzinc_(Zridge0);
- wwmax_(Wridge0max, angle);
- wwadd_(Wridge0, angle);
- }else {
- zzinc_(Zridgeok)
- wwmax_(Wridgeokmax, angle);
- wwadd_(Wridgeok, angle);
- }
- }
- if (simplex != points) {
- FOREACHpoint_i_(points) {
- if (!qh_setin (simplex, point)) {
- facet= SETelemt_(centers, point_i, facetT);
- zinc_(Zdiststat);
- dist= qh_distnorm (dim, point, normal, &offset);
- if (dist < 0)
- dist= -dist;
- zzinc_(Zridge);
- wwmax_(Wridgemax, dist);
- wwadd_(Wridge, dist);
- trace4((qh ferr, "qh_detvnorm: points %d %d Voronoi vertex %d dist %2.2g\n",
- pointid, pointidA, facet->visitid, dist));
- }
- }
- }
- }
- *offsetp= offset;
- if (simplex != points)
- qh_settempfree (&simplex);
- qh_settempfree (&points);
- return normal;
-} /* detvnorm */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="detvridge">-</a>
-
- qh_detvridge( vertexA )
- determine Voronoi ridge from 'seen' neighbors of vertexA
- include one vertex-at-infinite if an !neighbor->visitid
-
- returns:
- temporary set of centers (facets, i.e., Voronoi vertices)
- sorted by center id
-*/
-setT *qh_detvridge (vertexT *vertex) {
- setT *centers= qh_settemp (qh TEMPsize);
- setT *tricenters= qh_settemp (qh TEMPsize);
- facetT *neighbor, **neighborp;
- boolT firstinf= True;
-
- FOREACHneighbor_(vertex) {
- if (neighbor->seen) {
- if (neighbor->visitid) {
- if (!neighbor->tricoplanar || qh_setunique (&tricenters, neighbor->center))
- qh_setappend (¢ers, neighbor);
- }else if (firstinf) {
- firstinf= False;
- qh_setappend (¢ers, neighbor);
- }
- }
- }
- qsort (SETaddr_(centers, facetT), qh_setsize (centers),
- sizeof (facetT *), qh_compare_facetvisit);
- qh_settempfree (&tricenters);
- return centers;
-} /* detvridge */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="detvridge3">-</a>
-
- qh_detvridge3( atvertex, vertex )
- determine 3-d Voronoi ridge from 'seen' neighbors of atvertex and vertex
- include one vertex-at-infinite for !neighbor->visitid
- assumes all facet->seen2= True
-
- returns:
- temporary set of centers (facets, i.e., Voronoi vertices)
- listed in adjacency order (not oriented)
- all facet->seen2= True
-
- design:
- mark all neighbors of atvertex
- for each adjacent neighbor of both atvertex and vertex
- if neighbor selected
- add neighbor to set of Voronoi vertices
-*/
-setT *qh_detvridge3 (vertexT *atvertex, vertexT *vertex) {
- setT *centers= qh_settemp (qh TEMPsize);
- setT *tricenters= qh_settemp (qh TEMPsize);
- facetT *neighbor, **neighborp, *facet= NULL;
- boolT firstinf= True;
-
- FOREACHneighbor_(atvertex)
- neighbor->seen2= False;
- FOREACHneighbor_(vertex) {
- if (!neighbor->seen2) {
- facet= neighbor;
- break;
- }
- }
- while (facet) {
- facet->seen2= True;
- if (neighbor->seen) {
- if (facet->visitid) {
- if (!facet->tricoplanar || qh_setunique (&tricenters, facet->center))
- qh_setappend (¢ers, facet);
- }else if (firstinf) {
- firstinf= False;
- qh_setappend (¢ers, facet);
- }
- }
- FOREACHneighbor_(facet) {
- if (!neighbor->seen2) {
- if (qh_setin (vertex->neighbors, neighbor))
- break;
- else
- neighbor->seen2= True;
- }
- }
- facet= neighbor;
- }
- if (qh CHECKfrequently) {
- FOREACHneighbor_(vertex) {
- if (!neighbor->seen2) {
- fprintf (stderr, "qh_detvridge3: neigbors of vertex p%d are not connected at facet %d\n",
- qh_pointid (vertex->point), neighbor->id);
- qh_errexit (qh_ERRqhull, neighbor, NULL);
- }
- }
- }
- FOREACHneighbor_(atvertex)
- neighbor->seen2= True;
- qh_settempfree (&tricenters);
- return centers;
-} /* detvridge3 */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="eachvoronoi">-</a>
-
- qh_eachvoronoi( fp, printvridge, vertex, visitall, innerouter, inorder )
- if visitall,
- visit all Voronoi ridges for vertex (i.e., an input site)
- else
- visit all unvisited Voronoi ridges for vertex
- all vertex->seen= False if unvisited
- assumes
- all facet->seen= False
- all facet->seen2= True (for qh_detvridge3)
- all facet->visitid == 0 if vertex_at_infinity
- == index of Voronoi vertex
- >= qh.num_facets if ignored
- innerouter:
- qh_RIDGEall-- both inner (bounded) and outer (unbounded) ridges
- qh_RIDGEinner- only inner
- qh_RIDGEouter- only outer
-
- if inorder
- orders vertices for 3-d Voronoi diagrams
-
- returns:
- number of visited ridges (does not include previously visited ridges)
-
- if printvridge,
- calls printvridge( fp, vertex, vertexA, centers)
- fp== any pointer (assumes FILE*)
- vertex,vertexA= pair of input sites that define a Voronoi ridge
- centers= set of facets (i.e., Voronoi vertices)
- ->visitid == index or 0 if vertex_at_infinity
- ordered for 3-d Voronoi diagram
- notes:
- uses qh.vertex_visit
-
- see:
- qh_eachvoronoi_all()
-
- design:
- mark selected neighbors of atvertex
- for each selected neighbor (either Voronoi vertex or vertex-at-infinity)
- for each unvisited vertex
- if atvertex and vertex share more than d-1 neighbors
- bump totalcount
- if printvridge defined
- build the set of shared neighbors (i.e., Voronoi vertices)
- call printvridge
-*/
-int qh_eachvoronoi (FILE *fp, printvridgeT printvridge, vertexT *atvertex, boolT visitall, qh_RIDGE innerouter, boolT inorder) {
- boolT unbounded;
- int count;
- facetT *neighbor, **neighborp, *neighborA, **neighborAp;
- setT *centers;
- setT *tricenters= qh_settemp (qh TEMPsize);
-
- vertexT *vertex, **vertexp;
- boolT firstinf;
- unsigned int numfacets= (unsigned int)qh num_facets;
- int totridges= 0;
-
- qh vertex_visit++;
- atvertex->seen= True;
- if (visitall) {
- FORALLvertices
- vertex->seen= False;
- }
- FOREACHneighbor_(atvertex) {
- if (neighbor->visitid < numfacets)
- neighbor->seen= True;
- }
- FOREACHneighbor_(atvertex) {
- if (neighbor->seen) {
- FOREACHvertex_(neighbor->vertices) {
- if (vertex->visitid != qh vertex_visit && !vertex->seen) {
- vertex->visitid= qh vertex_visit;
- count= 0;
- firstinf= True;
- qh_settruncate (tricenters, 0);
- FOREACHneighborA_(vertex) {
- if (neighborA->seen) {
- if (neighborA->visitid) {
- if (!neighborA->tricoplanar || qh_setunique (&tricenters, neighborA->center))
- count++;
- }else if (firstinf) {
- count++;
- firstinf= False;
- }
- }
- }
- if (count >= qh hull_dim - 1) { /* e.g., 3 for 3-d Voronoi */
- if (firstinf) {
- if (innerouter == qh_RIDGEouter)
- continue;
- unbounded= False;
- }else {
- if (innerouter == qh_RIDGEinner)
- continue;
- unbounded= True;
- }
- totridges++;
- trace4((qh ferr, "qh_eachvoronoi: Voronoi ridge of %d vertices between sites %d and %d\n",
- count, qh_pointid (atvertex->point), qh_pointid (vertex->point)));
- if (printvridge) {
- if (inorder && qh hull_dim == 3+1) /* 3-d Voronoi diagram */
- centers= qh_detvridge3 (atvertex, vertex);
- else
- centers= qh_detvridge (vertex);
- (*printvridge) (fp, atvertex, vertex, centers, unbounded);
- qh_settempfree (¢ers);
- }
- }
- }
- }
- }
- }
- FOREACHneighbor_(atvertex)
- neighbor->seen= False;
- qh_settempfree (&tricenters);
- return totridges;
-} /* eachvoronoi */
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="eachvoronoi_all">-</a>
-
- qh_eachvoronoi_all( fp, printvridge, isupper, innerouter, inorder )
- visit all Voronoi ridges
-
- innerouter:
- see qh_eachvoronoi()
-
- if inorder
- orders vertices for 3-d Voronoi diagrams
-
- returns
- total number of ridges
-
- if isupper == facet->upperdelaunay (i.e., a Vornoi vertex)
- facet->visitid= Voronoi vertex index (same as 'o' format)
- else
- facet->visitid= 0
-
- if printvridge,
- calls printvridge( fp, vertex, vertexA, centers)
- [see qh_eachvoronoi]
-
- notes:
- Not used for qhull.exe
- same effect as qh_printvdiagram but ridges not sorted by point id
-*/
-int qh_eachvoronoi_all (FILE *fp, printvridgeT printvridge, boolT isupper, qh_RIDGE innerouter, boolT inorder) {
- facetT *facet;
- vertexT *vertex;
- int numcenters= 1; /* vertex 0 is vertex-at-infinity */
- int totridges= 0;
-
- qh_clearcenters (qh_ASvoronoi);
- qh_vertexneighbors();
- maximize_(qh visit_id, (unsigned) qh num_facets);
- FORALLfacets {
- facet->visitid= 0;
- facet->seen= False;
- facet->seen2= True;
- }
- FORALLfacets {
- if (facet->upperdelaunay == isupper)
- facet->visitid= numcenters++;
- }
- FORALLvertices
- vertex->seen= False;
- FORALLvertices {
- if (qh GOODvertex > 0 && qh_pointid(vertex->point)+1 != qh GOODvertex)
- continue;
- totridges += qh_eachvoronoi (fp, printvridge, vertex,
- !qh_ALL, innerouter, inorder);
- }
- return totridges;
-} /* eachvoronoi_all */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="facet2point">-</a>
-
- qh_facet2point( facet, point0, point1, mindist )
- return two projected temporary vertices for a 2-d facet
- may be non-simplicial
-
- returns:
- point0 and point1 oriented and projected to the facet
- returns mindist (maximum distance below plane)
-*/
-void qh_facet2point(facetT *facet, pointT **point0, pointT **point1, realT *mindist) {
- vertexT *vertex0, *vertex1;
- realT dist;
-
- if (facet->toporient ^ qh_ORIENTclock) {
- vertex0= SETfirstt_(facet->vertices, vertexT);
- vertex1= SETsecondt_(facet->vertices, vertexT);
- }else {
- vertex1= SETfirstt_(facet->vertices, vertexT);
- vertex0= SETsecondt_(facet->vertices, vertexT);
- }
- zadd_(Zdistio, 2);
- qh_distplane(vertex0->point, facet, &dist);
- *mindist= dist;
- *point0= qh_projectpoint(vertex0->point, facet, dist);
- qh_distplane(vertex1->point, facet, &dist);
- minimize_(*mindist, dist);
- *point1= qh_projectpoint(vertex1->point, facet, dist);
-} /* facet2point */
-
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="facetvertices">-</a>
-
- qh_facetvertices( facetlist, facets, allfacets )
- returns temporary set of vertices in a set and/or list of facets
- if allfacets, ignores qh_skipfacet()
-
- returns:
- vertices with qh.vertex_visit
-
- notes:
- optimized for allfacets of facet_list
-
- design:
- if allfacets of facet_list
- create vertex set from vertex_list
- else
- for each selected facet in facets or facetlist
- append unvisited vertices to vertex set
-*/
-setT *qh_facetvertices (facetT *facetlist, setT *facets, boolT allfacets) {
- setT *vertices;
- facetT *facet, **facetp;
- vertexT *vertex, **vertexp;
-
- qh vertex_visit++;
- if (facetlist == qh facet_list && allfacets && !facets) {
- vertices= qh_settemp (qh num_vertices);
- FORALLvertices {
- vertex->visitid= qh vertex_visit;
- qh_setappend (&vertices, vertex);
- }
- }else {
- vertices= qh_settemp (qh TEMPsize);
- FORALLfacet_(facetlist) {
- if (!allfacets && qh_skipfacet (facet))
- continue;
- FOREACHvertex_(facet->vertices) {
- if (vertex->visitid != qh vertex_visit) {
- vertex->visitid= qh vertex_visit;
- qh_setappend (&vertices, vertex);
- }
- }
- }
- }
- FOREACHfacet_(facets) {
- if (!allfacets && qh_skipfacet (facet))
- continue;
- FOREACHvertex_(facet->vertices) {
- if (vertex->visitid != qh vertex_visit) {
- vertex->visitid= qh vertex_visit;
- qh_setappend (&vertices, vertex);
- }
- }
- }
- return vertices;
-} /* facetvertices */
-
-/*-<a href="qh-geom.htm#TOC"
- >-------------------------------</a><a name="geomplanes">-</a>
-
- qh_geomplanes( facet, outerplane, innerplane )
- return outer and inner planes for Geomview
- qh.PRINTradius is size of vertices and points (includes qh.JOGGLEmax)
-
- notes:
- assume precise calculations in io.c with roundoff covered by qh_GEOMepsilon
-*/
-void qh_geomplanes (facetT *facet, realT *outerplane, realT *innerplane) {
- realT radius;
-
- if (qh MERGING || qh JOGGLEmax < REALmax/2) {
- qh_outerinner (facet, outerplane, innerplane);
- radius= qh PRINTradius;
- if (qh JOGGLEmax < REALmax/2)
- radius -= qh JOGGLEmax * sqrt (qh hull_dim); /* already accounted for in qh_outerinner() */
- *outerplane += radius;
- *innerplane -= radius;
- if (qh PRINTcoplanar || qh PRINTspheres) {
- *outerplane += qh MAXabs_coord * qh_GEOMepsilon;
- *innerplane -= qh MAXabs_coord * qh_GEOMepsilon;
- }
- }else
- *innerplane= *outerplane= 0;
-} /* geomplanes */
-
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="markkeep">-</a>
-
- qh_markkeep( facetlist )
- mark good facets that meet qh.KEEParea, qh.KEEPmerge, and qh.KEEPminArea
- ignores visible facets (not part of convex hull)
-
- returns:
- may clear facet->good
- recomputes qh.num_good
-
- design:
- get set of good facets
- if qh.KEEParea
- sort facets by area
- clear facet->good for all but n largest facets
- if qh.KEEPmerge
- sort facets by merge count
- clear facet->good for all but n most merged facets
- if qh.KEEPminarea
- clear facet->good if area too small
- update qh.num_good
-*/
-void qh_markkeep (facetT *facetlist) {
- facetT *facet, **facetp;
- setT *facets= qh_settemp (qh num_facets);
- int size, count;
-
- trace2((qh ferr, "qh_markkeep: only keep %d largest and/or %d most merged facets and/or min area %.2g\n",
- qh KEEParea, qh KEEPmerge, qh KEEPminArea));
- FORALLfacet_(facetlist) {
- if (!facet->visible && facet->good)
- qh_setappend (&facets, facet);
- }
- size= qh_setsize (facets);
- if (qh KEEParea) {
- qsort (SETaddr_(facets, facetT), size,
- sizeof (facetT *), qh_compare_facetarea);
- if ((count= size - qh KEEParea) > 0) {
- FOREACHfacet_(facets) {
- facet->good= False;
- if (--count == 0)
- break;
- }
- }
- }
- if (qh KEEPmerge) {
- qsort (SETaddr_(facets, facetT), size,
- sizeof (facetT *), qh_compare_facetmerge);
- if ((count= size - qh KEEPmerge) > 0) {
- FOREACHfacet_(facets) {
- facet->good= False;
- if (--count == 0)
- break;
- }
- }
- }
- if (qh KEEPminArea < REALmax/2) {
- FOREACHfacet_(facets) {
- if (!facet->isarea || facet->f.area < qh KEEPminArea)
- facet->good= False;
- }
- }
- qh_settempfree (&facets);
- count= 0;
- FORALLfacet_(facetlist) {
- if (facet->good)
- count++;
- }
- qh num_good= count;
-} /* markkeep */
-
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="markvoronoi">-</a>
-
- qh_markvoronoi( facetlist, facets, printall, islower, numcenters )
- mark voronoi vertices for printing by site pairs
-
- returns:
- temporary set of vertices indexed by pointid
- islower set if printing lower hull (i.e., at least one facet is lower hull)
- numcenters= total number of Voronoi vertices
- bumps qh.printoutnum for vertex-at-infinity
- clears all facet->seen and sets facet->seen2
-
- if selected
- facet->visitid= Voronoi vertex id
- else if upper hull (or 'Qu' and lower hull)
- facet->visitid= 0
- else
- facet->visitid >= qh num_facets
-
- notes:
- ignores qh.ATinfinity, if defined
-*/
-setT *qh_markvoronoi (facetT *facetlist, setT *facets, boolT printall, boolT *islowerp, int *numcentersp) {
- int numcenters=0;
- facetT *facet, **facetp;
- setT *vertices;
- boolT islower= False;
-
- qh printoutnum++;
- qh_clearcenters (qh_ASvoronoi); /* in case, qh_printvdiagram2 called by user */
- qh_vertexneighbors();
- vertices= qh_pointvertex();
- if (qh ATinfinity)
- SETelem_(vertices, qh num_points-1)= NULL;
- qh visit_id++;
- maximize_(qh visit_id, (unsigned) qh num_facets);
- FORALLfacet_(facetlist) {
- if (printall || !qh_skipfacet (facet)) {
- if (!facet->upperdelaunay) {
- islower= True;
- break;
- }
- }
- }
- FOREACHfacet_(facets) {
- if (printall || !qh_skipfacet (facet)) {
- if (!facet->upperdelaunay) {
- islower= True;
- break;
- }
- }
- }
- FORALLfacets {
- if (facet->normal && (facet->upperdelaunay == islower))
- facet->visitid= 0; /* facetlist or facets may overwrite */
- else
- facet->visitid= qh visit_id;
- facet->seen= False;
- facet->seen2= True;
- }
- numcenters++; /* qh_INFINITE */
- FORALLfacet_(facetlist) {
- if (printall || !qh_skipfacet (facet))
- facet->visitid= numcenters++;
- }
- FOREACHfacet_(facets) {
- if (printall || !qh_skipfacet (facet))
- facet->visitid= numcenters++;
- }
- *islowerp= islower;
- *numcentersp= numcenters;
- trace2((qh ferr, "qh_markvoronoi: islower %d numcenters %d\n", islower, numcenters));
- return vertices;
-} /* markvoronoi */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="order_vertexneighbors">-</a>
-
- qh_order_vertexneighbors( vertex )
- order facet neighbors of a 2-d or 3-d vertex by adjacency
-
- notes:
- does not orient the neighbors
-
- design:
- initialize a new neighbor set with the first facet in vertex->neighbors
- while vertex->neighbors non-empty
- select next neighbor in the previous facet's neighbor set
- set vertex->neighbors to the new neighbor set
-*/
-void qh_order_vertexneighbors(vertexT *vertex) {
- setT *newset;
- facetT *facet, *neighbor, **neighborp;
-
- trace4((qh ferr, "qh_order_vertexneighbors: order neighbors of v%d for 3-d\n", vertex->id));
- newset= qh_settemp (qh_setsize (vertex->neighbors));
- facet= (facetT*)qh_setdellast (vertex->neighbors);
- qh_setappend (&newset, facet);
- while (qh_setsize (vertex->neighbors)) {
- FOREACHneighbor_(vertex) {
- if (qh_setin (facet->neighbors, neighbor)) {
- qh_setdel(vertex->neighbors, neighbor);
- qh_setappend (&newset, neighbor);
- facet= neighbor;
- break;
- }
- }
- if (!neighbor) {
- fprintf (qh ferr, "qhull internal error (qh_order_vertexneighbors): no neighbor of v%d for f%d\n",
- vertex->id, facet->id);
- qh_errexit (qh_ERRqhull, facet, NULL);
- }
- }
- qh_setfree (&vertex->neighbors);
- qh_settemppop ();
- vertex->neighbors= newset;
-} /* order_vertexneighbors */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printafacet">-</a>
-
- qh_printafacet( fp, format, facet, printall )
- print facet to fp in given output format (see qh.PRINTout)
-
- returns:
- nop if !printall and qh_skipfacet()
- nop if visible facet and NEWfacets and format != PRINTfacets
- must match qh_countfacets
-
- notes
- preserves qh.visit_id
- facet->normal may be null if PREmerge/MERGEexact and STOPcone before merge
-
- see
- qh_printbegin() and qh_printend()
-
- design:
- test for printing facet
- call appropriate routine for format
- or output results directly
-*/
-void qh_printafacet(FILE *fp, int format, facetT *facet, boolT printall) {
- realT color[4], offset, dist, outerplane, innerplane;
- boolT zerodiv;
- coordT *point, *normp, *coordp, **pointp, *feasiblep;
- int k;
- vertexT *vertex, **vertexp;
- facetT *neighbor, **neighborp;
-
- if (!printall && qh_skipfacet (facet))
- return;
- if (facet->visible && qh NEWfacets && format != qh_PRINTfacets)
- return;
- qh printoutnum++;
- switch (format) {
- case qh_PRINTarea:
- if (facet->isarea) {
- fprintf (fp, qh_REAL_1, facet->f.area);
- fprintf (fp, "\n");
- }else
- fprintf (fp, "0\n");
- break;
- case qh_PRINTcoplanars:
- fprintf (fp, "%d", qh_setsize (facet->coplanarset));
- FOREACHpoint_(facet->coplanarset)
- fprintf (fp, " %d", qh_pointid (point));
- fprintf (fp, "\n");
- break;
- case qh_PRINTcentrums:
- qh_printcenter (fp, format, NULL, facet);
- break;
- case qh_PRINTfacets:
- qh_printfacet (fp, facet);
- break;
- case qh_PRINTfacets_xridge:
- qh_printfacetheader (fp, facet);
- break;
- case qh_PRINTgeom: /* either 2 , 3, or 4-d by qh_printbegin */
- if (!facet->normal)
- break;
- for (k= qh hull_dim; k--; ) {
- color[k]= (facet->normal[k]+1.0)/2.0;
- maximize_(color[k], -1.0);
- minimize_(color[k], +1.0);
- }
- qh_projectdim3 (color, color);
- if (qh PRINTdim != qh hull_dim)
- qh_normalize2 (color, 3, True, NULL, NULL);
- if (qh hull_dim <= 2)
- qh_printfacet2geom (fp, facet, color);
- else if (qh hull_dim == 3) {
- if (facet->simplicial)
- qh_printfacet3geom_simplicial (fp, facet, color);
- else
- qh_printfacet3geom_nonsimplicial (fp, facet, color);
- }else {
- if (facet->simplicial)
- qh_printfacet4geom_simplicial (fp, facet, color);
- else
- qh_printfacet4geom_nonsimplicial (fp, facet, color);
- }
- break;
- case qh_PRINTids:
- fprintf (fp, "%d\n", facet->id);
- break;
- case qh_PRINTincidences:
- case qh_PRINToff:
- case qh_PRINTtriangles:
- if (qh hull_dim == 3 && format != qh_PRINTtriangles)
- qh_printfacet3vertex (fp, facet, format);
- else if (facet->simplicial || qh hull_dim == 2 || format == qh_PRINToff)
- qh_printfacetNvertex_simplicial (fp, facet, format);
- else
- qh_printfacetNvertex_nonsimplicial (fp, facet, qh printoutvar++, format);
- break;
- case qh_PRINTinner:
- qh_outerinner (facet, NULL, &innerplane);
- offset= facet->offset - innerplane;
- goto LABELprintnorm;
- break; /* prevent warning */
- case qh_PRINTmerges:
- fprintf (fp, "%d\n", facet->nummerge);
- break;
- case qh_PRINTnormals:
- offset= facet->offset;
- goto LABELprintnorm;
- break; /* prevent warning */
- case qh_PRINTouter:
- qh_outerinner (facet, &outerplane, NULL);
- offset= facet->offset - outerplane;
- LABELprintnorm:
- if (!facet->normal) {
- fprintf (fp, "no normal for facet f%d\n", facet->id);
- break;
- }
- if (qh CDDoutput) {
- fprintf (fp, qh_REAL_1, -offset);
- for (k=0; k < qh hull_dim; k++)
- fprintf (fp, qh_REAL_1, -facet->normal[k]);
- }else {
- for (k=0; k < qh hull_dim; k++)
- fprintf (fp, qh_REAL_1, facet->normal[k]);
- fprintf (fp, qh_REAL_1, offset);
- }
- fprintf (fp, "\n");
- break;
- case qh_PRINTmathematica: /* either 2 or 3-d by qh_printbegin */
- case qh_PRINTmaple:
- if (qh hull_dim == 2)
- qh_printfacet2math (fp, facet, format, qh printoutvar++);
- else
- qh_printfacet3math (fp, facet, format, qh printoutvar++);
- break;
- case qh_PRINTneighbors:
- fprintf (fp, "%d", qh_setsize (facet->neighbors));
- FOREACHneighbor_(facet)
- fprintf (fp, " %d",
- neighbor->visitid ? neighbor->visitid - 1: - neighbor->id);
- fprintf (fp, "\n");
- break;
- case qh_PRINTpointintersect:
- if (!qh feasible_point) {
- fprintf (fp, "qhull input error (qh_printafacet): option 'Fp' needs qh feasible_point\n");
- qh_errexit( qh_ERRinput, NULL, NULL);
- }
- if (facet->offset > 0)
- goto LABELprintinfinite;
- point= coordp= (coordT*)qh_memalloc (qh normal_size);
- normp= facet->normal;
- feasiblep= qh feasible_point;
- if (facet->offset < -qh MINdenom) {
- for (k= qh hull_dim; k--; )
- *(coordp++)= (*(normp++) / - facet->offset) + *(feasiblep++);
- }else {
- for (k= qh hull_dim; k--; ) {
- *(coordp++)= qh_divzero (*(normp++), facet->offset, qh MINdenom_1,
- &zerodiv) + *(feasiblep++);
- if (zerodiv) {
- qh_memfree (point, qh normal_size);
- goto LABELprintinfinite;
- }
- }
- }
- qh_printpoint (fp, NULL, point);
- qh_memfree (point, qh normal_size);
- break;
- LABELprintinfinite:
- for (k= qh hull_dim; k--; )
- fprintf (fp, qh_REAL_1, qh_INFINITE);
- fprintf (fp, "\n");
- break;
- case qh_PRINTpointnearest:
- FOREACHpoint_(facet->coplanarset) {
- int id, id2;
- vertex= qh_nearvertex (facet, point, &dist);
- id= qh_pointid (vertex->point);
- id2= qh_pointid (point);
- fprintf (fp, "%d %d %d " qh_REAL_1 "\n", id, id2, facet->id, dist);
- }
- break;
- case qh_PRINTpoints: /* VORONOI only by qh_printbegin */
- if (qh CDDoutput)
- fprintf (fp, "1 ");
- qh_printcenter (fp, format, NULL, facet);
- break;
- case qh_PRINTvertices:
- fprintf (fp, "%d", qh_setsize (facet->vertices));
- FOREACHvertex_(facet->vertices)
- fprintf (fp, " %d", qh_pointid (vertex->point));
- fprintf (fp, "\n");
- break;
- }
-} /* printafacet */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printbegin">-</a>
-
- qh_printbegin( )
- prints header for all output formats
-
- returns:
- checks for valid format
-
- notes:
- uses qh.visit_id for 3/4off
- changes qh.interior_point if printing centrums
- qh_countfacets clears facet->visitid for non-good facets
-
- see
- qh_printend() and qh_printafacet()
-
- design:
- count facets and related statistics
- print header for format
-*/
-void qh_printbegin (FILE *fp, int format, facetT *facetlist, setT *facets, boolT printall) {
- int numfacets, numsimplicial, numridges, totneighbors, numcoplanars, numtricoplanars;
- int i, num;
- facetT *facet, **facetp;
- vertexT *vertex, **vertexp;
- setT *vertices;
- pointT *point, **pointp, *pointtemp;
-
- qh printoutnum= 0;
- qh_countfacets (facetlist, facets, printall, &numfacets, &numsimplicial,
- &totneighbors, &numridges, &numcoplanars, &numtricoplanars);
- switch (format) {
- case qh_PRINTnone:
- break;
- case qh_PRINTarea:
- fprintf (fp, "%d\n", numfacets);
- break;
- case qh_PRINTcoplanars:
- fprintf (fp, "%d\n", numfacets);
- break;
- case qh_PRINTcentrums:
- if (qh CENTERtype == qh_ASnone)
- qh_clearcenters (qh_AScentrum);
- fprintf (fp, "%d\n%d\n", qh hull_dim, numfacets);
- break;
- case qh_PRINTfacets:
- case qh_PRINTfacets_xridge:
- if (facetlist)
- qh_printvertexlist (fp, "Vertices and facets:\n", facetlist, facets, printall);
- break;
- case qh_PRINTgeom:
- if (qh hull_dim > 4) /* qh_initqhull_globals also checks */
- goto LABELnoformat;
- if (qh VORONOI && qh hull_dim > 3) /* PRINTdim == DROPdim == hull_dim-1 */
- goto LABELnoformat;
- if (qh hull_dim == 2 && (qh PRINTridges || qh DOintersections))
- fprintf (qh ferr, "qhull warning: output for ridges and intersections not implemented in 2-d\n");
- if (qh hull_dim == 4 && (qh PRINTinner || qh PRINTouter ||
- (qh PRINTdim == 4 && qh PRINTcentrums)))
- fprintf (qh ferr, "qhull warning: output for outer/inner planes and centrums not implemented in 4-d\n");
- if (qh PRINTdim == 4 && (qh PRINTspheres))
- fprintf (qh ferr, "qhull warning: output for vertices not implemented in 4-d\n");
- if (qh PRINTdim == 4 && qh DOintersections && qh PRINTnoplanes)
- fprintf (qh ferr, "qhull warning: 'Gnh' generates no output in 4-d\n");
- if (qh PRINTdim == 2) {
- fprintf(fp, "{appearance {linewidth 3} LIST # %s | %s\n",
- qh rbox_command, qh qhull_command);
- }else if (qh PRINTdim == 3) {
- fprintf(fp, "{appearance {+edge -evert linewidth 2} LIST # %s | %s\n",
- qh rbox_command, qh qhull_command);
- }else if (qh PRINTdim == 4) {
- qh visit_id++;
- num= 0;
- FORALLfacet_(facetlist) /* get number of ridges to be printed */
- qh_printend4geom (NULL, facet, &num, printall);
- FOREACHfacet_(facets)
- qh_printend4geom (NULL, facet, &num, printall);
- qh ridgeoutnum= num;
- qh printoutvar= 0; /* counts number of ridges in output */
- fprintf (fp, "LIST # %s | %s\n", qh rbox_command, qh qhull_command);
- }
- if (qh PRINTdots) {
- qh printoutnum++;
- num= qh num_points + qh_setsize (qh other_points);
- if (qh DELAUNAY && qh ATinfinity)
- num--;
- if (qh PRINTdim == 4)
- fprintf (fp, "4VECT %d %d 1\n", num, num);
- else
- fprintf (fp, "VECT %d %d 1\n", num, num);
- for (i= num; i--; ) {
- if (i % 20 == 0)
- fprintf (fp, "\n");
- fprintf (fp, "1 ");
- }
- fprintf (fp, "# 1 point per line\n1 ");
- for (i= num-1; i--; ) {
- if (i % 20 == 0)
- fprintf (fp, "\n");
- fprintf (fp, "0 ");
- }
- fprintf (fp, "# 1 color for all\n");
- FORALLpoints {
- if (!qh DELAUNAY || !qh ATinfinity || qh_pointid(point) != qh num_points-1) {
- if (qh PRINTdim == 4)
- qh_printpoint (fp, NULL, point);
- else
- qh_printpoint3 (fp, point);
- }
- }
- FOREACHpoint_(qh other_points) {
- if (qh PRINTdim == 4)
- qh_printpoint (fp, NULL, point);
- else
- qh_printpoint3 (fp, point);
- }
- fprintf (fp, "0 1 1 1 # color of points\n");
- }
- if (qh PRINTdim == 4 && !qh PRINTnoplanes)
- /* 4dview loads up multiple 4OFF objects slowly */
- fprintf(fp, "4OFF %d %d 1\n", 3*qh ridgeoutnum, qh ridgeoutnum);
- qh PRINTcradius= 2 * qh DISTround; /* include test DISTround */
- if (qh PREmerge) {
- maximize_(qh PRINTcradius, qh premerge_centrum + qh DISTround);
- }else if (qh POSTmerge)
- maximize_(qh PRINTcradius, qh postmerge_centrum + qh DISTround);
- qh PRINTradius= qh PRINTcradius;
- if (qh PRINTspheres + qh PRINTcoplanar)
- maximize_(qh PRINTradius, qh MAXabs_coord * qh_MINradius);
- if (qh premerge_cos < REALmax/2) {
- maximize_(qh PRINTradius, (1- qh premerge_cos) * qh MAXabs_coord);
- }else if (!qh PREmerge && qh POSTmerge && qh postmerge_cos < REALmax/2) {
- maximize_(qh PRINTradius, (1- qh postmerge_cos) * qh MAXabs_coord);
- }
- maximize_(qh PRINTradius, qh MINvisible);
- if (qh JOGGLEmax < REALmax/2)
- qh PRINTradius += qh JOGGLEmax * sqrt (qh hull_dim);
- if (qh PRINTdim != 4 &&
- (qh PRINTcoplanar || qh PRINTspheres || qh PRINTcentrums)) {
- vertices= qh_facetvertices (facetlist, facets, printall);
- if (qh PRINTspheres && qh PRINTdim <= 3)
- qh_printspheres (fp, vertices, qh PRINTradius);
- if (qh PRINTcoplanar || qh PRINTcentrums) {
- qh firstcentrum= True;
- if (qh PRINTcoplanar&& !qh PRINTspheres) {
- FOREACHvertex_(vertices)
- qh_printpointvect2 (fp, vertex->point, NULL,
- qh interior_point, qh PRINTradius);
- }
- FORALLfacet_(facetlist) {
- if (!printall && qh_skipfacet(facet))
- continue;
- if (!facet->normal)
- continue;
- if (qh PRINTcentrums && qh PRINTdim <= 3)
- qh_printcentrum (fp, facet, qh PRINTcradius);
- if (!qh PRINTcoplanar)
- continue;
- FOREACHpoint_(facet->coplanarset)
- qh_printpointvect2 (fp, point, facet->normal, NULL, qh PRINTradius);
- FOREACHpoint_(facet->outsideset)
- qh_printpointvect2 (fp, point, facet->normal, NULL, qh PRINTradius);
- }
- FOREACHfacet_(facets) {
- if (!printall && qh_skipfacet(facet))
- continue;
- if (!facet->normal)
- continue;
- if (qh PRINTcentrums && qh PRINTdim <= 3)
- qh_printcentrum (fp, facet, qh PRINTcradius);
- if (!qh PRINTcoplanar)
- continue;
- FOREACHpoint_(facet->coplanarset)
- qh_printpointvect2 (fp, point, facet->normal, NULL, qh PRINTradius);
- FOREACHpoint_(facet->outsideset)
- qh_printpointvect2 (fp, point, facet->normal, NULL, qh PRINTradius);
- }
- }
- qh_settempfree (&vertices);
- }
- qh visit_id++; /* for printing hyperplane intersections */
- break;
- case qh_PRINTids:
- fprintf (fp, "%d\n", numfacets);
- break;
- case qh_PRINTincidences:
- if (qh VORONOI && qh PRINTprecision)
- fprintf (qh ferr, "qhull warning: writing Delaunay. Use 'p' or 'o' for Voronoi centers\n");
- qh printoutvar= qh vertex_id; /* centrum id for non-simplicial facets */
- if (qh hull_dim <= 3)
- fprintf(fp, "%d\n", numfacets);
- else
- fprintf(fp, "%d\n", numsimplicial+numridges);
- break;
- case qh_PRINTinner:
- case qh_PRINTnormals:
- case qh_PRINTouter:
- if (qh CDDoutput)
- fprintf (fp, "%s | %s\nbegin\n %d %d real\n", qh rbox_command,
- qh qhull_command, numfacets, qh hull_dim+1);
- else
- fprintf (fp, "%d\n%d\n", qh hull_dim+1, numfacets);
- break;
- case qh_PRINTmathematica:
- case qh_PRINTmaple:
- if (qh hull_dim > 3) /* qh_initbuffers also checks */
- goto LABELnoformat;
- if (qh VORONOI)
- fprintf (qh ferr, "qhull warning: output is the Delaunay triangulation\n");
- if (format == qh_PRINTmaple) {
- if (qh hull_dim == 2)
- fprintf(fp, "PLOT(CURVES(\n");
- else
- fprintf(fp, "PLOT3D(POLYGONS(\n");
- }else
- fprintf(fp, "{\n");
- qh printoutvar= 0; /* counts number of facets for notfirst */
- break;
- case qh_PRINTmerges:
- fprintf (fp, "%d\n", numfacets);
- break;
- case qh_PRINTpointintersect:
- fprintf (fp, "%d\n%d\n", qh hull_dim, numfacets);
- break;
- case qh_PRINTneighbors:
- fprintf (fp, "%d\n", numfacets);
- break;
- case qh_PRINToff:
- case qh_PRINTtriangles:
- if (qh VORONOI)
- goto LABELnoformat;
- num = qh hull_dim;
- if (format == qh_PRINToff || qh hull_dim == 2)
- fprintf (fp, "%d\n%d %d %d\n", num,
- qh num_points+qh_setsize (qh other_points), numfacets, totneighbors/2);
- else { /* qh_PRINTtriangles */
- qh printoutvar= qh num_points+qh_setsize (qh other_points); /* first centrum */
- if (qh DELAUNAY)
- num--; /* drop last dimension */
- fprintf (fp, "%d\n%d %d %d\n", num, qh printoutvar
- + numfacets - numsimplicial, numsimplicial + numridges, totneighbors/2);
- }
- FORALLpoints
- qh_printpointid (qh fout, NULL, num, point, -1);
- FOREACHpoint_(qh other_points)
- qh_printpointid (qh fout, NULL, num, point, -1);
- if (format == qh_PRINTtriangles && qh hull_dim > 2) {
- FORALLfacets {
- if (!facet->simplicial && facet->visitid)
- qh_printcenter (qh fout, format, NULL, facet);
- }
- }
- break;
- case qh_PRINTpointnearest:
- fprintf (fp, "%d\n", numcoplanars);
- break;
- case qh_PRINTpoints:
- if (!qh VORONOI)
- goto LABELnoformat;
- if (qh CDDoutput)
- fprintf (fp, "%s | %s\nbegin\n%d %d real\n", qh rbox_command,
- qh qhull_command, numfacets, qh hull_dim);
- else
- fprintf (fp, "%d\n%d\n", qh hull_dim-1, numfacets);
- break;
- case qh_PRINTvertices:
- fprintf (fp, "%d\n", numfacets);
- break;
- case qh_PRINTsummary:
- default:
- LABELnoformat:
- fprintf (qh ferr, "qhull internal error (qh_printbegin): can not use this format for dimension %d\n",
- qh hull_dim);
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
-} /* printbegin */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printcenter">-</a>
-
- qh_printcenter( fp, string, facet )
- print facet->center as centrum or Voronoi center
- string may be NULL. Don't include '%' codes.
- nop if qh CENTERtype neither CENTERvoronoi nor CENTERcentrum
- if upper envelope of Delaunay triangulation and point at-infinity
- prints qh_INFINITE instead;
-
- notes:
- defines facet->center if needed
- if format=PRINTgeom, adds a 0 if would otherwise be 2-d
-*/
-void qh_printcenter (FILE *fp, int format, char *string, facetT *facet) {
- int k, num;
-
- if (qh CENTERtype != qh_ASvoronoi && qh CENTERtype != qh_AScentrum)
- return;
- if (string)
- fprintf (fp, string, facet->id);
- if (qh CENTERtype == qh_ASvoronoi) {
- num= qh hull_dim-1;
- if (!facet->normal || !facet->upperdelaunay || !qh ATinfinity) {
- if (!facet->center)
- facet->center= qh_facetcenter (facet->vertices);
- for (k=0; k < num; k++)
- fprintf (fp, qh_REAL_1, facet->center[k]);
- }else {
- for (k=0; k < num; k++)
- fprintf (fp, qh_REAL_1, qh_INFINITE);
- }
- }else /* qh CENTERtype == qh_AScentrum */ {
- num= qh hull_dim;
- if (format == qh_PRINTtriangles && qh DELAUNAY)
- num--;
- if (!facet->center)
- facet->center= qh_getcentrum (facet);
- for (k=0; k < num; k++)
- fprintf (fp, qh_REAL_1, facet->center[k]);
- }
- if (format == qh_PRINTgeom && num == 2)
- fprintf (fp, " 0\n");
- else
- fprintf (fp, "\n");
-} /* printcenter */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printcentrum">-</a>
-
- qh_printcentrum( fp, facet, radius )
- print centrum for a facet in OOGL format
- radius defines size of centrum
- 2-d or 3-d only
-
- returns:
- defines facet->center if needed
-*/
-void qh_printcentrum (FILE *fp, facetT *facet, realT radius) {
- pointT *centrum, *projpt;
- boolT tempcentrum= False;
- realT xaxis[4], yaxis[4], normal[4], dist;
- realT green[3]={0, 1, 0};
- vertexT *apex;
- int k;
-
- if (qh CENTERtype == qh_AScentrum) {
- if (!facet->center)
- facet->center= qh_getcentrum (facet);
- centrum= facet->center;
- }else {
- centrum= qh_getcentrum (facet);
- tempcentrum= True;
- }
- fprintf (fp, "{appearance {-normal -edge normscale 0} ");
- if (qh firstcentrum) {
- qh firstcentrum= False;
- fprintf (fp, "{INST geom { define centrum CQUAD # f%d\n\
--0.3 -0.3 0.0001 0 0 1 1\n\
- 0.3 -0.3 0.0001 0 0 1 1\n\
- 0.3 0.3 0.0001 0 0 1 1\n\
--0.3 0.3 0.0001 0 0 1 1 } transform { \n", facet->id);
- }else
- fprintf (fp, "{INST geom { : centrum } transform { # f%d\n", facet->id);
- apex= SETfirstt_(facet->vertices, vertexT);
- qh_distplane(apex->point, facet, &dist);
- projpt= qh_projectpoint(apex->point, facet, dist);
- for (k= qh hull_dim; k--; ) {
- xaxis[k]= projpt[k] - centrum[k];
- normal[k]= facet->normal[k];
- }
- if (qh hull_dim == 2) {
- xaxis[2]= 0;
- normal[2]= 0;
- }else if (qh hull_dim == 4) {
- qh_projectdim3 (xaxis, xaxis);
- qh_projectdim3 (normal, normal);
- qh_normalize2 (normal, qh PRINTdim, True, NULL, NULL);
- }
- qh_crossproduct (3, xaxis, normal, yaxis);
- fprintf (fp, "%8.4g %8.4g %8.4g 0\n", xaxis[0], xaxis[1], xaxis[2]);
- fprintf (fp, "%8.4g %8.4g %8.4g 0\n", yaxis[0], yaxis[1], yaxis[2]);
- fprintf (fp, "%8.4g %8.4g %8.4g 0\n", normal[0], normal[1], normal[2]);
- qh_printpoint3 (fp, centrum);
- fprintf (fp, "1 }}}\n");
- qh_memfree (projpt, qh normal_size);
- qh_printpointvect (fp, centrum, facet->normal, NULL, radius, green);
- if (tempcentrum)
- qh_memfree (centrum, qh normal_size);
-} /* printcentrum */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printend">-</a>
-
- qh_printend( fp, format )
- prints trailer for all output formats
-
- see:
- qh_printbegin() and qh_printafacet()
-
-*/
-void qh_printend (FILE *fp, int format, facetT *facetlist, setT *facets, boolT printall) {
- int num;
- facetT *facet, **facetp;
-
- if (!qh printoutnum)
- fprintf (qh ferr, "qhull warning: no facets printed\n");
- switch (format) {
- case qh_PRINTgeom:
- if (qh hull_dim == 4 && qh DROPdim < 0 && !qh PRINTnoplanes) {
- qh visit_id++;
- num= 0;
- FORALLfacet_(facetlist)
- qh_printend4geom (fp, facet,&num, printall);
- FOREACHfacet_(facets)
- qh_printend4geom (fp, facet, &num, printall);
- if (num != qh ridgeoutnum || qh printoutvar != qh ridgeoutnum) {
- fprintf (qh ferr, "qhull internal error (qh_printend): number of ridges %d != number printed %d and at end %d\n", qh ridgeoutnum, qh printoutvar, num);
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- }else
- fprintf(fp, "}\n");
- break;
- case qh_PRINTinner:
- case qh_PRINTnormals:
- case qh_PRINTouter:
- if (qh CDDoutput)
- fprintf (fp, "end\n");
- break;
- case qh_PRINTmaple:
- fprintf(fp, "));\n");
- break;
- case qh_PRINTmathematica:
- fprintf(fp, "}\n");
- break;
- case qh_PRINTpoints:
- if (qh CDDoutput)
- fprintf (fp, "end\n");
- break;
- }
-} /* printend */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printend4geom">-</a>
-
- qh_printend4geom( fp, facet, numridges, printall )
- helper function for qh_printbegin/printend
-
- returns:
- number of printed ridges
-
- notes:
- just counts printed ridges if fp=NULL
- uses facet->visitid
- must agree with qh_printfacet4geom...
-
- design:
- computes color for facet from its normal
- prints each ridge of facet
-*/
-void qh_printend4geom (FILE *fp, facetT *facet, int *nump, boolT printall) {
- realT color[3];
- int i, num= *nump;
- facetT *neighbor, **neighborp;
- ridgeT *ridge, **ridgep;
-
- if (!printall && qh_skipfacet(facet))
- return;
- if (qh PRINTnoplanes || (facet->visible && qh NEWfacets))
- return;
- if (!facet->normal)
- return;
- if (fp) {
- for (i=0; i < 3; i++) {
- color[i]= (facet->normal[i]+1.0)/2.0;
- maximize_(color[i], -1.0);
- minimize_(color[i], +1.0);
- }
- }
- facet->visitid= qh visit_id;
- if (facet->simplicial) {
- FOREACHneighbor_(facet) {
- if (neighbor->visitid != qh visit_id) {
- if (fp)
- fprintf (fp, "3 %d %d %d %8.4g %8.4g %8.4g 1 # f%d f%d\n",
- 3*num, 3*num+1, 3*num+2, color[0], color[1], color[2],
- facet->id, neighbor->id);
- num++;
- }
- }
- }else {
- FOREACHridge_(facet->ridges) {
- neighbor= otherfacet_(ridge, facet);
- if (neighbor->visitid != qh visit_id) {
- if (fp)
- fprintf (fp, "3 %d %d %d %8.4g %8.4g %8.4g 1 #r%d f%d f%d\n",
- 3*num, 3*num+1, 3*num+2, color[0], color[1], color[2],
- ridge->id, facet->id, neighbor->id);
- num++;
- }
- }
- }
- *nump= num;
-} /* printend4geom */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printextremes">-</a>
-
- qh_printextremes( fp, facetlist, facets, printall )
- print extreme points for convex hulls or halfspace intersections
-
- notes:
- #points, followed by ids, one per line
-
- sorted by id
- same order as qh_printpoints_out if no coplanar/interior points
-*/
-void qh_printextremes (FILE *fp, facetT *facetlist, setT *facets, int printall) {
- setT *vertices, *points;
- pointT *point;
- vertexT *vertex, **vertexp;
- int id;
- int numpoints=0, point_i, point_n;
- int allpoints= qh num_points + qh_setsize (qh other_points);
-
- points= qh_settemp (allpoints);
- qh_setzero (points, 0, allpoints);
- vertices= qh_facetvertices (facetlist, facets, printall);
- FOREACHvertex_(vertices) {
- id= qh_pointid (vertex->point);
- if (id >= 0) {
- SETelem_(points, id)= vertex->point;
- numpoints++;
- }
- }
- qh_settempfree (&vertices);
- fprintf (fp, "%d\n", numpoints);
- FOREACHpoint_i_(points) {
- if (point)
- fprintf (fp, "%d\n", point_i);
- }
- qh_settempfree (&points);
-} /* printextremes */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printextremes_2d">-</a>
-
- qh_printextremes_2d( fp, facetlist, facets, printall )
- prints point ids for facets in qh_ORIENTclock order
-
- notes:
- #points, followed by ids, one per line
- if facetlist/facets are disjoint than the output includes skips
- errors if facets form a loop
- does not print coplanar points
-*/
-void qh_printextremes_2d (FILE *fp, facetT *facetlist, setT *facets, int printall) {
- int numfacets, numridges, totneighbors, numcoplanars, numsimplicial, numtricoplanars;
- setT *vertices;
- facetT *facet, *startfacet, *nextfacet;
- vertexT *vertexA, *vertexB;
-
- qh_countfacets (facetlist, facets, printall, &numfacets, &numsimplicial,
- &totneighbors, &numridges, &numcoplanars, &numtricoplanars); /* marks qh visit_id */
- vertices= qh_facetvertices (facetlist, facets, printall);
- fprintf(fp, "%d\n", qh_setsize (vertices));
- qh_settempfree (&vertices);
- if (!numfacets)
- return;
- facet= startfacet= facetlist ? facetlist : SETfirstt_(facets, facetT);
- qh vertex_visit++;
- qh visit_id++;
- do {
- if (facet->toporient ^ qh_ORIENTclock) {
- vertexA= SETfirstt_(facet->vertices, vertexT);
- vertexB= SETsecondt_(facet->vertices, vertexT);
- nextfacet= SETfirstt_(facet->neighbors, facetT);
- }else {
- vertexA= SETsecondt_(facet->vertices, vertexT);
- vertexB= SETfirstt_(facet->vertices, vertexT);
- nextfacet= SETsecondt_(facet->neighbors, facetT);
- }
- if (facet->visitid == qh visit_id) {
- fprintf(qh ferr, "qh_printextremes_2d: loop in facet list. facet %d nextfacet %d\n",
- facet->id, nextfacet->id);
- qh_errexit2 (qh_ERRqhull, facet, nextfacet);
- }
- if (facet->visitid) {
- if (vertexA->visitid != qh vertex_visit) {
- vertexA->visitid= qh vertex_visit;
- fprintf(fp, "%d\n", qh_pointid (vertexA->point));
- }
- if (vertexB->visitid != qh vertex_visit) {
- vertexB->visitid= qh vertex_visit;
- fprintf(fp, "%d\n", qh_pointid (vertexB->point));
- }
- }
- facet->visitid= qh visit_id;
- facet= nextfacet;
- }while (facet && facet != startfacet);
-} /* printextremes_2d */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printextremes_d">-</a>
-
- qh_printextremes_d( fp, facetlist, facets, printall )
- print extreme points of input sites for Delaunay triangulations
-
- notes:
- #points, followed by ids, one per line
-
- unordered
-*/
-void qh_printextremes_d (FILE *fp, facetT *facetlist, setT *facets, int printall) {
- setT *vertices;
- vertexT *vertex, **vertexp;
- boolT upperseen, lowerseen;
- facetT *neighbor, **neighborp;
- int numpoints=0;
-
- vertices= qh_facetvertices (facetlist, facets, printall);
- qh_vertexneighbors();
- FOREACHvertex_(vertices) {
- upperseen= lowerseen= False;
- FOREACHneighbor_(vertex) {
- if (neighbor->upperdelaunay)
- upperseen= True;
- else
- lowerseen= True;
- }
- if (upperseen && lowerseen) {
- vertex->seen= True;
- numpoints++;
- }else
- vertex->seen= False;
- }
- fprintf (fp, "%d\n", numpoints);
- FOREACHvertex_(vertices) {
- if (vertex->seen)
- fprintf (fp, "%d\n", qh_pointid (vertex->point));
- }
- qh_settempfree (&vertices);
-} /* printextremes_d */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printfacet">-</a>
-
- qh_printfacet( fp, facet )
- prints all fields of a facet to fp
-
- notes:
- ridges printed in neighbor order
-*/
-void qh_printfacet(FILE *fp, facetT *facet) {
-
- qh_printfacetheader (fp, facet);
- if (facet->ridges)
- qh_printfacetridges (fp, facet);
-} /* printfacet */
-
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printfacet2geom">-</a>
-
- qh_printfacet2geom( fp, facet, color )
- print facet as part of a 2-d VECT for Geomview
-
- notes:
- assume precise calculations in io.c with roundoff covered by qh_GEOMepsilon
- mindist is calculated within io.c. maxoutside is calculated elsewhere
- so a DISTround error may have occured.
-*/
-void qh_printfacet2geom(FILE *fp, facetT *facet, realT color[3]) {
- pointT *point0, *point1;
- realT mindist, innerplane, outerplane;
- int k;
-
- qh_facet2point (facet, &point0, &point1, &mindist);
- qh_geomplanes (facet, &outerplane, &innerplane);
- if (qh PRINTouter || (!qh PRINTnoplanes && !qh PRINTinner))
- qh_printfacet2geom_points(fp, point0, point1, facet, outerplane, color);
- if (qh PRINTinner || (!qh PRINTnoplanes && !qh PRINTouter &&
- outerplane - innerplane > 2 * qh MAXabs_coord * qh_GEOMepsilon)) {
- for(k= 3; k--; )
- color[k]= 1.0 - color[k];
- qh_printfacet2geom_points(fp, point0, point1, facet, innerplane, color);
- }
- qh_memfree (point1, qh normal_size);
- qh_memfree (point0, qh normal_size);
-} /* printfacet2geom */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printfacet2geom_points">-</a>
-
- qh_printfacet2geom_points( fp, point1, point2, facet, offset, color )
- prints a 2-d facet as a VECT with 2 points at some offset.
- The points are on the facet's plane.
-*/
-void qh_printfacet2geom_points(FILE *fp, pointT *point1, pointT *point2,
- facetT *facet, realT offset, realT color[3]) {
- pointT *p1= point1, *p2= point2;
-
- fprintf(fp, "VECT 1 2 1 2 1 # f%d\n", facet->id);
- if (offset != 0.0) {
- p1= qh_projectpoint (p1, facet, -offset);
- p2= qh_projectpoint (p2, facet, -offset);
- }
- fprintf(fp, "%8.4g %8.4g %8.4g\n%8.4g %8.4g %8.4g\n",
- p1[0], p1[1], 0.0, p2[0], p2[1], 0.0);
- if (offset != 0.0) {
- qh_memfree (p1, qh normal_size);
- qh_memfree (p2, qh normal_size);
- }
- fprintf(fp, "%8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
-} /* printfacet2geom_points */
-
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printfacet2math">-</a>
-
- qh_printfacet2math( fp, facet, format, notfirst )
- print 2-d Maple or Mathematica output for a facet
- may be non-simplicial
-
- notes:
- use %16.8f since Mathematica 2.2 does not handle exponential format
- see qh_printfacet3math
-*/
-void qh_printfacet2math(FILE *fp, facetT *facet, int format, int notfirst) {
- pointT *point0, *point1;
- realT mindist;
- char *pointfmt;
-
- qh_facet2point (facet, &point0, &point1, &mindist);
- if (notfirst)
- fprintf(fp, ",");
- if (format == qh_PRINTmaple)
- pointfmt= "[[%16.8f, %16.8f], [%16.8f, %16.8f]]\n";
- else
- pointfmt= "Line[{{%16.8f, %16.8f}, {%16.8f, %16.8f}}]\n";
- fprintf(fp, pointfmt, point0[0], point0[1], point1[0], point1[1]);
- qh_memfree (point1, qh normal_size);
- qh_memfree (point0, qh normal_size);
-} /* printfacet2math */
-
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printfacet3geom_nonsimplicial">-</a>
-
- qh_printfacet3geom_nonsimplicial( fp, facet, color )
- print Geomview OFF for a 3-d nonsimplicial facet.
- if DOintersections, prints ridges to unvisited neighbors (qh visit_id)
-
- notes
- uses facet->visitid for intersections and ridges
-*/
-void qh_printfacet3geom_nonsimplicial(FILE *fp, facetT *facet, realT color[3]) {
- ridgeT *ridge, **ridgep;
- setT *projectedpoints, *vertices;
- vertexT *vertex, **vertexp, *vertexA, *vertexB;
- pointT *projpt, *point, **pointp;
- facetT *neighbor;
- realT dist, outerplane, innerplane;
- int cntvertices, k;
- realT black[3]={0, 0, 0}, green[3]={0, 1, 0};
-
- qh_geomplanes (facet, &outerplane, &innerplane);
- vertices= qh_facet3vertex (facet); /* oriented */
- cntvertices= qh_setsize(vertices);
- projectedpoints= qh_settemp(cntvertices);
- FOREACHvertex_(vertices) {
- zinc_(Zdistio);
- qh_distplane(vertex->point, facet, &dist);
- projpt= qh_projectpoint(vertex->point, facet, dist);
- qh_setappend (&projectedpoints, projpt);
- }
- if (qh PRINTouter || (!qh PRINTnoplanes && !qh PRINTinner))
- qh_printfacet3geom_points(fp, projectedpoints, facet, outerplane, color);
- if (qh PRINTinner || (!qh PRINTnoplanes && !qh PRINTouter &&
- outerplane - innerplane > 2 * qh MAXabs_coord * qh_GEOMepsilon)) {
- for (k=3; k--; )
- color[k]= 1.0 - color[k];
- qh_printfacet3geom_points(fp, projectedpoints, facet, innerplane, color);
- }
- FOREACHpoint_(projectedpoints)
- qh_memfree (point, qh normal_size);
- qh_settempfree(&projectedpoints);
- qh_settempfree(&vertices);
- if ((qh DOintersections || qh PRINTridges)
- && (!facet->visible || !qh NEWfacets)) {
- facet->visitid= qh visit_id;
- FOREACHridge_(facet->ridges) {
- neighbor= otherfacet_(ridge, facet);
- if (neighbor->visitid != qh visit_id) {
- if (qh DOintersections)
- qh_printhyperplaneintersection(fp, facet, neighbor, ridge->vertices, black);
- if (qh PRINTridges) {
- vertexA= SETfirstt_(ridge->vertices, vertexT);
- vertexB= SETsecondt_(ridge->vertices, vertexT);
- qh_printline3geom (fp, vertexA->point, vertexB->point, green);
- }
- }
- }
- }
-} /* printfacet3geom_nonsimplicial */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printfacet3geom_points">-</a>
-
- qh_printfacet3geom_points( fp, points, facet, offset )
- prints a 3-d facet as OFF Geomview object.
- offset is relative to the facet's hyperplane
- Facet is determined as a list of points
-*/
-void qh_printfacet3geom_points(FILE *fp, setT *points, facetT *facet, realT offset, realT color[3]) {
- int k, n= qh_setsize(points), i;
- pointT *point, **pointp;
- setT *printpoints;
-
- fprintf(fp, "{ OFF %d 1 1 # f%d\n", n, facet->id);
- if (offset != 0.0) {
- printpoints= qh_settemp (n);
- FOREACHpoint_(points)
- qh_setappend (&printpoints, qh_projectpoint(point, facet, -offset));
- }else
- printpoints= points;
- FOREACHpoint_(printpoints) {
- for (k=0; k < qh hull_dim; k++) {
- if (k == qh DROPdim)
- fprintf(fp, "0 ");
- else
- fprintf(fp, "%8.4g ", point[k]);
- }
- if (printpoints != points)
- qh_memfree (point, qh normal_size);
- fprintf (fp, "\n");
- }
- if (printpoints != points)
- qh_settempfree (&printpoints);
- fprintf(fp, "%d ", n);
- for(i= 0; i < n; i++)
- fprintf(fp, "%d ", i);
- fprintf(fp, "%8.4g %8.4g %8.4g 1.0 }\n", color[0], color[1], color[2]);
-} /* printfacet3geom_points */
-
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printfacet3geom_simplicial">-</a>
-
- qh_printfacet3geom_simplicial( )
- print Geomview OFF for a 3-d simplicial facet.
-
- notes:
- may flip color
- uses facet->visitid for intersections and ridges
-
- assume precise calculations in io.c with roundoff covered by qh_GEOMepsilon
- innerplane may be off by qh DISTround. Maxoutside is calculated elsewhere
- so a DISTround error may have occured.
-*/
-void qh_printfacet3geom_simplicial(FILE *fp, facetT *facet, realT color[3]) {
- setT *points, *vertices;
- vertexT *vertex, **vertexp, *vertexA, *vertexB;
- facetT *neighbor, **neighborp;
- realT outerplane, innerplane;
- realT black[3]={0, 0, 0}, green[3]={0, 1, 0};
- int k;
-
- qh_geomplanes (facet, &outerplane, &innerplane);
- vertices= qh_facet3vertex (facet);
- points= qh_settemp (qh TEMPsize);
- FOREACHvertex_(vertices)
- qh_setappend(&points, vertex->point);
- if (qh PRINTouter || (!qh PRINTnoplanes && !qh PRINTinner))
- qh_printfacet3geom_points(fp, points, facet, outerplane, color);
- if (qh PRINTinner || (!qh PRINTnoplanes && !qh PRINTouter &&
- outerplane - innerplane > 2 * qh MAXabs_coord * qh_GEOMepsilon)) {
- for (k= 3; k--; )
- color[k]= 1.0 - color[k];
- qh_printfacet3geom_points(fp, points, facet, innerplane, color);
- }
- qh_settempfree(&points);
- qh_settempfree(&vertices);
- if ((qh DOintersections || qh PRINTridges)
- && (!facet->visible || !qh NEWfacets)) {
- facet->visitid= qh visit_id;
- FOREACHneighbor_(facet) {
- if (neighbor->visitid != qh visit_id) {
- vertices= qh_setnew_delnthsorted (facet->vertices, qh hull_dim,
- SETindex_(facet->neighbors, neighbor), 0);
- if (qh DOintersections)
- qh_printhyperplaneintersection(fp, facet, neighbor, vertices, black);
- if (qh PRINTridges) {
- vertexA= SETfirstt_(vertices, vertexT);
- vertexB= SETsecondt_(vertices, vertexT);
- qh_printline3geom (fp, vertexA->point, vertexB->point, green);
- }
- qh_setfree(&vertices);
- }
- }
- }
-} /* printfacet3geom_simplicial */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printfacet3math">-</a>
-
- qh_printfacet3math( fp, facet, notfirst )
- print 3-d Maple or Mathematica output for a facet
-
- notes:
- may be non-simplicial
- use %16.8f since Mathematica 2.2 does not handle exponential format
- see qh_printfacet2math
-*/
-void qh_printfacet3math (FILE *fp, facetT *facet, int format, int notfirst) {
- vertexT *vertex, **vertexp;
- setT *points, *vertices;
- pointT *point, **pointp;
- boolT firstpoint= True;
- realT dist;
- char *pointfmt, *endfmt;
-
- if (notfirst)
- fprintf(fp, ",\n");
- vertices= qh_facet3vertex (facet);
- points= qh_settemp (qh_setsize (vertices));
- FOREACHvertex_(vertices) {
- zinc_(Zdistio);
- qh_distplane(vertex->point, facet, &dist);
- point= qh_projectpoint(vertex->point, facet, dist);
- qh_setappend (&points, point);
- }
- if (format == qh_PRINTmaple) {
- fprintf(fp, "[");
- pointfmt= "[%16.8f, %16.8f, %16.8f]";
- endfmt= "]";
- }else {
- fprintf(fp, "Polygon[{");
- pointfmt= "{%16.8f, %16.8f, %16.8f}";
- endfmt= "}]";
- }
- FOREACHpoint_(points) {
- if (firstpoint)
- firstpoint= False;
- else
- fprintf(fp, ",\n");
- fprintf(fp, pointfmt, point[0], point[1], point[2]);
- }
- FOREACHpoint_(points)
- qh_memfree (point, qh normal_size);
- qh_settempfree(&points);
- qh_settempfree(&vertices);
- fprintf(fp, endfmt);
-} /* printfacet3math */
-
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printfacet3vertex">-</a>
-
- qh_printfacet3vertex( fp, facet, format )
- print vertices in a 3-d facet as point ids
-
- notes:
- prints number of vertices first if format == qh_PRINToff
- the facet may be non-simplicial
-*/
-void qh_printfacet3vertex(FILE *fp, facetT *facet, int format) {
- vertexT *vertex, **vertexp;
- setT *vertices;
-
- vertices= qh_facet3vertex (facet);
- if (format == qh_PRINToff)
- fprintf (fp, "%d ", qh_setsize (vertices));
- FOREACHvertex_(vertices)
- fprintf (fp, "%d ", qh_pointid(vertex->point));
- fprintf (fp, "\n");
- qh_settempfree(&vertices);
-} /* printfacet3vertex */
-
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printfacet4geom_nonsimplicial">-</a>
-
- qh_printfacet4geom_nonsimplicial( )
- print Geomview 4OFF file for a 4d nonsimplicial facet
- prints all ridges to unvisited neighbors (qh.visit_id)
- if qh.DROPdim
- prints in OFF format
-
- notes:
- must agree with printend4geom()
-*/
-void qh_printfacet4geom_nonsimplicial(FILE *fp, facetT *facet, realT color[3]) {
- facetT *neighbor;
- ridgeT *ridge, **ridgep;
- vertexT *vertex, **vertexp;
- pointT *point;
- int k;
- realT dist;
-
- facet->visitid= qh visit_id;
- if (qh PRINTnoplanes || (facet->visible && qh NEWfacets))
- return;
- FOREACHridge_(facet->ridges) {
- neighbor= otherfacet_(ridge, facet);
- if (neighbor->visitid == qh visit_id)
- continue;
- if (qh PRINTtransparent && !neighbor->good)
- continue;
- if (qh DOintersections)
- qh_printhyperplaneintersection(fp, facet, neighbor, ridge->vertices, color);
- else {
- if (qh DROPdim >= 0)
- fprintf(fp, "OFF 3 1 1 # f%d\n", facet->id);
- else {
- qh printoutvar++;
- fprintf (fp, "# r%d between f%d f%d\n", ridge->id, facet->id, neighbor->id);
- }
- FOREACHvertex_(ridge->vertices) {
- zinc_(Zdistio);
- qh_distplane(vertex->point,facet, &dist);
- point=qh_projectpoint(vertex->point,facet, dist);
- for(k= 0; k < qh hull_dim; k++) {
- if (k != qh DROPdim)
- fprintf(fp, "%8.4g ", point[k]);
- }
- fprintf (fp, "\n");
- qh_memfree (point, qh normal_size);
- }
- if (qh DROPdim >= 0)
- fprintf(fp, "3 0 1 2 %8.4g %8.4g %8.4g\n", color[0], color[1], color[2]);
- }
- }
-} /* printfacet4geom_nonsimplicial */
-
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printfacet4geom_simplicial">-</a>
-
- qh_printfacet4geom_simplicial( fp, facet, color )
- print Geomview 4OFF file for a 4d simplicial facet
- prints triangles for unvisited neighbors (qh.visit_id)
-
- notes:
- must agree with printend4geom()
-*/
-void qh_printfacet4geom_simplicial(FILE *fp, facetT *facet, realT color[3]) {
- setT *vertices;
- facetT *neighbor, **neighborp;
- vertexT *vertex, **vertexp;
- int k;
-
- facet->visitid= qh visit_id;
- if (qh PRINTnoplanes || (facet->visible && qh NEWfacets))
- return;
- FOREACHneighbor_(facet) {
- if (neighbor->visitid == qh visit_id)
- continue;
- if (qh PRINTtransparent && !neighbor->good)
- continue;
- vertices= qh_setnew_delnthsorted (facet->vertices, qh hull_dim,
- SETindex_(facet->neighbors, neighbor), 0);
- if (qh DOintersections)
- qh_printhyperplaneintersection(fp, facet, neighbor, vertices, color);
- else {
- if (qh DROPdim >= 0)
- fprintf(fp, "OFF 3 1 1 # ridge between f%d f%d\n",
- facet->id, neighbor->id);
- else {
- qh printoutvar++;
- fprintf (fp, "# ridge between f%d f%d\n", facet->id, neighbor->id);
- }
- FOREACHvertex_(vertices) {
- for(k= 0; k < qh hull_dim; k++) {
- if (k != qh DROPdim)
- fprintf(fp, "%8.4g ", vertex->point[k]);
- }
- fprintf (fp, "\n");
- }
- if (qh DROPdim >= 0)
- fprintf(fp, "3 0 1 2 %8.4g %8.4g %8.4g\n", color[0], color[1], color[2]);
- }
- qh_setfree(&vertices);
- }
-} /* printfacet4geom_simplicial */
-
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printfacetNvertex_nonsimplicial">-</a>
-
- qh_printfacetNvertex_nonsimplicial( fp, facet, id, format )
- print vertices for an N-d non-simplicial facet
- triangulates each ridge to the id
-*/
-void qh_printfacetNvertex_nonsimplicial(FILE *fp, facetT *facet, int id, int format) {
- vertexT *vertex, **vertexp;
- ridgeT *ridge, **ridgep;
-
- if (facet->visible && qh NEWfacets)
- return;
- FOREACHridge_(facet->ridges) {
- if (format == qh_PRINTtriangles)
- fprintf(fp, "%d ", qh hull_dim);
- fprintf(fp, "%d ", id);
- if ((ridge->top == facet) ^ qh_ORIENTclock) {
- FOREACHvertex_(ridge->vertices)
- fprintf(fp, "%d ", qh_pointid(vertex->point));
- }else {
- FOREACHvertexreverse12_(ridge->vertices)
- fprintf(fp, "%d ", qh_pointid(vertex->point));
- }
- fprintf(fp, "\n");
- }
-} /* printfacetNvertex_nonsimplicial */
-
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printfacetNvertex_simplicial">-</a>
-
- qh_printfacetNvertex_simplicial( fp, facet, format )
- print vertices for an N-d simplicial facet
- prints vertices for non-simplicial facets
- 2-d facets (orientation preserved by qh_mergefacet2d)
- PRINToff ('o') for 4-d and higher
-*/
-void qh_printfacetNvertex_simplicial(FILE *fp, facetT *facet, int format) {
- vertexT *vertex, **vertexp;
-
- if (format == qh_PRINToff || format == qh_PRINTtriangles)
- fprintf (fp, "%d ", qh_setsize (facet->vertices));
- if ((facet->toporient ^ qh_ORIENTclock)
- || (qh hull_dim > 2 && !facet->simplicial)) {
- FOREACHvertex_(facet->vertices)
- fprintf(fp, "%d ", qh_pointid(vertex->point));
- }else {
- FOREACHvertexreverse12_(facet->vertices)
- fprintf(fp, "%d ", qh_pointid(vertex->point));
- }
- fprintf(fp, "\n");
-} /* printfacetNvertex_simplicial */
-
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printfacetheader">-</a>
-
- qh_printfacetheader( fp, facet )
- prints header fields of a facet to fp
-
- notes:
- for 'f' output and debugging
-*/
-void qh_printfacetheader(FILE *fp, facetT *facet) {
- pointT *point, **pointp, *furthest;
- facetT *neighbor, **neighborp;
- realT dist;
-
- if (facet == qh_MERGEridge) {
- fprintf (fp, " MERGEridge\n");
- return;
- }else if (facet == qh_DUPLICATEridge) {
- fprintf (fp, " DUPLICATEridge\n");
- return;
- }else if (!facet) {
- fprintf (fp, " NULLfacet\n");
- return;
- }
- qh old_randomdist= qh RANDOMdist;
- qh RANDOMdist= False;
- fprintf(fp, "- f%d\n", facet->id);
- fprintf(fp, " - flags:");
- if (facet->toporient)
- fprintf(fp, " top");
- else
- fprintf(fp, " bottom");
- if (facet->simplicial)
- fprintf(fp, " simplicial");
- if (facet->tricoplanar)
- fprintf(fp, " tricoplanar");
- if (facet->upperdelaunay)
- fprintf(fp, " upperDelaunay");
- if (facet->visible)
- fprintf(fp, " visible");
- if (facet->newfacet)
- fprintf(fp, " new");
- if (facet->tested)
- fprintf(fp, " tested");
- if (!facet->good)
- fprintf(fp, " notG");
- if (facet->seen)
- fprintf(fp, " seen");
- if (facet->coplanar)
- fprintf(fp, " coplanar");
- if (facet->mergehorizon)
- fprintf(fp, " mergehorizon");
- if (facet->keepcentrum)
- fprintf(fp, " keepcentrum");
- if (facet->dupridge)
- fprintf(fp, " dupridge");
- if (facet->mergeridge && !facet->mergeridge2)
- fprintf(fp, " mergeridge1");
- if (facet->mergeridge2)
- fprintf(fp, " mergeridge2");
- if (facet->newmerge)
- fprintf(fp, " newmerge");
- if (facet->flipped)
- fprintf(fp, " flipped");
- if (facet->notfurthest)
- fprintf(fp, " notfurthest");
- if (facet->degenerate)
- fprintf(fp, " degenerate");
- if (facet->redundant)
- fprintf(fp, " redundant");
- fprintf(fp, "\n");
- if (facet->isarea)
- fprintf(fp, " - area: %2.2g\n", facet->f.area);
- else if (qh NEWfacets && facet->visible && facet->f.replace)
- fprintf(fp, " - replacement: f%d\n", facet->f.replace->id);
- else if (facet->newfacet) {
- if (facet->f.samecycle && facet->f.samecycle != facet)
- fprintf(fp, " - shares same visible/horizon as f%d\n", facet->f.samecycle->id);
- }else if (facet->tricoplanar /* !isarea */) {
- if (facet->f.triowner)
- fprintf(fp, " - owner of normal & centrum is facet f%d\n", facet->f.triowner->id);
- }else if (facet->f.newcycle)
- fprintf(fp, " - was horizon to f%d\n", facet->f.newcycle->id);
- if (facet->nummerge)
- fprintf(fp, " - merges: %d\n", facet->nummerge);
- qh_printpointid(fp, " - normal: ", qh hull_dim, facet->normal, -1);
- fprintf(fp, " - offset: %10.7g\n", facet->offset);
- if (qh CENTERtype == qh_ASvoronoi || facet->center)
- qh_printcenter (fp, qh_PRINTfacets, " - center: ", facet);
-#if qh_MAXoutside
- if (facet->maxoutside > qh DISTround)
- fprintf(fp, " - maxoutside: %10.7g\n", facet->maxoutside);
-#endif
- if (!SETempty_(facet->outsideset)) {
- furthest= (pointT*)qh_setlast(facet->outsideset);
- if (qh_setsize (facet->outsideset) < 6) {
- fprintf(fp, " - outside set (furthest p%d):\n", qh_pointid(furthest));
- FOREACHpoint_(facet->outsideset)
- qh_printpoint(fp, " ", point);
- }else if (qh_setsize (facet->outsideset) < 21) {
- qh_printpoints(fp, " - outside set:", facet->outsideset);
- }else {
- fprintf(fp, " - outside set: %d points.", qh_setsize(facet->outsideset));
- qh_printpoint(fp, " Furthest", furthest);
- }
-#if !qh_COMPUTEfurthest
- fprintf(fp, " - furthest distance= %2.2g\n", facet->furthestdist);
-#endif
- }
- if (!SETempty_(facet->coplanarset)) {
- furthest= (pointT*)qh_setlast(facet->coplanarset);
- if (qh_setsize (facet->coplanarset) < 6) {
- fprintf(fp, " - coplanar set (furthest p%d):\n", qh_pointid(furthest));
- FOREACHpoint_(facet->coplanarset)
- qh_printpoint(fp, " ", point);
- }else if (qh_setsize (facet->coplanarset) < 21) {
- qh_printpoints(fp, " - coplanar set:", facet->coplanarset);
- }else {
- fprintf(fp, " - coplanar set: %d points.", qh_setsize(facet->coplanarset));
- qh_printpoint(fp, " Furthest", furthest);
- }
- zinc_(Zdistio);
- qh_distplane (furthest, facet, &dist);
- fprintf(fp, " furthest distance= %2.2g\n", dist);
- }
- qh_printvertices (fp, " - vertices:", facet->vertices);
- fprintf(fp, " - neighboring facets: ");
- FOREACHneighbor_(facet) {
- if (neighbor == qh_MERGEridge)
- fprintf(fp, " MERGE");
- else if (neighbor == qh_DUPLICATEridge)
- fprintf(fp, " DUP");
- else
- fprintf(fp, " f%d", neighbor->id);
- }
- fprintf(fp, "\n");
- qh RANDOMdist= qh old_randomdist;
-} /* printfacetheader */
-
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printfacetridges">-</a>
-
- qh_printfacetridges( fp, facet )
- prints ridges of a facet to fp
-
- notes:
- ridges printed in neighbor order
- assumes the ridges exist
- for 'f' output
-*/
-void qh_printfacetridges(FILE *fp, facetT *facet) {
- facetT *neighbor, **neighborp;
- ridgeT *ridge, **ridgep;
- int numridges= 0;
-
-
- if (facet->visible && qh NEWfacets) {
- fprintf(fp, " - ridges (ids may be garbage):");
- FOREACHridge_(facet->ridges)
- fprintf(fp, " r%d", ridge->id);
- fprintf(fp, "\n");
- }else {
- fprintf(fp, " - ridges:\n");
- FOREACHridge_(facet->ridges)
- ridge->seen= False;
- if (qh hull_dim == 3) {
- ridge= SETfirstt_(facet->ridges, ridgeT);
- while (ridge && !ridge->seen) {
- ridge->seen= True;
- qh_printridge(fp, ridge);
- numridges++;
- ridge= qh_nextridge3d (ridge, facet, NULL);
- }
- }else {
- FOREACHneighbor_(facet) {
- FOREACHridge_(facet->ridges) {
- if (otherfacet_(ridge,facet) == neighbor) {
- ridge->seen= True;
- qh_printridge(fp, ridge);
- numridges++;
- }
- }
- }
- }
- if (numridges != qh_setsize (facet->ridges)) {
- fprintf (fp, " - all ridges:");
- FOREACHridge_(facet->ridges)
- fprintf (fp, " r%d", ridge->id);
- fprintf (fp, "\n");
- }
- FOREACHridge_(facet->ridges) {
- if (!ridge->seen)
- qh_printridge(fp, ridge);
- }
- }
-} /* printfacetridges */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printfacets">-</a>
-
- qh_printfacets( fp, format, facetlist, facets, printall )
- prints facetlist and/or facet set in output format
-
- notes:
- also used for specialized formats ('FO' and summary)
- turns off 'Rn' option since want actual numbers
-*/
-void qh_printfacets(FILE *fp, int format, facetT *facetlist, setT *facets, boolT printall) {
- int numfacets, numsimplicial, numridges, totneighbors, numcoplanars, numtricoplanars;
- facetT *facet, **facetp;
- setT *vertices;
- coordT *center;
- realT outerplane, innerplane;
-
- qh old_randomdist= qh RANDOMdist;
- qh RANDOMdist= False;
- if (qh CDDoutput && (format == qh_PRINTcentrums || format == qh_PRINTpointintersect || format == qh_PRINToff))
- fprintf (qh ferr, "qhull warning: CDD format is not available for centrums, halfspace\nintersections, and OFF file format.\n");
- if (format == qh_PRINTnone)
- ; /* print nothing */
- else if (format == qh_PRINTaverage) {
- vertices= qh_facetvertices (facetlist, facets, printall);
- center= qh_getcenter (vertices);
- fprintf (fp, "%d 1\n", qh hull_dim);
- qh_printpointid (fp, NULL, qh hull_dim, center, -1);
- qh_memfree (center, qh normal_size);
- qh_settempfree (&vertices);
- }else if (format == qh_PRINTextremes) {
- if (qh DELAUNAY)
- qh_printextremes_d (fp, facetlist, facets, printall);
- else if (qh hull_dim == 2)
- qh_printextremes_2d (fp, facetlist, facets, printall);
- else
- qh_printextremes (fp, facetlist, facets, printall);
- }else if (format == qh_PRINToptions)
- fprintf(fp, "Options selected for Qhull %s:\n%s\n", qh_version, qh qhull_options);
- else if (format == qh_PRINTpoints && !qh VORONOI)
- qh_printpoints_out (fp, facetlist, facets, printall);
- else if (format == qh_PRINTqhull)
- fprintf (fp, "%s | %s\n", qh rbox_command, qh qhull_command);
- else if (format == qh_PRINTsize) {
- fprintf (fp, "0\n2 ");
- fprintf (fp, qh_REAL_1, qh totarea);
- fprintf (fp, qh_REAL_1, qh totvol);
- fprintf (fp, "\n");
- }else if (format == qh_PRINTsummary) {
- qh_countfacets (facetlist, facets, printall, &numfacets, &numsimplicial,
- &totneighbors, &numridges, &numcoplanars, &numtricoplanars);
- vertices= qh_facetvertices (facetlist, facets, printall);
- fprintf (fp, "10 %d %d %d %d %d %d %d %d %d %d\n2 ", qh hull_dim,
- qh num_points + qh_setsize (qh other_points),
- qh num_vertices, qh num_facets - qh num_visible,
- qh_setsize (vertices), numfacets, numcoplanars,
- numfacets - numsimplicial, zzval_(Zdelvertextot),
- numtricoplanars);
- qh_settempfree (&vertices);
- qh_outerinner (NULL, &outerplane, &innerplane);
- fprintf (fp, qh_REAL_2n, outerplane, innerplane);
- }else if (format == qh_PRINTvneighbors)
- qh_printvneighbors (fp, facetlist, facets, printall);
- else if (qh VORONOI && format == qh_PRINToff)
- qh_printvoronoi (fp, format, facetlist, facets, printall);
- else if (qh VORONOI && format == qh_PRINTgeom) {
- qh_printbegin (fp, format, facetlist, facets, printall);
- qh_printvoronoi (fp, format, facetlist, facets, printall);
- qh_printend (fp, format, facetlist, facets, printall);
- }else if (qh VORONOI
- && (format == qh_PRINTvertices || format == qh_PRINTinner || format == qh_PRINTouter))
- qh_printvdiagram (fp, format, facetlist, facets, printall);
- else {
- qh_printbegin (fp, format, facetlist, facets, printall);
- FORALLfacet_(facetlist)
- qh_printafacet (fp, format, facet, printall);
- FOREACHfacet_(facets)
- qh_printafacet (fp, format, facet, printall);
- qh_printend (fp, format, facetlist, facets, printall);
- }
- qh RANDOMdist= qh old_randomdist;
-} /* printfacets */
-
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printhelp_degenerate">-</a>
-
- qh_printhelp_degenerate( fp )
- prints descriptive message for precision error
-
- notes:
- no message if qh_QUICKhelp
-*/
-void qh_printhelp_degenerate(FILE *fp) {
-
- if (qh MERGEexact || qh PREmerge || qh JOGGLEmax < REALmax/2)
- fprintf(fp, "\n\
-A Qhull error has occurred. Qhull should have corrected the above\n\
-precision error. Please send the input and all of the output to\n\
-qhull_bug@qhull.org\n");
- else if (!qh_QUICKhelp) {
- fprintf(fp, "\n\
-Precision problems were detected during construction of the convex hull.\n\
-This occurs because convex hull algorithms assume that calculations are\n\
-exact, but floating-point arithmetic has roundoff errors.\n\
-\n\
-To correct for precision problems, do not use 'Q0'. By default, Qhull\n\
-selects 'C-0' or 'Qx' and merges non-convex facets. With option 'QJ',\n\
-Qhull joggles the input to prevent precision problems. See \"Imprecision\n\
-in Qhull\" (qh-impre.htm).\n\
-\n\
-If you use 'Q0', the output may include\n\
-coplanar ridges, concave ridges, and flipped facets. In 4-d and higher,\n\
-Qhull may produce a ridge with four neighbors or two facets with the same \n\
-vertices. Qhull reports these events when they occur. It stops when a\n\
-concave ridge, flipped facet, or duplicate facet occurs.\n");
-#if REALfloat
- fprintf (fp, "\
-\n\
-Qhull is currently using single precision arithmetic. The following\n\
-will probably remove the precision problems:\n\
- - recompile qhull for double precision (#define REALfloat 0 in user.h).\n");
-#endif
- if (qh DELAUNAY && !qh SCALElast && qh MAXabs_coord > 1e4)
- fprintf( fp, "\
-\n\
-When computing the Delaunay triangulation of coordinates > 1.0,\n\
- - use 'Qbb' to scale the last coordinate to [0,m] (max previous coordinate)\n");
- if (qh DELAUNAY && !qh ATinfinity)
- fprintf( fp, "\
-When computing the Delaunay triangulation:\n\
- - use 'Qz' to add a point at-infinity. This reduces precision problems.\n");
-
- fprintf(fp, "\
-\n\
-If you need triangular output:\n\
- - use option 'Qt' to triangulate the output\n\
- - use option 'QJ' to joggle the input points and remove precision errors\n\
- - use option 'Ft'. It triangulates non-simplicial facets with added points.\n\
-\n\
-If you must use 'Q0',\n\
-try one or more of the following options. They can not guarantee an output.\n\
- - use 'QbB' to scale the input to a cube.\n\
- - use 'Po' to produce output and prevent partitioning for flipped facets\n\
- - use 'V0' to set min. distance to visible facet as 0 instead of roundoff\n\
- - use 'En' to specify a maximum roundoff error less than %2.2g.\n\
- - options 'Qf', 'Qbb', and 'QR0' may also help\n",
- qh DISTround);
- fprintf(fp, "\
-\n\
-To guarantee simplicial output:\n\
- - use option 'Qt' to triangulate the output\n\
- - use option 'QJ' to joggle the input points and remove precision errors\n\
- - use option 'Ft' to triangulate the output by adding points\n\
- - use exact arithmetic (see \"Imprecision in Qhull\", qh-impre.htm)\n\
-");
- }
-} /* printhelp_degenerate */
-
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printhelp_singular">-</a>
-
- qh_printhelp_singular( fp )
- prints descriptive message for singular input
-*/
-void qh_printhelp_singular(FILE *fp) {
- facetT *facet;
- vertexT *vertex, **vertexp;
- realT min, max, *coord, dist;
- int i,k;
-
- fprintf(fp, "\n\
-The input to qhull appears to be less than %d dimensional, or a\n\
-computation has overflowed.\n\n\
-Qhull could not construct a clearly convex simplex from points:\n",
- qh hull_dim);
- qh_printvertexlist (fp, "", qh facet_list, NULL, qh_ALL);
- if (!qh_QUICKhelp)
- fprintf(fp, "\n\
-The center point is coplanar with a facet, or a vertex is coplanar\n\
-with a neighboring facet. The maximum round off error for\n\
-computing distances is %2.2g. The center point, facets and distances\n\
-to the center point are as follows:\n\n", qh DISTround);
- qh_printpointid (fp, "center point", qh hull_dim, qh interior_point, -1);
- fprintf (fp, "\n");
- FORALLfacets {
- fprintf (fp, "facet");
- FOREACHvertex_(facet->vertices)
- fprintf (fp, " p%d", qh_pointid(vertex->point));
- zinc_(Zdistio);
- qh_distplane(qh interior_point, facet, &dist);
- fprintf (fp, " distance= %4.2g\n", dist);
- }
- if (!qh_QUICKhelp) {
- if (qh HALFspace)
- fprintf (fp, "\n\
-These points are the dual of the given halfspaces. They indicate that\n\
-the intersection is degenerate.\n");
- fprintf (fp,"\n\
-These points either have a maximum or minimum x-coordinate, or\n\
-they maximize the determinant for k coordinates. Trial points\n\
-are first selected from points that maximize a coordinate.\n");
- if (qh hull_dim >= qh_INITIALmax)
- fprintf (fp, "\n\
-Because of the high dimension, the min x-coordinate and max-coordinate\n\
-points are used if the determinant is non-zero. Option 'Qs' will\n\
-do a better, though much slower, job. Instead of 'Qs', you can change\n\
-the points by randomly rotating the input with 'QR0'.\n");
- }
- fprintf (fp, "\nThe min and max coordinates for each dimension are:\n");
- for (k=0; k < qh hull_dim; k++) {
- min= REALmax;
- max= -REALmin;
- for (i=qh num_points, coord= qh first_point+k; i--; coord += qh hull_dim) {
- maximize_(max, *coord);
- minimize_(min, *coord);
- }
- fprintf (fp, " %d: %8.4g %8.4g difference= %4.4g\n", k, min, max, max-min);
- }
- if (!qh_QUICKhelp) {
- fprintf (fp, "\n\
-If the input should be full dimensional, you have several options that\n\
-may determine an initial simplex:\n\
- - use 'QJ' to joggle the input and make it full dimensional\n\
- - use 'QbB' to scale the points to the unit cube\n\
- - use 'QR0' to randomly rotate the input for different maximum points\n\
- - use 'Qs' to search all points for the initial simplex\n\
- - use 'En' to specify a maximum roundoff error less than %2.2g.\n\
- - trace execution with 'T3' to see the determinant for each point.\n",
- qh DISTround);
-#if REALfloat
- fprintf (fp, "\
- - recompile qhull for double precision (#define REALfloat 0 in qhull.h).\n");
-#endif
- fprintf (fp, "\n\
-If the input is lower dimensional:\n\
- - use 'QJ' to joggle the input and make it full dimensional\n\
- - use 'Qbk:0Bk:0' to delete coordinate k from the input. You should\n\
- pick the coordinate with the least range. The hull will have the\n\
- correct topology.\n\
- - determine the flat containing the points, rotate the points\n\
- into a coordinate plane, and delete the other coordinates.\n\
- - add one or more points to make the input full dimensional.\n\
-");
- if (qh DELAUNAY && !qh ATinfinity)
- fprintf (fp, "\n\n\
-This is a Delaunay triangulation and the input is co-circular or co-spherical:\n\
- - use 'Qz' to add a point \"at infinity\" (i.e., above the paraboloid)\n\
- - or use 'QJ' to joggle the input and avoid co-circular data\n");
- }
-} /* printhelp_singular */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printhyperplaneintersection">-</a>
-
- qh_printhyperplaneintersection( fp, facet1, facet2, vertices, color )
- print Geomview OFF or 4OFF for the intersection of two hyperplanes in 3-d or 4-d
-*/
-void qh_printhyperplaneintersection(FILE *fp, facetT *facet1, facetT *facet2,
- setT *vertices, realT color[3]) {
- realT costheta, denominator, dist1, dist2, s, t, mindenom, p[4];
- vertexT *vertex, **vertexp;
- int i, k;
- boolT nearzero1, nearzero2;
-
- costheta= qh_getangle(facet1->normal, facet2->normal);
- denominator= 1 - costheta * costheta;
- i= qh_setsize(vertices);
- if (qh hull_dim == 3)
- fprintf(fp, "VECT 1 %d 1 %d 1 ", i, i);
- else if (qh hull_dim == 4 && qh DROPdim >= 0)
- fprintf(fp, "OFF 3 1 1 ");
- else
- qh printoutvar++;
- fprintf (fp, "# intersect f%d f%d\n", facet1->id, facet2->id);
- mindenom= 1 / (10.0 * qh MAXabs_coord);
- FOREACHvertex_(vertices) {
- zadd_(Zdistio, 2);
- qh_distplane(vertex->point, facet1, &dist1);
- qh_distplane(vertex->point, facet2, &dist2);
- s= qh_divzero (-dist1 + costheta * dist2, denominator,mindenom,&nearzero1);
- t= qh_divzero (-dist2 + costheta * dist1, denominator,mindenom,&nearzero2);
- if (nearzero1 || nearzero2)
- s= t= 0.0;
- for(k= qh hull_dim; k--; )
- p[k]= vertex->point[k] + facet1->normal[k] * s + facet2->normal[k] * t;
- if (qh PRINTdim <= 3) {
- qh_projectdim3 (p, p);
- fprintf(fp, "%8.4g %8.4g %8.4g # ", p[0], p[1], p[2]);
- }else
- fprintf(fp, "%8.4g %8.4g %8.4g %8.4g # ", p[0], p[1], p[2], p[3]);
- if (nearzero1+nearzero2)
- fprintf (fp, "p%d (coplanar facets)\n", qh_pointid (vertex->point));
- else
- fprintf (fp, "projected p%d\n", qh_pointid (vertex->point));
- }
- if (qh hull_dim == 3)
- fprintf(fp, "%8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
- else if (qh hull_dim == 4 && qh DROPdim >= 0)
- fprintf(fp, "3 0 1 2 %8.4g %8.4g %8.4g 1.0\n", color[0], color[1], color[2]);
-} /* printhyperplaneintersection */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printline3geom">-</a>
-
- qh_printline3geom( fp, pointA, pointB, color )
- prints a line as a VECT
- prints 0's for qh.DROPdim
-
- notes:
- if pointA == pointB,
- it's a 1 point VECT
-*/
-void qh_printline3geom (FILE *fp, pointT *pointA, pointT *pointB, realT color[3]) {
- int k;
- realT pA[4], pB[4];
-
- qh_projectdim3(pointA, pA);
- qh_projectdim3(pointB, pB);
- if ((fabs(pA[0] - pB[0]) > 1e-3) ||
- (fabs(pA[1] - pB[1]) > 1e-3) ||
- (fabs(pA[2] - pB[2]) > 1e-3)) {
- fprintf (fp, "VECT 1 2 1 2 1\n");
- for (k= 0; k < 3; k++)
- fprintf (fp, "%8.4g ", pB[k]);
- fprintf (fp, " # p%d\n", qh_pointid (pointB));
- }else
- fprintf (fp, "VECT 1 1 1 1 1\n");
- for (k=0; k < 3; k++)
- fprintf (fp, "%8.4g ", pA[k]);
- fprintf (fp, " # p%d\n", qh_pointid (pointA));
- fprintf (fp, "%8.4g %8.4g %8.4g 1\n", color[0], color[1], color[2]);
-}
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printneighborhood">-</a>
-
- qh_printneighborhood( fp, format, facetA, facetB, printall )
- print neighborhood of one or two facets
-
- notes:
- calls qh_findgood_all()
- bumps qh.visit_id
-*/
-void qh_printneighborhood (FILE *fp, int format, facetT *facetA, facetT *facetB, boolT printall) {
- facetT *neighbor, **neighborp, *facet;
- setT *facets;
-
- if (format == qh_PRINTnone)
- return;
- qh_findgood_all (qh facet_list);
- if (facetA == facetB)
- facetB= NULL;
- facets= qh_settemp (2*(qh_setsize (facetA->neighbors)+1));
- qh visit_id++;
- for (facet= facetA; facet; facet= ((facet == facetA) ? facetB : NULL)) {
- if (facet->visitid != qh visit_id) {
- facet->visitid= qh visit_id;
- qh_setappend (&facets, facet);
- }
- FOREACHneighbor_(facet) {
- if (neighbor->visitid == qh visit_id)
- continue;
- neighbor->visitid= qh visit_id;
- if (printall || !qh_skipfacet (neighbor))
- qh_setappend (&facets, neighbor);
- }
- }
- qh_printfacets (fp, format, NULL, facets, printall);
- qh_settempfree (&facets);
-} /* printneighborhood */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printpoint">-</a>
-
- qh_printpoint( fp, string, point )
- qh_printpointid( fp, string, dim, point, id )
- prints the coordinates of a point
-
- returns:
- if string is defined
- prints 'string p%d' (skips p%d if id=-1)
-
- notes:
- nop if point is NULL
- prints id unless it is undefined (-1)
-*/
-void qh_printpoint(FILE *fp, char *string, pointT *point) {
- int id= qh_pointid( point);
-
- qh_printpointid( fp, string, qh hull_dim, point, id);
-} /* printpoint */
-
-void qh_printpointid(FILE *fp, char *string, int dim, pointT *point, int id) {
- int k;
- realT r; /*bug fix*/
-
- if (!point)
- return;
- if (string) {
- fputs (string, fp);
- if (id != -1)
- fprintf(fp, " p%d: ", id);
- }
- for(k= dim; k--; ) {
- r= *point++;
- if (string)
- fprintf(fp, " %8.4g", r);
- else
- fprintf(fp, qh_REAL_1, r);
- }
- fprintf(fp, "\n");
-} /* printpointid */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printpoint3">-</a>
-
- qh_printpoint3( fp, point )
- prints 2-d, 3-d, or 4-d point as Geomview 3-d coordinates
-*/
-void qh_printpoint3 (FILE *fp, pointT *point) {
- int k;
- realT p[4];
-
- qh_projectdim3 (point, p);
- for (k=0; k < 3; k++)
- fprintf (fp, "%8.4g ", p[k]);
- fprintf (fp, " # p%d\n", qh_pointid (point));
-} /* printpoint3 */
-
-/*----------------------------------------
--printpoints- print pointids for a set of points starting at index
- see geom.c
-*/
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printpoints_out">-</a>
-
- qh_printpoints_out( fp, facetlist, facets, printall )
- prints vertices, coplanar/inside points, for facets by their point coordinates
- allows qh.CDDoutput
-
- notes:
- same format as qhull input
- if no coplanar/interior points,
- same order as qh_printextremes
-*/
-void qh_printpoints_out (FILE *fp, facetT *facetlist, setT *facets, int printall) {
- int allpoints= qh num_points + qh_setsize (qh other_points);
- int numpoints=0, point_i, point_n;
- setT *vertices, *points;
- facetT *facet, **facetp;
- pointT *point, **pointp;
- vertexT *vertex, **vertexp;
- int id;
-
- points= qh_settemp (allpoints);
- qh_setzero (points, 0, allpoints);
- vertices= qh_facetvertices (facetlist, facets, printall);
- FOREACHvertex_(vertices) {
- id= qh_pointid (vertex->point);
- if (id >= 0)
- SETelem_(points, id)= vertex->point;
- }
- if (qh KEEPinside || qh KEEPcoplanar || qh KEEPnearinside) {
- FORALLfacet_(facetlist) {
- if (!printall && qh_skipfacet(facet))
- continue;
- FOREACHpoint_(facet->coplanarset) {
- id= qh_pointid (point);
- if (id >= 0)
- SETelem_(points, id)= point;
- }
- }
- FOREACHfacet_(facets) {
- if (!printall && qh_skipfacet(facet))
- continue;
- FOREACHpoint_(facet->coplanarset) {
- id= qh_pointid (point);
- if (id >= 0)
- SETelem_(points, id)= point;
- }
- }
- }
- qh_settempfree (&vertices);
- FOREACHpoint_i_(points) {
- if (point)
- numpoints++;
- }
- if (qh CDDoutput)
- fprintf (fp, "%s | %s\nbegin\n%d %d real\n", qh rbox_command,
- qh qhull_command, numpoints, qh hull_dim + 1);
- else
- fprintf (fp, "%d\n%d\n", qh hull_dim, numpoints);
- FOREACHpoint_i_(points) {
- if (point) {
- if (qh CDDoutput)
- fprintf (fp, "1 ");
- qh_printpoint (fp, NULL, point);
- }
- }
- if (qh CDDoutput)
- fprintf (fp, "end\n");
- qh_settempfree (&points);
-} /* printpoints_out */
-
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printpointvect">-</a>
-
- qh_printpointvect( fp, point, normal, center, radius, color )
- prints a 2-d, 3-d, or 4-d point as 3-d VECT's relative to normal or to center point
-*/
-void qh_printpointvect (FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius, realT color[3]) {
- realT diff[4], pointA[4];
- int k;
-
- for (k= qh hull_dim; k--; ) {
- if (center)
- diff[k]= point[k]-center[k];
- else if (normal)
- diff[k]= normal[k];
- else
- diff[k]= 0;
- }
- if (center)
- qh_normalize2 (diff, qh hull_dim, True, NULL, NULL);
- for (k= qh hull_dim; k--; )
- pointA[k]= point[k]+diff[k] * radius;
- qh_printline3geom (fp, point, pointA, color);
-} /* printpointvect */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printpointvect2">-</a>
-
- qh_printpointvect2( fp, point, normal, center, radius )
- prints a 2-d, 3-d, or 4-d point as 2 3-d VECT's for an imprecise point
-*/
-void qh_printpointvect2 (FILE *fp, pointT *point, coordT *normal, pointT *center, realT radius) {
- realT red[3]={1, 0, 0}, yellow[3]={1, 1, 0};
-
- qh_printpointvect (fp, point, normal, center, radius, red);
- qh_printpointvect (fp, point, normal, center, -radius, yellow);
-} /* printpointvect2 */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printridge">-</a>
-
- qh_printridge( fp, ridge )
- prints the information in a ridge
-
- notes:
- for qh_printfacetridges()
-*/
-void qh_printridge(FILE *fp, ridgeT *ridge) {
-
- fprintf(fp, " - r%d", ridge->id);
- if (ridge->tested)
- fprintf (fp, " tested");
- if (ridge->nonconvex)
- fprintf (fp, " nonconvex");
- fprintf (fp, "\n");
- qh_printvertices (fp, " vertices:", ridge->vertices);
- if (ridge->top && ridge->bottom)
- fprintf(fp, " between f%d and f%d\n",
- ridge->top->id, ridge->bottom->id);
-} /* printridge */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printspheres">-</a>
-
- qh_printspheres( fp, vertices, radius )
- prints 3-d vertices as OFF spheres
-
- notes:
- inflated octahedron from Stuart Levy earth/mksphere2
-*/
-void qh_printspheres(FILE *fp, setT *vertices, realT radius) {
- vertexT *vertex, **vertexp;
-
- qh printoutnum++;
- fprintf (fp, "{appearance {-edge -normal normscale 0} {\n\
-INST geom {define vsphere OFF\n\
-18 32 48\n\
-\n\
-0 0 1\n\
-1 0 0\n\
-0 1 0\n\
--1 0 0\n\
-0 -1 0\n\
-0 0 -1\n\
-0.707107 0 0.707107\n\
-0 -0.707107 0.707107\n\
-0.707107 -0.707107 0\n\
--0.707107 0 0.707107\n\
--0.707107 -0.707107 0\n\
-0 0.707107 0.707107\n\
--0.707107 0.707107 0\n\
-0.707107 0.707107 0\n\
-0.707107 0 -0.707107\n\
-0 0.707107 -0.707107\n\
--0.707107 0 -0.707107\n\
-0 -0.707107 -0.707107\n\
-\n\
-3 0 6 11\n\
-3 0 7 6 \n\
-3 0 9 7 \n\
-3 0 11 9\n\
-3 1 6 8 \n\
-3 1 8 14\n\
-3 1 13 6\n\
-3 1 14 13\n\
-3 2 11 13\n\
-3 2 12 11\n\
-3 2 13 15\n\
-3 2 15 12\n\
-3 3 9 12\n\
-3 3 10 9\n\
-3 3 12 16\n\
-3 3 16 10\n\
-3 4 7 10\n\
-3 4 8 7\n\
-3 4 10 17\n\
-3 4 17 8\n\
-3 5 14 17\n\
-3 5 15 14\n\
-3 5 16 15\n\
-3 5 17 16\n\
-3 6 13 11\n\
-3 7 8 6\n\
-3 9 10 7\n\
-3 11 12 9\n\
-3 14 8 17\n\
-3 15 13 14\n\
-3 16 12 15\n\
-3 17 10 16\n} transforms { TLIST\n");
- FOREACHvertex_(vertices) {
- fprintf(fp, "%8.4g 0 0 0 # v%d\n 0 %8.4g 0 0\n0 0 %8.4g 0\n",
- radius, vertex->id, radius, radius);
- qh_printpoint3 (fp, vertex->point);
- fprintf (fp, "1\n");
- }
- fprintf (fp, "}}}\n");
-} /* printspheres */
-
-
-/*----------------------------------------------
--printsummary-
- see qhull.c
-*/
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printvdiagram">-</a>
-
- qh_printvdiagram( fp, format, facetlist, facets, printall )
- print voronoi diagram
- # of pairs of input sites
- #indices site1 site2 vertex1 ...
-
- sites indexed by input point id
- point 0 is the first input point
- vertices indexed by 'o' and 'p' order
- vertex 0 is the 'vertex-at-infinity'
- vertex 1 is the first Voronoi vertex
-
- see:
- qh_printvoronoi()
- qh_eachvoronoi_all()
-
- notes:
- if all facets are upperdelaunay,
- prints upper hull (furthest-site Voronoi diagram)
-*/
-void qh_printvdiagram (FILE *fp, int format, facetT *facetlist, setT *facets, boolT printall) {
- setT *vertices;
- int totcount, numcenters;
- boolT islower;
- qh_RIDGE innerouter= qh_RIDGEall;
- printvridgeT printvridge= NULL;
-
- if (format == qh_PRINTvertices) {
- innerouter= qh_RIDGEall;
- printvridge= qh_printvridge;
- }else if (format == qh_PRINTinner) {
- innerouter= qh_RIDGEinner;
- printvridge= qh_printvnorm;
- }else if (format == qh_PRINTouter) {
- innerouter= qh_RIDGEouter;
- printvridge= qh_printvnorm;
- }else {
- fprintf(qh ferr, "qh_printvdiagram: unknown print format %d.\n", format);
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- vertices= qh_markvoronoi (facetlist, facets, printall, &islower, &numcenters);
- totcount= qh_printvdiagram2 (NULL, NULL, vertices, innerouter, False);
- fprintf (fp, "%d\n", totcount);
- totcount= qh_printvdiagram2 (fp, printvridge, vertices, innerouter, True /* inorder*/);
- qh_settempfree (&vertices);
-#if 0 /* for testing qh_eachvoronoi_all */
- fprintf (fp, "\n");
- totcount= qh_eachvoronoi_all(fp, printvridge, qh UPPERdelaunay, innerouter, True /* inorder*/);
- fprintf (fp, "%d\n", totcount);
-#endif
-} /* printvdiagram */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printvdiagram2">-</a>
-
- qh_printvdiagram2( fp, printvridge, vertices, innerouter, inorder )
- visit all pairs of input sites (vertices) for selected Voronoi vertices
- vertices may include NULLs
-
- innerouter:
- qh_RIDGEall print inner ridges (bounded) and outer ridges (unbounded)
- qh_RIDGEinner print only inner ridges
- qh_RIDGEouter print only outer ridges
-
- inorder:
- print 3-d Voronoi vertices in order
-
- assumes:
- qh_markvoronoi marked facet->visitid for Voronoi vertices
- all facet->seen= False
- all facet->seen2= True
-
- returns:
- total number of Voronoi ridges
- if printvridge,
- calls printvridge( fp, vertex, vertexA, centers) for each ridge
- [see qh_eachvoronoi()]
-
- see:
- qh_eachvoronoi_all()
-*/
-int qh_printvdiagram2 (FILE *fp, printvridgeT printvridge, setT *vertices, qh_RIDGE innerouter, boolT inorder) {
- int totcount= 0;
- int vertex_i, vertex_n;
- vertexT *vertex;
-
- FORALLvertices
- vertex->seen= False;
- FOREACHvertex_i_(vertices) {
- if (vertex) {
- if (qh GOODvertex > 0 && qh_pointid(vertex->point)+1 != qh GOODvertex)
- continue;
- totcount += qh_eachvoronoi (fp, printvridge, vertex, !qh_ALL, innerouter, inorder);
- }
- }
- return totcount;
-} /* printvdiagram2 */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printvertex">-</a>
-
- qh_printvertex( fp, vertex )
- prints the information in a vertex
-*/
-void qh_printvertex(FILE *fp, vertexT *vertex) {
- pointT *point;
- int k, count= 0;
- facetT *neighbor, **neighborp;
- realT r; /*bug fix*/
-
- if (!vertex) {
- fprintf (fp, " NULLvertex\n");
- return;
- }
- fprintf(fp, "- p%d (v%d):", qh_pointid(vertex->point), vertex->id);
- point= vertex->point;
- if (point) {
- for(k= qh hull_dim; k--; ) {
- r= *point++;
- fprintf(fp, " %5.2g", r);
- }
- }
- if (vertex->deleted)
- fprintf(fp, " deleted");
- if (vertex->delridge)
- fprintf (fp, " ridgedeleted");
- fprintf(fp, "\n");
- if (vertex->neighbors) {
- fprintf(fp, " neighbors:");
- FOREACHneighbor_(vertex) {
- if (++count % 100 == 0)
- fprintf (fp, "\n ");
- fprintf(fp, " f%d", neighbor->id);
- }
- fprintf(fp, "\n");
- }
-} /* printvertex */
-
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printvertexlist">-</a>
-
- qh_printvertexlist( fp, string, facetlist, facets, printall )
- prints vertices used by a facetlist or facet set
- tests qh_skipfacet() if !printall
-*/
-void qh_printvertexlist (FILE *fp, char* string, facetT *facetlist,
- setT *facets, boolT printall) {
- vertexT *vertex, **vertexp;
- setT *vertices;
-
- vertices= qh_facetvertices (facetlist, facets, printall);
- fputs (string, fp);
- FOREACHvertex_(vertices)
- qh_printvertex(fp, vertex);
- qh_settempfree (&vertices);
-} /* printvertexlist */
-
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printvertices">-</a>
-
- qh_printvertices( fp, string, vertices )
- prints vertices in a set
-*/
-void qh_printvertices(FILE *fp, char* string, setT *vertices) {
- vertexT *vertex, **vertexp;
-
- fputs (string, fp);
- FOREACHvertex_(vertices)
- fprintf (fp, " p%d (v%d)", qh_pointid(vertex->point), vertex->id);
- fprintf(fp, "\n");
-} /* printvertices */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printvneighbors">-</a>
-
- qh_printvneighbors( fp, facetlist, facets, printall )
- print vertex neighbors of vertices in facetlist and facets ('FN')
-
- notes:
- qh_countfacets clears facet->visitid for non-printed facets
-
- design:
- collect facet count and related statistics
- if necessary, build neighbor sets for each vertex
- collect vertices in facetlist and facets
- build a point array for point->vertex and point->coplanar facet
- for each point
- list vertex neighbors or coplanar facet
-*/
-void qh_printvneighbors (FILE *fp, facetT* facetlist, setT *facets, boolT printall) {
- int numfacets, numsimplicial, numridges, totneighbors, numneighbors, numcoplanars, numtricoplanars;
- setT *vertices, *vertex_points, *coplanar_points;
- int numpoints= qh num_points + qh_setsize (qh other_points);
- vertexT *vertex, **vertexp;
- int vertex_i, vertex_n;
- facetT *facet, **facetp, *neighbor, **neighborp;
- pointT *point, **pointp;
-
- qh_countfacets (facetlist, facets, printall, &numfacets, &numsimplicial,
- &totneighbors, &numridges, &numcoplanars, &numtricoplanars); /* sets facet->visitid */
- fprintf (fp, "%d\n", numpoints);
- qh_vertexneighbors();
- vertices= qh_facetvertices (facetlist, facets, printall);
- vertex_points= qh_settemp (numpoints);
- coplanar_points= qh_settemp (numpoints);
- qh_setzero (vertex_points, 0, numpoints);
- qh_setzero (coplanar_points, 0, numpoints);
- FOREACHvertex_(vertices)
- qh_point_add (vertex_points, vertex->point, vertex);
- FORALLfacet_(facetlist) {
- FOREACHpoint_(facet->coplanarset)
- qh_point_add (coplanar_points, point, facet);
- }
- FOREACHfacet_(facets) {
- FOREACHpoint_(facet->coplanarset)
- qh_point_add (coplanar_points, point, facet);
- }
- FOREACHvertex_i_(vertex_points) {
- if (vertex) {
- numneighbors= qh_setsize (vertex->neighbors);
- fprintf (fp, "%d", numneighbors);
- if (qh hull_dim == 3)
- qh_order_vertexneighbors (vertex);
- else if (qh hull_dim >= 4)
- qsort (SETaddr_(vertex->neighbors, facetT), numneighbors,
- sizeof (facetT *), qh_compare_facetvisit);
- FOREACHneighbor_(vertex)
- fprintf (fp, " %d",
- neighbor->visitid ? neighbor->visitid - 1 : - neighbor->id);
- fprintf (fp, "\n");
- }else if ((facet= SETelemt_(coplanar_points, vertex_i, facetT)))
- fprintf (fp, "1 %d\n",
- facet->visitid ? facet->visitid - 1 : - facet->id);
- else
- fprintf (fp, "0\n");
- }
- qh_settempfree (&coplanar_points);
- qh_settempfree (&vertex_points);
- qh_settempfree (&vertices);
-} /* printvneighbors */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printvoronoi">-</a>
-
- qh_printvoronoi( fp, format, facetlist, facets, printall )
- print voronoi diagram in 'o' or 'G' format
- for 'o' format
- prints voronoi centers for each facet and for infinity
- for each vertex, lists ids of printed facets or infinity
- assumes facetlist and facets are disjoint
- for 'G' format
- prints an OFF object
- adds a 0 coordinate to center
- prints infinity but does not list in vertices
-
- see:
- qh_printvdiagram()
-
- notes:
- if 'o',
- prints a line for each point except "at-infinity"
- if all facets are upperdelaunay,
- reverses lower and upper hull
-*/
-void qh_printvoronoi (FILE *fp, int format, facetT *facetlist, setT *facets, boolT printall) {
- int k, numcenters, numvertices= 0, numneighbors, numinf, vid=1, vertex_i, vertex_n;
- facetT *facet, **facetp, *neighbor, **neighborp;
- setT *vertices;
- vertexT *vertex;
- boolT islower;
- unsigned int numfacets= (unsigned int) qh num_facets;
-
- vertices= qh_markvoronoi (facetlist, facets, printall, &islower, &numcenters);
- FOREACHvertex_i_(vertices) {
- if (vertex) {
- numvertices++;
- numneighbors = numinf = 0;
- FOREACHneighbor_(vertex) {
- if (neighbor->visitid == 0)
- numinf= 1;
- else if (neighbor->visitid < numfacets)
- numneighbors++;
- }
- if (numinf && !numneighbors) {
- SETelem_(vertices, vertex_i)= NULL;
- numvertices--;
- }
- }
- }
- if (format == qh_PRINTgeom)
- fprintf (fp, "{appearance {+edge -face} OFF %d %d 1 # Voronoi centers and cells\n",
- numcenters, numvertices);
- else
- fprintf (fp, "%d\n%d %d 1\n", qh hull_dim-1, numcenters, qh_setsize(vertices));
- if (format == qh_PRINTgeom) {
- for (k= qh hull_dim-1; k--; )
- fprintf (fp, qh_REAL_1, 0.0);
- fprintf (fp, " 0 # infinity not used\n");
- }else {
- for (k= qh hull_dim-1; k--; )
- fprintf (fp, qh_REAL_1, qh_INFINITE);
- fprintf (fp, "\n");
- }
- FORALLfacet_(facetlist) {
- if (facet->visitid && facet->visitid < numfacets) {
- if (format == qh_PRINTgeom)
- fprintf (fp, "# %d f%d\n", vid++, facet->id);
- qh_printcenter (fp, format, NULL, facet);
- }
- }
- FOREACHfacet_(facets) {
- if (facet->visitid && facet->visitid < numfacets) {
- if (format == qh_PRINTgeom)
- fprintf (fp, "# %d f%d\n", vid++, facet->id);
- qh_printcenter (fp, format, NULL, facet);
- }
- }
- FOREACHvertex_i_(vertices) {
- numneighbors= 0;
- numinf=0;
- if (vertex) {
- if (qh hull_dim == 3)
- qh_order_vertexneighbors(vertex);
- else if (qh hull_dim >= 4)
- qsort (SETaddr_(vertex->neighbors, vertexT),
- qh_setsize (vertex->neighbors),
- sizeof (facetT *), qh_compare_facetvisit);
- FOREACHneighbor_(vertex) {
- if (neighbor->visitid == 0)
- numinf= 1;
- else if (neighbor->visitid < numfacets)
- numneighbors++;
- }
- }
- if (format == qh_PRINTgeom) {
- if (vertex) {
- fprintf (fp, "%d", numneighbors);
- if (vertex) {
- FOREACHneighbor_(vertex) {
- if (neighbor->visitid && neighbor->visitid < numfacets)
- fprintf (fp, " %d", neighbor->visitid);
- }
- }
- fprintf (fp, " # p%d (v%d)\n", vertex_i, vertex->id);
- }else
- fprintf (fp, " # p%d is coplanar or isolated\n", vertex_i);
- }else {
- if (numinf)
- numneighbors++;
- fprintf (fp, "%d", numneighbors);
- if (vertex) {
- FOREACHneighbor_(vertex) {
- if (neighbor->visitid == 0) {
- if (numinf) {
- numinf= 0;
- fprintf (fp, " %d", neighbor->visitid);
- }
- }else if (neighbor->visitid < numfacets)
- fprintf (fp, " %d", neighbor->visitid);
- }
- }
- fprintf (fp, "\n");
- }
- }
- if (format == qh_PRINTgeom)
- fprintf (fp, "}\n");
- qh_settempfree (&vertices);
-} /* printvoronoi */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printvnorm">-</a>
-
- qh_printvnorm( fp, vertex, vertexA, centers, unbounded )
- print one separating plane of the Voronoi diagram for a pair of input sites
- unbounded==True if centers includes vertex-at-infinity
-
- assumes:
- qh_ASvoronoi and qh_vertexneighbors() already set
-
- see:
- qh_printvdiagram()
- qh_eachvoronoi()
-*/
-void qh_printvnorm (FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded) {
- pointT *normal;
- realT offset;
- int k;
-
- normal= qh_detvnorm (vertex, vertexA, centers, &offset);
- fprintf (fp, "%d %d %d ",
- 2+qh hull_dim, qh_pointid (vertex->point), qh_pointid (vertexA->point));
- for (k= 0; k< qh hull_dim-1; k++)
- fprintf (fp, qh_REAL_1, normal[k]);
- fprintf (fp, qh_REAL_1, offset);
- fprintf (fp, "\n");
-} /* printvnorm */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="printvridge">-</a>
-
- qh_printvridge( fp, vertex, vertexA, centers, unbounded )
- print one ridge of the Voronoi diagram for a pair of input sites
- unbounded==True if centers includes vertex-at-infinity
-
- see:
- qh_printvdiagram()
-
- notes:
- the user may use a different function
-*/
-void qh_printvridge (FILE *fp, vertexT *vertex, vertexT *vertexA, setT *centers, boolT unbounded) {
- facetT *facet, **facetp;
-
- fprintf (fp, "%d %d %d", qh_setsize (centers)+2,
- qh_pointid (vertex->point), qh_pointid (vertexA->point));
- FOREACHfacet_(centers)
- fprintf (fp, " %d", facet->visitid);
- fprintf (fp, "\n");
-} /* printvridge */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="projectdim3">-</a>
-
- qh_projectdim3( source, destination )
- project 2-d 3-d or 4-d point to a 3-d point
- uses qh.DROPdim and qh.hull_dim
- source and destination may be the same
-
- notes:
- allocate 4 elements to destination just in case
-*/
-void qh_projectdim3 (pointT *source, pointT *destination) {
- int i,k;
-
- for (k= 0, i=0; k < qh hull_dim; k++) {
- if (qh hull_dim == 4) {
- if (k != qh DROPdim)
- destination[i++]= source[k];
- }else if (k == qh DROPdim)
- destination[i++]= 0;
- else
- destination[i++]= source[k];
- }
- while (i < 3)
- destination[i++]= 0.0;
-} /* projectdim3 */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="readfeasible">-</a>
-
- qh_readfeasible( dim, remainder )
- read feasible point from remainder string and qh.fin
-
- returns:
- number of lines read from qh.fin
- sets qh.FEASIBLEpoint with malloc'd coordinates
-
- notes:
- checks for qh.HALFspace
- assumes dim > 1
-
- see:
- qh_setfeasible
-*/
-int qh_readfeasible (int dim, char *remainder) {
- boolT isfirst= True;
- int linecount= 0, tokcount= 0;
- char *s, *t, firstline[qh_MAXfirst+1];
- coordT *coords, value;
-
- if (!qh HALFspace) {
- fprintf (qh ferr, "qhull input error: feasible point (dim 1 coords) is only valid for halfspace intersection\n");
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- if (qh feasible_string)
- fprintf (qh ferr, "qhull input warning: feasible point (dim 1 coords) overrides 'Hn,n,n' feasible point for halfspace intersection\n");
- if (!(qh feasible_point= (coordT*)malloc (dim* sizeof(coordT)))) {
- fprintf(qh ferr, "qhull error: insufficient memory for feasible point\n");
- qh_errexit(qh_ERRmem, NULL, NULL);
- }
- coords= qh feasible_point;
- while ((s= (isfirst ? remainder : fgets(firstline, qh_MAXfirst, qh fin)))) {
- if (isfirst)
- isfirst= False;
- else
- linecount++;
- while (*s) {
- while (isspace(*s))
- s++;
- value= qh_strtod (s, &t);
- if (s == t)
- break;
- s= t;
- *(coords++)= value;
- if (++tokcount == dim) {
- while (isspace (*s))
- s++;
- qh_strtod (s, &t);
- if (s != t) {
- fprintf (qh ferr, "qhull input error: coordinates for feasible point do not finish out the line: %s\n",
- s);
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- return linecount;
- }
- }
- }
- fprintf (qh ferr, "qhull input error: only %d coordinates. Could not read %d-d feasible point.\n",
- tokcount, dim);
- qh_errexit (qh_ERRinput, NULL, NULL);
- return 0;
-} /* readfeasible */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="readpoints">-</a>
-
- qh_readpoints( numpoints, dimension, ismalloc )
- read points from qh.fin into qh.first_point, qh.num_points
- qh.fin is lines of coordinates, one per vertex, first line number of points
- if 'rbox D4',
- gives message
- if qh.ATinfinity,
- adds point-at-infinity for Delaunay triangulations
-
- returns:
- number of points, array of point coordinates, dimension, ismalloc True
- if qh.DELAUNAY & !qh.PROJECTinput, projects points to paraboloid
- and clears qh.PROJECTdelaunay
- if qh.HALFspace, reads optional feasible point, reads halfspaces,
- converts to dual.
-
- for feasible point in "cdd format" in 3-d:
- 3 1
- coordinates
- comments
- begin
- n 4 real/integer
- ...
- end
-
- notes:
- dimension will change in qh_initqhull_globals if qh.PROJECTinput
- uses malloc() since qh_mem not initialized
- FIXUP: this routine needs rewriting
-*/
-coordT *qh_readpoints(int *numpoints, int *dimension, boolT *ismalloc) {
- coordT *points, *coords, *infinity= NULL;
- realT paraboloid, maxboloid= -REALmax, value;
- realT *coordp= NULL, *offsetp= NULL, *normalp= NULL;
- char *s, *t, firstline[qh_MAXfirst+1];
- int diminput=0, numinput=0, dimfeasible= 0, newnum, k, tempi;
- int firsttext=0, firstshort=0, firstlong=0, firstpoint=0;
- int tokcount= 0, linecount=0, maxcount, coordcount=0;
- boolT islong, isfirst= True, wasbegin= False;
- boolT isdelaunay= qh DELAUNAY && !qh PROJECTinput;
-
- if (qh CDDinput) {
- while ((s= fgets(firstline, qh_MAXfirst, qh fin))) {
- linecount++;
- if (qh HALFspace && linecount == 1 && isdigit(*s)) {
- dimfeasible= qh_strtol (s, &s);
- while (isspace(*s))
- s++;
- if (qh_strtol (s, &s) == 1)
- linecount += qh_readfeasible (dimfeasible, s);
- else
- dimfeasible= 0;
- }else if (!memcmp (firstline, "begin", 5) || !memcmp (firstline, "BEGIN", 5))
- break;
- else if (!*qh rbox_command)
- strncat(qh rbox_command, s, sizeof (qh rbox_command)-1);
- }
- if (!s) {
- fprintf (qh ferr, "qhull input error: missing \"begin\" for cdd-formated input\n");
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- }
- while(!numinput && (s= fgets(firstline, qh_MAXfirst, qh fin))) {
- linecount++;
- if (!memcmp (s, "begin", 5) || !memcmp (s, "BEGIN", 5))
- wasbegin= True;
- while (*s) {
- while (isspace(*s))
- s++;
- if (!*s)
- break;
- if (!isdigit(*s)) {
- if (!*qh rbox_command) {
- strncat(qh rbox_command, s, sizeof (qh rbox_command)-1);
- firsttext= linecount;
- }
- break;
- }
- if (!diminput)
- diminput= qh_strtol (s, &s);
- else {
- numinput= qh_strtol (s, &s);
- if (numinput == 1 && diminput >= 2 && qh HALFspace && !qh CDDinput) {
- linecount += qh_readfeasible (diminput, s); /* checks if ok */
- dimfeasible= diminput;
- diminput= numinput= 0;
- }else
- break;
- }
- }
- }
- if (!s) {
- fprintf(qh ferr, "qhull input error: short input file. Did not find dimension and number of points\n");
- qh_errexit(qh_ERRinput, NULL, NULL);
- }
- if (diminput > numinput) {
- tempi= diminput; /* exchange dim and n, e.g., for cdd input format */
- diminput= numinput;
- numinput= tempi;
- }
- if (diminput < 2) {
- fprintf(qh ferr,"qhull input error: dimension %d (first number) should be at least 2\n",
- diminput);
- qh_errexit(qh_ERRinput, NULL, NULL);
- }
- if (isdelaunay) {
- qh PROJECTdelaunay= False;
- if (qh CDDinput)
- *dimension= diminput;
- else
- *dimension= diminput+1;
- *numpoints= numinput;
- if (qh ATinfinity)
- (*numpoints)++;
- }else if (qh HALFspace) {
- *dimension= diminput - 1;
- *numpoints= numinput;
- if (diminput < 3) {
- fprintf(qh ferr,"qhull input error: dimension %d (first number, includes offset) should be at least 3 for halfspaces\n",
- diminput);
- qh_errexit(qh_ERRinput, NULL, NULL);
- }
- if (dimfeasible) {
- if (dimfeasible != *dimension) {
- fprintf(qh ferr,"qhull input error: dimension %d of feasible point is not one less than dimension %d for halfspaces\n",
- dimfeasible, diminput);
- qh_errexit(qh_ERRinput, NULL, NULL);
- }
- }else
- qh_setfeasible (*dimension);
- }else {
- if (qh CDDinput)
- *dimension= diminput-1;
- else
- *dimension= diminput;
- *numpoints= numinput;
- }
- qh normal_size= *dimension * sizeof(coordT); /* for tracing with qh_printpoint */
- if (qh HALFspace) {
- qh half_space= coordp= (coordT*) malloc (qh normal_size + sizeof(coordT));
- if (qh CDDinput) {
- offsetp= qh half_space;
- normalp= offsetp + 1;
- }else {
- normalp= qh half_space;
- offsetp= normalp + *dimension;
- }
- }
- qh maxline= diminput * (qh_REALdigits + 5);
- maximize_(qh maxline, 500);
- qh line= (char*)malloc ((qh maxline+1) * sizeof (char));
- *ismalloc= True; /* use malloc since memory not setup */
- coords= points= qh temp_malloc=
- (coordT*)malloc((*numpoints)*(*dimension)*sizeof(coordT));
- if (!coords || !qh line || (qh HALFspace && !qh half_space)) {
- fprintf(qh ferr, "qhull error: insufficient memory to read %d points\n",
- numinput);
- qh_errexit(qh_ERRmem, NULL, NULL);
- }
- if (isdelaunay && qh ATinfinity) {
- infinity= points + numinput * (*dimension);
- for (k= (*dimension) - 1; k--; )
- infinity[k]= 0.0;
- }
- maxcount= numinput * diminput;
- paraboloid= 0.0;
- while ((s= (isfirst ? s : fgets(qh line, qh maxline, qh fin)))) {
- if (!isfirst) {
- linecount++;
- if (*s == 'e' || *s == 'E') {
- if (!memcmp (s, "end", 3) || !memcmp (s, "END", 3)) {
- if (qh CDDinput )
- break;
- else if (wasbegin)
- fprintf (qh ferr, "qhull input warning: the input appears to be in cdd format. If so, use 'Fd'\n");
- }
- }
- }
- islong= False;
- while (*s) {
- while (isspace(*s))
- s++;
- value= qh_strtod (s, &t);
- if (s == t) {
- if (!*qh rbox_command)
- strncat(qh rbox_command, s, sizeof (qh rbox_command)-1);
- if (*s && !firsttext)
- firsttext= linecount;
- if (!islong && !firstshort && coordcount)
- firstshort= linecount;
- break;
- }
- if (!firstpoint)
- firstpoint= linecount;
- s= t;
- if (++tokcount > maxcount)
- continue;
- if (qh HALFspace) {
- if (qh CDDinput)
- *(coordp++)= -value; /* both coefficients and offset */
- else
- *(coordp++)= value;
- }else {
- *(coords++)= value;
- if (qh CDDinput && !coordcount) {
- if (value != 1.0) {
- fprintf (qh ferr, "qhull input error: for cdd format, point at line %d does not start with '1'\n",
- linecount);
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- coords--;
- }else if (isdelaunay) {
- paraboloid += value * value;
- if (qh ATinfinity) {
- if (qh CDDinput)
- infinity[coordcount-1] += value;
- else
- infinity[coordcount] += value;
- }
- }
- }
- if (++coordcount == diminput) {
- coordcount= 0;
- if (isdelaunay) {
- *(coords++)= paraboloid;
- maximize_(maxboloid, paraboloid);
- paraboloid= 0.0;
- }else if (qh HALFspace) {
- if (!qh_sethalfspace (*dimension, coords, &coords, normalp, offsetp, qh feasible_point)) {
- fprintf (qh ferr, "The halfspace was on line %d\n", linecount);
- if (wasbegin)
- fprintf (qh ferr, "The input appears to be in cdd format. If so, you should use option 'Fd'\n");
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- coordp= qh half_space;
- }
- while (isspace(*s))
- s++;
- if (*s) {
- islong= True;
- if (!firstlong)
- firstlong= linecount;
- }
- }
- }
- if (!islong && !firstshort && coordcount)
- firstshort= linecount;
- if (!isfirst && s - qh line >= qh maxline) {
- fprintf(qh ferr, "qhull input error: line %d contained more than %d characters\n",
- linecount, (int) (s - qh line));
- qh_errexit(qh_ERRinput, NULL, NULL);
- }
- isfirst= False;
- }
- if (tokcount != maxcount) {
- newnum= fmin_(numinput, tokcount/diminput);
- fprintf(qh ferr,"\
-qhull warning: instead of %d %d-dimensional points, input contains\n\
-%d points and %d extra coordinates. Line %d is the first\npoint",
- numinput, diminput, tokcount/diminput, tokcount % diminput, firstpoint);
- if (firsttext)
- fprintf(qh ferr, ", line %d is the first comment", firsttext);
- if (firstshort)
- fprintf(qh ferr, ", line %d is the first short\nline", firstshort);
- if (firstlong)
- fprintf(qh ferr, ", line %d is the first long line", firstlong);
- fprintf(qh ferr, ". Continue with %d points.\n", newnum);
- numinput= newnum;
- if (isdelaunay && qh ATinfinity) {
- for (k= tokcount % diminput; k--; )
- infinity[k] -= *(--coords);
- *numpoints= newnum+1;
- }else {
- coords -= tokcount % diminput;
- *numpoints= newnum;
- }
- }
- if (isdelaunay && qh ATinfinity) {
- for (k= (*dimension) -1; k--; )
- infinity[k] /= numinput;
- if (coords == infinity)
- coords += (*dimension) -1;
- else {
- for (k= 0; k < (*dimension) -1; k++)
- *(coords++)= infinity[k];
- }
- *(coords++)= maxboloid * 1.1;
- }
- if (qh rbox_command[0]) {
- qh rbox_command[strlen(qh rbox_command)-1]= '\0';
- if (!strcmp (qh rbox_command, "./rbox D4"))
- fprintf (qh ferr, "\n\
-This is the qhull test case. If any errors or core dumps occur,\n\
-recompile qhull with 'make new'. If errors still occur, there is\n\
-an incompatibility. You should try a different compiler. You can also\n\
-change the choices in user.h. If you discover the source of the problem,\n\
-please send mail to qhull_bug@qhull.org.\n\
-\n\
-Type 'qhull' for a short list of options.\n");
- }
- free (qh line);
- qh line= NULL;
- if (qh half_space) {
- free (qh half_space);
- qh half_space= NULL;
- }
- qh temp_malloc= NULL;
- trace1((qh ferr,"qh_readpoints: read in %d %d-dimensional points\n",
- numinput, diminput));
- return(points);
-} /* readpoints */
-
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="setfeasible">-</a>
-
- qh_setfeasible( dim )
- set qh.FEASIBLEpoint from qh.feasible_string in "n,n,n" or "n n n" format
-
- notes:
- "n,n,n" already checked by qh_initflags()
- see qh_readfeasible()
-*/
-void qh_setfeasible (int dim) {
- int tokcount= 0;
- char *s;
- coordT *coords, value;
-
- if (!(s= qh feasible_string)) {
- fprintf(qh ferr, "\
-qhull input error: halfspace intersection needs a feasible point.\n\
-Either prepend the input with 1 point or use 'Hn,n,n'. See manual.\n");
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- if (!(qh feasible_point= (pointT*)malloc (dim* sizeof(coordT)))) {
- fprintf(qh ferr, "qhull error: insufficient memory for 'Hn,n,n'\n");
- qh_errexit(qh_ERRmem, NULL, NULL);
- }
- coords= qh feasible_point;
- while (*s) {
- value= qh_strtod (s, &s);
- if (++tokcount > dim) {
- fprintf (qh ferr, "qhull input warning: more coordinates for 'H%s' than dimension %d\n",
- qh feasible_string, dim);
- break;
- }
- *(coords++)= value;
- if (*s)
- s++;
- }
- while (++tokcount <= dim)
- *(coords++)= 0.0;
-} /* setfeasible */
-
-/*-<a href="qh-io.htm#TOC"
- >-------------------------------</a><a name="skipfacet">-</a>
-
- qh_skipfacet( facet )
- returns 'True' if this facet is not to be printed
-
- notes:
- based on the user provided slice thresholds and 'good' specifications
-*/
-boolT qh_skipfacet(facetT *facet) {
- facetT *neighbor, **neighborp;
-
- if (qh PRINTneighbors) {
- if (facet->good)
- return !qh PRINTgood;
- FOREACHneighbor_(facet) {
- if (neighbor->good)
- return False;
- }
- return True;
- }else if (qh PRINTgood)
- return !facet->good;
- else if (!facet->normal)
- return True;
- return (!qh_inthresholds (facet->normal, NULL));
-} /* skipfacet */
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/io.h b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/io.h
deleted file mode 100644
index a2ca04499c442309eeddfeb3ad4557af40f3b707..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/io.h
+++ /dev/null
@@ -1,154 +0,0 @@
-/*<html><pre> -<a href="qh-io.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- io.h
- declarations of Input/Output functions
-
- see README, qhull.h and io.c
-
- copyright (c) 1993-2003, The Geometry Center
-*/
-
-#ifndef qhDEFio
-#define qhDEFio 1
-
-/*============ constants and flags ==================*/
-
-/*-<a href="qh-io.htm#TOC"
- >--------------------------------</a><a name="qh_MAXfirst">-</a>
-
- qh_MAXfirst
- maximum length of first two lines of stdin
-*/
-#define qh_MAXfirst 200
-
-/*-<a href="qh-io.htm#TOC"
- >--------------------------------</a><a name="qh_MINradius">-</a>
-
- qh_MINradius
- min radius for Gp and Gv, fraction of maxcoord
-*/
-#define qh_MINradius 0.02
-
-/*-<a href="qh-io.htm#TOC"
- >--------------------------------</a><a name="qh_GEOMepsilon">-</a>
-
- qh_GEOMepsilon
- adjust outer planes for 'lines closer' and geomview roundoff.
- This prevents bleed through.
-*/
-#define qh_GEOMepsilon 2e-3
-
-/*-<a href="qh-io.htm#TOC"
- >--------------------------------</a><a name="qh_WHITESPACE">-</a>
-
- qh_WHITESPACE
- possible values of white space
-*/
-#define qh_WHITESPACE " \n\t\v\r\f"
-
-
-/*-<a href="qh-io.htm#TOC"
- >--------------------------------</a><a name="RIDGE">-</a>
-
- qh_RIDGE
- to select which ridges to print in qh_eachvoronoi
-*/
-typedef enum
-{
- qh_RIDGEall = 0, qh_RIDGEinner, qh_RIDGEouter
-}
-qh_RIDGE;
-
-/*-<a href="qh-io.htm#TOC"
- >--------------------------------</a><a name="printvridgeT">-</a>
-
- printvridgeT
- prints results of qh_printvdiagram
-
- see:
- <a href="io.c#printvridge">qh_printvridge</a> for an example
-*/
-typedef void (*printvridgeT)(FILE* fp, vertexT* vertex, vertexT* vertexA, setT* centers, boolT unbounded);
-
-/*============== -prototypes in alphabetical order =========*/
-
-void dfacet(unsigned id);
-void dvertex(unsigned id);
-int qh_compare_facetarea(const void* p1, const void* p2);
-int qh_compare_facetmerge(const void* p1, const void* p2);
-int qh_compare_facetvisit(const void* p1, const void* p2);
-int qh_compare_vertexpoint(const void* p1, const void* p2); /* not used */
-
-void qh_countfacets(facetT* facetlist, setT* facets, boolT printall,
- int* numfacetsp, int* numsimplicialp, int* totneighborsp,
- int* numridgesp, int* numcoplanarsp, int* numnumtricoplanarsp);
-pointT* qh_detvnorm(vertexT* vertex, vertexT* vertexA, setT* centers, realT* offsetp);
-setT* qh_detvridge(vertexT* vertex);
-setT* qh_detvridge3(vertexT* atvertex, vertexT* vertex);
-int qh_eachvoronoi(FILE* fp, printvridgeT printvridge, vertexT* atvertex, boolT visitall, qh_RIDGE innerouter, boolT inorder);
-int qh_eachvoronoi_all(FILE* fp, printvridgeT printvridge, boolT isupper, qh_RIDGE innerouter, boolT inorder);
-void qh_facet2point(facetT* facet, pointT** point0, pointT** point1, realT* mindist);
-setT* qh_facetvertices(facetT* facetlist, setT* facets, boolT allfacets);
-void qh_geomplanes(facetT* facet, realT* outerplane, realT* innerplane);
-void qh_markkeep(facetT* facetlist);
-setT* qh_markvoronoi(facetT* facetlist, setT* facets, boolT printall, boolT* islowerp, int* numcentersp);
-void qh_order_vertexneighbors(vertexT* vertex);
-void qh_printafacet(FILE* fp, int format, facetT* facet, boolT printall);
-void qh_printbegin(FILE* fp, int format, facetT* facetlist, setT* facets, boolT printall);
-void qh_printcenter(FILE* fp, int format, char* string, facetT* facet);
-void qh_printcentrum(FILE* fp, facetT* facet, realT radius);
-void qh_printend(FILE* fp, int format, facetT* facetlist, setT* facets, boolT printall);
-void qh_printend4geom(FILE* fp, facetT* facet, int* num, boolT printall);
-void qh_printextremes(FILE* fp, facetT* facetlist, setT* facets, int printall);
-void qh_printextremes_2d(FILE* fp, facetT* facetlist, setT* facets, int printall);
-void qh_printextremes_d(FILE* fp, facetT* facetlist, setT* facets, int printall);
-void qh_printfacet(FILE* fp, facetT* facet);
-void qh_printfacet2math(FILE* fp, facetT* facet, int format, int notfirst);
-void qh_printfacet2geom(FILE* fp, facetT* facet, realT color[3]);
-void qh_printfacet2geom_points(FILE* fp, pointT* point1, pointT* point2,
- facetT* facet, realT offset, realT color[3]);
-void qh_printfacet3math(FILE* fp, facetT* facet, int format, int notfirst);
-void qh_printfacet3geom_nonsimplicial(FILE* fp, facetT* facet, realT color[3]);
-void qh_printfacet3geom_points(FILE* fp, setT* points, facetT* facet, realT offset, realT color[3]);
-void qh_printfacet3geom_simplicial(FILE* fp, facetT* facet, realT color[3]);
-void qh_printfacet3vertex(FILE* fp, facetT* facet, int format);
-void qh_printfacet4geom_nonsimplicial(FILE* fp, facetT* facet, realT color[3]);
-void qh_printfacet4geom_simplicial(FILE* fp, facetT* facet, realT color[3]);
-void qh_printfacetNvertex_nonsimplicial(FILE* fp, facetT* facet, int id, int format);
-void qh_printfacetNvertex_simplicial(FILE* fp, facetT* facet, int format);
-void qh_printfacetheader(FILE* fp, facetT* facet);
-void qh_printfacetridges(FILE* fp, facetT* facet);
-void qh_printfacets(FILE* fp, int format, facetT* facetlist, setT* facets, boolT printall);
-void qh_printhelp_degenerate(FILE* fp);
-void qh_printhelp_singular(FILE* fp);
-void qh_printhyperplaneintersection(FILE* fp, facetT* facet1, facetT* facet2,
- setT* vertices, realT color[3]);
-void qh_printneighborhood(FILE* fp, int format, facetT* facetA, facetT* facetB, boolT printall);
-void qh_printline3geom(FILE* fp, pointT* pointA, pointT* pointB, realT color[3]);
-void qh_printpoint(FILE* fp, char* string, pointT* point);
-void qh_printpointid(FILE* fp, char* string, int dim, pointT* point, int id);
-void qh_printpoint3(FILE* fp, pointT* point);
-void qh_printpoints_out(FILE* fp, facetT* facetlist, setT* facets, int printall);
-void qh_printpointvect(FILE* fp, pointT* point, coordT* normal, pointT* center, realT radius, realT color[3]);
-void qh_printpointvect2(FILE* fp, pointT* point, coordT* normal, pointT* center, realT radius);
-void qh_printridge(FILE* fp, ridgeT* ridge);
-void qh_printspheres(FILE* fp, setT* vertices, realT radius);
-void qh_printvdiagram(FILE* fp, int format, facetT* facetlist, setT* facets, boolT printall);
-int qh_printvdiagram2(FILE* fp, printvridgeT printvridge, setT* vertices, qh_RIDGE innerouter, boolT inorder);
-void qh_printvertex(FILE* fp, vertexT* vertex);
-void qh_printvertexlist(FILE* fp, char* string, facetT* facetlist,
- setT* facets, boolT printall);
-void qh_printvertices(FILE* fp, char* string, setT* vertices);
-void qh_printvneighbors(FILE* fp, facetT* facetlist, setT* facets, boolT printall);
-void qh_printvoronoi(FILE* fp, int format, facetT* facetlist, setT* facets, boolT printall);
-void qh_printvnorm(FILE* fp, vertexT* vertex, vertexT* vertexA, setT* centers, boolT unbounded);
-void qh_printvridge(FILE* fp, vertexT* vertex, vertexT* vertexA, setT* centers, boolT unbounded);
-void qh_produce_output(void);
-void qh_projectdim3(pointT* source, pointT* destination);
-int qh_readfeasible(int dim, char* remainder);
-coordT* qh_readpoints(int* numpoints, int* dimension, boolT* ismalloc);
-void qh_setfeasible(int dim);
-boolT qh_skipfacet(facetT* facet);
-
-#endif /* qhDEFio */
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/mem.c b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/mem.c
deleted file mode 100644
index f7fdde46cd3ebb6532977f7d0a15be58bfb61815..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/mem.c
+++ /dev/null
@@ -1,452 +0,0 @@
-/*<html><pre> -<a href="qh-mem.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- mem.c
- memory management routines for qhull
-
- This is a standalone program.
-
- To initialize memory:
-
- qh_meminit (stderr);
- qh_meminitbuffers (qh IStracing, qh_MEMalign, 7, qh_MEMbufsize,qh_MEMinitbuf);
- qh_memsize(sizeof(facetT));
- qh_memsize(sizeof(facetT));
- ...
- qh_memsetup();
-
- To free up all memory buffers:
- qh_memfreeshort (&curlong, &totlong);
-
- if qh_NOmem,
- malloc/free is used instead of mem.c
-
- notes:
- uses Quickfit algorithm (freelists for commonly allocated sizes)
- assumes small sizes for freelists (it discards the tail of memory buffers)
-
- see:
- qh-mem.htm and mem.h
- global.c (qh_initbuffers) for an example of using mem.c
-
- copyright (c) 1993-2003 The Geometry Center
-*/
-
-#include <stdio.h>
-#include <stdlib.h>
-#include <string.h>
-#include "mem.h"
-
-#ifndef qhDEFqhull
-typedef struct ridgeT ridgeT;
-typedef struct facetT facetT;
-void qh_errexit(int exitcode, facetT *, ridgeT *);
-#endif
-
-/*============ -global data structure ==============
- see mem.h for definition
-*/
-
-qhmemT qhmem;
-/*= {0};
-/ * remove "= {0}" if this causes a compiler error */
-
-#ifndef qh_NOmem
-
-/*============= internal functions ==============*/
-
-static int qh_intcompare(const void *i, const void *j);
-
-/*========== functions in alphabetical order ======== */
-
-/*-<a href="qh-mem.htm#TOC"
- >-------------------------------</a><a name="intcompare">-</a>
-
- qh_intcompare( i, j )
- used by qsort and bsearch to compare two integers
-*/
-static int qh_intcompare(const void *i, const void *j) {
- return(*((int *)i) - *((int *)j));
-} /* intcompare */
-
-
-/*-<a href="qh-mem.htm#TOC"
- >--------------------------------</a><a name="memalloc">-</a>
-
- qh_memalloc( insize )
- returns object of insize bytes
- qhmem is the global memory structure
-
- returns:
- pointer to allocated memory
- errors if insufficient memory
-
- notes:
- use explicit type conversion to avoid type warnings on some compilers
- actual object may be larger than insize
- use qh_memalloc_() for inline code for quick allocations
- logs allocations if 'T5'
-
- design:
- if size < qhmem.LASTsize
- if qhmem.freelists[size] non-empty
- return first object on freelist
- else
- round up request to size of qhmem.freelists[size]
- allocate new allocation buffer if necessary
- allocate object from allocation buffer
- else
- allocate object with malloc()
-*/
-void *qh_memalloc(int insize) {
- void **freelistp, *newbuffer;
- int index, size;
- int outsize, bufsize;
- void *object;
-
- if ((unsigned) insize <= (unsigned) qhmem.LASTsize) {
- index= qhmem.indextable[insize];
- freelistp= qhmem.freelists+index;
- if ((object= *freelistp)) {
- qhmem.cntquick++;
- *freelistp= *((void **)*freelistp); /* replace freelist with next object */
- return (object);
- }else {
- outsize= qhmem.sizetable[index];
- qhmem.cntshort++;
- if (outsize > qhmem .freesize) {
- if (!qhmem.curbuffer)
- bufsize= qhmem.BUFinit;
- else
- bufsize= qhmem.BUFsize;
- qhmem.totshort += bufsize;
- if (!(newbuffer= malloc(bufsize))) {
- fprintf(qhmem.ferr, "qhull error (qh_memalloc): insufficient memory\n");
- qh_errexit(qhmem_ERRmem, NULL, NULL);
- }
- *((void **)newbuffer)= qhmem.curbuffer; /* prepend newbuffer to curbuffer
- list */
- qhmem.curbuffer= newbuffer;
- size= (sizeof(void **) + qhmem.ALIGNmask) & ~qhmem.ALIGNmask;
- qhmem.freemem= (void *)((char *)newbuffer+size);
- qhmem.freesize= bufsize - size;
- }
- object= qhmem.freemem;
- qhmem.freemem= (void *)((char *)qhmem.freemem + outsize);
- qhmem.freesize -= outsize;
- return object;
- }
- }else { /* long allocation */
- if (!qhmem.indextable) {
- fprintf (qhmem.ferr, "qhull internal error (qh_memalloc): qhmem has not been initialized.\n");
- qh_errexit(qhmem_ERRqhull, NULL, NULL);
- }
- outsize= insize;
- qhmem .cntlong++;
- qhmem .curlong++;
- qhmem .totlong += outsize;
- if (qhmem.maxlong < qhmem.totlong)
- qhmem.maxlong= qhmem.totlong;
- if (!(object= malloc(outsize))) {
- fprintf(qhmem.ferr, "qhull error (qh_memalloc): insufficient memory\n");
- qh_errexit(qhmem_ERRmem, NULL, NULL);
- }
- if (qhmem.IStracing >= 5)
- fprintf (qhmem.ferr, "qh_memalloc long: %d bytes at %p\n", outsize, object);
- }
- return (object);
-} /* memalloc */
-
-
-/*-<a href="qh-mem.htm#TOC"
- >--------------------------------</a><a name="memfree">-</a>
-
- qh_memfree( object, size )
- free up an object of size bytes
- size is insize from qh_memalloc
-
- notes:
- object may be NULL
- type checking warns if using (void **)object
- use qh_memfree_() for quick free's of small objects
-
- design:
- if size <= qhmem.LASTsize
- append object to corresponding freelist
- else
- call free(object)
-*/
-void qh_memfree(void *object, int size) {
- void **freelistp;
-
- if (!object)
- return;
- if (size <= qhmem.LASTsize) {
- qhmem .freeshort++;
- freelistp= qhmem.freelists + qhmem.indextable[size];
- *((void **)object)= *freelistp;
- *freelistp= object;
- }else {
- qhmem .freelong++;
- qhmem .totlong -= size;
- free (object);
- if (qhmem.IStracing >= 5)
- fprintf (qhmem.ferr, "qh_memfree long: %d bytes at %p\n", size, object);
- }
-} /* memfree */
-
-
-/*-<a href="qh-mem.htm#TOC"
- >-------------------------------</a><a name="memfreeshort">-</a>
-
- qh_memfreeshort( curlong, totlong )
- frees up all short and qhmem memory allocations
-
- returns:
- number and size of current long allocations
-*/
-void qh_memfreeshort (int *curlong, int *totlong) {
- void *buffer, *nextbuffer;
- FILE *ferr;
-
- *curlong= qhmem .cntlong - qhmem .freelong;
- *totlong= qhmem .totlong;
- for(buffer= qhmem.curbuffer; buffer; buffer= nextbuffer) {
- nextbuffer= *((void **) buffer);
- free(buffer);
- }
- qhmem.curbuffer= NULL;
- if (qhmem .LASTsize) {
- free (qhmem .indextable);
- free (qhmem .freelists);
- free (qhmem .sizetable);
- }
- ferr= qhmem.ferr;
- memset((char *)&qhmem, 0, sizeof qhmem); /* every field is 0, FALSE, NULL */
- qhmem.ferr= ferr;
-} /* memfreeshort */
-
-
-/*-<a href="qh-mem.htm#TOC"
- >--------------------------------</a><a name="meminit">-</a>
-
- qh_meminit( ferr )
- initialize qhmem and test sizeof( void*)
-*/
-void qh_meminit (FILE *ferr) {
-
- memset((char *)&qhmem, 0, sizeof qhmem); /* every field is 0, FALSE, NULL */
- qhmem.ferr= ferr;
- if (sizeof(void*) < sizeof(int)) {
- fprintf (ferr, "qhull internal error (qh_meminit): sizeof(void*) < sizeof(int). qset.c will not work\n");
- exit (1); /* can not use qh_errexit() */
- }
-} /* meminit */
-
-/*-<a href="qh-mem.htm#TOC"
- >-------------------------------</a><a name="meminitbuffers">-</a>
-
- qh_meminitbuffers( tracelevel, alignment, numsizes, bufsize, bufinit )
- initialize qhmem
- if tracelevel >= 5, trace memory allocations
- alignment= desired address alignment for memory allocations
- numsizes= number of freelists
- bufsize= size of additional memory buffers for short allocations
- bufinit= size of initial memory buffer for short allocations
-*/
-void qh_meminitbuffers (int tracelevel, int alignment, int numsizes, int bufsize, int bufinit) {
-
- qhmem.IStracing= tracelevel;
- qhmem.NUMsizes= numsizes;
- qhmem.BUFsize= bufsize;
- qhmem.BUFinit= bufinit;
- qhmem.ALIGNmask= alignment-1;
- if (qhmem.ALIGNmask & ~qhmem.ALIGNmask) {
- fprintf (qhmem.ferr, "qhull internal error (qh_meminit): memory alignment %d is not a power of 2\n", alignment);
- qh_errexit (qhmem_ERRqhull, NULL, NULL);
- }
- qhmem.sizetable= (int *) calloc (numsizes, sizeof(int));
- qhmem.freelists= (void **) calloc (numsizes, sizeof(void *));
- if (!qhmem.sizetable || !qhmem.freelists) {
- fprintf(qhmem.ferr, "qhull error (qh_meminit): insufficient memory\n");
- qh_errexit (qhmem_ERRmem, NULL, NULL);
- }
- if (qhmem.IStracing >= 1)
- fprintf (qhmem.ferr, "qh_meminitbuffers: memory initialized with alignment %d\n", alignment);
-} /* meminitbuffers */
-
-/*-<a href="qh-mem.htm#TOC"
- >-------------------------------</a><a name="memsetup">-</a>
-
- qh_memsetup()
- set up memory after running memsize()
-*/
-void qh_memsetup (void) {
- int k,i;
-
- qsort(qhmem.sizetable, qhmem.TABLEsize, sizeof(int), qh_intcompare);
- qhmem.LASTsize= qhmem.sizetable[qhmem.TABLEsize-1];
- if (qhmem .LASTsize >= qhmem .BUFsize || qhmem.LASTsize >= qhmem .BUFinit) {
- fprintf (qhmem.ferr, "qhull error (qh_memsetup): largest mem size %d is >= buffer size %d or initial buffer size %d\n",
- qhmem .LASTsize, qhmem .BUFsize, qhmem .BUFinit);
- qh_errexit(qhmem_ERRmem, NULL, NULL);
- }
- if (!(qhmem.indextable= (int *)malloc((qhmem.LASTsize+1) * sizeof(int)))) {
- fprintf(qhmem.ferr, "qhull error (qh_memsetup): insufficient memory\n");
- qh_errexit(qhmem_ERRmem, NULL, NULL);
- }
- for(k=qhmem.LASTsize+1; k--; )
- qhmem.indextable[k]= k;
- i= 0;
- for(k= 0; k <= qhmem.LASTsize; k++) {
- if (qhmem.indextable[k] <= qhmem.sizetable[i])
- qhmem.indextable[k]= i;
- else
- qhmem.indextable[k]= ++i;
- }
-} /* memsetup */
-
-/*-<a href="qh-mem.htm#TOC"
- >-------------------------------</a><a name="memsize">-</a>
-
- qh_memsize( size )
- define a free list for this size
-*/
-void qh_memsize(int size) {
- int k;
-
- if (qhmem .LASTsize) {
- fprintf (qhmem .ferr, "qhull error (qh_memsize): called after qhmem_setup\n");
- qh_errexit (qhmem_ERRqhull, NULL, NULL);
- }
- size= (size + qhmem.ALIGNmask) & ~qhmem.ALIGNmask;
- for(k= qhmem.TABLEsize; k--; ) {
- if (qhmem.sizetable[k] == size)
- return;
- }
- if (qhmem.TABLEsize < qhmem.NUMsizes)
- qhmem.sizetable[qhmem.TABLEsize++]= size;
- else
- fprintf(qhmem.ferr, "qhull warning (memsize): free list table has room for only %d sizes\n", qhmem.NUMsizes);
-} /* memsize */
-
-
-/*-<a href="qh-mem.htm#TOC"
- >-------------------------------</a><a name="memstatistics">-</a>
-
- qh_memstatistics( fp )
- print out memory statistics
-
- notes:
- does not account for wasted memory at the end of each block
-*/
-void qh_memstatistics (FILE *fp) {
- int i, count, totfree= 0;
- void *object;
-
- for (i=0; i < qhmem.TABLEsize; i++) {
- count=0;
- for (object= qhmem .freelists[i]; object; object= *((void **)object))
- count++;
- totfree += qhmem.sizetable[i] * count;
- }
- fprintf (fp, "\nmemory statistics:\n\
-%7d quick allocations\n\
-%7d short allocations\n\
-%7d long allocations\n\
-%7d short frees\n\
-%7d long frees\n\
-%7d bytes of short memory in use\n\
-%7d bytes of short memory in freelists\n\
-%7d bytes of long memory allocated (except for input)\n\
-%7d bytes of long memory in use (in %d pieces)\n\
-%7d bytes per memory buffer (initially %d bytes)\n",
- qhmem .cntquick, qhmem.cntshort, qhmem.cntlong,
- qhmem .freeshort, qhmem.freelong,
- qhmem .totshort - qhmem .freesize - totfree,
- totfree,
- qhmem .maxlong, qhmem .totlong, qhmem .cntlong - qhmem .freelong,
- qhmem .BUFsize, qhmem .BUFinit);
- if (qhmem.cntlarger) {
- fprintf (fp, "%7d calls to qh_setlarger\n%7.2g average copy size\n",
- qhmem.cntlarger, ((float) qhmem.totlarger)/ qhmem.cntlarger);
- fprintf (fp, " freelists (bytes->count):");
- }
- for (i=0; i < qhmem.TABLEsize; i++) {
- count=0;
- for (object= qhmem .freelists[i]; object; object= *((void **)object))
- count++;
- fprintf (fp, " %d->%d", qhmem.sizetable[i], count);
- }
- fprintf (fp, "\n\n");
-} /* memstatistics */
-
-
-/*-<a href="qh-mem.htm#TOC"
- >-------------------------------</a><a name="NOmem">-</a>
-
- qh_NOmem
- turn off quick-fit memory allocation
-
- notes:
- uses malloc() and free() instead
-*/
-#else /* qh_NOmem */
-
-void *qh_memalloc(int insize) {
- void *object;
-
- if (!(object= malloc(insize))) {
- fprintf(qhmem.ferr, "qhull error (qh_memalloc): insufficient memory\n");
- qh_errexit(qhmem_ERRmem, NULL, NULL);
- }
- if (qhmem.IStracing >= 5)
- fprintf (qhmem.ferr, "qh_memalloc long: %d bytes at %p\n", insize, object);
- return object;
-}
-
-void qh_memfree(void *object, int size) {
-
- if (!object)
- return;
- free (object);
- if (qhmem.IStracing >= 5)
- fprintf (qhmem.ferr, "qh_memfree long: %d bytes at %p\n", size, object);
-}
-
-void qh_memfreeshort (int *curlong, int *totlong) {
-
- memset((char *)&qhmem, 0, sizeof qhmem); /* every field is 0, FALSE, NULL */
- *curlong= 0;
- *totlong= 0;
-}
-
-void qh_meminit (FILE *ferr) {
-
- memset((char *)&qhmem, 0, sizeof qhmem); /* every field is 0, FALSE, NULL */
- qhmem.ferr= ferr;
- if (sizeof(void*) < sizeof(int)) {
- fprintf (ferr, "qhull internal error (qh_meminit): sizeof(void*) < sizeof(int). qset.c will not work\n");
- qh_errexit (qhmem_ERRqhull, NULL, NULL);
- }
-}
-
-void qh_meminitbuffers (int tracelevel, int alignment, int numsizes, int bufsize, int bufinit) {
-
- qhmem.IStracing= tracelevel;
-
-}
-
-void qh_memsetup (void) {
-
-}
-
-void qh_memsize(int size) {
-
-}
-
-void qh_memstatistics (FILE *fp) {
-
-}
-
-#endif /* qh_NOmem */
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/mem.h b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/mem.h
deleted file mode 100644
index 3283efe89efa77d661b47bf603c50317c611d5f8..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/mem.h
+++ /dev/null
@@ -1,173 +0,0 @@
-/*<html><pre> -<a href="qh-mem.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- mem.h
- prototypes for memory management functions
-
- see qh-mem.htm, mem.c and qset.h
-
- for error handling, writes message and calls
- qh_errexit (qhmem_ERRmem, NULL, NULL) if insufficient memory
- and
- qh_errexit (qhmem_ERRqhull, NULL, NULL) otherwise
-
- copyright (c) 1993-2003, The Geometry Center
-*/
-
-#pragma once
-
-/*-<a href="qh-mem.htm#TOC"
- >-------------------------------</a><a name="NOmem">-</a>
-
- qh_NOmem
- turn off quick-fit memory allocation
-
- notes:
- mem.c implements Quickfit memory allocation for about 20% time
- savings. If it fails on your machine, try to locate the
- problem, and send the answer to qhull@qhull.org. If this can
- not be done, define qh_NOmem to use malloc/free instead.
-
- #define qh_NOmem
-*/
-
-/*-------------------------------------------
- to avoid bus errors, memory allocation must consider alignment requirements.
- malloc() automatically takes care of alignment. Since mem.c manages
- its own memory, we need to explicitly specify alignment in
- qh_meminitbuffers().
-
- A safe choice is sizeof(double). sizeof(float) may be used if doubles
- do not occur in data structures and pointers are the same size. Be careful
- of machines (e.g., DEC Alpha) with large pointers. If gcc is available,
- use __alignof__(double) or fmax_(__alignof__(float), __alignof__(void *)).
-
- see <a href="user.h#MEMalign">qh_MEMalign</a> in user.h for qhull's alignment
-*/
-
-#define qhmem_ERRmem 4 /* matches qh_ERRmem in qhull.h */
-#define qhmem_ERRqhull 5 /* matches qh_ERRqhull in qhull.h */
-
-/*-<a href="qh-mem.htm#TOC"
- >--------------------------------</a><a name="ptr_intT">-</a>
-
- ptr_intT
- for casting a void* to an integer-type
-
- notes:
- On 64-bit machines, a pointer may be larger than an 'int'.
- qh_meminit() checks that 'long' holds a 'void*'
-*/
-typedef unsigned long ptr_intT;
-
-/*-<a href="qh-mem.htm#TOC"
- >--------------------------------</a><a name="qhmemT">-</a>
-
- qhmemT
- global memory structure for mem.c
-
- notes:
- users should ignore qhmem except for writing extensions
- qhmem is allocated in mem.c
-
- qhmem could be swapable like qh and qhstat, but then
- multiple qh's and qhmem's would need to keep in synch.
- A swapable qhmem would also waste memory buffers. As long
- as memory operations are atomic, there is no problem with
- multiple qh structures being active at the same time.
- If you need separate address spaces, you can swap the
- contents of qhmem.
-*/
-typedef struct qhmemT qhmemT;
-extern qhmemT qhmem;
-
-struct qhmemT /* global memory management variables */
-{
- int BUFsize; /* size of memory allocation buffer */
- int BUFinit; /* initial size of memory allocation buffer */
- int TABLEsize; /* actual number of sizes in free list table */
- int NUMsizes; /* maximum number of sizes in free list table */
- int LASTsize; /* last size in free list table */
- int ALIGNmask; /* worst-case alignment, must be 2^n-1 */
- void** freelists; /* free list table, linked by offset 0 */
- int* sizetable; /* size of each freelist */
- int* indextable; /* size->index table */
- void* curbuffer; /* current buffer, linked by offset 0 */
- void* freemem; /* free memory in curbuffer */
- int freesize; /* size of free memory in bytes */
- void* tempstack; /* stack of temporary memory, managed by users */
- FILE* ferr; /* file for reporting errors */
- int IStracing; /* =5 if tracing memory allocations */
- int cntquick; /* count of quick allocations */
- /* remove statistics doesn't effect speed */
- int cntshort; /* count of short allocations */
- int cntlong; /* count of long allocations */
- int curlong; /* current count of inuse, long allocations */
- int freeshort; /* count of short memfrees */
- int freelong; /* count of long memfrees */
- int totshort; /* total size of short allocations */
- int totlong; /* total size of long allocations */
- int maxlong; /* maximum totlong */
- int cntlarger; /* count of setlarger's */
- int totlarger; /* total copied by setlarger */
-};
-
-
-/*==================== -macros ====================*/
-
-/*-<a href="qh-mem.htm#TOC"
- >--------------------------------</a><a name="memalloc_">-</a>
-
- qh_memalloc_(size, object, type)
- returns object of size bytes
- assumes size<=qhmem.LASTsize and void **freelistp is a temp
-*/
-
-#ifdef qh_NOmem
-#define qh_memalloc_(size, freelistp, object, type) {\
- object= (type*)qh_memalloc (size); }
-#else /* !qh_NOmem */
-
-#define qh_memalloc_(size, freelistp, object, type) {\
- freelistp= qhmem.freelists + qhmem.indextable[size];\
- if ((object= (type*)*freelistp)) {\
- qhmem.cntquick++; \
- *freelistp= *((void **)*freelistp);\
- }else object= (type*)qh_memalloc (size);}
-#endif
-
-/*-<a href="qh-mem.htm#TOC"
- >--------------------------------</a><a name="memfree_">-</a>
-
- qh_memfree_(object, size)
- free up an object
-
- notes:
- object may be NULL
- assumes size<=qhmem.LASTsize and void **freelistp is a temp
-*/
-#ifdef qh_NOmem
-#define qh_memfree_(object, size, freelistp) {\
- qh_memfree (object, size); }
-#else /* !qh_NOmem */
-
-#define qh_memfree_(object, size, freelistp) {\
- if (object) { \
- qhmem .freeshort++;\
- freelistp= qhmem.freelists + qhmem.indextable[size];\
- *((void **)object)= *freelistp;\
- *freelistp= object;}}
-#endif
-
-/*=============== prototypes in alphabetical order ============*/
-
-void* qh_memalloc(int insize);
-void qh_memfree(void* object, int size);
-void qh_memfreeshort(int* curlong, int* totlong);
-void qh_meminit(FILE* ferr);
-void qh_meminitbuffers(int tracelevel, int alignment, int numsizes,
- int bufsize, int bufinit);
-void qh_memsetup(void);
-void qh_memsize(int size);
-void qh_memstatistics(FILE* fp);
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/merge.c b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/merge.c
deleted file mode 100644
index cb683dea1b28cd7944ff36ec15c192d4fb608d52..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/merge.c
+++ /dev/null
@@ -1,3619 +0,0 @@
-/*<html><pre> -<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="TOP">-</a>
-
- merge.c
- merges non-convex facets
-
- see qh-merge.htm and merge.h
-
- other modules call qh_premerge() and qh_postmerge()
-
- the user may call qh_postmerge() to perform additional merges.
-
- To remove deleted facets and vertices (qhull() in qhull.c):
- qh_partitionvisible (!qh_ALL, &numoutside); // visible_list, newfacet_list
- qh_deletevisible (); // qh.visible_list
- qh_resetlists (False, qh_RESETvisible); // qh.visible_list newvertex_list newfacet_list
-
- assumes qh.CENTERtype= centrum
-
- merges occur in qh_mergefacet and in qh_mergecycle
- vertex->neighbors not set until the first merge occurs
-
- copyright (c) 1993-2003 The Geometry Center
-*/
-
-#include "qhull_a.h"
-
-#ifndef qh_NOmerge
-
-/*===== functions (alphabetical after premerge and postmerge) ======*/
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="premerge">-</a>
-
- qh_premerge( apex, maxcentrum )
- pre-merge nonconvex facets in qh.newfacet_list for apex
- maxcentrum defines coplanar and concave (qh_test_appendmerge)
-
- returns:
- deleted facets added to qh.visible_list with facet->visible set
-
- notes:
- uses globals, qh.MERGEexact, qh.PREmerge
-
- design:
- mark duplicate ridges in qh.newfacet_list
- merge facet cycles in qh.newfacet_list
- merge duplicate ridges and concave facets in qh.newfacet_list
- check merged facet cycles for degenerate and redundant facets
- merge degenerate and redundant facets
- collect coplanar and concave facets
- merge concave, coplanar, degenerate, and redundant facets
-*/
-void qh_premerge (vertexT *apex, realT maxcentrum, realT maxangle) {
- boolT othermerge= False;
- facetT *newfacet;
-
- if (qh ZEROcentrum && qh_checkzero(!qh_ALL))
- return;
- trace2((qh ferr, "qh_premerge: premerge centrum %2.2g angle %2.2g for apex v%d facetlist f%d\n",
- maxcentrum, maxangle, apex->id, getid_(qh newfacet_list)));
- if (qh IStracing >= 4 && qh num_facets < 50)
- qh_printlists();
- qh centrum_radius= maxcentrum;
- qh cos_max= maxangle;
- qh degen_mergeset= qh_settemp (qh TEMPsize);
- qh facet_mergeset= qh_settemp (qh TEMPsize);
- if (qh hull_dim >=3) {
- qh_mark_dupridges (qh newfacet_list); /* facet_mergeset */
- qh_mergecycle_all (qh newfacet_list, &othermerge);
- qh_forcedmerges (&othermerge /* qh facet_mergeset */);
- FORALLnew_facets { /* test samecycle merges */
- if (!newfacet->simplicial && !newfacet->mergeridge)
- qh_degen_redundant_neighbors (newfacet, NULL);
- }
- if (qh_merge_degenredundant())
- othermerge= True;
- }else /* qh hull_dim == 2 */
- qh_mergecycle_all (qh newfacet_list, &othermerge);
- qh_flippedmerges (qh newfacet_list, &othermerge);
- if (!qh MERGEexact || zzval_(Ztotmerge)) {
- zinc_(Zpremergetot);
- qh POSTmerging= False;
- qh_getmergeset_initial (qh newfacet_list);
- qh_all_merges (othermerge, False);
- }
- qh_settempfree(&qh facet_mergeset);
- qh_settempfree(&qh degen_mergeset);
-} /* premerge */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="postmerge">-</a>
-
- qh_postmerge( reason, maxcentrum, maxangle, vneighbors )
- post-merge nonconvex facets as defined by maxcentrum and maxangle
- 'reason' is for reporting progress
- if vneighbors,
- calls qh_test_vneighbors at end of qh_all_merge
- if firstmerge,
- calls qh_reducevertices before qh_getmergeset
-
- returns:
- if first call (qh.visible_list != qh.facet_list),
- builds qh.facet_newlist, qh.newvertex_list
- deleted facets added to qh.visible_list with facet->visible
- qh.visible_list == qh.facet_list
-
- notes:
-
-
- design:
- if first call
- set qh.visible_list and qh.newfacet_list to qh.facet_list
- add all facets to qh.newfacet_list
- mark non-simplicial facets, facet->newmerge
- set qh.newvertext_list to qh.vertex_list
- add all vertices to qh.newvertex_list
- if a pre-merge occured
- set vertex->delridge {will retest the ridge}
- if qh.MERGEexact
- call qh_reducevertices()
- if no pre-merging
- merge flipped facets
- determine non-convex facets
- merge all non-convex facets
-*/
-void qh_postmerge (char *reason, realT maxcentrum, realT maxangle,
- boolT vneighbors) {
- facetT *newfacet;
- boolT othermerges= False;
- vertexT *vertex;
-
- if (qh REPORTfreq || qh IStracing) {
- qh_buildtracing (NULL, NULL);
- qh_printsummary (qh ferr);
- if (qh PRINTstatistics)
- qh_printallstatistics (qh ferr, "reason");
- fprintf (qh ferr, "\n%s with 'C%.2g' and 'A%.2g'\n",
- reason, maxcentrum, maxangle);
- }
- trace2((qh ferr, "qh_postmerge: postmerge. test vneighbors? %d\n",
- vneighbors));
- qh centrum_radius= maxcentrum;
- qh cos_max= maxangle;
- qh POSTmerging= True;
- qh degen_mergeset= qh_settemp (qh TEMPsize);
- qh facet_mergeset= qh_settemp (qh TEMPsize);
- if (qh visible_list != qh facet_list) { /* first call */
- qh NEWfacets= True;
- qh visible_list= qh newfacet_list= qh facet_list;
- FORALLnew_facets {
- newfacet->newfacet= True;
- if (!newfacet->simplicial)
- newfacet->newmerge= True;
- zinc_(Zpostfacets);
- }
- qh newvertex_list= qh vertex_list;
- FORALLvertices
- vertex->newlist= True;
- if (qh VERTEXneighbors) { /* a merge has occurred */
- FORALLvertices
- vertex->delridge= True; /* test for redundant, needed? */
- if (qh MERGEexact) {
- if (qh hull_dim <= qh_DIMreduceBuild)
- qh_reducevertices(); /* was skipped during pre-merging */
- }
- }
- if (!qh PREmerge && !qh MERGEexact)
- qh_flippedmerges (qh newfacet_list, &othermerges);
- }
- qh_getmergeset_initial (qh newfacet_list);
- qh_all_merges (False, vneighbors);
- qh_settempfree(&qh facet_mergeset);
- qh_settempfree(&qh degen_mergeset);
-} /* post_merge */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="all_merges">-</a>
-
- qh_all_merges( othermerge, vneighbors )
- merge all non-convex facets
-
- set othermerge if already merged facets (for qh_reducevertices)
- if vneighbors
- tests vertex neighbors for convexity at end
- qh.facet_mergeset lists the non-convex ridges in qh_newfacet_list
- qh.degen_mergeset is defined
- if qh.MERGEexact && !qh.POSTmerging,
- does not merge coplanar facets
-
- returns:
- deleted facets added to qh.visible_list with facet->visible
- deleted vertices added qh.delvertex_list with vertex->delvertex
-
- notes:
- unless !qh.MERGEindependent,
- merges facets in independent sets
- uses qh.newfacet_list as argument since merges call qh_removefacet()
-
- design:
- while merges occur
- for each merge in qh.facet_mergeset
- unless one of the facets was already merged in this pass
- merge the facets
- test merged facets for additional merges
- add merges to qh.facet_mergeset
- if vertices record neighboring facets
- rename redundant vertices
- update qh.facet_mergeset
- if vneighbors ??
- tests vertex neighbors for convexity at end
-*/
-void qh_all_merges (boolT othermerge, boolT vneighbors) {
- facetT *facet1, *facet2;
- mergeT *merge;
- boolT wasmerge= True, isreduce;
- void **freelistp; /* used !qh_NOmem */
- vertexT *vertex;
- mergeType mergetype;
- int numcoplanar=0, numconcave=0, numdegenredun= 0, numnewmerges= 0;
-
- trace2((qh ferr, "qh_all_merges: starting to merge facets beginning from f%d\n",
- getid_(qh newfacet_list)));
- while (True) {
- wasmerge= False;
- while (qh_setsize (qh facet_mergeset)) {
- while ((merge= (mergeT*)qh_setdellast(qh facet_mergeset))) {
- facet1= merge->facet1;
- facet2= merge->facet2;
- mergetype= merge->type;
- qh_memfree_(merge, sizeof(mergeT), freelistp);
- if (facet1->visible || facet2->visible) /*deleted facet*/
- continue;
- if ((facet1->newfacet && !facet1->tested)
- || (facet2->newfacet && !facet2->tested)) {
- if (qh MERGEindependent && mergetype <= MRGanglecoplanar)
- continue; /* perform independent sets of merges */
- }
- qh_merge_nonconvex (facet1, facet2, mergetype);
- numdegenredun += qh_merge_degenredundant();
- numnewmerges++;
- wasmerge= True;
- if (mergetype == MRGconcave)
- numconcave++;
- else /* MRGcoplanar or MRGanglecoplanar */
- numcoplanar++;
- } /* while setdellast */
- if (qh POSTmerging && qh hull_dim <= qh_DIMreduceBuild
- && numnewmerges > qh_MAXnewmerges) {
- numnewmerges= 0;
- qh_reducevertices(); /* otherwise large post merges too slow */
- }
- qh_getmergeset (qh newfacet_list); /* facet_mergeset */
- } /* while mergeset */
- if (qh VERTEXneighbors) {
- isreduce= False;
- if (qh hull_dim >=4 && qh POSTmerging) {
- FORALLvertices
- vertex->delridge= True;
- isreduce= True;
- }
- if ((wasmerge || othermerge) && (!qh MERGEexact || qh POSTmerging)
- && qh hull_dim <= qh_DIMreduceBuild) {
- othermerge= False;
- isreduce= True;
- }
- if (isreduce) {
- if (qh_reducevertices()) {
- qh_getmergeset (qh newfacet_list); /* facet_mergeset */
- continue;
- }
- }
- }
- if (vneighbors && qh_test_vneighbors(/* qh newfacet_list */))
- continue;
- break;
- } /* while (True) */
- if (qh CHECKfrequently && !qh MERGEexact) {
- qh old_randomdist= qh RANDOMdist;
- qh RANDOMdist= False;
- qh_checkconvex (qh newfacet_list, qh_ALGORITHMfault);
- /* qh_checkconnect (); [this is slow and it changes the facet order] */
- qh RANDOMdist= qh old_randomdist;
- }
- trace1((qh ferr, "qh_all_merges: merged %d coplanar facets %d concave facets and %d degen or redundant facets.\n",
- numcoplanar, numconcave, numdegenredun));
- if (qh IStracing >= 4 && qh num_facets < 50)
- qh_printlists ();
-} /* all_merges */
-
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="appendmergeset">-</a>
-
- qh_appendmergeset( facet, neighbor, mergetype, angle )
- appends an entry to qh.facet_mergeset or qh.degen_mergeset
-
- angle ignored if NULL or !qh.ANGLEmerge
-
- returns:
- merge appended to facet_mergeset or degen_mergeset
- sets ->degenerate or ->redundant if degen_mergeset
-
- see:
- qh_test_appendmerge()
-
- design:
- allocate merge entry
- if regular merge
- append to qh.facet_mergeset
- else if degenerate merge and qh.facet_mergeset is all degenerate
- append to qh.degen_mergeset
- else if degenerate merge
- prepend to qh.degen_mergeset
- else if redundant merge
- append to qh.degen_mergeset
-*/
-void qh_appendmergeset(facetT *facet, facetT *neighbor, mergeType mergetype, realT *angle) {
- mergeT *merge, *lastmerge;
- void **freelistp; /* used !qh_NOmem */
-
- if (facet->redundant)
- return;
- if (facet->degenerate && mergetype == MRGdegen)
- return;
- qh_memalloc_(sizeof(mergeT), freelistp, merge, mergeT);
- merge->facet1= facet;
- merge->facet2= neighbor;
- merge->type= mergetype;
- if (angle && qh ANGLEmerge)
- merge->angle= *angle;
- if (mergetype < MRGdegen)
- qh_setappend (&(qh facet_mergeset), merge);
- else if (mergetype == MRGdegen) {
- facet->degenerate= True;
- if (!(lastmerge= (mergeT*)qh_setlast (qh degen_mergeset))
- || lastmerge->type == MRGdegen)
- qh_setappend (&(qh degen_mergeset), merge);
- else
- qh_setaddnth (&(qh degen_mergeset), 0, merge);
- }else if (mergetype == MRGredundant) {
- facet->redundant= True;
- qh_setappend (&(qh degen_mergeset), merge);
- }else /* mergetype == MRGmirror */ {
- if (facet->redundant || neighbor->redundant) {
- fprintf(qh ferr, "qhull error (qh_appendmergeset): facet f%d or f%d is already a mirrored facet\n",
- facet->id, neighbor->id);
- qh_errexit2 (qh_ERRqhull, facet, neighbor);
- }
- if (!qh_setequal (facet->vertices, neighbor->vertices)) {
- fprintf(qh ferr, "qhull error (qh_appendmergeset): mirrored facets f%d and f%d do not have the same vertices\n",
- facet->id, neighbor->id);
- qh_errexit2 (qh_ERRqhull, facet, neighbor);
- }
- facet->redundant= True;
- neighbor->redundant= True;
- qh_setappend (&(qh degen_mergeset), merge);
- }
-} /* appendmergeset */
-
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="basevertices">-</a>
-
- qh_basevertices( samecycle )
- return temporary set of base vertices for samecycle
- samecycle is first facet in the cycle
- assumes apex is SETfirst_( samecycle->vertices )
-
- returns:
- vertices (settemp)
- all ->seen are cleared
-
- notes:
- uses qh_vertex_visit;
-
- design:
- for each facet in samecycle
- for each unseen vertex in facet->vertices
- append to result
-*/
-setT *qh_basevertices (facetT *samecycle) {
- facetT *same;
- vertexT *apex, *vertex, **vertexp;
- setT *vertices= qh_settemp (qh TEMPsize);
-
- apex= SETfirstt_(samecycle->vertices, vertexT);
- apex->visitid= ++qh vertex_visit;
- FORALLsame_cycle_(samecycle) {
- if (same->mergeridge)
- continue;
- FOREACHvertex_(same->vertices) {
- if (vertex->visitid != qh vertex_visit) {
- qh_setappend (&vertices, vertex);
- vertex->visitid= qh vertex_visit;
- vertex->seen= False;
- }
- }
- }
- trace4((qh ferr, "qh_basevertices: found %d vertices\n",
- qh_setsize (vertices)));
- return vertices;
-} /* basevertices */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="checkconnect">-</a>
-
- qh_checkconnect()
- check that new facets are connected
- new facets are on qh.newfacet_list
-
- notes:
- this is slow and it changes the order of the facets
- uses qh.visit_id
-
- design:
- move first new facet to end of qh.facet_list
- for all newly appended facets
- append unvisited neighbors to end of qh.facet_list
- for all new facets
- report error if unvisited
-*/
-void qh_checkconnect (void /* qh newfacet_list */) {
- facetT *facet, *newfacet, *errfacet= NULL, *neighbor, **neighborp;
-
- facet= qh newfacet_list;
- qh_removefacet (facet);
- qh_appendfacet (facet);
- facet->visitid= ++qh visit_id;
- FORALLfacet_(facet) {
- FOREACHneighbor_(facet) {
- if (neighbor->visitid != qh visit_id) {
- qh_removefacet (neighbor);
- qh_appendfacet (neighbor);
- neighbor->visitid= qh visit_id;
- }
- }
- }
- FORALLnew_facets {
- if (newfacet->visitid == qh visit_id)
- break;
- fprintf(qh ferr, "qhull error: f%d is not attached to the new facets\n",
- newfacet->id);
- errfacet= newfacet;
- }
- if (errfacet)
- qh_errexit (qh_ERRqhull, errfacet, NULL);
-} /* checkconnect */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="checkzero">-</a>
-
- qh_checkzero( testall )
- check that facets are clearly convex for qh.DISTround with qh.MERGEexact
-
- if testall,
- test all facets for qh.MERGEexact post-merging
- else
- test qh.newfacet_list
-
- if qh.MERGEexact,
- allows coplanar ridges
- skips convexity test while qh.ZEROall_ok
-
- returns:
- True if all facets !flipped, !dupridge, normal
- if all horizon facets are simplicial
- if all vertices are clearly below neighbor
- if all opposite vertices of horizon are below
- clears qh.ZEROall_ok if any problems or coplanar facets
-
- notes:
- uses qh.vertex_visit
- horizon facets may define multiple new facets
-
- design:
- for all facets in qh.newfacet_list or qh.facet_list
- check for flagged faults (flipped, etc.)
- for all facets in qh.newfacet_list or qh.facet_list
- for each neighbor of facet
- skip horizon facets for qh.newfacet_list
- test the opposite vertex
- if qh.newfacet_list
- test the other vertices in the facet's horizon facet
-*/
-boolT qh_checkzero (boolT testall) {
- facetT *facet, *neighbor, **neighborp;
- facetT *horizon, *facetlist;
- int neighbor_i;
- vertexT *vertex, **vertexp;
- realT dist;
-
- if (testall)
- facetlist= qh facet_list;
- else {
- facetlist= qh newfacet_list;
- FORALLfacet_(facetlist) {
- horizon= SETfirstt_(facet->neighbors, facetT);
- if (!horizon->simplicial)
- goto LABELproblem;
- if (facet->flipped || facet->dupridge || !facet->normal)
- goto LABELproblem;
- }
- if (qh MERGEexact && qh ZEROall_ok) {
- trace2((qh ferr, "qh_checkzero: skip convexity check until first pre-merge\n"));
- return True;
- }
- }
- FORALLfacet_(facetlist) {
- qh vertex_visit++;
- neighbor_i= 0;
- horizon= NULL;
- FOREACHneighbor_(facet) {
- if (!neighbor_i && !testall) {
- horizon= neighbor;
- neighbor_i++;
- continue; /* horizon facet tested in qh_findhorizon */
- }
- vertex= SETelemt_(facet->vertices, neighbor_i++, vertexT);
- vertex->visitid= qh vertex_visit;
- zzinc_(Zdistzero);
- qh_distplane (vertex->point, neighbor, &dist);
- if (dist >= -qh DISTround) {
- qh ZEROall_ok= False;
- if (!qh MERGEexact || testall || dist > qh DISTround)
- goto LABELnonconvex;
- }
- }
- if (!testall) {
- FOREACHvertex_(horizon->vertices) {
- if (vertex->visitid != qh vertex_visit) {
- zzinc_(Zdistzero);
- qh_distplane (vertex->point, facet, &dist);
- if (dist >= -qh DISTround) {
- qh ZEROall_ok= False;
- if (!qh MERGEexact || dist > qh DISTround)
- goto LABELnonconvex;
- }
- break;
- }
- }
- }
- }
- trace2((qh ferr, "qh_checkzero: testall %d, facets are %s\n", testall,
- (qh MERGEexact && !testall) ?
- "not concave, flipped, or duplicate ridged" : "clearly convex"));
- return True;
-
- LABELproblem:
- qh ZEROall_ok= False;
- trace2((qh ferr, "qh_checkzero: facet f%d needs pre-merging\n",
- facet->id));
- return False;
-
- LABELnonconvex:
- trace2((qh ferr, "qh_checkzero: facet f%d and f%d are not clearly convex. v%d dist %.2g\n",
- facet->id, neighbor->id, vertex->id, dist));
- return False;
-} /* checkzero */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="compareangle">-</a>
-
- qh_compareangle( angle1, angle2 )
- used by qsort() to order merges by angle
-*/
-int qh_compareangle(const void *p1, const void *p2) {
- mergeT *a= *((mergeT **)p1), *b= *((mergeT **)p2);
-
- return ((a->angle > b->angle) ? 1 : -1);
-} /* compareangle */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="comparemerge">-</a>
-
- qh_comparemerge( merge1, merge2 )
- used by qsort() to order merges
-*/
-int qh_comparemerge(const void *p1, const void *p2) {
- mergeT *a= *((mergeT **)p1), *b= *((mergeT **)p2);
-
- return (a->type - b->type);
-} /* comparemerge */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="comparevisit">-</a>
-
- qh_comparevisit( vertex1, vertex2 )
- used by qsort() to order vertices by their visitid
-*/
-int qh_comparevisit (const void *p1, const void *p2) {
- vertexT *a= *((vertexT **)p1), *b= *((vertexT **)p2);
-
- return (a->visitid - b->visitid);
-} /* comparevisit */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="copynonconvex">-</a>
-
- qh_copynonconvex( atridge )
- set non-convex flag on other ridges (if any) between same neighbors
-
- notes:
- may be faster if use smaller ridge set
-
- design:
- for each ridge of atridge's top facet
- if ridge shares the same neighbor
- set nonconvex flag
-*/
-void qh_copynonconvex (ridgeT *atridge) {
- facetT *facet, *otherfacet;
- ridgeT *ridge, **ridgep;
-
- facet= atridge->top;
- otherfacet= atridge->bottom;
- FOREACHridge_(facet->ridges) {
- if (otherfacet == otherfacet_(ridge, facet) && ridge != atridge) {
- ridge->nonconvex= True;
- trace4((qh ferr, "qh_copynonconvex: moved nonconvex flag from r%d to r%d\n",
- atridge->id, ridge->id));
- break;
- }
- }
-} /* copynonconvex */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="degen_redundant_facet">-</a>
-
- qh_degen_redundant_facet( facet )
- check facet for degen. or redundancy
-
- notes:
- bumps vertex_visit
- called if a facet was redundant but no longer is (qh_merge_degenredundant)
- qh_appendmergeset() only appends first reference to facet (i.e., redundant)
-
- see:
- qh_degen_redundant_neighbors()
-
- design:
- test for redundant neighbor
- test for degenerate facet
-*/
-void qh_degen_redundant_facet (facetT *facet) {
- vertexT *vertex, **vertexp;
- facetT *neighbor, **neighborp;
-
- trace4((qh ferr, "qh_degen_redundant_facet: test facet f%d for degen/redundant\n",
- facet->id));
- FOREACHneighbor_(facet) {
- qh vertex_visit++;
- FOREACHvertex_(neighbor->vertices)
- vertex->visitid= qh vertex_visit;
- FOREACHvertex_(facet->vertices) {
- if (vertex->visitid != qh vertex_visit)
- break;
- }
- if (!vertex) {
- qh_appendmergeset (facet, neighbor, MRGredundant, NULL);
- trace2((qh ferr, "qh_degen_redundant_facet: f%d is contained in f%d. merge\n", facet->id, neighbor->id));
- return;
- }
- }
- if (qh_setsize (facet->neighbors) < qh hull_dim) {
- qh_appendmergeset (facet, facet, MRGdegen, NULL);
- trace2((qh ferr, "qh_degen_redundant_neighbors: f%d is degenerate.\n", facet->id));
- }
-} /* degen_redundant_facet */
-
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="degen_redundant_neighbors">-</a>
-
- qh_degen_redundant_neighbors( facet, delfacet, )
- append degenerate and redundant neighbors to facet_mergeset
- if delfacet,
- only checks neighbors of both delfacet and facet
- also checks current facet for degeneracy
-
- notes:
- bumps vertex_visit
- called for each qh_mergefacet() and qh_mergecycle()
- merge and statistics occur in merge_nonconvex
- qh_appendmergeset() only appends first reference to facet (i.e., redundant)
- it appends redundant facets after degenerate ones
-
- a degenerate facet has fewer than hull_dim neighbors
- a redundant facet's vertices is a subset of its neighbor's vertices
- tests for redundant merges first (appendmergeset is nop for others)
- in a merge, only needs to test neighbors of merged facet
-
- see:
- qh_merge_degenredundant() and qh_degen_redundant_facet()
-
- design:
- test for degenerate facet
- test for redundant neighbor
- test for degenerate neighbor
-*/
-void qh_degen_redundant_neighbors (facetT *facet, facetT *delfacet) {
- vertexT *vertex, **vertexp;
- facetT *neighbor, **neighborp;
- int size;
-
- trace4((qh ferr, "qh_degen_redundant_neighbors: test neighbors of f%d with delfacet f%d\n",
- facet->id, getid_(delfacet)));
- if ((size= qh_setsize (facet->neighbors)) < qh hull_dim) {
- qh_appendmergeset (facet, facet, MRGdegen, NULL);
- trace2((qh ferr, "qh_degen_redundant_neighbors: f%d is degenerate with %d neighbors.\n", facet->id, size));
- }
- if (!delfacet)
- delfacet= facet;
- qh vertex_visit++;
- FOREACHvertex_(facet->vertices)
- vertex->visitid= qh vertex_visit;
- FOREACHneighbor_(delfacet) {
- /* uses early out instead of checking vertex count */
- if (neighbor == facet)
- continue;
- FOREACHvertex_(neighbor->vertices) {
- if (vertex->visitid != qh vertex_visit)
- break;
- }
- if (!vertex) {
- qh_appendmergeset (neighbor, facet, MRGredundant, NULL);
- trace2((qh ferr, "qh_degen_redundant_neighbors: f%d is contained in f%d. merge\n", neighbor->id, facet->id));
- }
- }
- FOREACHneighbor_(delfacet) { /* redundant merges occur first */
- if (neighbor == facet)
- continue;
- if ((size= qh_setsize (neighbor->neighbors)) < qh hull_dim) {
- qh_appendmergeset (neighbor, neighbor, MRGdegen, NULL);
- trace2((qh ferr, "qh_degen_redundant_neighbors: f%d is degenerate with %d neighbors. Neighbor of f%d.\n", neighbor->id, size, facet->id));
- }
- }
-} /* degen_redundant_neighbors */
-
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="find_newvertex">-</a>
-
- qh_find_newvertex( oldvertex, vertices, ridges )
- locate new vertex for renaming old vertex
- vertices is a set of possible new vertices
- vertices sorted by number of deleted ridges
-
- returns:
- newvertex or NULL
- each ridge includes both vertex and oldvertex
- vertices sorted by number of deleted ridges
-
- notes:
- modifies vertex->visitid
- new vertex is in one of the ridges
- renaming will not cause a duplicate ridge
- renaming will minimize the number of deleted ridges
- newvertex may not be adjacent in the dual (though unlikely)
-
- design:
- for each vertex in vertices
- set vertex->visitid to number of references in ridges
- remove unvisited vertices
- set qh.vertex_visit above all possible values
- sort vertices by number of references in ridges
- add each ridge to qh.hash_table
- for each vertex in vertices
- look for a vertex that would not cause a duplicate ridge after a rename
-*/
-vertexT *qh_find_newvertex (vertexT *oldvertex, setT *vertices, setT *ridges) {
- vertexT *vertex, **vertexp;
- setT *newridges;
- ridgeT *ridge, **ridgep;
- int size, hashsize;
- int hash;
-
-#ifndef qh_NOtrace
- if (qh IStracing >= 4) {
- fprintf (qh ferr, "qh_find_newvertex: find new vertex for v%d from ",
- oldvertex->id);
- FOREACHvertex_(vertices)
- fprintf (qh ferr, "v%d ", vertex->id);
- FOREACHridge_(ridges)
- fprintf (qh ferr, "r%d ", ridge->id);
- fprintf (qh ferr, "\n");
- }
-#endif
- FOREACHvertex_(vertices)
- vertex->visitid= 0;
- FOREACHridge_(ridges) {
- FOREACHvertex_(ridge->vertices)
- vertex->visitid++;
- }
- FOREACHvertex_(vertices) {
- if (!vertex->visitid) {
- qh_setdelnth (vertices, SETindex_(vertices,vertex));
- vertexp--; /* repeat since deleted this vertex */
- }
- }
- qh vertex_visit += qh_setsize (ridges);
- if (!qh_setsize (vertices)) {
- trace4((qh ferr, "qh_find_newvertex: vertices not in ridges for v%d\n",
- oldvertex->id));
- return NULL;
- }
- qsort (SETaddr_(vertices, vertexT), qh_setsize (vertices),
- sizeof (vertexT *), qh_comparevisit);
- /* can now use qh vertex_visit */
- if (qh PRINTstatistics) {
- size= qh_setsize (vertices);
- zinc_(Zintersect);
- zadd_(Zintersecttot, size);
- zmax_(Zintersectmax, size);
- }
- hashsize= qh_newhashtable (qh_setsize (ridges));
- FOREACHridge_(ridges)
- qh_hashridge (qh hash_table, hashsize, ridge, oldvertex);
- FOREACHvertex_(vertices) {
- newridges= qh_vertexridges (vertex);
- FOREACHridge_(newridges) {
- if (qh_hashridge_find (qh hash_table, hashsize, ridge, vertex, oldvertex, &hash)) {
- zinc_(Zdupridge);
- break;
- }
- }
- qh_settempfree (&newridges);
- if (!ridge)
- break; /* found a rename */
- }
- if (vertex) {
- /* counted in qh_renamevertex */
- trace2((qh ferr, "qh_find_newvertex: found v%d for old v%d from %d vertices and %d ridges.\n",
- vertex->id, oldvertex->id, qh_setsize (vertices), qh_setsize (ridges)));
- }else {
- zinc_(Zfindfail);
- trace0((qh ferr, "qh_find_newvertex: no vertex for renaming v%d (all duplicated ridges) during p%d\n",
- oldvertex->id, qh furthest_id));
- }
- qh_setfree (&qh hash_table);
- return vertex;
-} /* find_newvertex */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="findbest_test">-</a>
-
- qh_findbest_test( testcentrum, facet, neighbor, bestfacet, dist, mindist, maxdist )
- test neighbor of facet for qh_findbestneighbor()
- if testcentrum,
- tests centrum (assumes it is defined)
- else
- tests vertices
-
- returns:
- if a better facet (i.e., vertices/centrum of facet closer to neighbor)
- updates bestfacet, dist, mindist, and maxdist
-*/
-void qh_findbest_test (boolT testcentrum, facetT *facet, facetT *neighbor,
- facetT **bestfacet, realT *distp, realT *mindistp, realT *maxdistp) {
- realT dist, mindist, maxdist;
-
- if (testcentrum) {
- zzinc_(Zbestdist);
- qh_distplane(facet->center, neighbor, &dist);
- dist *= qh hull_dim; /* estimate furthest vertex */
- if (dist < 0) {
- maxdist= 0;
- mindist= dist;
- dist= -dist;
- }else
- maxdist= dist;
- }else
- dist= qh_getdistance (facet, neighbor, &mindist, &maxdist);
- if (dist < *distp) {
- *bestfacet= neighbor;
- *mindistp= mindist;
- *maxdistp= maxdist;
- *distp= dist;
- }
-} /* findbest_test */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="findbestneighbor">-</a>
-
- qh_findbestneighbor( facet, dist, mindist, maxdist )
- finds best neighbor (least dist) of a facet for merging
-
- returns:
- returns min and max distances and their max absolute value
-
- notes:
- avoids merging old into new
- assumes ridge->nonconvex only set on one ridge between a pair of facets
- could use an early out predicate but not worth it
-
- design:
- if a large facet
- will test centrum
- else
- will test vertices
- if a large facet
- test nonconvex neighbors for best merge
- else
- test all neighbors for the best merge
- if testing centrum
- get distance information
-*/
-facetT *qh_findbestneighbor(facetT *facet, realT *distp, realT *mindistp, realT *maxdistp) {
- facetT *neighbor, **neighborp, *bestfacet= NULL;
- ridgeT *ridge, **ridgep;
- boolT nonconvex= True, testcentrum= False;
- int size= qh_setsize (facet->vertices);
-
- *distp= REALmax;
- if (size > qh_BESTcentrum2 * qh hull_dim + qh_BESTcentrum) {
- testcentrum= True;
- zinc_(Zbestcentrum);
- if (!facet->center)
- facet->center= qh_getcentrum (facet);
- }
- if (size > qh hull_dim + qh_BESTnonconvex) {
- FOREACHridge_(facet->ridges) {
- if (ridge->nonconvex) {
- neighbor= otherfacet_(ridge, facet);
- qh_findbest_test (testcentrum, facet, neighbor,
- &bestfacet, distp, mindistp, maxdistp);
- }
- }
- }
- if (!bestfacet) {
- nonconvex= False;
- FOREACHneighbor_(facet)
- qh_findbest_test (testcentrum, facet, neighbor,
- &bestfacet, distp, mindistp, maxdistp);
- }
- if (!bestfacet) {
- fprintf (qh ferr, "qhull internal error (qh_findbestneighbor): no neighbors for f%d\n", facet->id);
-
- qh_errexit (qh_ERRqhull, facet, NULL);
- }
- if (testcentrum)
- qh_getdistance (facet, bestfacet, mindistp, maxdistp);
- trace3((qh ferr, "qh_findbestneighbor: f%d is best neighbor for f%d testcentrum? %d nonconvex? %d dist %2.2g min %2.2g max %2.2g\n",
- bestfacet->id, facet->id, testcentrum, nonconvex, *distp, *mindistp, *maxdistp));
- return(bestfacet);
-} /* findbestneighbor */
-
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="flippedmerges">-</a>
-
- qh_flippedmerges( facetlist, wasmerge )
- merge flipped facets into best neighbor
- assumes qh.facet_mergeset at top of temporary stack
-
- returns:
- no flipped facets on facetlist
- sets wasmerge if merge occurred
- degen/redundant merges passed through
-
- notes:
- othermerges not needed since qh.facet_mergeset is empty before & after
- keep it in case of change
-
- design:
- append flipped facets to qh.facetmergeset
- for each flipped merge
- find best neighbor
- merge facet into neighbor
- merge degenerate and redundant facets
- remove flipped merges from qh.facet_mergeset
-*/
-void qh_flippedmerges(facetT *facetlist, boolT *wasmerge) {
- facetT *facet, *neighbor, *facet1;
- realT dist, mindist, maxdist;
- mergeT *merge, **mergep;
- setT *othermerges;
- int nummerge=0;
-
- trace4((qh ferr, "qh_flippedmerges: begin\n"));
- FORALLfacet_(facetlist) {
- if (facet->flipped && !facet->visible)
- qh_appendmergeset (facet, facet, MRGflip, NULL);
- }
- othermerges= qh_settemppop(); /* was facet_mergeset */
- qh facet_mergeset= qh_settemp (qh TEMPsize);
- qh_settemppush (othermerges);
- FOREACHmerge_(othermerges) {
- facet1= merge->facet1;
- if (merge->type != MRGflip || facet1->visible)
- continue;
- if (qh TRACEmerge-1 == zzval_(Ztotmerge))
- qhmem.IStracing= qh IStracing= qh TRACElevel;
- neighbor= qh_findbestneighbor (facet1, &dist, &mindist, &maxdist);
- trace0((qh ferr, "qh_flippedmerges: merge flipped f%d into f%d dist %2.2g during p%d\n",
- facet1->id, neighbor->id, dist, qh furthest_id));
- qh_mergefacet (facet1, neighbor, &mindist, &maxdist, !qh_MERGEapex);
- nummerge++;
- if (qh PRINTstatistics) {
- zinc_(Zflipped);
- wadd_(Wflippedtot, dist);
- wmax_(Wflippedmax, dist);
- }
- qh_merge_degenredundant();
- }
- FOREACHmerge_(othermerges) {
- if (merge->facet1->visible || merge->facet2->visible)
- qh_memfree (merge, sizeof(mergeT));
- else
- qh_setappend (&qh facet_mergeset, merge);
- }
- qh_settempfree (&othermerges);
- if (nummerge)
- *wasmerge= True;
- trace1((qh ferr, "qh_flippedmerges: merged %d flipped facets into a good neighbor\n", nummerge));
-} /* flippedmerges */
-
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="forcedmerges">-</a>
-
- qh_forcedmerges( wasmerge )
- merge duplicated ridges
-
- returns:
- removes all duplicate ridges on facet_mergeset
- wasmerge set if merge
- qh.facet_mergeset may include non-forced merges (none for now)
- qh.degen_mergeset includes degen/redun merges
-
- notes:
- duplicate ridges occur when the horizon is pinched,
- i.e. a subridge occurs in more than two horizon ridges.
- could rename vertices that pinch the horizon
- assumes qh_merge_degenredundant() has not be called
- othermerges isn't needed since facet_mergeset is empty afterwards
- keep it in case of change
-
- design:
- for each duplicate ridge
- find current facets by chasing f.replace links
- determine best direction for facet
- merge one facet into the other
- remove duplicate ridges from qh.facet_mergeset
-*/
-void qh_forcedmerges(boolT *wasmerge) {
- facetT *facet1, *facet2;
- mergeT *merge, **mergep;
- realT dist1, dist2, mindist1, mindist2, maxdist1, maxdist2;
- setT *othermerges;
- int nummerge=0, numflip=0;
-
- if (qh TRACEmerge-1 == zzval_(Ztotmerge))
- qhmem.IStracing= qh IStracing= qh TRACElevel;
- trace4((qh ferr, "qh_forcedmerges: begin\n"));
- othermerges= qh_settemppop(); /* was facet_mergeset */
- qh facet_mergeset= qh_settemp (qh TEMPsize);
- qh_settemppush (othermerges);
- FOREACHmerge_(othermerges) {
- if (merge->type != MRGridge)
- continue;
- facet1= merge->facet1;
- facet2= merge->facet2;
- while (facet1->visible) /* must exist, no qh_merge_degenredunant */
- facet1= facet1->f.replace; /* previously merged facet */
- while (facet2->visible)
- facet2= facet2->f.replace; /* previously merged facet */
- if (facet1 == facet2)
- continue;
- if (!qh_setin (facet2->neighbors, facet1)) {
- fprintf (qh ferr, "qhull internal error (qh_forcedmerges): f%d and f%d had a duplicate ridge but as f%d and f%d they are no longer neighbors\n",
- merge->facet1->id, merge->facet2->id, facet1->id, facet2->id);
- qh_errexit2 (qh_ERRqhull, facet1, facet2);
- }
- if (qh TRACEmerge-1 == zzval_(Ztotmerge))
- qhmem.IStracing= qh IStracing= qh TRACElevel;
- dist1= qh_getdistance (facet1, facet2, &mindist1, &maxdist1);
- dist2= qh_getdistance (facet2, facet1, &mindist2, &maxdist2);
- trace0((qh ferr, "qh_forcedmerges: duplicate ridge between f%d and f%d, dist %2.2g and reverse dist %2.2g during p%d\n",
- facet1->id, facet2->id, dist1, dist2, qh furthest_id));
- if (dist1 < dist2)
- qh_mergefacet (facet1, facet2, &mindist1, &maxdist1, !qh_MERGEapex);
- else {
- qh_mergefacet (facet2, facet1, &mindist2, &maxdist2, !qh_MERGEapex);
- dist1= dist2;
- facet1= facet2;
- }
- if (facet1->flipped) {
- zinc_(Zmergeflipdup);
- numflip++;
- }else
- nummerge++;
- if (qh PRINTstatistics) {
- zinc_(Zduplicate);
- wadd_(Wduplicatetot, dist1);
- wmax_(Wduplicatemax, dist1);
- }
- }
- FOREACHmerge_(othermerges) {
- if (merge->type == MRGridge)
- qh_memfree (merge, sizeof(mergeT));
- else
- qh_setappend (&qh facet_mergeset, merge);
- }
- qh_settempfree (&othermerges);
- if (nummerge)
- *wasmerge= True;
- trace1((qh ferr, "qh_forcedmerges: merged %d facets and %d flipped facets across duplicated ridges\n",
- nummerge, numflip));
-} /* forcedmerges */
-
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="getmergeset">-</a>
-
- qh_getmergeset( facetlist )
- determines nonconvex facets on facetlist
- tests !tested ridges and nonconvex ridges of !tested facets
-
- returns:
- returns sorted qh.facet_mergeset of facet-neighbor pairs to be merged
- all ridges tested
-
- notes:
- assumes no nonconvex ridges with both facets tested
- uses facet->tested/ridge->tested to prevent duplicate tests
- can not limit tests to modified ridges since the centrum changed
- uses qh.visit_id
-
- see:
- qh_getmergeset_initial()
-
- design:
- for each facet on facetlist
- for each ridge of facet
- if untested ridge
- test ridge for convexity
- if non-convex
- append ridge to qh.facet_mergeset
- sort qh.facet_mergeset by angle
-*/
-void qh_getmergeset(facetT *facetlist) {
- facetT *facet, *neighbor, **neighborp;
- ridgeT *ridge, **ridgep;
- int nummerges;
-
- nummerges= qh_setsize (qh facet_mergeset);
- trace4((qh ferr, "qh_getmergeset: started.\n"));
- qh visit_id++;
- FORALLfacet_(facetlist) {
- if (facet->tested)
- continue;
- facet->visitid= qh visit_id;
- facet->tested= True; /* must be non-simplicial due to merge */
- FOREACHneighbor_(facet)
- neighbor->seen= False;
- FOREACHridge_(facet->ridges) {
- if (ridge->tested && !ridge->nonconvex)
- continue;
- /* if tested & nonconvex, need to append merge */
- neighbor= otherfacet_(ridge, facet);
- if (neighbor->seen) {
- ridge->tested= True;
- ridge->nonconvex= False;
- }else if (neighbor->visitid != qh visit_id) {
- ridge->tested= True;
- ridge->nonconvex= False;
- neighbor->seen= True; /* only one ridge is marked nonconvex */
- if (qh_test_appendmerge (facet, neighbor))
- ridge->nonconvex= True;
- }
- }
- }
- nummerges= qh_setsize (qh facet_mergeset);
- if (qh ANGLEmerge)
- qsort(SETaddr_(qh facet_mergeset, mergeT), nummerges,sizeof(mergeT *),qh_compareangle);
- else
- qsort(SETaddr_(qh facet_mergeset, mergeT), nummerges,sizeof(mergeT *),qh_comparemerge);
- if (qh POSTmerging) {
- zadd_(Zmergesettot2, nummerges);
- }else {
- zadd_(Zmergesettot, nummerges);
- zmax_(Zmergesetmax, nummerges);
- }
- trace2((qh ferr, "qh_getmergeset: %d merges found\n", nummerges));
-} /* getmergeset */
-
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="getmergeset_initial">-</a>
-
- qh_getmergeset_initial( facetlist )
- determine initial qh.facet_mergeset for facets
- tests all facet/neighbor pairs on facetlist
-
- returns:
- sorted qh.facet_mergeset with nonconvex ridges
- sets facet->tested, ridge->tested, and ridge->nonconvex
-
- notes:
- uses visit_id, assumes ridge->nonconvex is False
-
- see:
- qh_getmergeset()
-
- design:
- for each facet on facetlist
- for each untested neighbor of facet
- test facet and neighbor for convexity
- if non-convex
- append merge to qh.facet_mergeset
- mark one of the ridges as nonconvex
- sort qh.facet_mergeset by angle
-*/
-void qh_getmergeset_initial (facetT *facetlist) {
- facetT *facet, *neighbor, **neighborp;
- ridgeT *ridge, **ridgep;
- int nummerges;
-
- qh visit_id++;
- FORALLfacet_(facetlist) {
- facet->visitid= qh visit_id;
- facet->tested= True;
- FOREACHneighbor_(facet) {
- if (neighbor->visitid != qh visit_id) {
- if (qh_test_appendmerge (facet, neighbor)) {
- FOREACHridge_(neighbor->ridges) {
- if (facet == otherfacet_(ridge, neighbor)) {
- ridge->nonconvex= True;
- break; /* only one ridge is marked nonconvex */
- }
- }
- }
- }
- }
- FOREACHridge_(facet->ridges)
- ridge->tested= True;
- }
- nummerges= qh_setsize (qh facet_mergeset);
- if (qh ANGLEmerge)
- qsort(SETaddr_(qh facet_mergeset, mergeT), nummerges,sizeof(mergeT *),qh_compareangle);
- else
- qsort(SETaddr_(qh facet_mergeset, mergeT), nummerges,sizeof(mergeT *),qh_comparemerge);
- if (qh POSTmerging) {
- zadd_(Zmergeinittot2, nummerges);
- }else {
- zadd_(Zmergeinittot, nummerges);
- zmax_(Zmergeinitmax, nummerges);
- }
- trace2((qh ferr, "qh_getmergeset_initial: %d merges found\n", nummerges));
-} /* getmergeset_initial */
-
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="hashridge">-</a>
-
- qh_hashridge( hashtable, hashsize, ridge, oldvertex )
- add ridge to hashtable without oldvertex
-
- notes:
- assumes hashtable is large enough
-
- design:
- determine hash value for ridge without oldvertex
- find next empty slot for ridge
-*/
-void qh_hashridge (setT *hashtable, int hashsize, ridgeT *ridge, vertexT *oldvertex) {
- int hash;
- ridgeT *ridgeA;
-
- hash= (int)qh_gethash (hashsize, ridge->vertices, qh hull_dim-1, 0, oldvertex);
- while (True) {
- if (!(ridgeA= SETelemt_(hashtable, hash, ridgeT))) {
- SETelem_(hashtable, hash)= ridge;
- break;
- }else if (ridgeA == ridge)
- break;
- if (++hash == hashsize)
- hash= 0;
- }
-} /* hashridge */
-
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="hashridge_find">-</a>
-
- qh_hashridge_find( hashtable, hashsize, ridge, vertex, oldvertex, hashslot )
- returns matching ridge without oldvertex in hashtable
- for ridge without vertex
- if oldvertex is NULL
- matches with any one skip
-
- returns:
- matching ridge or NULL
- if no match,
- if ridge already in table
- hashslot= -1
- else
- hashslot= next NULL index
-
- notes:
- assumes hashtable is large enough
- can't match ridge to itself
-
- design:
- get hash value for ridge without vertex
- for each hashslot
- return match if ridge matches ridgeA without oldvertex
-*/
-ridgeT *qh_hashridge_find (setT *hashtable, int hashsize, ridgeT *ridge,
- vertexT *vertex, vertexT *oldvertex, int *hashslot) {
- int hash;
- ridgeT *ridgeA;
-
- *hashslot= 0;
- zinc_(Zhashridge);
- hash= (int)qh_gethash (hashsize, ridge->vertices, qh hull_dim-1, 0, vertex);
- while ((ridgeA= SETelemt_(hashtable, hash, ridgeT))) {
- if (ridgeA == ridge)
- *hashslot= -1;
- else {
- zinc_(Zhashridgetest);
- if (qh_setequal_except (ridge->vertices, vertex, ridgeA->vertices, oldvertex))
- return ridgeA;
- }
- if (++hash == hashsize)
- hash= 0;
- }
- if (!*hashslot)
- *hashslot= hash;
- return NULL;
-} /* hashridge_find */
-
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="makeridges">-</a>
-
- qh_makeridges( facet )
- creates explicit ridges between simplicial facets
-
- returns:
- facet with ridges and without qh_MERGEridge
- ->simplicial is False
-
- notes:
- allows qh_MERGEridge flag
- uses existing ridges
- duplicate neighbors ok if ridges already exist (qh_mergecycle_ridges)
-
- see:
- qh_mergecycle_ridges()
-
- design:
- look for qh_MERGEridge neighbors
- mark neighbors that already have ridges
- for each unprocessed neighbor of facet
- create a ridge for neighbor and facet
- if any qh_MERGEridge neighbors
- delete qh_MERGEridge flags (already handled by qh_mark_dupridges)
-*/
-void qh_makeridges(facetT *facet) {
- facetT *neighbor, **neighborp;
- ridgeT *ridge, **ridgep;
- int neighbor_i, neighbor_n;
- boolT toporient, mergeridge= False;
-
- if (!facet->simplicial)
- return;
- trace4((qh ferr, "qh_makeridges: make ridges for f%d\n", facet->id));
- facet->simplicial= False;
- FOREACHneighbor_(facet) {
- if (neighbor == qh_MERGEridge)
- mergeridge= True;
- else
- neighbor->seen= False;
- }
- FOREACHridge_(facet->ridges)
- otherfacet_(ridge, facet)->seen= True;
- FOREACHneighbor_i_(facet) {
- if (neighbor == qh_MERGEridge)
- continue; /* fixed by qh_mark_dupridges */
- else if (!neighbor->seen) { /* no current ridges */
- ridge= qh_newridge();
- ridge->vertices= qh_setnew_delnthsorted (facet->vertices, qh hull_dim,
- neighbor_i, 0);
- toporient= facet->toporient ^ (neighbor_i & 0x1);
- if (toporient) {
- ridge->top= facet;
- ridge->bottom= neighbor;
- }else {
- ridge->top= neighbor;
- ridge->bottom= facet;
- }
-#if 0 /* this also works */
- flip= (facet->toporient ^ neighbor->toporient)^(skip1 & 0x1) ^ (skip2 & 0x1);
- if (facet->toporient ^ (skip1 & 0x1) ^ flip) {
- ridge->top= neighbor;
- ridge->bottom= facet;
- }else {
- ridge->top= facet;
- ridge->bottom= neighbor;
- }
-#endif
- qh_setappend(&(facet->ridges), ridge);
- qh_setappend(&(neighbor->ridges), ridge);
- }
- }
- if (mergeridge) {
- while (qh_setdel (facet->neighbors, qh_MERGEridge))
- ; /* delete each one */
- }
-} /* makeridges */
-
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="mark_dupridges">-</a>
-
- qh_mark_dupridges( facetlist )
- add duplicated ridges to qh.facet_mergeset
- facet->dupridge is true
-
- returns:
- duplicate ridges on qh.facet_mergeset
- ->mergeridge/->mergeridge2 set
- duplicate ridges marked by qh_MERGEridge and both sides facet->dupridge
- no MERGEridges in neighbor sets
-
- notes:
- duplicate ridges occur when the horizon is pinched,
- i.e. a subridge occurs in more than two horizon ridges.
- could rename vertices that pinch the horizon
- uses qh.visit_id
-
- design:
- for all facets on facetlist
- if facet contains a duplicate ridge
- for each neighbor of facet
- if neighbor marked qh_MERGEridge (one side of the merge)
- set facet->mergeridge
- else
- if neighbor contains a duplicate ridge
- and the back link is qh_MERGEridge
- append duplicate ridge to qh.facet_mergeset
- for each duplicate ridge
- make ridge sets in preparation for merging
- remove qh_MERGEridge from neighbor set
- for each duplicate ridge
- restore the missing neighbor from the neighbor set that was qh_MERGEridge
- add the missing ridge for this neighbor
-*/
-void qh_mark_dupridges(facetT *facetlist) {
- facetT *facet, *neighbor, **neighborp;
- int nummerge=0;
- mergeT *merge, **mergep;
-
-
- trace4((qh ferr, "qh_mark_dupridges: identify duplicate ridges\n"));
- FORALLfacet_(facetlist) {
- if (facet->dupridge) {
- FOREACHneighbor_(facet) {
- if (neighbor == qh_MERGEridge) {
- facet->mergeridge= True;
- continue;
- }
- if (neighbor->dupridge
- && !qh_setin (neighbor->neighbors, facet)) { /* qh_MERGEridge */
- qh_appendmergeset (facet, neighbor, MRGridge, NULL);
- facet->mergeridge2= True;
- facet->mergeridge= True;
- nummerge++;
- }
- }
- }
- }
- if (!nummerge)
- return;
- FORALLfacet_(facetlist) { /* gets rid of qh_MERGEridge */
- if (facet->mergeridge && !facet->mergeridge2)
- qh_makeridges (facet);
- }
- FOREACHmerge_(qh facet_mergeset) { /* restore the missing neighbors */
- if (merge->type == MRGridge) {
- qh_setappend (&merge->facet2->neighbors, merge->facet1);
- qh_makeridges (merge->facet1); /* and the missing ridges */
- }
- }
- trace1((qh ferr, "qh_mark_dupridges: found %d duplicated ridges\n",
- nummerge));
-} /* mark_dupridges */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="maydropneighbor">-</a>
-
- qh_maydropneighbor( facet )
- drop neighbor relationship if no ridge between facet and neighbor
-
- returns:
- neighbor sets updated
- appends degenerate facets to qh.facet_mergeset
-
- notes:
- won't cause redundant facets since vertex inclusion is the same
- may drop vertex and neighbor if no ridge
- uses qh.visit_id
-
- design:
- visit all neighbors with ridges
- for each unvisited neighbor of facet
- delete neighbor and facet from the neighbor sets
- if neighbor becomes degenerate
- append neighbor to qh.degen_mergeset
- if facet is degenerate
- append facet to qh.degen_mergeset
-*/
-void qh_maydropneighbor (facetT *facet) {
- ridgeT *ridge, **ridgep;
- realT angledegen= qh_ANGLEdegen;
- facetT *neighbor, **neighborp;
-
- qh visit_id++;
- trace4((qh ferr, "qh_maydropneighbor: test f%d for no ridges to a neighbor\n",
- facet->id));
- FOREACHridge_(facet->ridges) {
- ridge->top->visitid= qh visit_id;
- ridge->bottom->visitid= qh visit_id;
- }
- FOREACHneighbor_(facet) {
- if (neighbor->visitid != qh visit_id) {
- trace0((qh ferr, "qh_maydropneighbor: facets f%d and f%d are no longer neighbors during p%d\n",
- facet->id, neighbor->id, qh furthest_id));
- zinc_(Zdropneighbor);
- qh_setdel (facet->neighbors, neighbor);
- neighborp--; /* repeat, deleted a neighbor */
- qh_setdel (neighbor->neighbors, facet);
- if (qh_setsize (neighbor->neighbors) < qh hull_dim) {
- zinc_(Zdropdegen);
- qh_appendmergeset (neighbor, neighbor, MRGdegen, &angledegen);
- trace2((qh ferr, "qh_maydropneighbors: f%d is degenerate.\n", neighbor->id));
- }
- }
- }
- if (qh_setsize (facet->neighbors) < qh hull_dim) {
- zinc_(Zdropdegen);
- qh_appendmergeset (facet, facet, MRGdegen, &angledegen);
- trace2((qh ferr, "qh_maydropneighbors: f%d is degenerate.\n", facet->id));
- }
-} /* maydropneighbor */
-
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="merge_degenredundant">-</a>
-
- qh_merge_degenredundant()
- merge all degenerate and redundant facets
- qh.degen_mergeset contains merges from qh_degen_redundant_neighbors()
-
- returns:
- number of merges performed
- resets facet->degenerate/redundant
- if deleted (visible) facet has no neighbors
- sets ->f.replace to NULL
-
- notes:
- redundant merges happen before degenerate ones
- merging and renaming vertices can result in degen/redundant facets
-
- design:
- for each merge on qh.degen_mergeset
- if redundant merge
- if non-redundant facet merged into redundant facet
- recheck facet for redundancy
- else
- merge redundant facet into other facet
-*/
-int qh_merge_degenredundant (void) {
- int size;
- mergeT *merge;
- facetT *bestneighbor, *facet1, *facet2;
- realT dist, mindist, maxdist;
- vertexT *vertex, **vertexp;
- int nummerges= 0;
- mergeType mergetype;
-
- while ((merge= (mergeT*)qh_setdellast (qh degen_mergeset))) {
- facet1= merge->facet1;
- facet2= merge->facet2;
- mergetype= merge->type;
- qh_memfree (merge, sizeof(mergeT));
- if (facet1->visible)
- continue;
- facet1->degenerate= False;
- facet1->redundant= False;
- if (qh TRACEmerge-1 == zzval_(Ztotmerge))
- qhmem.IStracing= qh IStracing= qh TRACElevel;
- if (mergetype == MRGredundant) {
- zinc_(Zneighbor);
- while (facet2->visible) {
- if (!facet2->f.replace) {
- fprintf (qh ferr, "qhull internal error (qh_merge_degenredunant): f%d redundant but f%d has no replacement\n",
- facet1->id, facet2->id);
- qh_errexit2 (qh_ERRqhull, facet1, facet2);
- }
- facet2= facet2->f.replace;
- }
- if (facet1 == facet2) {
- qh_degen_redundant_facet (facet1); /* in case of others */
- continue;
- }
- trace2((qh ferr, "qh_merge_degenredundant: facet f%d is contained in f%d, will merge\n",
- facet1->id, facet2->id));
- qh_mergefacet(facet1, facet2, NULL, NULL, !qh_MERGEapex);
- /* merge distance is already accounted for */
- nummerges++;
- }else { /* mergetype == MRGdegen, other merges may have fixed */
- if (!(size= qh_setsize (facet1->neighbors))) {
- zinc_(Zdelfacetdup);
- trace2((qh ferr, "qh_merge_degenredundant: facet f%d has no neighbors. Deleted\n", facet1->id));
- qh_willdelete (facet1, NULL);
- FOREACHvertex_(facet1->vertices) {
- qh_setdel (vertex->neighbors, facet1);
- if (!SETfirst_(vertex->neighbors)) {
- zinc_(Zdegenvertex);
- trace2((qh ferr, "qh_merge_degenredundant: deleted v%d because f%d has no neighbors\n",
- vertex->id, facet1->id));
- vertex->deleted= True;
- qh_setappend (&qh del_vertices, vertex);
- }
- }
- nummerges++;
- }else if (size < qh hull_dim) {
- bestneighbor= qh_findbestneighbor(facet1, &dist, &mindist, &maxdist);
- trace2((qh ferr, "qh_merge_degenredundant: facet f%d has %d neighbors, merge into f%d dist %2.2g\n",
- facet1->id, size, bestneighbor->id, dist));
- qh_mergefacet(facet1, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
- nummerges++;
- if (qh PRINTstatistics) {
- zinc_(Zdegen);
- wadd_(Wdegentot, dist);
- wmax_(Wdegenmax, dist);
- }
- } /* else, another merge fixed the degeneracy and redundancy tested */
- }
- }
- return nummerges;
-} /* merge_degenredundant */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="merge_nonconvex">-</a>
-
- qh_merge_nonconvex( facet1, facet2, mergetype )
- remove non-convex ridge between facet1 into facet2
- mergetype gives why the facet's are non-convex
-
- returns:
- merges one of the facets into the best neighbor
-
- design:
- if one of the facets is a new facet
- prefer merging new facet into old facet
- find best neighbors for both facets
- merge the nearest facet into its best neighbor
- update the statistics
-*/
-void qh_merge_nonconvex (facetT *facet1, facetT *facet2, mergeType mergetype) {
- facetT *bestfacet, *bestneighbor, *neighbor;
- realT dist, dist2, mindist, mindist2, maxdist, maxdist2;
-
- if (qh TRACEmerge-1 == zzval_(Ztotmerge))
- qhmem.IStracing= qh IStracing= qh TRACElevel;
- trace3((qh ferr, "qh_merge_nonconvex: merge #%d for f%d and f%d type %d\n",
- zzval_(Ztotmerge) + 1, facet1->id, facet2->id, mergetype));
- /* concave or coplanar */
- if (!facet1->newfacet) {
- bestfacet= facet2; /* avoid merging old facet if new is ok */
- facet2= facet1;
- facet1= bestfacet;
- }else
- bestfacet= facet1;
- bestneighbor= qh_findbestneighbor(bestfacet, &dist, &mindist, &maxdist);
- neighbor= qh_findbestneighbor(facet2, &dist2, &mindist2, &maxdist2);
- if (dist < dist2) {
- qh_mergefacet(bestfacet, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
- }else if (qh AVOIDold && !facet2->newfacet
- && ((mindist >= -qh MAXcoplanar && maxdist <= qh max_outside)
- || dist * 1.5 < dist2)) {
- zinc_(Zavoidold);
- wadd_(Wavoidoldtot, dist);
- wmax_(Wavoidoldmax, dist);
- trace2((qh ferr, "qh_merge_nonconvex: avoid merging old facet f%d dist %2.2g. Use f%d dist %2.2g instead\n",
- facet2->id, dist2, facet1->id, dist2));
- qh_mergefacet(bestfacet, bestneighbor, &mindist, &maxdist, !qh_MERGEapex);
- }else {
- qh_mergefacet(facet2, neighbor, &mindist2, &maxdist2, !qh_MERGEapex);
- dist= dist2;
- }
- if (qh PRINTstatistics) {
- if (mergetype == MRGanglecoplanar) {
- zinc_(Zacoplanar);
- wadd_(Wacoplanartot, dist);
- wmax_(Wacoplanarmax, dist);
- }else if (mergetype == MRGconcave) {
- zinc_(Zconcave);
- wadd_(Wconcavetot, dist);
- wmax_(Wconcavemax, dist);
- }else { /* MRGcoplanar */
- zinc_(Zcoplanar);
- wadd_(Wcoplanartot, dist);
- wmax_(Wcoplanarmax, dist);
- }
- }
-} /* merge_nonconvex */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="mergecycle">-</a>
-
- qh_mergecycle( samecycle, newfacet )
- merge a cycle of facets starting at samecycle into a newfacet
- newfacet is a horizon facet with ->normal
- samecycle facets are simplicial from an apex
-
- returns:
- initializes vertex neighbors on first merge
- samecycle deleted (placed on qh.visible_list)
- newfacet at end of qh.facet_list
- deleted vertices on qh.del_vertices
-
- see:
- qh_mergefacet()
- called by qh_mergecycle_all() for multiple, same cycle facets
-
- design:
- make vertex neighbors if necessary
- make ridges for newfacet
- merge neighbor sets of samecycle into newfacet
- merge ridges of samecycle into newfacet
- merge vertex neighbors of samecycle into newfacet
- make apex of samecycle the apex of newfacet
- if newfacet wasn't a new facet
- add its vertices to qh.newvertex_list
- delete samecycle facets a make newfacet a newfacet
-*/
-void qh_mergecycle (facetT *samecycle, facetT *newfacet) {
- int traceonce= False, tracerestore= 0;
- vertexT *apex;
-#ifndef qh_NOtrace
- facetT *same;
-#endif
-
- if (newfacet->tricoplanar) {
- if (!qh TRInormals) {
- fprintf (qh ferr, "qh_mergecycle: does not work for tricoplanar facets. Use option 'Q11'\n");
- qh_errexit (qh_ERRqhull, newfacet, NULL);
- }
- newfacet->tricoplanar= False;
- newfacet->keepcentrum= False;
- }
- if (!qh VERTEXneighbors)
- qh_vertexneighbors();
- zzinc_(Ztotmerge);
- if (qh REPORTfreq2 && qh POSTmerging) {
- if (zzval_(Ztotmerge) > qh mergereport + qh REPORTfreq2)
- qh_tracemerging();
- }
-#ifndef qh_NOtrace
- if (qh TRACEmerge == zzval_(Ztotmerge))
- qhmem.IStracing= qh IStracing= qh TRACElevel;
- trace2((qh ferr, "qh_mergecycle: merge #%d for facets from cycle f%d into coplanar horizon f%d\n",
- zzval_(Ztotmerge), samecycle->id, newfacet->id));
- if (newfacet == qh tracefacet) {
- tracerestore= qh IStracing;
- qh IStracing= 4;
- fprintf (qh ferr, "qh_mergecycle: ========= trace merge %d of samecycle %d into trace f%d, furthest is p%d\n",
- zzval_(Ztotmerge), samecycle->id, newfacet->id, qh furthest_id);
- traceonce= True;
- }
- if (qh IStracing >=4) {
- fprintf (qh ferr, " same cycle:");
- FORALLsame_cycle_(samecycle)
- fprintf(qh ferr, " f%d", same->id);
- fprintf (qh ferr, "\n");
- }
- if (qh IStracing >=4)
- qh_errprint ("MERGING CYCLE", samecycle, newfacet, NULL, NULL);
-#endif /* !qh_NOtrace */
- apex= SETfirstt_(samecycle->vertices, vertexT);
- qh_makeridges (newfacet);
- qh_mergecycle_neighbors (samecycle, newfacet);
- qh_mergecycle_ridges (samecycle, newfacet);
- qh_mergecycle_vneighbors (samecycle, newfacet);
- if (SETfirstt_(newfacet->vertices, vertexT) != apex)
- qh_setaddnth (&newfacet->vertices, 0, apex); /* apex has last id */
- if (!newfacet->newfacet)
- qh_newvertices (newfacet->vertices);
- qh_mergecycle_facets (samecycle, newfacet);
- qh_tracemerge (samecycle, newfacet);
- /* check for degen_redundant_neighbors after qh_forcedmerges() */
- if (traceonce) {
- fprintf (qh ferr, "qh_mergecycle: end of trace facet\n");
- qh IStracing= tracerestore;
- }
-} /* mergecycle */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="mergecycle_all">-</a>
-
- qh_mergecycle_all( facetlist, wasmerge )
- merge all samecycles of coplanar facets into horizon
- don't merge facets with ->mergeridge (these already have ->normal)
- all facets are simplicial from apex
- all facet->cycledone == False
-
- returns:
- all newfacets merged into coplanar horizon facets
- deleted vertices on qh.del_vertices
- sets wasmerge if any merge
-
- see:
- calls qh_mergecycle for multiple, same cycle facets
-
- design:
- for each facet on facetlist
- skip facets with duplicate ridges and normals
- check that facet is in a samecycle (->mergehorizon)
- if facet only member of samecycle
- sets vertex->delridge for all vertices except apex
- merge facet into horizon
- else
- mark all facets in samecycle
- remove facets with duplicate ridges from samecycle
- merge samecycle into horizon (deletes facets from facetlist)
-*/
-void qh_mergecycle_all (facetT *facetlist, boolT *wasmerge) {
- facetT *facet, *same, *prev, *horizon;
- facetT *samecycle= NULL, *nextfacet, *nextsame;
- vertexT *apex, *vertex, **vertexp;
- int cycles=0, total=0, facets, nummerge;
-
- trace2((qh ferr, "qh_mergecycle_all: begin\n"));
- for (facet= facetlist; facet && (nextfacet= facet->next); facet= nextfacet) {
- if (facet->normal)
- continue;
- if (!facet->mergehorizon) {
- fprintf (qh ferr, "qh_mergecycle_all: f%d without normal\n", facet->id);
- qh_errexit (qh_ERRqhull, facet, NULL);
- }
- horizon= SETfirstt_(facet->neighbors, facetT);
- if (facet->f.samecycle == facet) {
- zinc_(Zonehorizon);
- /* merge distance done in qh_findhorizon */
- apex= SETfirstt_(facet->vertices, vertexT);
- FOREACHvertex_(facet->vertices) {
- if (vertex != apex)
- vertex->delridge= True;
- }
- horizon->f.newcycle= NULL;
- qh_mergefacet (facet, horizon, NULL, NULL, qh_MERGEapex);
- }else {
- samecycle= facet;
- facets= 0;
- prev= facet;
- for (same= facet->f.samecycle; same; /* FORALLsame_cycle_(facet) */
- same= (same == facet ? NULL :nextsame)) { /* ends at facet */
- nextsame= same->f.samecycle;
- if (same->cycledone || same->visible)
- qh_infiniteloop (same);
- same->cycledone= True;
- if (same->normal) {
- prev->f.samecycle= same->f.samecycle; /* unlink ->mergeridge */
- same->f.samecycle= NULL;
- }else {
- prev= same;
- facets++;
- }
- }
- while (nextfacet && nextfacet->cycledone) /* will delete samecycle */
- nextfacet= nextfacet->next;
- horizon->f.newcycle= NULL;
- qh_mergecycle (samecycle, horizon);
- nummerge= horizon->nummerge + facets;
- if (nummerge > qh_MAXnummerge)
- horizon->nummerge= qh_MAXnummerge;
- else
- horizon->nummerge= nummerge;
- zzinc_(Zcyclehorizon);
- total += facets;
- zzadd_(Zcyclefacettot, facets);
- zmax_(Zcyclefacetmax, facets);
- }
- cycles++;
- }
- if (cycles)
- *wasmerge= True;
- trace1((qh ferr, "qh_mergecycle_all: merged %d same cycles or facets into coplanar horizons\n", cycles));
-} /* mergecycle_all */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="mergecycle_facets">-</a>
-
- qh_mergecycle_facets( samecycle, newfacet )
- finish merge of samecycle into newfacet
-
- returns:
- samecycle prepended to visible_list for later deletion and partitioning
- each facet->f.replace == newfacet
-
- newfacet moved to end of qh.facet_list
- makes newfacet a newfacet (get's facet1->id if it was old)
- sets newfacet->newmerge
- clears newfacet->center (unless merging into a large facet)
- clears newfacet->tested and ridge->tested for facet1
-
- adds neighboring facets to facet_mergeset if redundant or degenerate
-
- design:
- make newfacet a new facet and set its flags
- move samecycle facets to qh.visible_list for later deletion
- unless newfacet is large
- remove its centrum
-*/
-void qh_mergecycle_facets (facetT *samecycle, facetT *newfacet) {
- facetT *same, *next;
-
- trace4((qh ferr, "qh_mergecycle_facets: make newfacet new and samecycle deleted\n"));
- qh_removefacet(newfacet); /* append as a newfacet to end of qh facet_list */
- qh_appendfacet(newfacet);
- newfacet->newfacet= True;
- newfacet->simplicial= False;
- newfacet->newmerge= True;
-
- for (same= samecycle->f.samecycle; same; same= (same == samecycle ? NULL : next)) {
- next= same->f.samecycle; /* reused by willdelete */
- qh_willdelete (same, newfacet);
- }
- if (newfacet->center
- && qh_setsize (newfacet->vertices) <= qh hull_dim + qh_MAXnewcentrum) {
- qh_memfree (newfacet->center, qh normal_size);
- newfacet->center= NULL;
- }
- trace3((qh ferr, "qh_mergecycle_facets: merged facets from cycle f%d into f%d\n",
- samecycle->id, newfacet->id));
-} /* mergecycle_facets */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="mergecycle_neighbors">-</a>
-
- qh_mergecycle_neighbors( samecycle, newfacet )
- add neighbors for samecycle facets to newfacet
-
- returns:
- newfacet with updated neighbors and vice-versa
- newfacet has ridges
- all neighbors of newfacet marked with qh.visit_id
- samecycle facets marked with qh.visit_id-1
- ridges updated for simplicial neighbors of samecycle with a ridge
-
- notes:
- assumes newfacet not in samecycle
- usually, samecycle facets are new, simplicial facets without internal ridges
- not so if horizon facet is coplanar to two different samecycles
-
- see:
- qh_mergeneighbors()
-
- design:
- check samecycle
- delete neighbors from newfacet that are also in samecycle
- for each neighbor of a facet in samecycle
- if neighbor is simplicial
- if first visit
- move the neighbor relation to newfacet
- update facet links for its ridges
- else
- make ridges for neighbor
- remove samecycle reference
- else
- update neighbor sets
-*/
-void qh_mergecycle_neighbors(facetT *samecycle, facetT *newfacet) {
- facetT *same, *neighbor, **neighborp;
- int delneighbors= 0, newneighbors= 0;
- unsigned int samevisitid;
- ridgeT *ridge, **ridgep;
-
- samevisitid= ++qh visit_id;
- FORALLsame_cycle_(samecycle) {
- if (same->visitid == samevisitid || same->visible)
- qh_infiniteloop (samecycle);
- same->visitid= samevisitid;
- }
- newfacet->visitid= ++qh visit_id;
- trace4((qh ferr, "qh_mergecycle_neighbors: delete shared neighbors from newfacet\n"));
- FOREACHneighbor_(newfacet) {
- if (neighbor->visitid == samevisitid) {
- SETref_(neighbor)= NULL; /* samecycle neighbors deleted */
- delneighbors++;
- }else
- neighbor->visitid= qh visit_id;
- }
- qh_setcompact (newfacet->neighbors);
-
- trace4((qh ferr, "qh_mergecycle_neighbors: update neighbors\n"));
- FORALLsame_cycle_(samecycle) {
- FOREACHneighbor_(same) {
- if (neighbor->visitid == samevisitid)
- continue;
- if (neighbor->simplicial) {
- if (neighbor->visitid != qh visit_id) {
- qh_setappend (&newfacet->neighbors, neighbor);
- qh_setreplace (neighbor->neighbors, same, newfacet);
- newneighbors++;
- neighbor->visitid= qh visit_id;
- FOREACHridge_(neighbor->ridges) { /* update ridge in case of qh_makeridges */
- if (ridge->top == same) {
- ridge->top= newfacet;
- break;
- }else if (ridge->bottom == same) {
- ridge->bottom= newfacet;
- break;
- }
- }
- }else {
- qh_makeridges (neighbor);
- qh_setdel (neighbor->neighbors, same);
- /* same can't be horizon facet for neighbor */
- }
- }else { /* non-simplicial neighbor */
- qh_setdel (neighbor->neighbors, same);
- if (neighbor->visitid != qh visit_id) {
- qh_setappend (&neighbor->neighbors, newfacet);
- qh_setappend (&newfacet->neighbors, neighbor);
- neighbor->visitid= qh visit_id;
- newneighbors++;
- }
- }
- }
- }
- trace2((qh ferr, "qh_mergecycle_neighbors: deleted %d neighbors and added %d\n",
- delneighbors, newneighbors));
-} /* mergecycle_neighbors */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="mergecycle_ridges">-</a>
-
- qh_mergecycle_ridges( samecycle, newfacet )
- add ridges/neighbors for facets in samecycle to newfacet
- all new/old neighbors of newfacet marked with qh.visit_id
- facets in samecycle marked with qh.visit_id-1
- newfacet marked with qh.visit_id
-
- returns:
- newfacet has merged ridges
-
- notes:
- ridge already updated for simplicial neighbors of samecycle with a ridge
-
- see:
- qh_mergeridges()
- qh_makeridges()
-
- design:
- remove ridges between newfacet and samecycle
- for each facet in samecycle
- for each ridge in facet
- update facet pointers in ridge
- skip ridges processed in qh_mergecycle_neighors
- free ridges between newfacet and samecycle
- free ridges between facets of samecycle (on 2nd visit)
- append remaining ridges to newfacet
- if simpilicial facet
- for each neighbor of facet
- if simplicial facet
- and not samecycle facet or newfacet
- make ridge between neighbor and newfacet
-*/
-void qh_mergecycle_ridges(facetT *samecycle, facetT *newfacet) {
- facetT *same, *neighbor= NULL;
- int numold=0, numnew=0;
- int neighbor_i, neighbor_n;
- unsigned int samevisitid;
- ridgeT *ridge, **ridgep;
- boolT toporient;
- void **freelistp; /* used !qh_NOmem */
-
- trace4((qh ferr, "qh_mergecycle_ridges: delete shared ridges from newfacet\n"));
- samevisitid= qh visit_id -1;
- FOREACHridge_(newfacet->ridges) {
- neighbor= otherfacet_(ridge, newfacet);
- if (neighbor->visitid == samevisitid)
- SETref_(ridge)= NULL; /* ridge free'd below */
- }
- qh_setcompact (newfacet->ridges);
-
- trace4((qh ferr, "qh_mergecycle_ridges: add ridges to newfacet\n"));
- FORALLsame_cycle_(samecycle) {
- FOREACHridge_(same->ridges) {
- if (ridge->top == same) {
- ridge->top= newfacet;
- neighbor= ridge->bottom;
- }else if (ridge->bottom == same) {
- ridge->bottom= newfacet;
- neighbor= ridge->top;
- }else if (ridge->top == newfacet || ridge->bottom == newfacet) {
- qh_setappend (&newfacet->ridges, ridge);
- numold++; /* already set by qh_mergecycle_neighbors */
- continue;
- }else {
- fprintf (qh ferr, "qhull internal error (qh_mergecycle_ridges): bad ridge r%d\n", ridge->id);
- qh_errexit (qh_ERRqhull, NULL, ridge);
- }
- if (neighbor == newfacet) {
- qh_setfree(&(ridge->vertices));
- qh_memfree_(ridge, sizeof(ridgeT), freelistp);
- numold++;
- }else if (neighbor->visitid == samevisitid) {
- qh_setdel (neighbor->ridges, ridge);
- qh_setfree(&(ridge->vertices));
- qh_memfree_(ridge, sizeof(ridgeT), freelistp);
- numold++;
- }else {
- qh_setappend (&newfacet->ridges, ridge);
- numold++;
- }
- }
- if (same->ridges)
- qh_settruncate (same->ridges, 0);
- if (!same->simplicial)
- continue;
- FOREACHneighbor_i_(same) { /* note: !newfact->simplicial */
- if (neighbor->visitid != samevisitid && neighbor->simplicial) {
- ridge= qh_newridge();
- ridge->vertices= qh_setnew_delnthsorted (same->vertices, qh hull_dim,
- neighbor_i, 0);
- toporient= same->toporient ^ (neighbor_i & 0x1);
- if (toporient) {
- ridge->top= newfacet;
- ridge->bottom= neighbor;
- }else {
- ridge->top= neighbor;
- ridge->bottom= newfacet;
- }
- qh_setappend(&(newfacet->ridges), ridge);
- qh_setappend(&(neighbor->ridges), ridge);
- numnew++;
- }
- }
- }
-
- trace2((qh ferr, "qh_mergecycle_ridges: found %d old ridges and %d new ones\n",
- numold, numnew));
-} /* mergecycle_ridges */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="mergecycle_vneighbors">-</a>
-
- qh_mergecycle_vneighbors( samecycle, newfacet )
- create vertex neighbors for newfacet from vertices of facets in samecycle
- samecycle marked with visitid == qh.visit_id - 1
-
- returns:
- newfacet vertices with updated neighbors
- marks newfacet with qh.visit_id-1
- deletes vertices that are merged away
- sets delridge on all vertices (faster here than in mergecycle_ridges)
-
- see:
- qh_mergevertex_neighbors()
-
- design:
- for each vertex of samecycle facet
- set vertex->delridge
- delete samecycle facets from vertex neighbors
- append newfacet to vertex neighbors
- if vertex only in newfacet
- delete it from newfacet
- add it to qh.del_vertices for later deletion
-*/
-void qh_mergecycle_vneighbors (facetT *samecycle, facetT *newfacet) {
- facetT *neighbor, **neighborp;
- unsigned int mergeid;
- vertexT *vertex, **vertexp, *apex;
- setT *vertices;
-
- trace4((qh ferr, "qh_mergecycle_vneighbors: update vertex neighbors for newfacet\n"));
- mergeid= qh visit_id - 1;
- newfacet->visitid= mergeid;
- vertices= qh_basevertices (samecycle); /* temp */
- apex= SETfirstt_(samecycle->vertices, vertexT);
- qh_setappend (&vertices, apex);
- FOREACHvertex_(vertices) {
- vertex->delridge= True;
- FOREACHneighbor_(vertex) {
- if (neighbor->visitid == mergeid)
- SETref_(neighbor)= NULL;
- }
- qh_setcompact (vertex->neighbors);
- qh_setappend (&vertex->neighbors, newfacet);
- if (!SETsecond_(vertex->neighbors)) {
- zinc_(Zcyclevertex);
- trace2((qh ferr, "qh_mergecycle_vneighbors: deleted v%d when merging cycle f%d into f%d\n",
- vertex->id, samecycle->id, newfacet->id));
- qh_setdelsorted (newfacet->vertices, vertex);
- vertex->deleted= True;
- qh_setappend (&qh del_vertices, vertex);
- }
- }
- qh_settempfree (&vertices);
- trace3((qh ferr, "qh_mergecycle_vneighbors: merged vertices from cycle f%d into f%d\n",
- samecycle->id, newfacet->id));
-} /* mergecycle_vneighbors */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="mergefacet">-</a>
-
- qh_mergefacet( facet1, facet2, mindist, maxdist, mergeapex )
- merges facet1 into facet2
- mergeapex==qh_MERGEapex if merging new facet into coplanar horizon
-
- returns:
- qh.max_outside and qh.min_vertex updated
- initializes vertex neighbors on first merge
-
- returns:
- facet2 contains facet1's vertices, neighbors, and ridges
- facet2 moved to end of qh.facet_list
- makes facet2 a newfacet
- sets facet2->newmerge set
- clears facet2->center (unless merging into a large facet)
- clears facet2->tested and ridge->tested for facet1
-
- facet1 prepended to visible_list for later deletion and partitioning
- facet1->f.replace == facet2
-
- adds neighboring facets to facet_mergeset if redundant or degenerate
-
- notes:
- mindist/maxdist may be NULL
- traces merge if fmax_(maxdist,-mindist) > TRACEdist
-
- see:
- qh_mergecycle()
-
- design:
- trace merge and check for degenerate simplex
- make ridges for both facets
- update qh.max_outside, qh.max_vertex, qh.min_vertex
- update facet2->maxoutside and keepcentrum
- update facet2->nummerge
- update tested flags for facet2
- if facet1 is simplicial
- merge facet1 into facet2
- else
- merge facet1's neighbors into facet2
- merge facet1's ridges into facet2
- merge facet1's vertices into facet2
- merge facet1's vertex neighbors into facet2
- add facet2's vertices to qh.new_vertexlist
- unless qh_MERGEapex
- test facet2 for degenerate or redundant neighbors
- move facet1 to qh.visible_list for later deletion
- move facet2 to end of qh.newfacet_list
-*/
-void qh_mergefacet(facetT *facet1, facetT *facet2, realT *mindist, realT *maxdist, boolT mergeapex) {
- boolT traceonce= False;
- vertexT *vertex, **vertexp;
- int tracerestore=0, nummerge;
-
- if (facet1->tricoplanar || facet2->tricoplanar) {
- if (!qh TRInormals) {
- fprintf (qh ferr, "qh_mergefacet: does not work for tricoplanar facets. Use option 'Q11'\n");
- qh_errexit2 (qh_ERRqhull, facet1, facet2);
- }
- if (facet2->tricoplanar) {
- facet2->tricoplanar= False;
- facet2->keepcentrum= False;
- }
- }
- zzinc_(Ztotmerge);
- if (qh REPORTfreq2 && qh POSTmerging) {
- if (zzval_(Ztotmerge) > qh mergereport + qh REPORTfreq2)
- qh_tracemerging();
- }
-#ifndef qh_NOtrace
- if (qh build_cnt >= qh RERUN) {
- if (mindist && (-*mindist > qh TRACEdist || *maxdist > qh TRACEdist)) {
- tracerestore= 0;
- qh IStracing= qh TRACElevel;
- traceonce= True;
- fprintf (qh ferr, "qh_mergefacet: ========= trace wide merge #%d (%2.2g) for f%d into f%d, last point was p%d\n", zzval_(Ztotmerge),
- fmax_(-*mindist, *maxdist), facet1->id, facet2->id, qh furthest_id);
- }else if (facet1 == qh tracefacet || facet2 == qh tracefacet) {
- tracerestore= qh IStracing;
- qh IStracing= 4;
- traceonce= True;
- fprintf (qh ferr, "qh_mergefacet: ========= trace merge #%d involving f%d, furthest is p%d\n",
- zzval_(Ztotmerge), qh tracefacet_id, qh furthest_id);
- }
- }
- if (qh IStracing >= 2) {
- realT mergemin= -2;
- realT mergemax= -2;
-
- if (mindist) {
- mergemin= *mindist;
- mergemax= *maxdist;
- }
- fprintf (qh ferr, "qh_mergefacet: #%d merge f%d into f%d, mindist= %2.2g, maxdist= %2.2g\n",
- zzval_(Ztotmerge), facet1->id, facet2->id, mergemin, mergemax);
- }
-#endif /* !qh_NOtrace */
- if (facet1 == facet2 || facet1->visible || facet2->visible) {
- fprintf (qh ferr, "qhull internal error (qh_mergefacet): either f%d and f%d are the same or one is a visible facet\n",
- facet1->id, facet2->id);
- qh_errexit2 (qh_ERRqhull, facet1, facet2);
- }
- if (qh num_facets - qh num_visible <= qh hull_dim + 1) {
- fprintf(qh ferr, "\n\
-qhull precision error: Only %d facets remain. Can not merge another\n\
-pair. The input is too degenerate or the convexity constraints are\n\
-too strong.\n", qh hull_dim+1);
- if (qh hull_dim >= 5 && !qh MERGEexact)
- fprintf(qh ferr, "Option 'Qx' may avoid this problem.\n");
- qh_errexit(qh_ERRinput, NULL, NULL);
- }
- if (!qh VERTEXneighbors)
- qh_vertexneighbors();
- qh_makeridges(facet1);
- qh_makeridges(facet2);
- if (qh IStracing >=4)
- qh_errprint ("MERGING", facet1, facet2, NULL, NULL);
- if (mindist) {
- maximize_(qh max_outside, *maxdist);
- maximize_(qh max_vertex, *maxdist);
-#if qh_MAXoutside
- maximize_(facet2->maxoutside, *maxdist);
-#endif
- minimize_(qh min_vertex, *mindist);
- if (!facet2->keepcentrum
- && (*maxdist > qh WIDEfacet || *mindist < -qh WIDEfacet)) {
- facet2->keepcentrum= True;
- zinc_(Zwidefacet);
- }
- }
- nummerge= facet1->nummerge + facet2->nummerge + 1;
- if (nummerge >= qh_MAXnummerge)
- facet2->nummerge= qh_MAXnummerge;
- else
- facet2->nummerge= nummerge;
- facet2->newmerge= True;
- facet2->dupridge= False;
- qh_updatetested (facet1, facet2);
- if (qh hull_dim > 2 && qh_setsize (facet1->vertices) == qh hull_dim)
- qh_mergesimplex (facet1, facet2, mergeapex);
- else {
- qh vertex_visit++;
- FOREACHvertex_(facet2->vertices)
- vertex->visitid= qh vertex_visit;
- if (qh hull_dim == 2)
- qh_mergefacet2d(facet1, facet2);
- else {
- qh_mergeneighbors(facet1, facet2);
- qh_mergevertices(facet1->vertices, &facet2->vertices);
- }
- qh_mergeridges(facet1, facet2);
- qh_mergevertex_neighbors(facet1, facet2);
- if (!facet2->newfacet)
- qh_newvertices (facet2->vertices);
- }
- if (!mergeapex)
- qh_degen_redundant_neighbors (facet2, facet1);
- if (facet2->coplanar || !facet2->newfacet) {
- zinc_(Zmergeintohorizon);
- }else if (!facet1->newfacet && facet2->newfacet) {
- zinc_(Zmergehorizon);
- }else {
- zinc_(Zmergenew);
- }
- qh_willdelete (facet1, facet2);
- qh_removefacet(facet2); /* append as a newfacet to end of qh facet_list */
- qh_appendfacet(facet2);
- facet2->newfacet= True;
- facet2->tested= False;
- qh_tracemerge (facet1, facet2);
- if (traceonce) {
- fprintf (qh ferr, "qh_mergefacet: end of wide tracing\n");
- qh IStracing= tracerestore;
- }
-} /* mergefacet */
-
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="mergefacet2d">-</a>
-
- qh_mergefacet2d( facet1, facet2 )
- in 2d, merges neighbors and vertices of facet1 into facet2
-
- returns:
- build ridges for neighbors if necessary
- facet2 looks like a simplicial facet except for centrum, ridges
- neighbors are opposite the corresponding vertex
- maintains orientation of facet2
-
- notes:
- qh_mergefacet() retains non-simplicial structures
- they are not needed in 2d, but later routines may use them
- preserves qh.vertex_visit for qh_mergevertex_neighbors()
-
- design:
- get vertices and neighbors
- determine new vertices and neighbors
- set new vertices and neighbors and adjust orientation
- make ridges for new neighbor if needed
-*/
-void qh_mergefacet2d (facetT *facet1, facetT *facet2) {
- vertexT *vertex1A, *vertex1B, *vertex2A, *vertex2B, *vertexA, *vertexB;
- facetT *neighbor1A, *neighbor1B, *neighbor2A, *neighbor2B, *neighborA, *neighborB;
-
- vertex1A= SETfirstt_(facet1->vertices, vertexT);
- vertex1B= SETsecondt_(facet1->vertices, vertexT);
- vertex2A= SETfirstt_(facet2->vertices, vertexT);
- vertex2B= SETsecondt_(facet2->vertices, vertexT);
- neighbor1A= SETfirstt_(facet1->neighbors, facetT);
- neighbor1B= SETsecondt_(facet1->neighbors, facetT);
- neighbor2A= SETfirstt_(facet2->neighbors, facetT);
- neighbor2B= SETsecondt_(facet2->neighbors, facetT);
- if (vertex1A == vertex2A) {
- vertexA= vertex1B;
- vertexB= vertex2B;
- neighborA= neighbor2A;
- neighborB= neighbor1A;
- }else if (vertex1A == vertex2B) {
- vertexA= vertex1B;
- vertexB= vertex2A;
- neighborA= neighbor2B;
- neighborB= neighbor1A;
- }else if (vertex1B == vertex2A) {
- vertexA= vertex1A;
- vertexB= vertex2B;
- neighborA= neighbor2A;
- neighborB= neighbor1B;
- }else { /* 1B == 2B */
- vertexA= vertex1A;
- vertexB= vertex2A;
- neighborA= neighbor2B;
- neighborB= neighbor1B;
- }
- /* vertexB always from facet2, neighborB always from facet1 */
- if (vertexA->id > vertexB->id) {
- SETfirst_(facet2->vertices)= vertexA;
- SETsecond_(facet2->vertices)= vertexB;
- if (vertexB == vertex2A)
- facet2->toporient= !facet2->toporient;
- SETfirst_(facet2->neighbors)= neighborA;
- SETsecond_(facet2->neighbors)= neighborB;
- }else {
- SETfirst_(facet2->vertices)= vertexB;
- SETsecond_(facet2->vertices)= vertexA;
- if (vertexB == vertex2B)
- facet2->toporient= !facet2->toporient;
- SETfirst_(facet2->neighbors)= neighborB;
- SETsecond_(facet2->neighbors)= neighborA;
- }
- qh_makeridges (neighborB);
- qh_setreplace(neighborB->neighbors, facet1, facet2);
- trace4((qh ferr, "qh_mergefacet2d: merged v%d and neighbor f%d of f%d into f%d\n",
- vertexA->id, neighborB->id, facet1->id, facet2->id));
-} /* mergefacet2d */
-
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="mergeneighbors">-</a>
-
- qh_mergeneighbors( facet1, facet2 )
- merges the neighbors of facet1 into facet2
-
- see:
- qh_mergecycle_neighbors()
-
- design:
- for each neighbor of facet1
- if neighbor is also a neighbor of facet2
- if neighbor is simpilicial
- make ridges for later deletion as a degenerate facet
- update its neighbor set
- else
- move the neighbor relation to facet2
- remove the neighbor relation for facet1 and facet2
-*/
-void qh_mergeneighbors(facetT *facet1, facetT *facet2) {
- facetT *neighbor, **neighborp;
-
- trace4((qh ferr, "qh_mergeneighbors: merge neighbors of f%d and f%d\n",
- facet1->id, facet2->id));
- qh visit_id++;
- FOREACHneighbor_(facet2) {
- neighbor->visitid= qh visit_id;
- }
- FOREACHneighbor_(facet1) {
- if (neighbor->visitid == qh visit_id) {
- if (neighbor->simplicial) /* is degen, needs ridges */
- qh_makeridges (neighbor);
- if (SETfirstt_(neighbor->neighbors, facetT) != facet1) /*keep newfacet->horizon*/
- qh_setdel (neighbor->neighbors, facet1);
- else {
- qh_setdel(neighbor->neighbors, facet2);
- qh_setreplace(neighbor->neighbors, facet1, facet2);
- }
- }else if (neighbor != facet2) {
- qh_setappend(&(facet2->neighbors), neighbor);
- qh_setreplace(neighbor->neighbors, facet1, facet2);
- }
- }
- qh_setdel(facet1->neighbors, facet2); /* here for makeridges */
- qh_setdel(facet2->neighbors, facet1);
-} /* mergeneighbors */
-
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="mergeridges">-</a>
-
- qh_mergeridges( facet1, facet2 )
- merges the ridge set of facet1 into facet2
-
- returns:
- may delete all ridges for a vertex
- sets vertex->delridge on deleted ridges
-
- see:
- qh_mergecycle_ridges()
-
- design:
- delete ridges between facet1 and facet2
- mark (delridge) vertices on these ridges for later testing
- for each remaining ridge
- rename facet1 to facet2
-*/
-void qh_mergeridges(facetT *facet1, facetT *facet2) {
- ridgeT *ridge, **ridgep;
- vertexT *vertex, **vertexp;
-
- trace4((qh ferr, "qh_mergeridges: merge ridges of f%d and f%d\n",
- facet1->id, facet2->id));
- FOREACHridge_(facet2->ridges) {
- if ((ridge->top == facet1) || (ridge->bottom == facet1)) {
- FOREACHvertex_(ridge->vertices)
- vertex->delridge= True;
- qh_delridge(ridge); /* expensive in high-d, could rebuild */
- ridgep--; /*repeat*/
- }
- }
- FOREACHridge_(facet1->ridges) {
- if (ridge->top == facet1)
- ridge->top= facet2;
- else
- ridge->bottom= facet2;
- qh_setappend(&(facet2->ridges), ridge);
- }
-} /* mergeridges */
-
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="mergesimplex">-</a>
-
- qh_mergesimplex( facet1, facet2, mergeapex )
- merge simplicial facet1 into facet2
- mergeapex==qh_MERGEapex if merging samecycle into horizon facet
- vertex id is latest (most recently created)
- facet1 may be contained in facet2
- ridges exist for both facets
-
- returns:
- facet2 with updated vertices, ridges, neighbors
- updated neighbors for facet1's vertices
- facet1 not deleted
- sets vertex->delridge on deleted ridges
-
- notes:
- special case code since this is the most common merge
- called from qh_mergefacet()
-
- design:
- if qh_MERGEapex
- add vertices of facet2 to qh.new_vertexlist if necessary
- add apex to facet2
- else
- for each ridge between facet1 and facet2
- set vertex->delridge
- determine the apex for facet1 (i.e., vertex to be merged)
- unless apex already in facet2
- insert apex into vertices for facet2
- add vertices of facet2 to qh.new_vertexlist if necessary
- add apex to qh.new_vertexlist if necessary
- for each vertex of facet1
- if apex
- rename facet1 to facet2 in its vertex neighbors
- else
- delete facet1 from vertex neighors
- if only in facet2
- add vertex to qh.del_vertices for later deletion
- for each ridge of facet1
- delete ridges between facet1 and facet2
- append other ridges to facet2 after renaming facet to facet2
-*/
-void qh_mergesimplex(facetT *facet1, facetT *facet2, boolT mergeapex) {
- vertexT *vertex, **vertexp, *apex;
- ridgeT *ridge, **ridgep;
- boolT issubset= False;
- int vertex_i= -1, vertex_n;
- facetT *neighbor, **neighborp, *otherfacet;
-
- if (mergeapex) {
- if (!facet2->newfacet)
- qh_newvertices (facet2->vertices); /* apex is new */
- apex= SETfirstt_(facet1->vertices, vertexT);
- if (SETfirstt_(facet2->vertices, vertexT) != apex)
- qh_setaddnth (&facet2->vertices, 0, apex); /* apex has last id */
- else
- issubset= True;
- }else {
- zinc_(Zmergesimplex);
- FOREACHvertex_(facet1->vertices)
- vertex->seen= False;
- FOREACHridge_(facet1->ridges) {
- if (otherfacet_(ridge, facet1) == facet2) {
- FOREACHvertex_(ridge->vertices) {
- vertex->seen= True;
- vertex->delridge= True;
- }
- break;
- }
- }
- FOREACHvertex_(facet1->vertices) {
- if (!vertex->seen)
- break; /* must occur */
- }
- apex= vertex;
- trace4((qh ferr, "qh_mergesimplex: merge apex v%d of f%d into facet f%d\n",
- apex->id, facet1->id, facet2->id));
- FOREACHvertex_i_(facet2->vertices) {
- if (vertex->id < apex->id) {
- break;
- }else if (vertex->id == apex->id) {
- issubset= True;
- break;
- }
- }
- if (!issubset)
- qh_setaddnth (&facet2->vertices, vertex_i, apex);
- if (!facet2->newfacet)
- qh_newvertices (facet2->vertices);
- else if (!apex->newlist) {
- qh_removevertex (apex);
- qh_appendvertex (apex);
- }
- }
- trace4((qh ferr, "qh_mergesimplex: update vertex neighbors of f%d\n",
- facet1->id));
- FOREACHvertex_(facet1->vertices) {
- if (vertex == apex && !issubset)
- qh_setreplace (vertex->neighbors, facet1, facet2);
- else {
- qh_setdel (vertex->neighbors, facet1);
- if (!SETsecond_(vertex->neighbors))
- qh_mergevertex_del (vertex, facet1, facet2);
- }
- }
- trace4((qh ferr, "qh_mergesimplex: merge ridges and neighbors of f%d into f%d\n",
- facet1->id, facet2->id));
- qh visit_id++;
- FOREACHneighbor_(facet2)
- neighbor->visitid= qh visit_id;
- FOREACHridge_(facet1->ridges) {
- otherfacet= otherfacet_(ridge, facet1);
- if (otherfacet == facet2) {
- qh_setdel (facet2->ridges, ridge);
- qh_setfree(&(ridge->vertices));
- qh_memfree (ridge, sizeof(ridgeT));
- qh_setdel (facet2->neighbors, facet1);
- }else {
- qh_setappend (&facet2->ridges, ridge);
- if (otherfacet->visitid != qh visit_id) {
- qh_setappend (&facet2->neighbors, otherfacet);
- qh_setreplace (otherfacet->neighbors, facet1, facet2);
- otherfacet->visitid= qh visit_id;
- }else {
- if (otherfacet->simplicial) /* is degen, needs ridges */
- qh_makeridges (otherfacet);
- if (SETfirstt_(otherfacet->neighbors, facetT) != facet1)
- qh_setdel (otherfacet->neighbors, facet1);
- else { /*keep newfacet->neighbors->horizon*/
- qh_setdel(otherfacet->neighbors, facet2);
- qh_setreplace(otherfacet->neighbors, facet1, facet2);
- }
- }
- if (ridge->top == facet1) /* wait until after qh_makeridges */
- ridge->top= facet2;
- else
- ridge->bottom= facet2;
- }
- }
- SETfirst_(facet1->ridges)= NULL; /* it will be deleted */
- trace3((qh ferr, "qh_mergesimplex: merged simplex f%d apex v%d into facet f%d\n",
- facet1->id, getid_(apex), facet2->id));
-} /* mergesimplex */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="mergevertex_del">-</a>
-
- qh_mergevertex_del( vertex, facet1, facet2 )
- delete a vertex because of merging facet1 into facet2
-
- returns:
- deletes vertex from facet2
- adds vertex to qh.del_vertices for later deletion
-*/
-void qh_mergevertex_del (vertexT *vertex, facetT *facet1, facetT *facet2) {
-
- zinc_(Zmergevertex);
- trace2((qh ferr, "qh_mergevertex_del: deleted v%d when merging f%d into f%d\n",
- vertex->id, facet1->id, facet2->id));
- qh_setdelsorted (facet2->vertices, vertex);
- vertex->deleted= True;
- qh_setappend (&qh del_vertices, vertex);
-} /* mergevertex_del */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="mergevertex_neighbors">-</a>
-
- qh_mergevertex_neighbors( facet1, facet2 )
- merge the vertex neighbors of facet1 to facet2
-
- returns:
- if vertex is current qh.vertex_visit
- deletes facet1 from vertex->neighbors
- else
- renames facet1 to facet2 in vertex->neighbors
- deletes vertices if only one neighbor
-
- notes:
- assumes vertex neighbor sets are good
-*/
-void qh_mergevertex_neighbors(facetT *facet1, facetT *facet2) {
- vertexT *vertex, **vertexp;
-
- trace4((qh ferr, "qh_mergevertex_neighbors: merge vertex neighbors of f%d and f%d\n",
- facet1->id, facet2->id));
- if (qh tracevertex) {
- fprintf (qh ferr, "qh_mergevertex_neighbors: of f%d and f%d at furthest p%d f0= %p\n",
- facet1->id, facet2->id, qh furthest_id, qh tracevertex->neighbors->e[0].p);
- qh_errprint ("TRACE", NULL, NULL, NULL, qh tracevertex);
- }
- FOREACHvertex_(facet1->vertices) {
- if (vertex->visitid != qh vertex_visit)
- qh_setreplace(vertex->neighbors, facet1, facet2);
- else {
- qh_setdel(vertex->neighbors, facet1);
- if (!SETsecond_(vertex->neighbors))
- qh_mergevertex_del (vertex, facet1, facet2);
- }
- }
- if (qh tracevertex)
- qh_errprint ("TRACE", NULL, NULL, NULL, qh tracevertex);
-} /* mergevertex_neighbors */
-
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="mergevertices">-</a>
-
- qh_mergevertices( vertices1, vertices2 )
- merges the vertex set of facet1 into facet2
-
- returns:
- replaces vertices2 with merged set
- preserves vertex_visit for qh_mergevertex_neighbors
- updates qh.newvertex_list
-
- design:
- create a merged set of both vertices (in inverse id order)
-*/
-void qh_mergevertices(setT *vertices1, setT **vertices2) {
- int newsize= qh_setsize(vertices1)+qh_setsize(*vertices2) - qh hull_dim + 1;
- setT *mergedvertices;
- vertexT *vertex, **vertexp, **vertex2= SETaddr_(*vertices2, vertexT);
-
- mergedvertices= qh_settemp (newsize);
- FOREACHvertex_(vertices1) {
- if (!*vertex2 || vertex->id > (*vertex2)->id)
- qh_setappend (&mergedvertices, vertex);
- else {
- while (*vertex2 && (*vertex2)->id > vertex->id)
- qh_setappend (&mergedvertices, *vertex2++);
- if (!*vertex2 || (*vertex2)->id < vertex->id)
- qh_setappend (&mergedvertices, vertex);
- else
- qh_setappend (&mergedvertices, *vertex2++);
- }
- }
- while (*vertex2)
- qh_setappend (&mergedvertices, *vertex2++);
- if (newsize < qh_setsize (mergedvertices)) {
- fprintf (qh ferr, "qhull internal error (qh_mergevertices): facets did not share a ridge\n");
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- qh_setfree(vertices2);
- *vertices2= mergedvertices;
- qh_settemppop ();
-} /* mergevertices */
-
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="neighbor_intersections">-</a>
-
- qh_neighbor_intersections( vertex )
- return intersection of all vertices in vertex->neighbors except for vertex
-
- returns:
- returns temporary set of vertices
- does not include vertex
- NULL if a neighbor is simplicial
- NULL if empty set
-
- notes:
- used for renaming vertices
-
- design:
- initialize the intersection set with vertices of the first two neighbors
- delete vertex from the intersection
- for each remaining neighbor
- intersect its vertex set with the intersection set
- return NULL if empty
- return the intersection set
-*/
-setT *qh_neighbor_intersections (vertexT *vertex) {
- facetT *neighbor, **neighborp, *neighborA, *neighborB;
- setT *intersect;
- int neighbor_i, neighbor_n;
-
- FOREACHneighbor_(vertex) {
- if (neighbor->simplicial)
- return NULL;
- }
- neighborA= SETfirstt_(vertex->neighbors, facetT);
- neighborB= SETsecondt_(vertex->neighbors, facetT);
- zinc_(Zintersectnum);
- if (!neighborA)
- return NULL;
- if (!neighborB)
- intersect= qh_setcopy (neighborA->vertices, 0);
- else
- intersect= qh_vertexintersect_new (neighborA->vertices, neighborB->vertices);
- qh_settemppush (intersect);
- qh_setdelsorted (intersect, vertex);
- FOREACHneighbor_i_(vertex) {
- if (neighbor_i >= 2) {
- zinc_(Zintersectnum);
- qh_vertexintersect (&intersect, neighbor->vertices);
- if (!SETfirst_(intersect)) {
- zinc_(Zintersectfail);
- qh_settempfree (&intersect);
- return NULL;
- }
- }
- }
- trace3((qh ferr, "qh_neighbor_intersections: %d vertices in neighbor intersection of v%d\n",
- qh_setsize (intersect), vertex->id));
- return intersect;
-} /* neighbor_intersections */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="newvertices">-</a>
-
- qh_newvertices( vertices )
- add vertices to end of qh.vertex_list (marks as new vertices)
-
- returns:
- vertices on qh.newvertex_list
- vertex->newlist set
-*/
-void qh_newvertices (setT *vertices) {
- vertexT *vertex, **vertexp;
-
- FOREACHvertex_(vertices) {
- if (!vertex->newlist) {
- qh_removevertex (vertex);
- qh_appendvertex (vertex);
- }
- }
-} /* newvertices */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="reducevertices">-</a>
-
- qh_reducevertices()
- reduce extra vertices, shared vertices, and redundant vertices
- facet->newmerge is set if merged since last call
- if !qh.MERGEvertices, only removes extra vertices
-
- returns:
- True if also merged degen_redundant facets
- vertices are renamed if possible
- clears facet->newmerge and vertex->delridge
-
- notes:
- ignored if 2-d
-
- design:
- merge any degenerate or redundant facets
- for each newly merged facet
- remove extra vertices
- if qh.MERGEvertices
- for each newly merged facet
- for each vertex
- if vertex was on a deleted ridge
- rename vertex if it is shared
- remove delridge flag from new vertices
-*/
-boolT qh_reducevertices (void) {
- int numshare=0, numrename= 0;
- boolT degenredun= False;
- facetT *newfacet;
- vertexT *vertex, **vertexp;
-
- if (qh hull_dim == 2)
- return False;
- if (qh_merge_degenredundant())
- degenredun= True;
- LABELrestart:
- FORALLnew_facets {
- if (newfacet->newmerge) {
- if (!qh MERGEvertices)
- newfacet->newmerge= False;
- qh_remove_extravertices (newfacet);
- }
- }
- if (!qh MERGEvertices)
- return False;
- FORALLnew_facets {
- if (newfacet->newmerge) {
- newfacet->newmerge= False;
- FOREACHvertex_(newfacet->vertices) {
- if (vertex->delridge) {
- if (qh_rename_sharedvertex (vertex, newfacet)) {
- numshare++;
- vertexp--; /* repeat since deleted vertex */
- }
- }
- }
- }
- }
- FORALLvertex_(qh newvertex_list) {
- if (vertex->delridge && !vertex->deleted) {
- vertex->delridge= False;
- if (qh hull_dim >= 4 && qh_redundant_vertex (vertex)) {
- numrename++;
- if (qh_merge_degenredundant()) {
- degenredun= True;
- goto LABELrestart;
- }
- }
- }
- }
- trace1((qh ferr, "qh_reducevertices: renamed %d shared vertices and %d redundant vertices. Degen? %d\n",
- numshare, numrename, degenredun));
- return degenredun;
-} /* reducevertices */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="redundant_vertex">-</a>
-
- qh_redundant_vertex( vertex )
- detect and rename a redundant vertex
- vertices have full vertex->neighbors
-
- returns:
- returns true if find a redundant vertex
- deletes vertex (vertex->deleted)
-
- notes:
- only needed if vertex->delridge and hull_dim >= 4
- may add degenerate facets to qh.facet_mergeset
- doesn't change vertex->neighbors or create redundant facets
-
- design:
- intersect vertices of all facet neighbors of vertex
- determine ridges for these vertices
- if find a new vertex for vertex amoung these ridges and vertices
- rename vertex to the new vertex
-*/
-vertexT *qh_redundant_vertex (vertexT *vertex) {
- vertexT *newvertex= NULL;
- setT *vertices, *ridges;
-
- trace3((qh ferr, "qh_redundant_vertex: check if v%d can be renamed\n", vertex->id));
- if ((vertices= qh_neighbor_intersections (vertex))) {
- ridges= qh_vertexridges (vertex);
- if ((newvertex= qh_find_newvertex (vertex, vertices, ridges)))
- qh_renamevertex (vertex, newvertex, ridges, NULL, NULL);
- qh_settempfree (&ridges);
- qh_settempfree (&vertices);
- }
- return newvertex;
-} /* redundant_vertex */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="remove_extravertices">-</a>
-
- qh_remove_extravertices( facet )
- remove extra vertices from non-simplicial facets
-
- returns:
- returns True if it finds them
-
- design:
- for each vertex in facet
- if vertex not in a ridge (i.e., no longer used)
- delete vertex from facet
- delete facet from vertice's neighbors
- unless vertex in another facet
- add vertex to qh.del_vertices for later deletion
-*/
-boolT qh_remove_extravertices (facetT *facet) {
- ridgeT *ridge, **ridgep;
- vertexT *vertex, **vertexp;
- boolT foundrem= False;
-
- trace4((qh ferr, "qh_remove_extravertices: test f%d for extra vertices\n",
- facet->id));
- FOREACHvertex_(facet->vertices)
- vertex->seen= False;
- FOREACHridge_(facet->ridges) {
- FOREACHvertex_(ridge->vertices)
- vertex->seen= True;
- }
- FOREACHvertex_(facet->vertices) {
- if (!vertex->seen) {
- foundrem= True;
- zinc_(Zremvertex);
- qh_setdelsorted (facet->vertices, vertex);
- qh_setdel (vertex->neighbors, facet);
- if (!qh_setsize (vertex->neighbors)) {
- vertex->deleted= True;
- qh_setappend (&qh del_vertices, vertex);
- zinc_(Zremvertexdel);
- trace2((qh ferr, "qh_remove_extravertices: v%d deleted because it's lost all ridges\n", vertex->id));
- }else
- trace3((qh ferr, "qh_remove_extravertices: v%d removed from f%d because it's lost all ridges\n", vertex->id, facet->id));
- vertexp--; /*repeat*/
- }
- }
- return foundrem;
-} /* remove_extravertices */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="rename_sharedvertex">-</a>
-
- qh_rename_sharedvertex( vertex, facet )
- detect and rename if shared vertex in facet
- vertices have full ->neighbors
-
- returns:
- newvertex or NULL
- the vertex may still exist in other facets (i.e., a neighbor was pinched)
- does not change facet->neighbors
- updates vertex->neighbors
-
- notes:
- a shared vertex for a facet is only in ridges to one neighbor
- this may undo a pinched facet
-
- it does not catch pinches involving multiple facets. These appear
- to be difficult to detect, since an exhaustive search is too expensive.
-
- design:
- if vertex only has two neighbors
- determine the ridges that contain the vertex
- determine the vertices shared by both neighbors
- if can find a new vertex in this set
- rename the vertex to the new vertex
-*/
-vertexT *qh_rename_sharedvertex (vertexT *vertex, facetT *facet) {
- facetT *neighbor, **neighborp, *neighborA= NULL;
- setT *vertices, *ridges;
- vertexT *newvertex;
-
- if (qh_setsize (vertex->neighbors) == 2) {
- neighborA= SETfirstt_(vertex->neighbors, facetT);
- if (neighborA == facet)
- neighborA= SETsecondt_(vertex->neighbors, facetT);
- }else if (qh hull_dim == 3)
- return NULL;
- else {
- qh visit_id++;
- FOREACHneighbor_(facet)
- neighbor->visitid= qh visit_id;
- FOREACHneighbor_(vertex) {
- if (neighbor->visitid == qh visit_id) {
- if (neighborA)
- return NULL;
- neighborA= neighbor;
- }
- }
- if (!neighborA) {
- fprintf (qh ferr, "qhull internal error (qh_rename_sharedvertex): v%d's neighbors not in f%d\n",
- vertex->id, facet->id);
- qh_errprint ("ERRONEOUS", facet, NULL, NULL, vertex);
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- }
- /* the vertex is shared by facet and neighborA */
- ridges= qh_settemp (qh TEMPsize);
- neighborA->visitid= ++qh visit_id;
- qh_vertexridges_facet (vertex, facet, &ridges);
- trace2((qh ferr, "qh_rename_sharedvertex: p%d (v%d) is shared by f%d (%d ridges) and f%d\n",
- qh_pointid(vertex->point), vertex->id, facet->id, qh_setsize (ridges), neighborA->id));
- zinc_(Zintersectnum);
- vertices= qh_vertexintersect_new (facet->vertices, neighborA->vertices);
- qh_setdel (vertices, vertex);
- qh_settemppush (vertices);
- if ((newvertex= qh_find_newvertex (vertex, vertices, ridges)))
- qh_renamevertex (vertex, newvertex, ridges, facet, neighborA);
- qh_settempfree (&vertices);
- qh_settempfree (&ridges);
- return newvertex;
-} /* rename_sharedvertex */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="renameridgevertex">-</a>
-
- qh_renameridgevertex( ridge, oldvertex, newvertex )
- renames oldvertex as newvertex in ridge
-
- returns:
-
- design:
- delete oldvertex from ridge
- if newvertex already in ridge
- copy ridge->noconvex to another ridge if possible
- delete the ridge
- else
- insert newvertex into the ridge
- adjust the ridge's orientation
-*/
-void qh_renameridgevertex(ridgeT *ridge, vertexT *oldvertex, vertexT *newvertex) {
- int nth= 0, oldnth;
- facetT *temp;
- vertexT *vertex, **vertexp;
-
- oldnth= qh_setindex (ridge->vertices, oldvertex);
- qh_setdelnthsorted (ridge->vertices, oldnth);
- FOREACHvertex_(ridge->vertices) {
- if (vertex == newvertex) {
- zinc_(Zdelridge);
- if (ridge->nonconvex) /* only one ridge has nonconvex set */
- qh_copynonconvex (ridge);
- qh_delridge (ridge);
- trace2((qh ferr, "qh_renameridgevertex: ridge r%d deleted. It contained both v%d and v%d\n",
- ridge->id, oldvertex->id, newvertex->id));
- return;
- }
- if (vertex->id < newvertex->id)
- break;
- nth++;
- }
- qh_setaddnth(&ridge->vertices, nth, newvertex);
- if (abs(oldnth - nth)%2) {
- trace3((qh ferr, "qh_renameridgevertex: swapped the top and bottom of ridge r%d\n",
- ridge->id));
- temp= ridge->top;
- ridge->top= ridge->bottom;
- ridge->bottom= temp;
- }
-} /* renameridgevertex */
-
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="renamevertex">-</a>
-
- qh_renamevertex( oldvertex, newvertex, ridges, oldfacet, neighborA )
- renames oldvertex as newvertex in ridges
- gives oldfacet/neighborA if oldvertex is shared between two facets
-
- returns:
- oldvertex may still exist afterwards
-
-
- notes:
- can not change neighbors of newvertex (since it's a subset)
-
- design:
- for each ridge in ridges
- rename oldvertex to newvertex and delete degenerate ridges
- if oldfacet not defined
- for each neighbor of oldvertex
- delete oldvertex from neighbor's vertices
- remove extra vertices from neighbor
- add oldvertex to qh.del_vertices
- else if oldvertex only between oldfacet and neighborA
- delete oldvertex from oldfacet and neighborA
- add oldvertex to qh.del_vertices
- else oldvertex is in oldfacet and neighborA and other facets (i.e., pinched)
- delete oldvertex from oldfacet
- delete oldfacet from oldvertice's neighbors
- remove extra vertices (e.g., oldvertex) from neighborA
-*/
-void qh_renamevertex(vertexT *oldvertex, vertexT *newvertex, setT *ridges, facetT *oldfacet, facetT *neighborA) {
- facetT *neighbor, **neighborp;
- ridgeT *ridge, **ridgep;
- boolT istrace= False;
-
- if (qh IStracing >= 2 || oldvertex->id == qh tracevertex_id ||
- newvertex->id == qh tracevertex_id)
- istrace= True;
- FOREACHridge_(ridges)
- qh_renameridgevertex (ridge, oldvertex, newvertex);
- if (!oldfacet) {
- zinc_(Zrenameall);
- if (istrace)
- fprintf (qh ferr, "qh_renamevertex: renamed v%d to v%d in several facets\n",
- oldvertex->id, newvertex->id);
- FOREACHneighbor_(oldvertex) {
- qh_maydropneighbor (neighbor);
- qh_setdelsorted (neighbor->vertices, oldvertex);
- if (qh_remove_extravertices (neighbor))
- neighborp--; /* neighbor may be deleted */
- }
- if (!oldvertex->deleted) {
- oldvertex->deleted= True;
- qh_setappend (&qh del_vertices, oldvertex);
- }
- }else if (qh_setsize (oldvertex->neighbors) == 2) {
- zinc_(Zrenameshare);
- if (istrace)
- fprintf (qh ferr, "qh_renamevertex: renamed v%d to v%d in oldfacet f%d\n",
- oldvertex->id, newvertex->id, oldfacet->id);
- FOREACHneighbor_(oldvertex)
- qh_setdelsorted (neighbor->vertices, oldvertex);
- oldvertex->deleted= True;
- qh_setappend (&qh del_vertices, oldvertex);
- }else {
- zinc_(Zrenamepinch);
- if (istrace || qh IStracing)
- fprintf (qh ferr, "qh_renamevertex: renamed pinched v%d to v%d between f%d and f%d\n",
- oldvertex->id, newvertex->id, oldfacet->id, neighborA->id);
- qh_setdelsorted (oldfacet->vertices, oldvertex);
- qh_setdel (oldvertex->neighbors, oldfacet);
- qh_remove_extravertices (neighborA);
- }
-} /* renamevertex */
-
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="test_appendmerge">-</a>
-
- qh_test_appendmerge( facet, neighbor )
- tests facet/neighbor for convexity
- appends to mergeset if non-convex
- if pre-merging,
- nop if qh.SKIPconvex, or qh.MERGEexact and coplanar
-
- returns:
- true if appends facet/neighbor to mergeset
- sets facet->center as needed
- does not change facet->seen
-
- design:
- if qh.cos_max is defined
- if the angle between facet normals is too shallow
- append an angle-coplanar merge to qh.mergeset
- return True
- make facet's centrum if needed
- if facet's centrum is above the neighbor
- set isconcave
- else
- if facet's centrum is not below the neighbor
- set iscoplanar
- make neighbor's centrum if needed
- if neighbor's centrum is above the facet
- set isconcave
- else if neighbor's centrum is not below the facet
- set iscoplanar
- if isconcave or iscoplanar
- get angle if needed
- append concave or coplanar merge to qh.mergeset
-*/
-boolT qh_test_appendmerge (facetT *facet, facetT *neighbor) {
- realT dist, dist2= -REALmax, angle= -REALmax;
- boolT isconcave= False, iscoplanar= False, okangle= False;
-
- if (qh SKIPconvex && !qh POSTmerging)
- return False;
- if ((!qh MERGEexact || qh POSTmerging) && qh cos_max < REALmax/2) {
- angle= qh_getangle(facet->normal, neighbor->normal);
- zinc_(Zangletests);
- if (angle > qh cos_max) {
- zinc_(Zcoplanarangle);
- qh_appendmergeset(facet, neighbor, MRGanglecoplanar, &angle);
- trace2((qh ferr, "qh_test_appendmerge: coplanar angle %4.4g between f%d and f%d\n",
- angle, facet->id, neighbor->id));
- return True;
- }else
- okangle= True;
- }
- if (!facet->center)
- facet->center= qh_getcentrum (facet);
- zzinc_(Zcentrumtests);
- qh_distplane(facet->center, neighbor, &dist);
- if (dist > qh centrum_radius)
- isconcave= True;
- else {
- if (dist > -qh centrum_radius)
- iscoplanar= True;
- if (!neighbor->center)
- neighbor->center= qh_getcentrum (neighbor);
- zzinc_(Zcentrumtests);
- qh_distplane(neighbor->center, facet, &dist2);
- if (dist2 > qh centrum_radius)
- isconcave= True;
- else if (!iscoplanar && dist2 > -qh centrum_radius)
- iscoplanar= True;
- }
- if (!isconcave && (!iscoplanar || (qh MERGEexact && !qh POSTmerging)))
- return False;
- if (!okangle && qh ANGLEmerge) {
- angle= qh_getangle(facet->normal, neighbor->normal);
- zinc_(Zangletests);
- }
- if (isconcave) {
- zinc_(Zconcaveridge);
- if (qh ANGLEmerge)
- angle += qh_ANGLEconcave + 0.5;
- qh_appendmergeset(facet, neighbor, MRGconcave, &angle);
- trace0((qh ferr, "qh_test_appendmerge: concave f%d to f%d dist %4.4g and reverse dist %4.4g angle %4.4g during p%d\n",
- facet->id, neighbor->id, dist, dist2, angle, qh furthest_id));
- }else /* iscoplanar */ {
- zinc_(Zcoplanarcentrum);
- qh_appendmergeset(facet, neighbor, MRGcoplanar, &angle);
- trace2((qh ferr, "qh_test_appendmerge: coplanar f%d to f%d dist %4.4g, reverse dist %4.4g angle %4.4g\n",
- facet->id, neighbor->id, dist, dist2, angle));
- }
- return True;
-} /* test_appendmerge */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="test_vneighbors">-</a>
-
- qh_test_vneighbors()
- test vertex neighbors for convexity
- tests all facets on qh.newfacet_list
-
- returns:
- true if non-convex vneighbors appended to qh.facet_mergeset
- initializes vertex neighbors if needed
-
- notes:
- assumes all facet neighbors have been tested
- this can be expensive
- this does not guarantee that a centrum is below all facets
- but it is unlikely
- uses qh.visit_id
-
- design:
- build vertex neighbors if necessary
- for all new facets
- for all vertices
- for each unvisited facet neighbor of the vertex
- test new facet and neighbor for convexity
-*/
-boolT qh_test_vneighbors (void /* qh newfacet_list */) {
- facetT *newfacet, *neighbor, **neighborp;
- vertexT *vertex, **vertexp;
- int nummerges= 0;
-
- trace1((qh ferr, "qh_test_vneighbors: testing vertex neighbors for convexity\n"));
- if (!qh VERTEXneighbors)
- qh_vertexneighbors();
- FORALLnew_facets
- newfacet->seen= False;
- FORALLnew_facets {
- newfacet->seen= True;
- newfacet->visitid= qh visit_id++;
- FOREACHneighbor_(newfacet)
- newfacet->visitid= qh visit_id;
- FOREACHvertex_(newfacet->vertices) {
- FOREACHneighbor_(vertex) {
- if (neighbor->seen || neighbor->visitid == qh visit_id)
- continue;
- if (qh_test_appendmerge (newfacet, neighbor))
- nummerges++;
- }
- }
- }
- zadd_(Ztestvneighbor, nummerges);
- trace1((qh ferr, "qh_test_vneighbors: found %d non-convex, vertex neighbors\n",
- nummerges));
- return (nummerges > 0);
-} /* test_vneighbors */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="tracemerge">-</a>
-
- qh_tracemerge( facet1, facet2 )
- print trace message after merge
-*/
-void qh_tracemerge (facetT *facet1, facetT *facet2) {
- boolT waserror= False;
-
-#ifndef qh_NOtrace
- if (qh IStracing >= 4)
- qh_errprint ("MERGED", facet2, NULL, NULL, NULL);
- if (facet2 == qh tracefacet || (qh tracevertex && qh tracevertex->newlist)) {
- fprintf (qh ferr, "qh_tracemerge: trace facet and vertex after merge of f%d and f%d, furthest p%d\n", facet1->id, facet2->id, qh furthest_id);
- if (facet2 != qh tracefacet)
- qh_errprint ("TRACE", qh tracefacet,
- (qh tracevertex && qh tracevertex->neighbors) ?
- SETfirstt_(qh tracevertex->neighbors, facetT) : NULL,
- NULL, qh tracevertex);
- }
- if (qh tracevertex) {
- if (qh tracevertex->deleted)
- fprintf (qh ferr, "qh_tracemerge: trace vertex deleted at furthest p%d\n",
- qh furthest_id);
- else
- qh_checkvertex (qh tracevertex);
- }
- if (qh tracefacet) {
- qh_checkfacet (qh tracefacet, True, &waserror);
- if (waserror)
- qh_errexit (qh_ERRqhull, qh tracefacet, NULL);
- }
-#endif /* !qh_NOtrace */
- if (qh CHECKfrequently || qh IStracing >= 4) { /* can't check polygon here */
- qh_checkfacet (facet2, True, &waserror);
- if (waserror)
- qh_errexit(qh_ERRqhull, NULL, NULL);
- }
-} /* tracemerge */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="tracemerging">-</a>
-
- qh_tracemerging()
- print trace message during POSTmerging
-
- returns:
- updates qh.mergereport
-
- notes:
- called from qh_mergecycle() and qh_mergefacet()
-
- see:
- qh_buildtracing()
-*/
-void qh_tracemerging (void) {
- realT cpu;
- int total;
- time_t timedata;
- struct tm *tp;
-
- qh mergereport= zzval_(Ztotmerge);
- time (&timedata);
- tp= localtime (&timedata);
- cpu= qh_CPUclock;
- cpu /= qh_SECticks;
- total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
- fprintf (qh ferr, "\n\
-At %d:%d:%d & %2.5g CPU secs, qhull has merged %d facets. The hull\n\
- contains %d facets and %d vertices.\n",
- tp->tm_hour, tp->tm_min, tp->tm_sec, cpu,
- total, qh num_facets - qh num_visible,
- qh num_vertices-qh_setsize (qh del_vertices));
-} /* tracemerging */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="updatetested">-</a>
-
- qh_updatetested( facet1, facet2 )
- clear facet2->tested and facet1->ridge->tested for merge
-
- returns:
- deletes facet2->center unless it's already large
- if so, clears facet2->ridge->tested
-
- design:
- clear facet2->tested
- clear ridge->tested for facet1's ridges
- if facet2 has a centrum
- if facet2 is large
- set facet2->keepcentrum
- else if facet2 has 3 vertices due to many merges, or not large and post merging
- clear facet2->keepcentrum
- unless facet2->keepcentrum
- clear facet2->center to recompute centrum later
- clear ridge->tested for facet2's ridges
-*/
-void qh_updatetested (facetT *facet1, facetT *facet2) {
- ridgeT *ridge, **ridgep;
- int size;
-
- facet2->tested= False;
- FOREACHridge_(facet1->ridges)
- ridge->tested= False;
- if (!facet2->center)
- return;
- size= qh_setsize (facet2->vertices);
- if (!facet2->keepcentrum) {
- if (size > qh hull_dim + qh_MAXnewcentrum) {
- facet2->keepcentrum= True;
- zinc_(Zwidevertices);
- }
- }else if (size <= qh hull_dim + qh_MAXnewcentrum) {
- /* center and keepcentrum was set */
- if (size == qh hull_dim || qh POSTmerging)
- facet2->keepcentrum= False; /* if many merges need to recompute centrum */
- }
- if (!facet2->keepcentrum) {
- qh_memfree (facet2->center, qh normal_size);
- facet2->center= NULL;
- FOREACHridge_(facet2->ridges)
- ridge->tested= False;
- }
-} /* updatetested */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="vertexridges">-</a>
-
- qh_vertexridges( vertex )
- return temporary set of ridges adjacent to a vertex
- vertex->neighbors defined
-
- ntoes:
- uses qh.visit_id
- does not include implicit ridges for simplicial facets
-
- design:
- for each neighbor of vertex
- add ridges that include the vertex to ridges
-*/
-setT *qh_vertexridges (vertexT *vertex) {
- facetT *neighbor, **neighborp;
- setT *ridges= qh_settemp (qh TEMPsize);
- int size;
-
- qh visit_id++;
- FOREACHneighbor_(vertex)
- neighbor->visitid= qh visit_id;
- FOREACHneighbor_(vertex) {
- if (*neighborp) /* no new ridges in last neighbor */
- qh_vertexridges_facet (vertex, neighbor, &ridges);
- }
- if (qh PRINTstatistics || qh IStracing) {
- size= qh_setsize (ridges);
- zinc_(Zvertexridge);
- zadd_(Zvertexridgetot, size);
- zmax_(Zvertexridgemax, size);
- trace3((qh ferr, "qh_vertexridges: found %d ridges for v%d\n",
- size, vertex->id));
- }
- return ridges;
-} /* vertexridges */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="vertexridges_facet">-</a>
-
- qh_vertexridges_facet( vertex, facet, ridges )
- add adjacent ridges for vertex in facet
- neighbor->visitid==qh.visit_id if it hasn't been visited
-
- returns:
- ridges updated
- sets facet->visitid to qh.visit_id-1
-
- design:
- for each ridge of facet
- if ridge of visited neighbor (i.e., unprocessed)
- if vertex in ridge
- append ridge to vertex
- mark facet processed
-*/
-void qh_vertexridges_facet (vertexT *vertex, facetT *facet, setT **ridges) {
- ridgeT *ridge, **ridgep;
- facetT *neighbor;
-
- FOREACHridge_(facet->ridges) {
- neighbor= otherfacet_(ridge, facet);
- if (neighbor->visitid == qh visit_id
- && qh_setin (ridge->vertices, vertex))
- qh_setappend (ridges, ridge);
- }
- facet->visitid= qh visit_id-1;
-} /* vertexridges_facet */
-
-/*-<a href="qh-merge.htm#TOC"
- >-------------------------------</a><a name="willdelete">-</a>
-
- qh_willdelete( facet, replace )
- moves facet to visible list
- sets facet->f.replace to replace (may be NULL)
-
- returns:
- bumps qh.num_visible
-*/
-void qh_willdelete (facetT *facet, facetT *replace) {
-
- qh_removefacet(facet);
- qh_prependfacet (facet, &qh visible_list);
- qh num_visible++;
- facet->visible= True;
- facet->f.replace= replace;
-} /* willdelete */
-
-#else /* qh_NOmerge */
-void qh_premerge (vertexT *apex, realT maxcentrum, realT maxangle) {
-}
-void qh_postmerge (char *reason, realT maxcentrum, realT maxangle,
- boolT vneighbors) {
-}
-boolT qh_checkzero (boolT testall) {
- }
-#endif /* qh_NOmerge */
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/merge.h b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/merge.h
deleted file mode 100644
index 8b689576dbb05d1627d116b360599a866b2cc93c..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/merge.h
+++ /dev/null
@@ -1,176 +0,0 @@
-/*<html><pre> -<a href="qh-merge.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- merge.h
- header file for merge.c
-
- see qh-merge.htm and merge.c
-
- copyright (c) 1993-2003, The Geometry Center
-*/
-
-#ifndef qhDEFmerge
-#define qhDEFmerge 1
-
-
-/*============ -constants- ==============*/
-
-/*-<a href="qh-merge.htm#TOC"
- >--------------------------------</a><a name="qh_ANGLEredundant">-</a>
-
- qh_ANGLEredundant
- indicates redundant merge in mergeT->angle
-*/
-#define qh_ANGLEredundant 6.0
-
-/*-<a href="qh-merge.htm#TOC"
- >--------------------------------</a><a name="qh_ANGLEdegen">-</a>
-
- qh_ANGLEdegen
- indicates degenerate facet in mergeT->angle
-*/
-#define qh_ANGLEdegen 5.0
-
-/*-<a href="qh-merge.htm#TOC"
- >--------------------------------</a><a name="qh_ANGLEconcave">-</a>
-
- qh_ANGLEconcave
- offset to indicate concave facets in mergeT->angle
-
- notes:
- concave facets are assigned the range of [2,4] in mergeT->angle
- roundoff error may make the angle less than 2
-*/
-#define qh_ANGLEconcave 1.5
-
-/*-<a href="qh-merge.htm#TOC"
- >--------------------------------</a><a name="MRG">-</a>
-
- MRG... (mergeType)
- indicates the type of a merge (mergeT->type)
-*/
-typedef enum /* in sort order for facet_mergeset */
-{
- MRGnone = 0,
- MRGcoplanar, /* centrum coplanar */
- MRGanglecoplanar, /* angle coplanar */
- /* could detect half concave ridges */
- MRGconcave, /* concave ridge */
- MRGflip, /* flipped facet. facet1 == facet2 */
- MRGridge, /* duplicate ridge (qh_MERGEridge) */
- /* degen and redundant go onto degen_mergeset */
- MRGdegen, /* degenerate facet (not enough neighbors) facet1 == facet2 */
- MRGredundant, /* redundant facet (vertex subset) */
- /* merge_degenredundant assumes degen < redundant */
- MRGmirror, /* mirror facet from qh_triangulate */
- ENDmrg
-} mergeType;
-
-/*-<a href="qh-merge.htm#TOC"
- >--------------------------------</a><a name="qh_MERGEapex">-</a>
-
- qh_MERGEapex
- flag for qh_mergefacet() to indicate an apex merge
-*/
-#define qh_MERGEapex True
-
-/*============ -structures- ====================*/
-
-/*-<a href="qh-merge.htm#TOC"
- >--------------------------------</a><a name="mergeT">-</a>
-
- mergeT
- structure used to merge facets
-*/
-
-typedef struct mergeT mergeT;
-struct mergeT /* initialize in qh_appendmergeset */
-{
- realT angle; /* angle between normals of facet1 and facet2 */
- facetT* facet1; /* will merge facet1 into facet2 */
- facetT* facet2;
- mergeType type;
-};
-
-
-/*=========== -macros- =========================*/
-
-/*-<a href="qh-merge.htm#TOC"
- >--------------------------------</a><a name="FOREACHmerge_">-</a>
-
- FOREACHmerge_( merges ) {...}
- assign 'merge' to each merge in merges
-
- notes:
- uses 'mergeT *merge, **mergep;'
- if qh_mergefacet(),
- restart since qh.facet_mergeset may change
- see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
-*/
-#define FOREACHmerge_( merges ) FOREACHsetelement_(mergeT, merges, merge)
-
-/*============ prototypes in alphabetical order after pre/postmerge =======*/
-
-void qh_premerge(vertexT* apex, realT maxcentrum, realT maxangle);
-void qh_postmerge(char* reason, realT maxcentrum, realT maxangle,
- boolT vneighbors);
-void qh_all_merges(boolT othermerge, boolT vneighbors);
-void qh_appendmergeset(facetT* facet, facetT* neighbor, mergeType mergetype, realT* angle);
-setT* qh_basevertices(facetT* samecycle);
-void qh_checkconnect(void /* qh new_facets */);
-boolT qh_checkzero(boolT testall);
-int qh_compareangle(const void* p1, const void* p2);
-int qh_comparemerge(const void* p1, const void* p2);
-int qh_comparevisit(const void* p1, const void* p2);
-void qh_copynonconvex(ridgeT* atridge);
-void qh_degen_redundant_facet(facetT* facet);
-void qh_degen_redundant_neighbors(facetT* facet, facetT* delfacet);
-vertexT* qh_find_newvertex(vertexT* oldvertex, setT* vertices, setT* ridges);
-void qh_findbest_test(boolT testcentrum, facetT* facet, facetT* neighbor,
- facetT** bestfacet, realT* distp, realT* mindistp, realT* maxdistp);
-facetT* qh_findbestneighbor(facetT* facet, realT* distp, realT* mindistp, realT* maxdistp);
-void qh_flippedmerges(facetT* facetlist, boolT* wasmerge);
-void qh_forcedmerges(boolT* wasmerge);
-void qh_getmergeset(facetT* facetlist);
-void qh_getmergeset_initial(facetT* facetlist);
-void qh_hashridge(setT* hashtable, int hashsize, ridgeT* ridge, vertexT* oldvertex);
-ridgeT* qh_hashridge_find(setT* hashtable, int hashsize, ridgeT* ridge,
- vertexT* vertex, vertexT* oldvertex, int* hashslot);
-void qh_makeridges(facetT* facet);
-void qh_mark_dupridges(facetT* facetlist);
-void qh_maydropneighbor(facetT* facet);
-int qh_merge_degenredundant(void);
-void qh_merge_nonconvex(facetT* facet1, facetT* facet2, mergeType mergetype);
-void qh_mergecycle(facetT* samecycle, facetT* newfacet);
-void qh_mergecycle_all(facetT* facetlist, boolT* wasmerge);
-void qh_mergecycle_facets(facetT* samecycle, facetT* newfacet);
-void qh_mergecycle_neighbors(facetT* samecycle, facetT* newfacet);
-void qh_mergecycle_ridges(facetT* samecycle, facetT* newfacet);
-void qh_mergecycle_vneighbors(facetT* samecycle, facetT* newfacet);
-void qh_mergefacet(facetT* facet1, facetT* facet2, realT* mindist, realT* maxdist, boolT mergeapex);
-void qh_mergefacet2d(facetT* facet1, facetT* facet2);
-void qh_mergeneighbors(facetT* facet1, facetT* facet2);
-void qh_mergeridges(facetT* facet1, facetT* facet2);
-void qh_mergesimplex(facetT* facet1, facetT* facet2, boolT mergeapex);
-void qh_mergevertex_del(vertexT* vertex, facetT* facet1, facetT* facet2);
-void qh_mergevertex_neighbors(facetT* facet1, facetT* facet2);
-void qh_mergevertices(setT* vertices1, setT** vertices);
-setT* qh_neighbor_intersections(vertexT* vertex);
-void qh_newvertices(setT* vertices);
-boolT qh_reducevertices(void);
-vertexT* qh_redundant_vertex(vertexT* vertex);
-boolT qh_remove_extravertices(facetT* facet);
-vertexT* qh_rename_sharedvertex(vertexT* vertex, facetT* facet);
-void qh_renameridgevertex(ridgeT* ridge, vertexT* oldvertex, vertexT* newvertex);
-void qh_renamevertex(vertexT* oldvertex, vertexT* newvertex, setT* ridges,
- facetT* oldfacet, facetT* neighborA);
-boolT qh_test_appendmerge(facetT* facet, facetT* neighbor);
-boolT qh_test_vneighbors(void /* qh newfacet_list */);
-void qh_tracemerge(facetT* facet1, facetT* facet2);
-void qh_tracemerging(void);
-void qh_updatetested(facetT* facet1, facetT* facet2);
-setT* qh_vertexridges(vertexT* vertex);
-void qh_vertexridges_facet(vertexT* vertex, facetT* facet, setT** ridges);
-void qh_willdelete(facetT* facet, facetT* replace);
-
-#endif /* qhDEFmerge */
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/poly.c b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/poly.c
deleted file mode 100644
index c2791341d506bf01a64d2d1bcd5a10584f5dbf70..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/poly.c
+++ /dev/null
@@ -1,1191 +0,0 @@
-/*<html><pre> -<a href="qh-poly.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- poly.c
- implements polygons and simplices
-
- see qh-poly.htm, poly.h and qhull.h
-
- infrequent code is in poly2.c
- (all but top 50 and their callers 12/3/95)
-
- copyright (c) 1993-2003, The Geometry Center
-*/
-
-#include "qhull_a.h"
-
-/*======== functions in alphabetical order ==========*/
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="appendfacet">-</a>
-
- qh_appendfacet( facet )
- appends facet to end of qh.facet_list,
-
- returns:
- updates qh.newfacet_list, facet_next, facet_list
- increments qh.numfacets
-
- notes:
- assumes qh.facet_list/facet_tail is defined (createsimplex)
-
- see:
- qh_removefacet()
-
-*/
-void qh_appendfacet(facetT *facet) {
- facetT *tail= qh facet_tail;
-
- if (tail == qh newfacet_list)
- qh newfacet_list= facet;
- if (tail == qh facet_next)
- qh facet_next= facet;
- facet->previous= tail->previous;
- facet->next= tail;
- if (tail->previous)
- tail->previous->next= facet;
- else
- qh facet_list= facet;
- tail->previous= facet;
- qh num_facets++;
- trace4((qh ferr, "qh_appendfacet: append f%d to facet_list\n", facet->id));
-} /* appendfacet */
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="appendvertex">-</a>
-
- qh_appendvertex( vertex )
- appends vertex to end of qh.vertex_list,
-
- returns:
- sets vertex->newlist
- updates qh.vertex_list, newvertex_list
- increments qh.num_vertices
-
- notes:
- assumes qh.vertex_list/vertex_tail is defined (createsimplex)
-
-*/
-void qh_appendvertex (vertexT *vertex) {
- vertexT *tail= qh vertex_tail;
-
- if (tail == qh newvertex_list)
- qh newvertex_list= vertex;
- vertex->newlist= True;
- vertex->previous= tail->previous;
- vertex->next= tail;
- if (tail->previous)
- tail->previous->next= vertex;
- else
- qh vertex_list= vertex;
- tail->previous= vertex;
- qh num_vertices++;
- trace4((qh ferr, "qh_appendvertex: append v%d to vertex_list\n", vertex->id));
-} /* appendvertex */
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="attachnewfacets">-</a>
-
- qh_attachnewfacets( )
- attach horizon facets to new facets in qh.newfacet_list
- newfacets have neighbor and ridge links to horizon but not vice versa
- only needed for qh.ONLYgood
-
- returns:
- set qh.NEWfacets
- horizon facets linked to new facets
- ridges changed from visible facets to new facets
- simplicial ridges deleted
- qh.visible_list, no ridges valid
- facet->f.replace is a newfacet (if any)
-
- design:
- delete interior ridges and neighbor sets by
- for each visible, non-simplicial facet
- for each ridge
- if last visit or if neighbor is simplicial
- if horizon neighbor
- delete ridge for horizon's ridge set
- delete ridge
- erase neighbor set
- attach horizon facets and new facets by
- for all new facets
- if corresponding horizon facet is simplicial
- locate corresponding visible facet {may be more than one}
- link visible facet to new facet
- replace visible facet with new facet in horizon
- else it's non-simplicial
- for all visible neighbors of the horizon facet
- link visible neighbor to new facet
- delete visible neighbor from horizon facet
- append new facet to horizon's neighbors
- the first ridge of the new facet is the horizon ridge
- link the new facet into the horizon ridge
-*/
-void qh_attachnewfacets (void ) {
- facetT *newfacet= NULL, *neighbor, **neighborp, *horizon, *visible;
- ridgeT *ridge, **ridgep;
-
- qh NEWfacets= True;
- trace3((qh ferr, "qh_attachnewfacets: delete interior ridges\n"));
- qh visit_id++;
- FORALLvisible_facets {
- visible->visitid= qh visit_id;
- if (visible->ridges) {
- FOREACHridge_(visible->ridges) {
- neighbor= otherfacet_(ridge, visible);
- if (neighbor->visitid == qh visit_id
- || (!neighbor->visible && neighbor->simplicial)) {
- if (!neighbor->visible) /* delete ridge for simplicial horizon */
- qh_setdel (neighbor->ridges, ridge);
- qh_setfree (&(ridge->vertices)); /* delete on 2nd visit */
- qh_memfree (ridge, sizeof(ridgeT));
- }
- }
- SETfirst_(visible->ridges)= NULL;
- }
- SETfirst_(visible->neighbors)= NULL;
- }
- trace1((qh ferr, "qh_attachnewfacets: attach horizon facets to new facets\n"));
- FORALLnew_facets {
- horizon= SETfirstt_(newfacet->neighbors, facetT);
- if (horizon->simplicial) {
- visible= NULL;
- FOREACHneighbor_(horizon) { /* may have more than one horizon ridge */
- if (neighbor->visible) {
- if (visible) {
- if (qh_setequal_skip (newfacet->vertices, 0, horizon->vertices,
- SETindex_(horizon->neighbors, neighbor))) {
- visible= neighbor;
- break;
- }
- }else
- visible= neighbor;
- }
- }
- if (visible) {
- visible->f.replace= newfacet;
- qh_setreplace (horizon->neighbors, visible, newfacet);
- }else {
- fprintf (qh ferr, "qhull internal error (qh_attachnewfacets): couldn't find visible facet for horizon f%d of newfacet f%d\n",
- horizon->id, newfacet->id);
- qh_errexit2 (qh_ERRqhull, horizon, newfacet);
- }
- }else { /* non-simplicial, with a ridge for newfacet */
- FOREACHneighbor_(horizon) { /* may hold for many new facets */
- if (neighbor->visible) {
- neighbor->f.replace= newfacet;
- qh_setdelnth (horizon->neighbors,
- SETindex_(horizon->neighbors, neighbor));
- neighborp--; /* repeat */
- }
- }
- qh_setappend (&horizon->neighbors, newfacet);
- ridge= SETfirstt_(newfacet->ridges, ridgeT);
- if (ridge->top == horizon)
- ridge->bottom= newfacet;
- else
- ridge->top= newfacet;
- }
- } /* newfacets */
- if (qh PRINTstatistics) {
- FORALLvisible_facets {
- if (!visible->f.replace)
- zinc_(Zinsidevisible);
- }
- }
-} /* attachnewfacets */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="checkflipped">-</a>
-
- qh_checkflipped( facet, dist, allerror )
- checks facet orientation to interior point
-
- if allerror set,
- tests against qh.DISTround
- else
- tests against 0 since tested against DISTround before
-
- returns:
- False if it flipped orientation (sets facet->flipped)
- distance if non-NULL
-*/
-boolT qh_checkflipped (facetT *facet, realT *distp, boolT allerror) {
- realT dist;
-
- if (facet->flipped && !distp)
- return False;
- zzinc_(Zdistcheck);
- qh_distplane(qh interior_point, facet, &dist);
- if (distp)
- *distp= dist;
- if ((allerror && dist > -qh DISTround)|| (!allerror && dist >= 0.0)) {
- facet->flipped= True;
- zzinc_(Zflippedfacets);
- trace0((qh ferr, "qh_checkflipped: facet f%d is flipped, distance= %6.12g during p%d\n",
- facet->id, dist, qh furthest_id));
- qh_precision ("flipped facet");
- return False;
- }
- return True;
-} /* checkflipped */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="delfacet">-</a>
-
- qh_delfacet( facet )
- removes facet from facet_list and frees up its memory
-
- notes:
- assumes vertices and ridges already freed
-*/
-void qh_delfacet(facetT *facet) {
- void **freelistp; /* used !qh_NOmem */
-
- trace4((qh ferr, "qh_delfacet: delete f%d\n", facet->id));
- if (facet == qh tracefacet)
- qh tracefacet= NULL;
- if (facet == qh GOODclosest)
- qh GOODclosest= NULL;
- qh_removefacet(facet);
- if (!facet->tricoplanar || facet->keepcentrum) {
- qh_memfree_(facet->normal, qh normal_size, freelistp);
- if (qh CENTERtype == qh_ASvoronoi) { /* uses macro calls */
- qh_memfree_(facet->center, qh center_size, freelistp);
- }else /* AScentrum */ {
- qh_memfree_(facet->center, qh normal_size, freelistp);
- }
- }
- qh_setfree(&(facet->neighbors));
- if (facet->ridges)
- qh_setfree(&(facet->ridges));
- qh_setfree(&(facet->vertices));
- if (facet->outsideset)
- qh_setfree(&(facet->outsideset));
- if (facet->coplanarset)
- qh_setfree(&(facet->coplanarset));
- qh_memfree_(facet, sizeof(facetT), freelistp);
-} /* delfacet */
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="deletevisible">-</a>
-
- qh_deletevisible()
- delete visible facets and vertices
-
- returns:
- deletes each facet and removes from facetlist
- at exit, qh.visible_list empty (== qh.newfacet_list)
-
- notes:
- ridges already deleted
- horizon facets do not reference facets on qh.visible_list
- new facets in qh.newfacet_list
- uses qh.visit_id;
-*/
-void qh_deletevisible (void /*qh visible_list*/) {
- facetT *visible, *nextfacet;
- vertexT *vertex, **vertexp;
- int numvisible= 0, numdel= qh_setsize(qh del_vertices);
-
- trace1((qh ferr, "qh_deletevisible: delete %d visible facets and %d vertices\n",
- qh num_visible, numdel));
- for (visible= qh visible_list; visible && visible->visible;
- visible= nextfacet) { /* deleting current */
- nextfacet= visible->next;
- numvisible++;
- qh_delfacet(visible);
- }
- if (numvisible != qh num_visible) {
- fprintf (qh ferr, "qhull internal error (qh_deletevisible): qh num_visible %d is not number of visible facets %d\n",
- qh num_visible, numvisible);
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- qh num_visible= 0;
- zadd_(Zvisfacettot, numvisible);
- zmax_(Zvisfacetmax, numvisible);
- zzadd_(Zdelvertextot, numdel);
- zmax_(Zdelvertexmax, numdel);
- FOREACHvertex_(qh del_vertices)
- qh_delvertex (vertex);
- qh_settruncate (qh del_vertices, 0);
-} /* deletevisible */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="facetintersect">-</a>
-
- qh_facetintersect( facetA, facetB, skipa, skipB, prepend )
- return vertices for intersection of two simplicial facets
- may include 1 prepended entry (if more, need to settemppush)
-
- returns:
- returns set of qh.hull_dim-1 + prepend vertices
- returns skipped index for each test and checks for exactly one
-
- notes:
- does not need settemp since set in quick memory
-
- see also:
- qh_vertexintersect and qh_vertexintersect_new
- use qh_setnew_delnthsorted to get nth ridge (no skip information)
-
- design:
- locate skipped vertex by scanning facet A's neighbors
- locate skipped vertex by scanning facet B's neighbors
- intersect the vertex sets
-*/
-setT *qh_facetintersect (facetT *facetA, facetT *facetB,
- int *skipA,int *skipB, int prepend) {
- setT *intersect;
- int dim= qh hull_dim, i, j;
- facetT **neighborsA, **neighborsB;
-
- neighborsA= SETaddr_(facetA->neighbors, facetT);
- neighborsB= SETaddr_(facetB->neighbors, facetT);
- i= j= 0;
- if (facetB == *neighborsA++)
- *skipA= 0;
- else if (facetB == *neighborsA++)
- *skipA= 1;
- else if (facetB == *neighborsA++)
- *skipA= 2;
- else {
- for (i= 3; i < dim; i++) {
- if (facetB == *neighborsA++) {
- *skipA= i;
- break;
- }
- }
- }
- if (facetA == *neighborsB++)
- *skipB= 0;
- else if (facetA == *neighborsB++)
- *skipB= 1;
- else if (facetA == *neighborsB++)
- *skipB= 2;
- else {
- for (j= 3; j < dim; j++) {
- if (facetA == *neighborsB++) {
- *skipB= j;
- break;
- }
- }
- }
- if (i >= dim || j >= dim) {
- fprintf (qh ferr, "qhull internal error (qh_facetintersect): f%d or f%d not in others neighbors\n",
- facetA->id, facetB->id);
- qh_errexit2 (qh_ERRqhull, facetA, facetB);
- }
- intersect= qh_setnew_delnthsorted (facetA->vertices, qh hull_dim, *skipA, prepend);
- trace4((qh ferr, "qh_facetintersect: f%d skip %d matches f%d skip %d\n",
- facetA->id, *skipA, facetB->id, *skipB));
- return(intersect);
-} /* facetintersect */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="gethash">-</a>
-
- qh_gethash( hashsize, set, size, firstindex, skipelem )
- return hashvalue for a set with firstindex and skipelem
-
- notes:
- assumes at least firstindex+1 elements
- assumes skipelem is NULL, in set, or part of hash
-
- hashes memory addresses which may change over different runs of the same data
- using sum for hash does badly in high d
-*/
-unsigned qh_gethash (int hashsize, setT *set, int size, int firstindex, void *skipelem) {
- void **elemp= SETelemaddr_(set, firstindex, void);
- ptr_intT hash = 0, elem;
- int i;
- // !! PATCHED TO 2010.1 version!!
- unsigned result;
- // !! PATCHED TO 2010.1 version!!
-
- switch (size-firstindex) {
- case 1:
- hash= (ptr_intT)(*elemp) - (ptr_intT) skipelem;
- break;
- case 2:
- hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] - (ptr_intT) skipelem;
- break;
- case 3:
- hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
- - (ptr_intT) skipelem;
- break;
- case 4:
- hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
- + (ptr_intT)elemp[3] - (ptr_intT) skipelem;
- break;
- case 5:
- hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
- + (ptr_intT)elemp[3] + (ptr_intT)elemp[4] - (ptr_intT) skipelem;
- break;
- case 6:
- hash= (ptr_intT)(*elemp) + (ptr_intT)elemp[1] + (ptr_intT)elemp[2]
- + (ptr_intT)elemp[3] + (ptr_intT)elemp[4]+ (ptr_intT)elemp[5]
- - (ptr_intT) skipelem;
- break;
- default:
- hash= 0;
- i= 3;
- do { /* this is about 10% in 10-d */
- if ((elem= (ptr_intT)*elemp++) != (ptr_intT)skipelem) {
- hash ^= (elem << i) + (elem >> (32-i));
- i += 3;
- if (i >= 32)
- i -= 32;
- }
- }while(*elemp);
- break;
- }
-
- // !! PATCHED TO 2010.1 version!!
- //hash %= (ptr_intT) hashsize;
- ///* hash= 0; for debugging purposes */
- //return hash;
- result= (unsigned)hash;
- result %= (unsigned)hashsize;
- /* result= 0; for debugging purposes */
- return result;
- // !! PATCHED TO 2010.1 version!!
-
-} /* gethash */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="makenewfacet">-</a>
-
- qh_makenewfacet( vertices, toporient, horizon )
- creates a toporient? facet from vertices
-
- returns:
- returns newfacet
- adds newfacet to qh.facet_list
- newfacet->vertices= vertices
- if horizon
- newfacet->neighbor= horizon, but not vice versa
- newvertex_list updated with vertices
-*/
-facetT *qh_makenewfacet(setT *vertices, boolT toporient,facetT *horizon) {
- facetT *newfacet;
- vertexT *vertex, **vertexp;
-
- FOREACHvertex_(vertices) {
- if (!vertex->newlist) {
- qh_removevertex (vertex);
- qh_appendvertex (vertex);
- }
- }
- newfacet= qh_newfacet();
- newfacet->vertices= vertices;
- newfacet->toporient= toporient;
- if (horizon)
- qh_setappend(&(newfacet->neighbors), horizon);
- qh_appendfacet(newfacet);
- return(newfacet);
-} /* makenewfacet */
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="makenewplanes">-</a>
-
- qh_makenewplanes()
- make new hyperplanes for facets on qh.newfacet_list
-
- returns:
- all facets have hyperplanes or are marked for merging
- doesn't create hyperplane if horizon is coplanar (will merge)
- updates qh.min_vertex if qh.JOGGLEmax
-
- notes:
- facet->f.samecycle is defined for facet->mergehorizon facets
-*/
-void qh_makenewplanes (void /* newfacet_list */) {
- facetT *newfacet;
-
- FORALLnew_facets {
- if (!newfacet->mergehorizon)
- qh_setfacetplane (newfacet);
- }
- if (qh JOGGLEmax < REALmax/2)
- minimize_(qh min_vertex, -wwval_(Wnewvertexmax));
-} /* makenewplanes */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="makenew_nonsimplicial">-</a>
-
- qh_makenew_nonsimplicial( visible, apex, numnew )
- make new facets for ridges of a visible facet
-
- returns:
- first newfacet, bumps numnew as needed
- attaches new facets if !qh.ONLYgood
- marks ridge neighbors for simplicial visible
- if (qh.ONLYgood)
- ridges on newfacet, horizon, and visible
- else
- ridge and neighbors between newfacet and horizon
- visible facet's ridges are deleted
-
- notes:
- qh.visit_id if visible has already been processed
- sets neighbor->seen for building f.samecycle
- assumes all 'seen' flags initially false
-
- design:
- for each ridge of visible facet
- get neighbor of visible facet
- if neighbor was already processed
- delete the ridge (will delete all visible facets later)
- if neighbor is a horizon facet
- create a new facet
- if neighbor coplanar
- adds newfacet to f.samecycle for later merging
- else
- updates neighbor's neighbor set
- (checks for non-simplicial facet with multiple ridges to visible facet)
- updates neighbor's ridge set
- (checks for simplicial neighbor to non-simplicial visible facet)
- (deletes ridge if neighbor is simplicial)
-
-*/
-#ifndef qh_NOmerge
-facetT *qh_makenew_nonsimplicial (facetT *visible, vertexT *apex, int *numnew) {
- void **freelistp; /* used !qh_NOmem */
- ridgeT *ridge, **ridgep;
- facetT *neighbor, *newfacet= NULL, *samecycle;
- setT *vertices;
- boolT toporient;
- int ridgeid;
-
- FOREACHridge_(visible->ridges) {
- ridgeid= ridge->id;
- neighbor= otherfacet_(ridge, visible);
- if (neighbor->visible) {
- if (!qh ONLYgood) {
- if (neighbor->visitid == qh visit_id) {
- qh_setfree (&(ridge->vertices)); /* delete on 2nd visit */
- qh_memfree_(ridge, sizeof(ridgeT), freelistp);
- }
- }
- }else { /* neighbor is an horizon facet */
- toporient= (ridge->top == visible);
- vertices= qh_setnew (qh hull_dim); /* makes sure this is quick */
- qh_setappend (&vertices, apex);
- qh_setappend_set (&vertices, ridge->vertices);
- newfacet= qh_makenewfacet(vertices, toporient, neighbor);
- (*numnew)++;
- if (neighbor->coplanar) {
- newfacet->mergehorizon= True;
- if (!neighbor->seen) {
- newfacet->f.samecycle= newfacet;
- neighbor->f.newcycle= newfacet;
- }else {
- samecycle= neighbor->f.newcycle;
- newfacet->f.samecycle= samecycle->f.samecycle;
- samecycle->f.samecycle= newfacet;
- }
- }
- if (qh ONLYgood) {
- if (!neighbor->simplicial)
- qh_setappend(&(newfacet->ridges), ridge);
- }else { /* qh_attachnewfacets */
- if (neighbor->seen) {
- if (neighbor->simplicial) {
- fprintf (qh ferr, "qhull internal error (qh_makenew_nonsimplicial): simplicial f%d sharing two ridges with f%d\n",
- neighbor->id, visible->id);
- qh_errexit2 (qh_ERRqhull, neighbor, visible);
- }
- qh_setappend (&(neighbor->neighbors), newfacet);
- }else
- qh_setreplace (neighbor->neighbors, visible, newfacet);
- if (neighbor->simplicial) {
- qh_setdel (neighbor->ridges, ridge);
- qh_setfree (&(ridge->vertices));
- qh_memfree (ridge, sizeof(ridgeT));
- }else {
- qh_setappend(&(newfacet->ridges), ridge);
- if (toporient)
- ridge->top= newfacet;
- else
- ridge->bottom= newfacet;
- }
- trace4((qh ferr, "qh_makenew_nonsimplicial: created facet f%d from v%d and r%d of horizon f%d\n",
- newfacet->id, apex->id, ridgeid, neighbor->id));
- }
- }
- neighbor->seen= True;
- } /* for each ridge */
- if (!qh ONLYgood)
- SETfirst_(visible->ridges)= NULL;
- return newfacet;
-} /* makenew_nonsimplicial */
-#else /* qh_NOmerge */
-facetT *qh_makenew_nonsimplicial (facetT *visible, vertexT *apex, int *numnew) {
- return NULL;
-}
-#endif /* qh_NOmerge */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="makenew_simplicial">-</a>
-
- qh_makenew_simplicial( visible, apex, numnew )
- make new facets for simplicial visible facet and apex
-
- returns:
- attaches new facets if (!qh.ONLYgood)
- neighbors between newfacet and horizon
-
- notes:
- nop if neighbor->seen or neighbor->visible (see qh_makenew_nonsimplicial)
-
- design:
- locate neighboring horizon facet for visible facet
- determine vertices and orientation
- create new facet
- if coplanar,
- add new facet to f.samecycle
- update horizon facet's neighbor list
-*/
-facetT *qh_makenew_simplicial (facetT *visible, vertexT *apex, int *numnew) {
- facetT *neighbor, **neighborp, *newfacet= NULL;
- setT *vertices;
- boolT flip, toporient;
- int horizonskip, visibleskip;
-
- FOREACHneighbor_(visible) {
- if (!neighbor->seen && !neighbor->visible) {
- vertices= qh_facetintersect(neighbor,visible, &horizonskip, &visibleskip, 1);
- SETfirst_(vertices)= apex;
- flip= ((horizonskip & 0x1) ^ (visibleskip & 0x1));
- if (neighbor->toporient)
- toporient= horizonskip & 0x1;
- else
- toporient= (horizonskip & 0x1) ^ 0x1;
- newfacet= qh_makenewfacet(vertices, toporient, neighbor);
- (*numnew)++;
- if (neighbor->coplanar && (qh PREmerge || qh MERGEexact)) {
-#ifndef qh_NOmerge
- newfacet->f.samecycle= newfacet;
- newfacet->mergehorizon= True;
-#endif
- }
- if (!qh ONLYgood)
- SETelem_(neighbor->neighbors, horizonskip)= newfacet;
- trace4((qh ferr, "qh_makenew_simplicial: create facet f%d top %d from v%d and horizon f%d skip %d top %d and visible f%d skip %d, flip? %d\n",
- newfacet->id, toporient, apex->id, neighbor->id, horizonskip,
- neighbor->toporient, visible->id, visibleskip, flip));
- }
- }
- return newfacet;
-} /* makenew_simplicial */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="matchneighbor">-</a>
-
- qh_matchneighbor( newfacet, newskip, hashsize, hashcount )
- either match subridge of newfacet with neighbor or add to hash_table
-
- returns:
- duplicate ridges are unmatched and marked by qh_DUPLICATEridge
-
- notes:
- ridge is newfacet->vertices w/o newskip vertex
- do not allocate memory (need to free hash_table cleanly)
- uses linear hash chains
-
- see also:
- qh_matchduplicates
-
- design:
- for each possible matching facet in qh.hash_table
- if vertices match
- set ismatch, if facets have opposite orientation
- if ismatch and matching facet doesn't have a match
- match the facets by updating their neighbor sets
- else
- indicate a duplicate ridge
- set facet hyperplane for later testing
- add facet to hashtable
- unless the other facet was already a duplicate ridge
- mark both facets with a duplicate ridge
- add other facet (if defined) to hash table
-*/
-void qh_matchneighbor (facetT *newfacet, int newskip, int hashsize, int *hashcount) {
- boolT newfound= False; /* True, if new facet is already in hash chain */
- boolT same, ismatch;
- int hash, scan;
- facetT *facet, *matchfacet;
- int skip, matchskip;
-
- hash= (int)qh_gethash (hashsize, newfacet->vertices, qh hull_dim, 1,
- SETelem_(newfacet->vertices, newskip));
- trace4((qh ferr, "qh_matchneighbor: newfacet f%d skip %d hash %d hashcount %d\n",
- newfacet->id, newskip, hash, *hashcount));
- zinc_(Zhashlookup);
- for (scan= hash; (facet= SETelemt_(qh hash_table, scan, facetT));
- scan= (++scan >= hashsize ? 0 : scan)) {
- if (facet == newfacet) {
- newfound= True;
- continue;
- }
- zinc_(Zhashtests);
- if (qh_matchvertices (1, newfacet->vertices, newskip, facet->vertices, &skip, &same)) {
- if (SETelem_(newfacet->vertices, newskip) ==
- SETelem_(facet->vertices, skip)) {
- qh_precision ("two facets with the same vertices");
- fprintf (qh ferr, "qhull precision error: Vertex sets are the same for f%d and f%d. Can not force output.\n",
- facet->id, newfacet->id);
- qh_errexit2 (qh_ERRprec, facet, newfacet);
- }
- ismatch= (same == (newfacet->toporient ^ facet->toporient));
- matchfacet= SETelemt_(facet->neighbors, skip, facetT);
- if (ismatch && !matchfacet) {
- SETelem_(facet->neighbors, skip)= newfacet;
- SETelem_(newfacet->neighbors, newskip)= facet;
- (*hashcount)--;
- trace4((qh ferr, "qh_matchneighbor: f%d skip %d matched with new f%d skip %d\n",
- facet->id, skip, newfacet->id, newskip));
- return;
- }
- if (!qh PREmerge && !qh MERGEexact) {
- qh_precision ("a ridge with more than two neighbors");
- fprintf (qh ferr, "qhull precision error: facets f%d, f%d and f%d meet at a ridge with more than 2 neighbors. Can not continue.\n",
- facet->id, newfacet->id, getid_(matchfacet));
- qh_errexit2 (qh_ERRprec, facet, newfacet);
- }
- SETelem_(newfacet->neighbors, newskip)= qh_DUPLICATEridge;
- newfacet->dupridge= True;
- if (!newfacet->normal)
- qh_setfacetplane (newfacet);
- qh_addhash (newfacet, qh hash_table, hashsize, hash);
- (*hashcount)++;
- if (!facet->normal)
- qh_setfacetplane (facet);
- if (matchfacet != qh_DUPLICATEridge) {
- SETelem_(facet->neighbors, skip)= qh_DUPLICATEridge;
- facet->dupridge= True;
- if (!facet->normal)
- qh_setfacetplane (facet);
- if (matchfacet) {
- matchskip= qh_setindex (matchfacet->neighbors, facet);
- SETelem_(matchfacet->neighbors, matchskip)= qh_DUPLICATEridge;
- matchfacet->dupridge= True;
- if (!matchfacet->normal)
- qh_setfacetplane (matchfacet);
- qh_addhash (matchfacet, qh hash_table, hashsize, hash);
- *hashcount += 2;
- }
- }
- trace4((qh ferr, "qh_matchneighbor: new f%d skip %d duplicates ridge for f%d skip %d matching f%d ismatch %d at hash %d\n",
- newfacet->id, newskip, facet->id, skip,
- (matchfacet == qh_DUPLICATEridge ? -2 : getid_(matchfacet)),
- ismatch, hash));
- return; /* end of duplicate ridge */
- }
- }
- if (!newfound)
- SETelem_(qh hash_table, scan)= newfacet; /* same as qh_addhash */
- (*hashcount)++;
- trace4((qh ferr, "qh_matchneighbor: no match for f%d skip %d at hash %d\n",
- newfacet->id, newskip, hash));
-} /* matchneighbor */
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="matchnewfacets">-</a>
-
- qh_matchnewfacets()
- match newfacets in qh.newfacet_list to their newfacet neighbors
-
- returns:
- qh.newfacet_list with full neighbor sets
- get vertices with nth neighbor by deleting nth vertex
- if qh.PREmerge/MERGEexact or qh.FORCEoutput
- sets facet->flippped if flipped normal (also prevents point partitioning)
- if duplicate ridges and qh.PREmerge/MERGEexact
- sets facet->dupridge
- missing neighbor links identifies extra ridges to be merging (qh_MERGEridge)
-
- notes:
- newfacets already have neighbor[0] (horizon facet)
- assumes qh.hash_table is NULL
- vertex->neighbors has not been updated yet
- do not allocate memory after qh.hash_table (need to free it cleanly)
-
- design:
- delete neighbor sets for all new facets
- initialize a hash table
- for all new facets
- match facet with neighbors
- if unmatched facets (due to duplicate ridges)
- for each new facet with a duplicate ridge
- match it with a facet
- check for flipped facets
-*/
-void qh_matchnewfacets (void /* qh newfacet_list */) {
- int numnew=0, hashcount=0, newskip;
- facetT *newfacet, *neighbor;
- int dim= qh hull_dim, hashsize, neighbor_i, neighbor_n;
- setT *neighbors;
-#ifndef qh_NOtrace
- int facet_i, facet_n, numfree= 0;
- facetT *facet;
-#endif
-
- trace1((qh ferr, "qh_matchnewfacets: match neighbors for new facets.\n"));
- FORALLnew_facets {
- numnew++;
- { /* inline qh_setzero (newfacet->neighbors, 1, qh hull_dim); */
- neighbors= newfacet->neighbors;
- neighbors->e[neighbors->maxsize].i= dim+1; /*may be overwritten*/
- memset ((char *)SETelemaddr_(neighbors, 1, void), 0, dim * SETelemsize);
- }
- }
- qh_newhashtable (numnew*(qh hull_dim-1)); /* twice what is normally needed,
- but every ridge could be DUPLICATEridge */
- hashsize= qh_setsize (qh hash_table);
- FORALLnew_facets {
- for (newskip=1; newskip<qh hull_dim; newskip++) /* furthest/horizon already matched */
- qh_matchneighbor (newfacet, newskip, hashsize, &hashcount);
-#if 0 /* use the following to trap hashcount errors */
- {
- int count= 0, k;
- facetT *facet, *neighbor;
-
- count= 0;
- FORALLfacet_(qh newfacet_list) { /* newfacet already in use */
- for (k=1; k < qh hull_dim; k++) {
- neighbor= SETelemt_(facet->neighbors, k, facetT);
- if (!neighbor || neighbor == qh_DUPLICATEridge)
- count++;
- }
- if (facet == newfacet)
- break;
- }
- if (count != hashcount) {
- fprintf (qh ferr, "qh_matchnewfacets: after adding facet %d, hashcount %d != count %d\n",
- newfacet->id, hashcount, count);
- qh_errexit (qh_ERRqhull, newfacet, NULL);
- }
- }
-#endif /* end of trap code */
- }
- if (hashcount) {
- FORALLnew_facets {
- if (newfacet->dupridge) {
- FOREACHneighbor_i_(newfacet) {
- if (neighbor == qh_DUPLICATEridge) {
- qh_matchduplicates (newfacet, neighbor_i, hashsize, &hashcount);
- /* this may report MERGEfacet */
- }
- }
- }
- }
- }
- if (hashcount) {
- fprintf (qh ferr, "qhull internal error (qh_matchnewfacets): %d neighbors did not match up\n",
- hashcount);
- qh_printhashtable (qh ferr);
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
-#ifndef qh_NOtrace
- if (qh IStracing >= 2) {
- FOREACHfacet_i_(qh hash_table) {
- if (!facet)
- numfree++;
- }
- fprintf (qh ferr, "qh_matchnewfacets: %d new facets, %d unused hash entries . hashsize %d\n",
- numnew, numfree, qh_setsize (qh hash_table));
- }
-#endif /* !qh_NOtrace */
- qh_setfree (&qh hash_table);
- if (qh PREmerge || qh MERGEexact) {
- if (qh IStracing >= 4)
- qh_printfacetlist (qh newfacet_list, NULL, qh_ALL);
- FORALLnew_facets {
- if (newfacet->normal)
- qh_checkflipped (newfacet, NULL, qh_ALL);
- }
- }else if (qh FORCEoutput)
- qh_checkflipped_all (qh newfacet_list); /* prints warnings for flipped */
-} /* matchnewfacets */
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="matchvertices">-</a>
-
- qh_matchvertices( firstindex, verticesA, skipA, verticesB, skipB, same )
- tests whether vertices match with a single skip
- starts match at firstindex since all new facets have a common vertex
-
- returns:
- true if matched vertices
- skip index for each set
- sets same iff vertices have the same orientation
-
- notes:
- assumes skipA is in A and both sets are the same size
-
- design:
- set up pointers
- scan both sets checking for a match
- test orientation
-*/
-boolT qh_matchvertices (int firstindex, setT *verticesA, int skipA,
- setT *verticesB, int *skipB, boolT *same) {
- vertexT **elemAp, **elemBp, **skipBp=NULL, **skipAp;
-
- elemAp= SETelemaddr_(verticesA, firstindex, vertexT);
- elemBp= SETelemaddr_(verticesB, firstindex, vertexT);
- skipAp= SETelemaddr_(verticesA, skipA, vertexT);
- do if (elemAp != skipAp) {
- while (*elemAp != *elemBp++) {
- if (skipBp)
- return False;
- skipBp= elemBp; /* one extra like FOREACH */
- }
- }while(*(++elemAp));
- if (!skipBp)
- skipBp= ++elemBp;
- *skipB= SETindex_(verticesB, skipB);
- *same= !(((ptr_intT)skipA & 0x1) ^ ((ptr_intT)*skipB & 0x1));
- trace4((qh ferr, "qh_matchvertices: matched by skip %d (v%d) and skip %d (v%d) same? %d\n",
- skipA, (*skipAp)->id, *skipB, (*(skipBp-1))->id, *same));
- return (True);
-} /* matchvertices */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="newfacet">-</a>
-
- qh_newfacet()
- return a new facet
-
- returns:
- all fields initialized or cleared (NULL)
- preallocates neighbors set
-*/
-facetT *qh_newfacet(void) {
- facetT *facet;
- void **freelistp; /* used !qh_NOmem */
-
- qh_memalloc_(sizeof(facetT), freelistp, facet, facetT);
- memset ((char *)facet, 0, sizeof(facetT));
- if (qh facet_id == qh tracefacet_id)
- qh tracefacet= facet;
- facet->id= qh facet_id++;
- facet->neighbors= qh_setnew(qh hull_dim);
-#if !qh_COMPUTEfurthest
- facet->furthestdist= 0.0;
-#endif
-#if qh_MAXoutside
- if (qh FORCEoutput && qh APPROXhull)
- facet->maxoutside= qh MINoutside;
- else
- facet->maxoutside= qh DISTround;
-#endif
- facet->simplicial= True;
- facet->good= True;
- facet->newfacet= True;
- trace4((qh ferr, "qh_newfacet: created facet f%d\n", facet->id));
- return (facet);
-} /* newfacet */
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="newridge">-</a>
-
- qh_newridge()
- return a new ridge
-*/
-ridgeT *qh_newridge(void) {
- ridgeT *ridge;
- void **freelistp; /* used !qh_NOmem */
-
- qh_memalloc_(sizeof(ridgeT), freelistp, ridge, ridgeT);
- memset ((char *)ridge, 0, sizeof(ridgeT));
- zinc_(Ztotridges);
- if (qh ridge_id == 0xFFFFFF) {
- fprintf(qh ferr, "\
-qhull warning: more than %d ridges. ID field overflows and two ridges\n\
-may have the same identifier. Otherwise output ok.\n", 0xFFFFFF);
- }
- ridge->id= qh ridge_id++;
- trace4((qh ferr, "qh_newridge: created ridge r%d\n", ridge->id));
- return (ridge);
-} /* newridge */
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="pointid">-</a>
-
- qh_pointid( )
- return id for a point,
- returns -3 if null, -2 if interior, or -1 if not known
-
- alternative code:
- unsigned long id;
- id= ((unsigned long)point - (unsigned long)qh.first_point)/qh.normal_size;
-
- notes:
- if point not in point array
- the code does a comparison of unrelated pointers.
-*/
-int qh_pointid (pointT *point) {
- long offset, id;
-
- if (!point)
- id= -3;
- else if (point == qh interior_point)
- id= -2;
- else if (point >= qh first_point
- && point < qh first_point + qh num_points * qh hull_dim) {
- offset= point - qh first_point;
- id= offset / qh hull_dim;
- }else if ((id= qh_setindex (qh other_points, point)) != -1)
- id += qh num_points;
- else
- id= -1;
- return (int) id;
-} /* pointid */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="removefacet">-</a>
-
- qh_removefacet( facet )
- unlinks facet from qh.facet_list,
-
- returns:
- updates qh.facet_list .newfacet_list .facet_next visible_list
- decrements qh.num_facets
-
- see:
- qh_appendfacet
-*/
-void qh_removefacet(facetT *facet) {
- facetT *next= facet->next, *previous= facet->previous;
-
- if (facet == qh newfacet_list)
- qh newfacet_list= next;
- if (facet == qh facet_next)
- qh facet_next= next;
- if (facet == qh visible_list)
- qh visible_list= next;
- if (previous) {
- previous->next= next;
- next->previous= previous;
- }else { /* 1st facet in qh facet_list */
- qh facet_list= next;
- qh facet_list->previous= NULL;
- }
- qh num_facets--;
- trace4((qh ferr, "qh_removefacet: remove f%d from facet_list\n", facet->id));
-} /* removefacet */
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="removevertex">-</a>
-
- qh_removevertex( vertex )
- unlinks vertex from qh.vertex_list,
-
- returns:
- updates qh.vertex_list .newvertex_list
- decrements qh.num_vertices
-*/
-void qh_removevertex(vertexT *vertex) {
- vertexT *next= vertex->next, *previous= vertex->previous;
-
- if (vertex == qh newvertex_list)
- qh newvertex_list= next;
- if (previous) {
- previous->next= next;
- next->previous= previous;
- }else { /* 1st vertex in qh vertex_list */
- qh vertex_list= vertex->next;
- qh vertex_list->previous= NULL;
- }
- qh num_vertices--;
- trace4((qh ferr, "qh_removevertex: remove v%d from vertex_list\n", vertex->id));
-} /* removevertex */
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="updatevertices">-</a>
-
- qh_updatevertices()
- update vertex neighbors and delete interior vertices
-
- returns:
- if qh.VERTEXneighbors, updates neighbors for each vertex
- if qh.newvertex_list,
- removes visible neighbors from vertex neighbors
- if qh.newfacet_list
- adds new facets to vertex neighbors
- if qh.visible_list
- interior vertices added to qh.del_vertices for later partitioning
-
- design:
- if qh.VERTEXneighbors
- deletes references to visible facets from vertex neighbors
- appends new facets to the neighbor list for each vertex
- checks all vertices of visible facets
- removes visible facets from neighbor lists
- marks unused vertices for deletion
-*/
-void qh_updatevertices (void /*qh newvertex_list, newfacet_list, visible_list*/) {
- facetT *newfacet= NULL, *neighbor, **neighborp, *visible;
- vertexT *vertex, **vertexp;
-
- trace3((qh ferr, "qh_updatevertices: delete interior vertices and update vertex->neighbors\n"));
- if (qh VERTEXneighbors) {
- FORALLvertex_(qh newvertex_list) {
- FOREACHneighbor_(vertex) {
- if (neighbor->visible)
- SETref_(neighbor)= NULL;
- }
- qh_setcompact (vertex->neighbors);
- }
- FORALLnew_facets {
- FOREACHvertex_(newfacet->vertices)
- qh_setappend (&vertex->neighbors, newfacet);
- }
- FORALLvisible_facets {
- FOREACHvertex_(visible->vertices) {
- if (!vertex->newlist && !vertex->deleted) {
- FOREACHneighbor_(vertex) { /* this can happen under merging */
- if (!neighbor->visible)
- break;
- }
- if (neighbor)
- qh_setdel (vertex->neighbors, visible);
- else {
- vertex->deleted= True;
- qh_setappend (&qh del_vertices, vertex);
- trace2((qh ferr, "qh_updatevertices: delete vertex p%d (v%d) in f%d\n",
- qh_pointid(vertex->point), vertex->id, visible->id));
- }
- }
- }
- }
- }else { /* !VERTEXneighbors */
- FORALLvisible_facets {
- FOREACHvertex_(visible->vertices) {
- if (!vertex->newlist && !vertex->deleted) {
- vertex->deleted= True;
- qh_setappend (&qh del_vertices, vertex);
- trace2((qh ferr, "qh_updatevertices: delete vertex p%d (v%d) in f%d\n",
- qh_pointid(vertex->point), vertex->id, visible->id));
- }
- }
- }
- }
-} /* updatevertices */
-
-
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/poly.h b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/poly.h
deleted file mode 100644
index 109b5b3eab4c055084faca92bd9fc8561ec59259..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/poly.h
+++ /dev/null
@@ -1,291 +0,0 @@
-/*<html><pre> -<a href="qh-poly.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- poly.h
- header file for poly.c and poly2.c
-
- see qh-poly.htm, qhull.h and poly.c
-
- copyright (c) 1993-2003, The Geometry Center
-*/
-
-#ifndef qhDEFpoly
-#define qhDEFpoly 1
-
-/*=============== constants ========================== */
-
-/*-<a href="qh-geom.htm#TOC"
- >--------------------------------</a><a name="ALGORITHMfault">-</a>
-
- ALGORITHMfault
- use as argument to checkconvex() to report errors during buildhull
-*/
-#define qh_ALGORITHMfault 0
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="DATAfault">-</a>
-
- DATAfault
- use as argument to checkconvex() to report errors during initialhull
-*/
-#define qh_DATAfault 1
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="DUPLICATEridge">-</a>
-
- DUPLICATEridge
- special value for facet->neighbor to indicate a duplicate ridge
-
- notes:
- set by matchneighbor, used by matchmatch and mark_dupridge
-*/
-#define qh_DUPLICATEridge ( facetT * ) 1L
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="MERGEridge">-</a>
-
- MERGEridge flag in facet
- special value for facet->neighbor to indicate a merged ridge
-
- notes:
- set by matchneighbor, used by matchmatch and mark_dupridge
-*/
-#define qh_MERGEridge ( facetT * ) 2L
-
-
-/*============ -structures- ====================*/
-
-/*=========== -macros- =========================*/
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FORALLfacet_">-</a>
-
- FORALLfacet_( facetlist ) { ... }
- assign 'facet' to each facet in facetlist
-
- notes:
- uses 'facetT *facet;'
- assumes last facet is a sentinel
-
- see:
- FORALLfacets
-*/
-#define FORALLfacet_( facetlist ) if ( facetlist ) for( facet=( facetlist );facet && facet->next;facet=facet->next )
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FORALLnew_facets">-</a>
-
- FORALLnew_facets { ... }
- assign 'newfacet' to each facet in qh.newfacet_list
-
- notes:
- uses 'facetT *newfacet;'
- at exit, newfacet==NULL
-*/
-#define FORALLnew_facets for( newfacet=qh newfacet_list;newfacet && newfacet->next;newfacet=newfacet->next )
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FORALLvertex_">-</a>
-
- FORALLvertex_( vertexlist ) { ... }
- assign 'vertex' to each vertex in vertexlist
-
- notes:
- uses 'vertexT *vertex;'
- at exit, vertex==NULL
-*/
-#define FORALLvertex_( vertexlist ) for ( vertex=( vertexlist );vertex && vertex->next;vertex= vertex->next )
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FORALLvisible_facets">-</a>
-
- FORALLvisible_facets { ... }
- assign 'visible' to each visible facet in qh.visible_list
-
- notes:
- uses 'vacetT *visible;'
- at exit, visible==NULL
-*/
-#define FORALLvisible_facets for (visible=qh visible_list; visible && visible->visible; visible= visible->next)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FORALLsame_">-</a>
-
- FORALLsame_( newfacet ) { ... }
- assign 'same' to each facet in newfacet->f.samecycle
-
- notes:
- uses 'facetT *same;'
- stops when it returns to newfacet
-*/
-#define FORALLsame_(newfacet) for (same= newfacet->f.samecycle; same != newfacet; same= same->f.samecycle)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FORALLsame_cycle_">-</a>
-
- FORALLsame_cycle_( newfacet ) { ... }
- assign 'same' to each facet in newfacet->f.samecycle
-
- notes:
- uses 'facetT *same;'
- at exit, same == NULL
-*/
-#define FORALLsame_cycle_(newfacet) \
- for (same= newfacet->f.samecycle; \
- same; same= (same == newfacet ? NULL : same->f.samecycle))
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHneighborA_">-</a>
-
- FOREACHneighborA_( facet ) { ... }
- assign 'neighborA' to each neighbor in facet->neighbors
-
- FOREACHneighborA_( vertex ) { ... }
- assign 'neighborA' to each neighbor in vertex->neighbors
-
- declare:
- facetT *neighborA, **neighborAp;
-
- see:
- <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
-*/
-#define FOREACHneighborA_(facet) FOREACHsetelement_(facetT, facet->neighbors, neighborA)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHvisible_">-</a>
-
- FOREACHvisible_( facets ) { ... }
- assign 'visible' to each facet in facets
-
- notes:
- uses 'facetT *facet, *facetp;'
- see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
-*/
-#define FOREACHvisible_(facets) FOREACHsetelement_(facetT, facets, visible)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHnewfacet_">-</a>
-
- FOREACHnewfacet_( facets ) { ... }
- assign 'newfacet' to each facet in facets
-
- notes:
- uses 'facetT *newfacet, *newfacetp;'
- see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
-*/
-#define FOREACHnewfacet_(facets) FOREACHsetelement_(facetT, facets, newfacet)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHvertexA_">-</a>
-
- FOREACHvertexA_( vertices ) { ... }
- assign 'vertexA' to each vertex in vertices
-
- notes:
- uses 'vertexT *vertexA, *vertexAp;'
- see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
-*/
-#define FOREACHvertexA_(vertices) FOREACHsetelement_(vertexT, vertices, vertexA)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHvertexreverse12_">-</a>
-
- FOREACHvertexreverse12_( vertices ) { ... }
- assign 'vertex' to each vertex in vertices
- reverse order of first two vertices
-
- notes:
- uses 'vertexT *vertex, *vertexp;'
- see <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
-*/
-#define FOREACHvertexreverse12_(vertices) FOREACHsetelementreverse12_(vertexT, vertices, vertex)
-
-
-/*=============== prototypes poly.c in alphabetical order ================*/
-
-void qh_appendfacet(facetT* facet);
-void qh_appendvertex(vertexT* vertex);
-void qh_attachnewfacets(void);
-boolT qh_checkflipped(facetT* facet, realT* dist, boolT allerror);
-void qh_delfacet(facetT* facet);
-void qh_deletevisible(void /*qh visible_list, qh horizon_list*/);
-setT* qh_facetintersect(facetT* facetA, facetT* facetB, int* skipAp, int* skipBp, int extra);
-unsigned qh_gethash(int hashsize, setT* set, int size, int firstindex, void* skipelem);
-facetT* qh_makenewfacet(setT* vertices, boolT toporient, facetT* facet);
-void qh_makenewplanes(void /* newfacet_list */);
-facetT* qh_makenew_nonsimplicial(facetT* visible, vertexT* apex, int* numnew);
-facetT* qh_makenew_simplicial(facetT* visible, vertexT* apex, int* numnew);
-void qh_matchneighbor(facetT* newfacet, int newskip, int hashsize,
- int* hashcount);
-void qh_matchnewfacets(void);
-boolT qh_matchvertices(int firstindex, setT* verticesA, int skipA,
- setT* verticesB, int* skipB, boolT* same);
-facetT* qh_newfacet(void);
-ridgeT* qh_newridge(void);
-int qh_pointid(pointT* point);
-void qh_removefacet(facetT* facet);
-void qh_removevertex(vertexT* vertex);
-void qh_updatevertices(void);
-
-
-/*========== -prototypes poly2.c in alphabetical order ===========*/
-
-void qh_addhash(void* newelem, setT* hashtable, int hashsize, unsigned hash);
-void qh_check_bestdist(void);
-void qh_check_maxout(void);
-void qh_check_output(void);
-void qh_check_point(pointT* point, facetT* facet, realT* maxoutside, realT* maxdist, facetT** errfacet1, facetT** errfacet2);
-void qh_check_points(void);
-void qh_checkconvex(facetT* facetlist, int fault);
-void qh_checkfacet(facetT* facet, boolT newmerge, boolT* waserrorp);
-void qh_checkflipped_all(facetT* facetlist);
-void qh_checkpolygon(facetT* facetlist);
-void qh_checkvertex(vertexT* vertex);
-void qh_clearcenters(qh_CENTER type);
-void qh_createsimplex(setT* vertices);
-void qh_delridge(ridgeT* ridge);
-void qh_delvertex(vertexT* vertex);
-setT* qh_facet3vertex(facetT* facet);
-facetT* qh_findbestfacet(pointT* point, boolT bestoutside,
- realT* bestdist, boolT* isoutside);
-facetT* qh_findbestlower(facetT* upperfacet, pointT* point, realT* bestdistp, int* numpart);
-facetT* qh_findfacet_all(pointT* point, realT* bestdist, boolT* isoutside,
- int* numpart);
-int qh_findgood(facetT* facetlist, int goodhorizon);
-void qh_findgood_all(facetT* facetlist);
-void qh_furthestnext(void /* qh facet_list */);
-void qh_furthestout(facetT* facet);
-void qh_infiniteloop(facetT* facet);
-void qh_initbuild(void);
-void qh_initialhull(setT* vertices);
-setT* qh_initialvertices(int dim, setT* maxpoints, pointT* points, int numpoints);
-vertexT* qh_isvertex(pointT* point, setT* vertices);
-vertexT* qh_makenewfacets(pointT* point /*horizon_list, visible_list*/);
-void qh_matchduplicates(facetT* atfacet, int atskip, int hashsize, int* hashcount);
-void qh_nearcoplanar(void /* qh.facet_list */);
-vertexT* qh_nearvertex(facetT* facet, pointT* point, realT* bestdistp);
-int qh_newhashtable(int newsize);
-vertexT* qh_newvertex(pointT* point);
-ridgeT* qh_nextridge3d(ridgeT* atridge, facetT* facet, vertexT** vertexp);
-void qh_outcoplanar(void /* facet_list */);
-pointT* qh_point(int id);
-void qh_point_add(setT* set, pointT* point, void* elem);
-setT* qh_pointfacet(void /*qh facet_list*/);
-setT* qh_pointvertex(void /*qh facet_list*/);
-void qh_prependfacet(facetT* facet, facetT** facetlist);
-void qh_printhashtable(FILE* fp);
-void qh_printlists(void);
-void qh_resetlists(boolT stats, boolT resetVisible /*qh newvertex_list newfacet_list visible_list*/);
-void qh_setvoronoi_all(void);
-void qh_triangulate(void /*qh facet_list*/);
-void qh_triangulate_facet(facetT* facetA, vertexT** first_vertex);
-void qh_triangulate_link(facetT* oldfacetA, facetT* facetA, facetT* oldfacetB, facetT* facetB);
-void qh_triangulate_mirror(facetT* facetA, facetT* facetB);
-void qh_triangulate_null(facetT* facetA);
-void qh_vertexintersect(setT** vertexsetA, setT* vertexsetB);
-setT* qh_vertexintersect_new(setT* vertexsetA, setT* vertexsetB);
-void qh_vertexneighbors(void /*qh facet_list*/);
-boolT qh_vertexsubset(setT* vertexsetA, setT* vertexsetB);
-
-
-#endif /* qhDEFpoly */
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/poly2.c b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/poly2.c
deleted file mode 100644
index 79ce4afa83a92b4836101a782ecb417a4ce8c5df..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/poly2.c
+++ /dev/null
@@ -1,3137 +0,0 @@
-/*<html><pre> -<a href="qh-poly.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- poly2.c
- implements polygons and simplices
-
- see qh-poly.htm, poly.h and qhull.h
-
- frequently used code is in poly.c
-
- copyright (c) 1993-2003, The Geometry Center
-*/
-
-#include "qhull_a.h"
-
-/*======== functions in alphabetical order ==========*/
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="addhash">-</a>
-
- qh_addhash( newelem, hashtable, hashsize, hash )
- add newelem to linear hash table at hash if not already there
-*/
-void qh_addhash (void* newelem, setT *hashtable, int hashsize, unsigned hash) {
- int scan;
- void *elem;
-
- for (scan= (int)hash; (elem= SETelem_(hashtable, scan));
- scan= (++scan >= hashsize ? 0 : scan)) {
- if (elem == newelem)
- break;
- }
- /* loop terminates because qh_HASHfactor >= 1.1 by qh_initbuffers */
- if (!elem)
- SETelem_(hashtable, scan)= newelem;
-} /* addhash */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="check_bestdist">-</a>
-
- qh_check_bestdist()
- check that all points are within max_outside of the nearest facet
- if qh.ONLYgood,
- ignores !good facets
-
- see:
- qh_check_maxout(), qh_outerinner()
-
- notes:
- only called from qh_check_points()
- seldom used since qh.MERGING is almost always set
- if notverified>0 at end of routine
- some points were well inside the hull. If the hull contains
- a lens-shaped component, these points were not verified. Use
- options 'Qi Tv' to verify all points. (Exhaustive check also verifies)
-
- design:
- determine facet for each point (if any)
- for each point
- start with the assigned facet or with the first facet
- find the best facet for the point and check all coplanar facets
- error if point is outside of facet
-*/
-void qh_check_bestdist (void) {
- boolT waserror= False, unassigned;
- facetT *facet, *bestfacet, *errfacet1= NULL, *errfacet2= NULL;
- facetT *facetlist;
- realT dist, maxoutside, maxdist= -REALmax;
- pointT *point;
- int numpart= 0, facet_i, facet_n, notgood= 0, notverified= 0;
- setT *facets;
-
- trace1((qh ferr, "qh_check_bestdist: check points below nearest facet. Facet_list f%d\n",
- qh facet_list->id));
- maxoutside= qh_maxouter();
- maxoutside += qh DISTround;
- /* one more qh.DISTround for check computation */
- trace1((qh ferr, "qh_check_bestdist: check that all points are within %2.2g of best facet\n", maxoutside));
- facets= qh_pointfacet (/*qh facet_list*/);
- if (!qh_QUICKhelp && qh PRINTprecision)
- fprintf (qh ferr, "\n\
-qhull output completed. Verifying that %d points are\n\
-below %2.2g of the nearest %sfacet.\n",
- qh_setsize(facets), maxoutside, (qh ONLYgood ? "good " : ""));
- FOREACHfacet_i_(facets) { /* for each point with facet assignment */
- if (facet)
- unassigned= False;
- else {
- unassigned= True;
- facet= qh facet_list;
- }
- point= qh_point(facet_i);
- if (point == qh GOODpointp)
- continue;
- qh_distplane(point, facet, &dist);
- numpart++;
- bestfacet= qh_findbesthorizon (!qh_IScheckmax, point, facet, qh_NOupper, &dist, &numpart);
- /* occurs after statistics reported */
- maximize_(maxdist, dist);
- if (dist > maxoutside) {
- if (qh ONLYgood && !bestfacet->good
- && !((bestfacet= qh_findgooddist (point, bestfacet, &dist, &facetlist))
- && dist > maxoutside))
- notgood++;
- else {
- waserror= True;
- fprintf(qh ferr, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
- facet_i, bestfacet->id, dist, maxoutside);
- if (errfacet1 != bestfacet) {
- errfacet2= errfacet1;
- errfacet1= bestfacet;
- }
- }
- }else if (unassigned && dist < -qh MAXcoplanar)
- notverified++;
- }
- qh_settempfree (&facets);
- if (notverified && !qh DELAUNAY && !qh_QUICKhelp && qh PRINTprecision)
- fprintf(qh ferr, "\n%d points were well inside the hull. If the hull contains\n\
-a lens-shaped component, these points were not verified. Use\n\
-options 'Qci Tv' to verify all points.\n", notverified);
- if (maxdist > qh outside_err) {
- fprintf( qh ferr, "qhull precision error (qh_check_bestdist): a coplanar point is %6.2g from convex hull. The maximum value (qh.outside_err) is %6.2g\n",
- maxdist, qh outside_err);
- qh_errexit2 (qh_ERRprec, errfacet1, errfacet2);
- }else if (waserror && qh outside_err > REALmax/2)
- qh_errexit2 (qh_ERRprec, errfacet1, errfacet2);
- else if (waserror)
- ; /* the error was logged to qh.ferr but does not effect the output */
- trace0((qh ferr, "qh_check_bestdist: max distance outside %2.2g\n", maxdist));
-} /* check_bestdist */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="check_maxout">-</a>
-
- qh_check_maxout()
- updates qh.max_outside by checking all points against bestfacet
- if qh.ONLYgood, ignores !good facets
-
- returns:
- updates facet->maxoutside via qh_findbesthorizon()
- sets qh.maxoutdone
- if printing qh.min_vertex (qh_outerinner),
- it is updated to the current vertices
- removes inside/coplanar points from coplanarset as needed
-
- notes:
- defines coplanar as min_vertex instead of MAXcoplanar
- may not need to check near-inside points because of qh.MAXcoplanar
- and qh.KEEPnearinside (before it was -DISTround)
-
- see also:
- qh_check_bestdist()
-
- design:
- if qh.min_vertex is needed
- for all neighbors of all vertices
- test distance from vertex to neighbor
- determine facet for each point (if any)
- for each point with an assigned facet
- find the best facet for the point and check all coplanar facets
- (updates outer planes)
- remove near-inside points from coplanar sets
-*/
-#ifndef qh_NOmerge
-void qh_check_maxout (void) {
- facetT *facet, *bestfacet, *neighbor, **neighborp, *facetlist;
- realT dist, maxoutside, minvertex, old_maxoutside;
- pointT *point;
- int numpart= 0, facet_i, facet_n, notgood= 0;
- setT *facets, *vertices;
- vertexT *vertex;
-
- trace1((qh ferr, "qh_check_maxout: check and update maxoutside for each facet.\n"));
- maxoutside= minvertex= 0;
- if (qh VERTEXneighbors
- && (qh PRINTsummary || qh KEEPinside || qh KEEPcoplanar
- || qh TRACElevel || qh PRINTstatistics
- || qh PRINTout[0] == qh_PRINTsummary || qh PRINTout[0] == qh_PRINTnone)) {
- trace1((qh ferr, "qh_check_maxout: determine actual maxoutside and minvertex\n"));
- vertices= qh_pointvertex (/*qh facet_list*/);
- FORALLvertices {
- FOREACHneighbor_(vertex) {
- zinc_(Zdistvertex); /* distance also computed by main loop below */
- qh_distplane (vertex->point, neighbor, &dist);
- minimize_(minvertex, dist);
- if (-dist > qh TRACEdist || dist > qh TRACEdist
- || neighbor == qh tracefacet || vertex == qh tracevertex)
- fprintf (qh ferr, "qh_check_maxout: p%d (v%d) is %.2g from f%d\n",
- qh_pointid (vertex->point), vertex->id, dist, neighbor->id);
- }
- }
- if (qh MERGING) {
- wmin_(Wminvertex, qh min_vertex);
- }
- qh min_vertex= minvertex;
- qh_settempfree (&vertices);
- }
- facets= qh_pointfacet (/*qh facet_list*/);
- do {
- old_maxoutside= fmax_(qh max_outside, maxoutside);
- FOREACHfacet_i_(facets) { /* for each point with facet assignment */
- if (facet) {
- point= qh_point(facet_i);
- if (point == qh GOODpointp)
- continue;
- zinc_(Ztotcheck);
- qh_distplane(point, facet, &dist);
- numpart++;
- bestfacet= qh_findbesthorizon (qh_IScheckmax, point, facet, !qh_NOupper, &dist, &numpart);
- if (bestfacet && dist > maxoutside) {
- if (qh ONLYgood && !bestfacet->good
- && !((bestfacet= qh_findgooddist (point, bestfacet, &dist, &facetlist))
- && dist > maxoutside))
- notgood++;
- else
- maxoutside= dist;
- }
- if (dist > qh TRACEdist || (bestfacet && bestfacet == qh tracefacet))
- fprintf (qh ferr, "qh_check_maxout: p%d is %.2g above f%d\n",
- qh_pointid (point), dist, bestfacet->id);
- }
- }
- }while
- (maxoutside > 2*old_maxoutside);
- /* if qh.maxoutside increases substantially, qh_SEARCHdist is not valid
- e.g., RBOX 5000 s Z1 G1e-13 t1001200614 | qhull */
- zzadd_(Zcheckpart, numpart);
- qh_settempfree (&facets);
- wval_(Wmaxout)= maxoutside - qh max_outside;
- wmax_(Wmaxoutside, qh max_outside);
- qh max_outside= maxoutside;
- qh_nearcoplanar (/*qh.facet_list*/);
- qh maxoutdone= True;
- trace1((qh ferr, "qh_check_maxout: maxoutside %2.2g, min_vertex %2.2g, outside of not good %d\n",
- maxoutside, qh min_vertex, notgood));
-} /* check_maxout */
-#else /* qh_NOmerge */
-void qh_check_maxout (void) {
-}
-#endif
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="check_output">-</a>
-
- qh_check_output()
- performs the checks at the end of qhull algorithm
- Maybe called after voronoi output. Will recompute otherwise centrums are Voronoi centers instead
-*/
-void qh_check_output (void) {
- int i;
-
- if (qh STOPcone)
- return;
- if (qh VERIFYoutput | qh IStracing | qh CHECKfrequently) {
- qh_checkpolygon (qh facet_list);
- qh_checkflipped_all (qh facet_list);
- qh_checkconvex (qh facet_list, qh_ALGORITHMfault);
- }else if (!qh MERGING && qh_newstats (qhstat precision, &i)) {
- qh_checkflipped_all (qh facet_list);
- qh_checkconvex (qh facet_list, qh_ALGORITHMfault);
- }
-} /* check_output */
-
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="check_point">-</a>
-
- qh_check_point( point, facet, maxoutside, maxdist, errfacet1, errfacet2 )
- check that point is less than maxoutside from facet
-*/
-void qh_check_point (pointT *point, facetT *facet, realT *maxoutside, realT *maxdist, facetT **errfacet1, facetT **errfacet2) {
- realT dist;
-
- /* occurs after statistics reported */
- qh_distplane(point, facet, &dist);
- if (dist > *maxoutside) {
- if (*errfacet1 != facet) {
- *errfacet2= *errfacet1;
- *errfacet1= facet;
- }
- fprintf(qh ferr, "qhull precision error: point p%d is outside facet f%d, distance= %6.8g maxoutside= %6.8g\n",
- qh_pointid(point), facet->id, dist, *maxoutside);
- }
- maximize_(*maxdist, dist);
-} /* qh_check_point */
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="check_points">-</a>
-
- qh_check_points()
- checks that all points are inside all facets
-
- notes:
- if many points and qh_check_maxout not called (i.e., !qh.MERGING),
- calls qh_findbesthorizon (seldom done).
- ignores flipped facets
- maxoutside includes 2 qh.DISTrounds
- one qh.DISTround for the computed distances in qh_check_points
- qh_printafacet and qh_printsummary needs only one qh.DISTround
- the computation for qh.VERIFYdirect does not account for qh.other_points
-
- design:
- if many points
- use qh_check_bestdist()
- else
- for all facets
- for all points
- check that point is inside facet
-*/
-void qh_check_points (void) {
- facetT *facet, *errfacet1= NULL, *errfacet2= NULL;
- realT total, maxoutside, maxdist= -REALmax;
- pointT *point, **pointp, *pointtemp;
- boolT testouter;
-
- maxoutside= qh_maxouter();
- maxoutside += qh DISTround;
- /* one more qh.DISTround for check computation */
- trace1((qh ferr, "qh_check_points: check all points below %2.2g of all facet planes\n",
- maxoutside));
- if (qh num_good) /* miss counts other_points and !good facets */
- total= (float) qh num_good * qh num_points;
- else
- total= (float) qh num_facets * qh num_points;
- if (total >= qh_VERIFYdirect && !qh maxoutdone) {
- if (!qh_QUICKhelp && qh SKIPcheckmax && qh MERGING)
- fprintf (qh ferr, "\n\
-qhull input warning: merging without checking outer planes ('Q5' or 'Po').\n\
-Verify may report that a point is outside of a facet.\n");
- qh_check_bestdist();
- }else {
- if (qh_MAXoutside && qh maxoutdone)
- testouter= True;
- else
- testouter= False;
- if (!qh_QUICKhelp) {
- if (qh MERGEexact)
- fprintf (qh ferr, "\n\
-qhull input warning: exact merge ('Qx'). Verify may report that a point\n\
-is outside of a facet. See qh-optq.htm#Qx\n");
- else if (qh SKIPcheckmax || qh NOnearinside)
- fprintf (qh ferr, "\n\
-qhull input warning: no outer plane check ('Q5') or no processing of\n\
-near-inside points ('Q8'). Verify may report that a point is outside\n\
-of a facet.\n");
- }
- if (qh PRINTprecision) {
- if (testouter)
- fprintf (qh ferr, "\n\
-Output completed. Verifying that all points are below outer planes of\n\
-all %sfacets. Will make %2.0f distance computations.\n",
- (qh ONLYgood ? "good " : ""), total);
- else
- fprintf (qh ferr, "\n\
-Output completed. Verifying that all points are below %2.2g of\n\
-all %sfacets. Will make %2.0f distance computations.\n",
- maxoutside, (qh ONLYgood ? "good " : ""), total);
- }
- FORALLfacets {
- if (!facet->good && qh ONLYgood)
- continue;
- if (facet->flipped)
- continue;
- if (!facet->normal) {
- fprintf( qh ferr, "qhull warning (qh_check_points): missing normal for facet f%d\n", facet->id);
- continue;
- }
- if (testouter) {
-#if qh_MAXoutside
- maxoutside= facet->maxoutside + 2* qh DISTround;
- /* one DISTround to actual point and another to computed point */
-#endif
- }
- FORALLpoints {
- if (point != qh GOODpointp)
- qh_check_point (point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
- }
- FOREACHpoint_(qh other_points) {
- if (point != qh GOODpointp)
- qh_check_point (point, facet, &maxoutside, &maxdist, &errfacet1, &errfacet2);
- }
- }
- if (maxdist > qh outside_err) {
- fprintf( qh ferr, "qhull precision error (qh_check_points): a coplanar point is %6.2g from convex hull. The maximum value (qh.outside_err) is %6.2g\n",
- maxdist, qh outside_err );
- qh_errexit2( qh_ERRprec, errfacet1, errfacet2 );
- }else if (errfacet1 && qh outside_err > REALmax/2)
- qh_errexit2( qh_ERRprec, errfacet1, errfacet2 );
- else if (errfacet1)
- ; /* the error was logged to qh.ferr but does not effect the output */
- trace0((qh ferr, "qh_check_points: max distance outside %2.2g\n", maxdist));
- }
-} /* check_points */
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="checkconvex">-</a>
-
- qh_checkconvex( facetlist, fault )
- check that each ridge in facetlist is convex
- fault = qh_DATAfault if reporting errors
- = qh_ALGORITHMfault otherwise
-
- returns:
- counts Zconcaveridges and Zcoplanarridges
- errors if concaveridge or if merging an coplanar ridge
-
- note:
- if not merging,
- tests vertices for neighboring simplicial facets
- else if ZEROcentrum,
- tests vertices for neighboring simplicial facets
- else
- tests centrums of neighboring facets
-
- design:
- for all facets
- report flipped facets
- if ZEROcentrum and simplicial neighbors
- test vertices for neighboring simplicial facets
- else
- test centrum against all neighbors
-*/
-void qh_checkconvex(facetT *facetlist, int fault) {
- facetT *facet, *neighbor, **neighborp, *errfacet1=NULL, *errfacet2=NULL;
- vertexT *vertex;
- realT dist;
- pointT *centrum;
- boolT waserror= False, centrum_warning= False, tempcentrum= False, allsimplicial;
- int neighbor_i;
-
- trace1((qh ferr, "qh_checkconvex: check all ridges are convex\n"));
- if (!qh RERUN) {
- zzval_(Zconcaveridges)= 0;
- zzval_(Zcoplanarridges)= 0;
- }
- FORALLfacet_(facetlist) {
- if (facet->flipped) {
- qh_precision ("flipped facet");
- fprintf (qh ferr, "qhull precision error: f%d is flipped (interior point is outside)\n",
- facet->id);
- errfacet1= facet;
- waserror= True;
- continue;
- }
- if (qh MERGING && (!qh ZEROcentrum || !facet->simplicial || facet->tricoplanar))
- allsimplicial= False;
- else {
- allsimplicial= True;
- neighbor_i= 0;
- FOREACHneighbor_(facet) {
- vertex= SETelemt_(facet->vertices, neighbor_i++, vertexT);
- if (!neighbor->simplicial || neighbor->tricoplanar) {
- allsimplicial= False;
- continue;
- }
- qh_distplane (vertex->point, neighbor, &dist);
- if (dist > -qh DISTround) {
- if (fault == qh_DATAfault) {
- qh_precision ("coplanar or concave ridge");
- fprintf (qh ferr, "qhull precision error: initial simplex is not convex. Distance=%.2g\n", dist);
- qh_errexit(qh_ERRsingular, NULL, NULL);
- }
- if (dist > qh DISTround) {
- zzinc_(Zconcaveridges);
- qh_precision ("concave ridge");
- fprintf (qh ferr, "qhull precision error: f%d is concave to f%d, since p%d (v%d) is %6.4g above\n",
- facet->id, neighbor->id, qh_pointid(vertex->point), vertex->id, dist);
- errfacet1= facet;
- errfacet2= neighbor;
- waserror= True;
- }else if (qh ZEROcentrum) {
- if (dist > 0) { /* qh_checkzero checks that dist < - qh DISTround */
- zzinc_(Zcoplanarridges);
- qh_precision ("coplanar ridge");
- fprintf (qh ferr, "qhull precision error: f%d is clearly not convex to f%d, since p%d (v%d) is %6.4g above\n",
- facet->id, neighbor->id, qh_pointid(vertex->point), vertex->id, dist);
- errfacet1= facet;
- errfacet2= neighbor;
- waserror= True;
- }
- }else {
- zzinc_(Zcoplanarridges);
- qh_precision ("coplanar ridge");
- trace0((qh ferr, "qhull precision error: f%d may be coplanar to f%d, since p%d (v%d) is within %6.4g during p%d\n",
- facet->id, neighbor->id, qh_pointid(vertex->point), vertex->id, dist, qh furthest_id));
- }
- }
- }
- }
- if (!allsimplicial) {
- if (qh CENTERtype == qh_AScentrum) {
- if (!facet->center)
- facet->center= qh_getcentrum (facet);
- centrum= facet->center;
- }else {
- if (!centrum_warning && (!facet->simplicial || facet->tricoplanar)) {
- centrum_warning= True;
- fprintf (qh ferr, "qhull note: recomputing centrums for convexity test. This may lead to false, precision errors.\n");
- }
- centrum= qh_getcentrum(facet);
- tempcentrum= True;
- }
- FOREACHneighbor_(facet) {
- if (qh ZEROcentrum && facet->simplicial && neighbor->simplicial)
- continue;
- if (facet->tricoplanar || neighbor->tricoplanar)
- continue;
- zzinc_(Zdistconvex);
- qh_distplane (centrum, neighbor, &dist);
- if (dist > qh DISTround) {
- zzinc_(Zconcaveridges);
- qh_precision ("concave ridge");
- fprintf (qh ferr, "qhull precision error: f%d is concave to f%d. Centrum of f%d is %6.4g above f%d\n",
- facet->id, neighbor->id, facet->id, dist, neighbor->id);
- errfacet1= facet;
- errfacet2= neighbor;
- waserror= True;
- }else if (dist >= 0.0) { /* if arithmetic always rounds the same,
- can test against centrum radius instead */
- zzinc_(Zcoplanarridges);
- qh_precision ("coplanar ridge");
- fprintf (qh ferr, "qhull precision error: f%d is coplanar or concave to f%d. Centrum of f%d is %6.4g above f%d\n",
- facet->id, neighbor->id, facet->id, dist, neighbor->id);
- errfacet1= facet;
- errfacet2= neighbor;
- waserror= True;
- }
- }
- if (tempcentrum)
- qh_memfree(centrum, qh normal_size);
- }
- }
- if (waserror && !qh FORCEoutput)
- qh_errexit2 (qh_ERRprec, errfacet1, errfacet2);
-} /* checkconvex */
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="checkfacet">-</a>
-
- qh_checkfacet( facet, newmerge, waserror )
- checks for consistency errors in facet
- newmerge set if from merge.c
-
- returns:
- sets waserror if any error occurs
-
- checks:
- vertex ids are inverse sorted
- unless newmerge, at least hull_dim neighbors and vertices (exactly if simplicial)
- if non-simplicial, at least as many ridges as neighbors
- neighbors are not duplicated
- ridges are not duplicated
- in 3-d, ridges=verticies
- (qh.hull_dim-1) ridge vertices
- neighbors are reciprocated
- ridge neighbors are facet neighbors and a ridge for every neighbor
- simplicial neighbors match facetintersect
- vertex intersection matches vertices of common ridges
- vertex neighbors and facet vertices agree
- all ridges have distinct vertex sets
-
- notes:
- uses neighbor->seen
-
- design:
- check sets
- check vertices
- check sizes of neighbors and vertices
- check for qh_MERGEridge and qh_DUPLICATEridge flags
- check neighbor set
- check ridge set
- check ridges, neighbors, and vertices
-*/
-void qh_checkfacet(facetT *facet, boolT newmerge, boolT *waserrorp) {
- facetT *neighbor, **neighborp, *errother=NULL;
- ridgeT *ridge, **ridgep, *errridge= NULL, *ridge2;
- vertexT *vertex, **vertexp;
- unsigned previousid= INT_MAX;
- int numneighbors, numvertices, numridges=0, numRvertices=0;
- boolT waserror= False;
- int skipA, skipB, ridge_i, ridge_n, i;
- setT *intersection;
-
- if (facet->visible) {
- fprintf (qh ferr, "qhull internal error (qh_checkfacet): facet f%d is on the visible_list\n",
- facet->id);
- qh_errexit (qh_ERRqhull, facet, NULL);
- }
- if (!facet->normal) {
- fprintf (qh ferr, "qhull internal error (qh_checkfacet): facet f%d does not have a normal\n",
- facet->id);
- waserror= True;
- }
- qh_setcheck (facet->vertices, "vertices for f", facet->id);
- qh_setcheck (facet->ridges, "ridges for f", facet->id);
- qh_setcheck (facet->outsideset, "outsideset for f", facet->id);
- qh_setcheck (facet->coplanarset, "coplanarset for f", facet->id);
- qh_setcheck (facet->neighbors, "neighbors for f", facet->id);
- FOREACHvertex_(facet->vertices) {
- if (vertex->deleted) {
- fprintf(qh ferr, "qhull internal error (qh_checkfacet): deleted vertex v%d in f%d\n", vertex->id, facet->id);
- qh_errprint ("ERRONEOUS", NULL, NULL, NULL, vertex);
- waserror= True;
- }
- if (vertex->id >= previousid) {
- fprintf(qh ferr, "qhull internal error (qh_checkfacet): vertices of f%d are not in descending id order at v%d\n", facet->id, vertex->id);
- waserror= True;
- break;
- }
- previousid= vertex->id;
- }
- numneighbors= qh_setsize(facet->neighbors);
- numvertices= qh_setsize(facet->vertices);
- numridges= qh_setsize(facet->ridges);
- if (facet->simplicial) {
- if (numvertices+numneighbors != 2*qh hull_dim
- && !facet->degenerate && !facet->redundant) {
- fprintf(qh ferr, "qhull internal error (qh_checkfacet): for simplicial facet f%d, #vertices %d + #neighbors %d != 2*qh hull_dim\n",
- facet->id, numvertices, numneighbors);
- qh_setprint (qh ferr, "", facet->neighbors);
- waserror= True;
- }
- }else { /* non-simplicial */
- if (!newmerge
- &&(numvertices < qh hull_dim || numneighbors < qh hull_dim)
- && !facet->degenerate && !facet->redundant) {
- fprintf(qh ferr, "qhull internal error (qh_checkfacet): for facet f%d, #vertices %d or #neighbors %d < qh hull_dim\n",
- facet->id, numvertices, numneighbors);
- waserror= True;
- }
- /* in 3-d, can get a vertex twice in an edge list, e.g., RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv TP624 TW1e-13 T4 */
- if (numridges < numneighbors
- ||(qh hull_dim == 3 && numvertices > numridges && !qh NEWfacets)
- ||(qh hull_dim == 2 && numridges + numvertices + numneighbors != 6)) {
- if (!facet->degenerate && !facet->redundant) {
- fprintf(qh ferr, "qhull internal error (qh_checkfacet): for facet f%d, #ridges %d < #neighbors %d or (3-d) > #vertices %d or (2-d) not all 2\n",
- facet->id, numridges, numneighbors, numvertices);
- waserror= True;
- }
- }
- }
- FOREACHneighbor_(facet) {
- if (neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge) {
- fprintf(qh ferr, "qhull internal error (qh_checkfacet): facet f%d still has a MERGE or DUP neighbor\n", facet->id);
- qh_errexit (qh_ERRqhull, facet, NULL);
- }
- neighbor->seen= True;
- }
- FOREACHneighbor_(facet) {
- if (!qh_setin(neighbor->neighbors, facet)) {
- fprintf(qh ferr, "qhull internal error (qh_checkfacet): facet f%d has neighbor f%d, but f%d does not have neighbor f%d\n",
- facet->id, neighbor->id, neighbor->id, facet->id);
- errother= neighbor;
- waserror= True;
- }
- if (!neighbor->seen) {
- fprintf(qh ferr, "qhull internal error (qh_checkfacet): facet f%d has a duplicate neighbor f%d\n",
- facet->id, neighbor->id);
- errother= neighbor;
- waserror= True;
- }
- neighbor->seen= False;
- }
- FOREACHridge_(facet->ridges) {
- qh_setcheck (ridge->vertices, "vertices for r", ridge->id);
- ridge->seen= False;
- }
- FOREACHridge_(facet->ridges) {
- if (ridge->seen) {
- fprintf(qh ferr, "qhull internal error (qh_checkfacet): facet f%d has a duplicate ridge r%d\n",
- facet->id, ridge->id);
- errridge= ridge;
- waserror= True;
- }
- ridge->seen= True;
- numRvertices= qh_setsize(ridge->vertices);
- if (numRvertices != qh hull_dim - 1) {
- fprintf(qh ferr, "qhull internal error (qh_checkfacet): ridge between f%d and f%d has %d vertices\n",
- ridge->top->id, ridge->bottom->id, numRvertices);
- errridge= ridge;
- waserror= True;
- }
- neighbor= otherfacet_(ridge, facet);
- neighbor->seen= True;
- if (!qh_setin(facet->neighbors, neighbor)) {
- fprintf(qh ferr, "qhull internal error (qh_checkfacet): for facet f%d, neighbor f%d of ridge r%d not in facet\n",
- facet->id, neighbor->id, ridge->id);
- errridge= ridge;
- waserror= True;
- }
- }
- if (!facet->simplicial) {
- FOREACHneighbor_(facet) {
- if (!neighbor->seen) {
- fprintf(qh ferr, "qhull internal error (qh_checkfacet): facet f%d does not have a ridge for neighbor f%d\n",
- facet->id, neighbor->id);
- errother= neighbor;
- waserror= True;
- }
- intersection= qh_vertexintersect_new(facet->vertices, neighbor->vertices);
- qh_settemppush (intersection);
- FOREACHvertex_(facet->vertices) {
- vertex->seen= False;
- vertex->seen2= False;
- }
- FOREACHvertex_(intersection)
- vertex->seen= True;
- FOREACHridge_(facet->ridges) {
- if (neighbor != otherfacet_(ridge, facet))
- continue;
- FOREACHvertex_(ridge->vertices) {
- if (!vertex->seen) {
- fprintf (qh ferr, "qhull internal error (qh_checkfacet): vertex v%d in r%d not in f%d intersect f%d\n",
- vertex->id, ridge->id, facet->id, neighbor->id);
- qh_errexit (qh_ERRqhull, facet, ridge);
- }
- vertex->seen2= True;
- }
- }
- if (!newmerge) {
- FOREACHvertex_(intersection) {
- if (!vertex->seen2) {
- if (qh IStracing >=3 || !qh MERGING) {
- fprintf (qh ferr, "qhull precision error (qh_checkfacet): vertex v%d in f%d intersect f%d but\n\
- not in a ridge. This is ok under merging. Last point was p%d\n",
- vertex->id, facet->id, neighbor->id, qh furthest_id);
- if (!qh FORCEoutput && !qh MERGING) {
- qh_errprint ("ERRONEOUS", facet, neighbor, NULL, vertex);
- if (!qh MERGING)
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- }
- }
- }
- }
- qh_settempfree (&intersection);
- }
- }else { /* simplicial */
- FOREACHneighbor_(facet) {
- if (neighbor->simplicial) {
- skipA= SETindex_(facet->neighbors, neighbor);
- skipB= qh_setindex (neighbor->neighbors, facet);
- if (!qh_setequal_skip (facet->vertices, skipA, neighbor->vertices, skipB)) {
- fprintf (qh ferr, "qhull internal error (qh_checkfacet): facet f%d skip %d and neighbor f%d skip %d do not match \n",
- facet->id, skipA, neighbor->id, skipB);
- errother= neighbor;
- waserror= True;
- }
- }
- }
- }
- if (qh hull_dim < 5 && (qh IStracing > 2 || qh CHECKfrequently)) {
- FOREACHridge_i_(facet->ridges) { /* expensive */
- for (i= ridge_i+1; i < ridge_n; i++) {
- ridge2= SETelemt_(facet->ridges, i, ridgeT);
- if (qh_setequal (ridge->vertices, ridge2->vertices)) {
- fprintf (qh ferr, "qh_checkfacet: ridges r%d and r%d have the same vertices\n",
- ridge->id, ridge2->id);
- errridge= ridge;
- waserror= True;
- }
- }
- }
- }
- if (waserror) {
- qh_errprint("ERRONEOUS", facet, errother, errridge, NULL);
- *waserrorp= True;
- }
-} /* checkfacet */
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="checkflipped_all">-</a>
-
- qh_checkflipped_all( facetlist )
- checks orientation of facets in list against interior point
-*/
-void qh_checkflipped_all (facetT *facetlist) {
- facetT *facet;
- boolT waserror= False;
- realT dist;
-
- if (facetlist == qh facet_list)
- zzval_(Zflippedfacets)= 0;
- FORALLfacet_(facetlist) {
- if (facet->normal && !qh_checkflipped (facet, &dist, !qh_ALL)) {
- fprintf(qh ferr, "qhull precision error: facet f%d is flipped, distance= %6.12g\n",
- facet->id, dist);
- if (!qh FORCEoutput) {
- qh_errprint("ERRONEOUS", facet, NULL, NULL, NULL);
- waserror= True;
- }
- }
- }
- if (waserror) {
- fprintf (qh ferr, "\n\
-A flipped facet occurs when its distance to the interior point is\n\
-greater than %2.2g, the maximum roundoff error.\n", -qh DISTround);
- qh_errexit(qh_ERRprec, NULL, NULL);
- }
-} /* checkflipped_all */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="checkpolygon">-</a>
-
- qh_checkpolygon( facetlist )
- checks the correctness of the structure
-
- notes:
- call with either qh.facet_list or qh.newfacet_list
- checks num_facets and num_vertices if qh.facet_list
-
- design:
- for each facet
- checks facet and outside set
- initializes vertexlist
- for each facet
- checks vertex set
- if checking all facets (qh.facetlist)
- check facet count
- if qh.VERTEXneighbors
- check vertex neighbors and count
- check vertex count
-*/
-void qh_checkpolygon(facetT *facetlist) {
- facetT *facet;
- vertexT *vertex, **vertexp, *vertexlist;
- int numfacets= 0, numvertices= 0, numridges= 0;
- int totvneighbors= 0, totvertices= 0;
- boolT waserror= False, nextseen= False, visibleseen= False;
-
- trace1((qh ferr, "qh_checkpolygon: check all facets from f%d\n", facetlist->id));
- if (facetlist != qh facet_list || qh ONLYgood)
- nextseen= True;
- FORALLfacet_(facetlist) {
- if (facet == qh visible_list)
- visibleseen= True;
- if (!facet->visible) {
- if (!nextseen) {
- if (facet == qh facet_next)
- nextseen= True;
- else if (qh_setsize (facet->outsideset)) {
- if (!qh NARROWhull
-#if !qh_COMPUTEfurthest
- || facet->furthestdist >= qh MINoutside
-#endif
- ) {
- fprintf (qh ferr, "qhull internal error (qh_checkpolygon): f%d has outside points before qh facet_next\n",
- facet->id);
- qh_errexit (qh_ERRqhull, facet, NULL);
- }
- }
- }
- numfacets++;
- qh_checkfacet(facet, False, &waserror);
- }
- }
- if (qh visible_list && !visibleseen && facetlist == qh facet_list) {
- fprintf (qh ferr, "qhull internal error (qh_checkpolygon): visible list f%d no longer on facet list\n", qh visible_list->id);
- qh_printlists();
- qh_errexit (qh_ERRqhull, qh visible_list, NULL);
- }
- if (facetlist == qh facet_list)
- vertexlist= qh vertex_list;
- else if (facetlist == qh newfacet_list)
- vertexlist= qh newvertex_list;
- else
- vertexlist= NULL;
- FORALLvertex_(vertexlist) {
- vertex->seen= False;
- vertex->visitid= 0;
- }
- FORALLfacet_(facetlist) {
- if (facet->visible)
- continue;
- if (facet->simplicial)
- numridges += qh hull_dim;
- else
- numridges += qh_setsize (facet->ridges);
- FOREACHvertex_(facet->vertices) {
- vertex->visitid++;
- if (!vertex->seen) {
- vertex->seen= True;
- numvertices++;
- if (qh_pointid (vertex->point) == -1) {
- fprintf (qh ferr, "qhull internal error (qh_checkpolygon): unknown point %p for vertex v%d first_point %p\n",
- vertex->point, vertex->id, qh first_point);
- waserror= True;
- }
- }
- }
- }
- qh vertex_visit += numfacets;
- if (facetlist == qh facet_list) {
- if (numfacets != qh num_facets - qh num_visible) {
- fprintf(qh ferr, "qhull internal error (qh_checkpolygon): actual number of facets is %d, cumulative facet count is %d - %d visible facets\n",
- numfacets, qh num_facets, qh num_visible);
- waserror= True;
- }
- qh vertex_visit++;
- if (qh VERTEXneighbors) {
- FORALLvertices {
- qh_setcheck (vertex->neighbors, "neighbors for v", vertex->id);
- if (vertex->deleted)
- continue;
- totvneighbors += qh_setsize (vertex->neighbors);
- }
- FORALLfacet_(facetlist)
- totvertices += qh_setsize (facet->vertices);
- if (totvneighbors != totvertices) {
- fprintf(qh ferr, "qhull internal error (qh_checkpolygon): vertex neighbors inconsistent. Totvneighbors %d, totvertices %d\n",
- totvneighbors, totvertices);
- waserror= True;
- }
- }
- if (numvertices != qh num_vertices - qh_setsize(qh del_vertices)) {
- fprintf(qh ferr, "qhull internal error (qh_checkpolygon): actual number of vertices is %d, cumulative vertex count is %d\n",
- numvertices, qh num_vertices - qh_setsize(qh del_vertices));
- waserror= True;
- }
- if (qh hull_dim == 2 && numvertices != numfacets) {
- fprintf (qh ferr, "qhull internal error (qh_checkpolygon): #vertices %d != #facets %d\n",
- numvertices, numfacets);
- waserror= True;
- }
- if (qh hull_dim == 3 && numvertices + numfacets - numridges/2 != 2) {
- fprintf (qh ferr, "qhull warning: #vertices %d + #facets %d - #edges %d != 2\n\
- A vertex appears twice in a edge list. May occur during merging.",
- numvertices, numfacets, numridges/2);
- /* occurs if lots of merging and a vertex ends up twice in an edge list. e.g., RBOX 1000 s W1e-13 t995849315 D2 | QHULL d Tc Tv */
- }
- }
- if (waserror)
- qh_errexit(qh_ERRqhull, NULL, NULL);
-} /* checkpolygon */
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="checkvertex">-</a>
-
- qh_checkvertex( vertex )
- check vertex for consistency
- checks vertex->neighbors
-
- notes:
- neighbors checked efficiently in checkpolygon
-*/
-void qh_checkvertex (vertexT *vertex) {
- boolT waserror= False;
- facetT *neighbor, **neighborp, *errfacet=NULL;
-
- if (qh_pointid (vertex->point) == -1) {
- fprintf (qh ferr, "qhull internal error (qh_checkvertex): unknown point id %p\n", vertex->point);
- waserror= True;
- }
- if (vertex->id >= qh vertex_id) {
- fprintf (qh ferr, "qhull internal error (qh_checkvertex): unknown vertex id %d\n", vertex->id);
- waserror= True;
- }
- if (!waserror && !vertex->deleted) {
- if (qh_setsize (vertex->neighbors)) {
- FOREACHneighbor_(vertex) {
- if (!qh_setin (neighbor->vertices, vertex)) {
- fprintf (qh ferr, "qhull internal error (qh_checkvertex): neighbor f%d does not contain v%d\n", neighbor->id, vertex->id);
- errfacet= neighbor;
- waserror= True;
- }
- }
- }
- }
- if (waserror) {
- qh_errprint ("ERRONEOUS", NULL, NULL, NULL, vertex);
- qh_errexit (qh_ERRqhull, errfacet, NULL);
- }
-} /* checkvertex */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="clearcenters">-</a>
-
- qh_clearcenters( type )
- clear old data from facet->center
-
- notes:
- sets new centertype
- nop if CENTERtype is the same
-*/
-void qh_clearcenters (qh_CENTER type) {
- facetT *facet;
-
- if (qh CENTERtype != type) {
- FORALLfacets {
- if (qh CENTERtype == qh_ASvoronoi){
- if (facet->center) {
- qh_memfree (facet->center, qh center_size);
- facet->center= NULL;
- }
- }else /* qh CENTERtype == qh_AScentrum */ {
- if (facet->center) {
- qh_memfree (facet->center, qh normal_size);
- facet->center= NULL;
- }
- }
- }
- qh CENTERtype= type;
- }
- trace2((qh ferr, "qh_clearcenters: switched to center type %d\n", type));
-} /* clearcenters */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="createsimplex">-</a>
-
- qh_createsimplex( vertices )
- creates a simplex from a set of vertices
-
- returns:
- initializes qh.facet_list to the simplex
- initializes qh.newfacet_list, .facet_tail
- initializes qh.vertex_list, .newvertex_list, .vertex_tail
-
- design:
- initializes lists
- for each vertex
- create a new facet
- for each new facet
- create its neighbor set
-*/
-void qh_createsimplex(setT *vertices) {
- facetT *facet= NULL, *newfacet;
- boolT toporient= True;
- int vertex_i, vertex_n, nth;
- setT *newfacets= qh_settemp (qh hull_dim+1);
- vertexT *vertex;
-
- qh facet_list= qh newfacet_list= qh facet_tail= qh_newfacet();
- qh num_facets= qh num_vertices= qh num_visible= 0;
- qh vertex_list= qh newvertex_list= qh vertex_tail= qh_newvertex(NULL);
- FOREACHvertex_i_(vertices) {
- newfacet= qh_newfacet();
- newfacet->vertices= qh_setnew_delnthsorted (vertices, vertex_n,
- vertex_i, 0);
- newfacet->toporient= toporient;
- qh_appendfacet(newfacet);
- newfacet->newfacet= True;
- qh_appendvertex (vertex);
- qh_setappend (&newfacets, newfacet);
- toporient ^= True;
- }
- FORALLnew_facets {
- nth= 0;
- FORALLfacet_(qh newfacet_list) {
- if (facet != newfacet)
- SETelem_(newfacet->neighbors, nth++)= facet;
- }
- qh_settruncate (newfacet->neighbors, qh hull_dim);
- }
- qh_settempfree (&newfacets);
- trace1((qh ferr, "qh_createsimplex: created simplex\n"));
-} /* createsimplex */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="delridge">-</a>
-
- qh_delridge( ridge )
- deletes ridge from data structures it belongs to
- frees up its memory
-
- notes:
- in merge.c, caller sets vertex->delridge for each vertex
- ridges also freed in qh_freeqhull
-*/
-void qh_delridge(ridgeT *ridge) {
- void **freelistp; /* used !qh_NOmem */
-
- qh_setdel(ridge->top->ridges, ridge);
- qh_setdel(ridge->bottom->ridges, ridge);
- qh_setfree(&(ridge->vertices));
- qh_memfree_(ridge, sizeof(ridgeT), freelistp);
-} /* delridge */
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="delvertex">-</a>
-
- qh_delvertex( vertex )
- deletes a vertex and frees its memory
-
- notes:
- assumes vertex->adjacencies have been updated if needed
- unlinks from vertex_list
-*/
-void qh_delvertex (vertexT *vertex) {
-
- if (vertex == qh tracevertex)
- qh tracevertex= NULL;
- qh_removevertex (vertex);
- qh_setfree (&vertex->neighbors);
- qh_memfree(vertex, sizeof(vertexT));
-} /* delvertex */
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="facet3vertex">-</a>
-
- qh_facet3vertex( )
- return temporary set of 3-d vertices in qh_ORIENTclock order
-
- design:
- if simplicial facet
- build set from facet->vertices with facet->toporient
- else
- for each ridge in order
- build set from ridge's vertices
-*/
-setT *qh_facet3vertex (facetT *facet) {
- ridgeT *ridge, *firstridge;
- vertexT *vertex;
- int cntvertices, cntprojected=0;
- setT *vertices;
-
- cntvertices= qh_setsize(facet->vertices);
- vertices= qh_settemp (cntvertices);
- if (facet->simplicial) {
- if (cntvertices != 3) {
- fprintf (qh ferr, "qhull internal error (qh_facet3vertex): only %d vertices for simplicial facet f%d\n",
- cntvertices, facet->id);
- qh_errexit(qh_ERRqhull, facet, NULL);
- }
- qh_setappend (&vertices, SETfirst_(facet->vertices));
- if (facet->toporient ^ qh_ORIENTclock)
- qh_setappend (&vertices, SETsecond_(facet->vertices));
- else
- qh_setaddnth (&vertices, 0, SETsecond_(facet->vertices));
- qh_setappend (&vertices, SETelem_(facet->vertices, 2));
- }else {
- ridge= firstridge= SETfirstt_(facet->ridges, ridgeT); /* no infinite */
- while ((ridge= qh_nextridge3d (ridge, facet, &vertex))) {
- qh_setappend (&vertices, vertex);
- if (++cntprojected > cntvertices || ridge == firstridge)
- break;
- }
- if (!ridge || cntprojected != cntvertices) {
- fprintf (qh ferr, "qhull internal error (qh_facet3vertex): ridges for facet %d don't match up. got at least %d\n",
- facet->id, cntprojected);
- qh_errexit(qh_ERRqhull, facet, ridge);
- }
- }
- return vertices;
-} /* facet3vertex */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="findbestfacet">-</a>
-
- qh_findbestfacet( point, bestoutside, bestdist, isoutside )
- find facet that is furthest below a point
-
- for Delaunay triangulations,
- Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
- Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
-
- returns:
- if bestoutside is set (e.g., qh_ALL)
- returns best facet that is not upperdelaunay
- if Delaunay and inside, point is outside circumsphere of bestfacet
- else
- returns first facet below point
- if point is inside, returns nearest, !upperdelaunay facet
- distance to facet
- isoutside set if outside of facet
-
- notes:
- For tricoplanar facets, this finds one of the tricoplanar facets closest
- to the point. For Delaunay triangulations, the point may be inside a
- different tricoplanar facet. See <a href="../html/qh-in.htm#findfacet">locate a facet with qh_findbestfacet()</a>
-
- If inside, qh_findbestfacet performs an exhaustive search
- this may be too conservative. Sometimes it is clearly required.
-
- qh_findbestfacet is not used by qhull.
- uses qh.visit_id and qh.coplanarset
-
- see:
- <a href="geom.c#findbest">qh_findbest</a>
-*/
-facetT *qh_findbestfacet (pointT *point, boolT bestoutside,
- realT *bestdist, boolT *isoutside) {
- facetT *bestfacet= NULL;
- int numpart, totpart= 0;
-
- bestfacet= qh_findbest (point, qh facet_list,
- bestoutside, !qh_ISnewfacets, bestoutside /* qh_NOupper */,
- bestdist, isoutside, &totpart);
- if (*bestdist < -qh DISTround) {
- bestfacet= qh_findfacet_all (point, bestdist, isoutside, &numpart);
- totpart += numpart;
- if ((isoutside && bestoutside)
- || (!isoutside && bestfacet->upperdelaunay)) {
- bestfacet= qh_findbest (point, bestfacet,
- bestoutside, False, bestoutside,
- bestdist, isoutside, &totpart);
- totpart += numpart;
- }
- }
- trace3((qh ferr, "qh_findbestfacet: f%d dist %2.2g isoutside %d totpart %d\n",
- bestfacet->id, *bestdist, *isoutside, totpart));
- return bestfacet;
-} /* findbestfacet */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="findbestlower">-</a>
-
- qh_findbestlower( facet, point, bestdist, numpart )
- returns best non-upper, non-flipped neighbor of facet for point
- if needed, searches vertex neighbors
-
- returns:
- returns bestdist and updates numpart
-
- notes:
- if Delaunay and inside, point is outside of circumsphere of bestfacet
- called by qh_findbest() for points above an upperdelaunay facet
-
-*/
-facetT *qh_findbestlower (facetT *upperfacet, pointT *point, realT *bestdistp, int *numpart) {
- facetT *neighbor, **neighborp, *bestfacet= NULL;
- realT bestdist= -REALmax/2 /* avoid underflow */;
- realT dist;
- vertexT *vertex;
-
- zinc_(Zbestlower);
- FOREACHneighbor_(upperfacet) {
- if (neighbor->upperdelaunay || neighbor->flipped)
- continue;
- (*numpart)++;
- qh_distplane (point, neighbor, &dist);
- if (dist > bestdist) {
- bestfacet= neighbor;
- bestdist= dist;
- }
- }
- if (!bestfacet) {
- zinc_(Zbestlowerv);
- /* rarely called, numpart does not count nearvertex computations */
- vertex= qh_nearvertex (upperfacet, point, &dist);
- qh_vertexneighbors();
- FOREACHneighbor_(vertex) {
- if (neighbor->upperdelaunay || neighbor->flipped)
- continue;
- (*numpart)++;
- qh_distplane (point, neighbor, &dist);
- if (dist > bestdist) {
- bestfacet= neighbor;
- bestdist= dist;
- }
- }
- }
- if (!bestfacet) {
- fprintf(qh ferr, "\n\
-qh_findbestlower: all neighbors of facet %d are flipped or upper Delaunay.\n\
-Please report this error to qhull_bug@qhull.org with the input and all of the output.\n",
- upperfacet->id);
- qh_errexit (qh_ERRqhull, upperfacet, NULL);
- }
- *bestdistp= bestdist;
- trace3((qh ferr, "qh_findbestlower: f%d dist %2.2g for f%d p%d\n",
- bestfacet->id, bestdist, upperfacet->id, qh_pointid(point)));
- return bestfacet;
-} /* findbestlower */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="findfacet_all">-</a>
-
- qh_findfacet_all( point, bestdist, isoutside, numpart )
- exhaustive search for facet below a point
-
- for Delaunay triangulations,
- Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
- Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
-
- returns:
- returns first facet below point
- if point is inside,
- returns nearest facet
- distance to facet
- isoutside if point is outside of the hull
- number of distance tests
-*/
-facetT *qh_findfacet_all (pointT *point, realT *bestdist, boolT *isoutside,
- int *numpart) {
- facetT *bestfacet= NULL, *facet;
- realT dist;
- int totpart= 0;
-
- *bestdist= REALmin;
- *isoutside= False;
- FORALLfacets {
- if (facet->flipped || !facet->normal)
- continue;
- totpart++;
- qh_distplane (point, facet, &dist);
- if (dist > *bestdist) {
- *bestdist= dist;
- bestfacet= facet;
- if (dist > qh MINoutside) {
- *isoutside= True;
- break;
- }
- }
- }
- *numpart= totpart;
- trace3((qh ferr, "qh_findfacet_all: f%d dist %2.2g isoutside %d totpart %d\n",
- getid_(bestfacet), *bestdist, *isoutside, totpart));
- return bestfacet;
-} /* findfacet_all */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="findgood">-</a>
-
- qh_findgood( facetlist, goodhorizon )
- identify good facets for qh.PRINTgood
- if qh.GOODvertex>0
- facet includes point as vertex
- if !match, returns goodhorizon
- inactive if qh.MERGING
- if qh.GOODpoint
- facet is visible or coplanar (>0) or not visible (<0)
- if qh.GOODthreshold
- facet->normal matches threshold
- if !goodhorizon and !match,
- selects facet with closest angle
- sets GOODclosest
-
- returns:
- number of new, good facets found
- determines facet->good
- may update qh.GOODclosest
-
- notes:
- qh_findgood_all further reduces the good region
-
- design:
- count good facets
- mark good facets for qh.GOODpoint
- mark good facets for qh.GOODthreshold
- if necessary
- update qh.GOODclosest
-*/
-int qh_findgood (facetT *facetlist, int goodhorizon) {
- facetT *facet, *bestfacet= NULL;
- realT angle, bestangle= REALmax, dist;
- int numgood=0;
-
- FORALLfacet_(facetlist) {
- if (facet->good)
- numgood++;
- }
- if (qh GOODvertex>0 && !qh MERGING) {
- FORALLfacet_(facetlist) {
- if (!qh_isvertex (qh GOODvertexp, facet->vertices)) {
- facet->good= False;
- numgood--;
- }
- }
- }
- if (qh GOODpoint && numgood) {
- FORALLfacet_(facetlist) {
- if (facet->good && facet->normal) {
- zinc_(Zdistgood);
- qh_distplane (qh GOODpointp, facet, &dist);
- if ((qh GOODpoint > 0) ^ (dist > 0.0)) {
- facet->good= False;
- numgood--;
- }
- }
- }
- }
- if (qh GOODthreshold && (numgood || goodhorizon || qh GOODclosest)) {
- FORALLfacet_(facetlist) {
- if (facet->good && facet->normal) {
- if (!qh_inthresholds (facet->normal, &angle)) {
- facet->good= False;
- numgood--;
- if (angle < bestangle) {
- bestangle= angle;
- bestfacet= facet;
- }
- }
- }
- }
- if (!numgood && (!goodhorizon || qh GOODclosest)) {
- if (qh GOODclosest) {
- if (qh GOODclosest->visible)
- qh GOODclosest= NULL;
- else {
- qh_inthresholds (qh GOODclosest->normal, &angle);
- if (angle < bestangle)
- bestfacet= qh GOODclosest;
- }
- }
- if (bestfacet && bestfacet != qh GOODclosest) {
- if (qh GOODclosest)
- qh GOODclosest->good= False;
- qh GOODclosest= bestfacet;
- bestfacet->good= True;
- numgood++;
- trace2((qh ferr, "qh_findgood: f%d is closest (%2.2g) to thresholds\n",
- bestfacet->id, bestangle));
- return numgood;
- }
- }else if (qh GOODclosest) { /* numgood > 0 */
- qh GOODclosest->good= False;
- qh GOODclosest= NULL;
- }
- }
- zadd_(Zgoodfacet, numgood);
- trace2((qh ferr, "qh_findgood: found %d good facets with %d good horizon\n",
- numgood, goodhorizon));
- if (!numgood && qh GOODvertex>0 && !qh MERGING)
- return goodhorizon;
- return numgood;
-} /* findgood */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="findgood_all">-</a>
-
- qh_findgood_all( facetlist )
- apply other constraints for good facets (used by qh.PRINTgood)
- if qh.GOODvertex
- facet includes (>0) or doesn't include (<0) point as vertex
- if last good facet and ONLYgood, prints warning and continues
- if qh.SPLITthresholds
- facet->normal matches threshold, or if none, the closest one
- calls qh_findgood
- nop if good not used
-
- returns:
- clears facet->good if not good
- sets qh.num_good
-
- notes:
- this is like qh_findgood but more restrictive
-
- design:
- uses qh_findgood to mark good facets
- marks facets for qh.GOODvertex
- marks facets for qh.SPLITthreholds
-*/
-void qh_findgood_all (facetT *facetlist) {
- facetT *facet, *bestfacet=NULL;
- realT angle, bestangle= REALmax;
- int numgood=0, startgood;
-
- if (!qh GOODvertex && !qh GOODthreshold && !qh GOODpoint
- && !qh SPLITthresholds)
- return;
- if (!qh ONLYgood)
- qh_findgood (qh facet_list, 0);
- FORALLfacet_(facetlist) {
- if (facet->good)
- numgood++;
- }
- if (qh GOODvertex <0 || (qh GOODvertex > 0 && qh MERGING)) {
- FORALLfacet_(facetlist) {
- if (facet->good && ((qh GOODvertex > 0) ^ !!qh_isvertex (qh GOODvertexp, facet->vertices))) {
- if (!--numgood) {
- if (qh ONLYgood) {
- fprintf (qh ferr, "qhull warning: good vertex p%d does not match last good facet f%d. Ignored.\n",
- qh_pointid(qh GOODvertexp), facet->id);
- return;
- }else if (qh GOODvertex > 0)
- fprintf (qh ferr, "qhull warning: point p%d is not a vertex ('QV%d').\n",
- qh GOODvertex-1, qh GOODvertex-1);
- else
- fprintf (qh ferr, "qhull warning: point p%d is a vertex for every facet ('QV-%d').\n",
- -qh GOODvertex - 1, -qh GOODvertex - 1);
- }
- facet->good= False;
- }
- }
- }
- startgood= numgood;
- if (qh SPLITthresholds) {
- FORALLfacet_(facetlist) {
- if (facet->good) {
- if (!qh_inthresholds (facet->normal, &angle)) {
- facet->good= False;
- numgood--;
- if (angle < bestangle) {
- bestangle= angle;
- bestfacet= facet;
- }
- }
- }
- }
- if (!numgood && bestfacet) {
- bestfacet->good= True;
- numgood++;
- trace0((qh ferr, "qh_findgood_all: f%d is closest (%2.2g) to thresholds\n",
- bestfacet->id, bestangle));
- return;
- }
- }
- qh num_good= numgood;
- trace0((qh ferr, "qh_findgood_all: %d good facets remain out of %d facets\n",
- numgood, startgood));
-} /* findgood_all */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="furthestnext">-</a>
-
- qh_furthestnext()
- set qh.facet_next to facet with furthest of all furthest points
- searches all facets on qh.facet_list
-
- notes:
- this may help avoid precision problems
-*/
-void qh_furthestnext (void /* qh facet_list */) {
- facetT *facet, *bestfacet= NULL;
- realT dist, bestdist= -REALmax;
-
- FORALLfacets {
- if (facet->outsideset) {
-#if qh_COMPUTEfurthest
- pointT *furthest;
- furthest= (pointT*)qh_setlast (facet->outsideset);
- zinc_(Zcomputefurthest);
- qh_distplane (furthest, facet, &dist);
-#else
- dist= facet->furthestdist;
-#endif
- if (dist > bestdist) {
- bestfacet= facet;
- bestdist= dist;
- }
- }
- }
- if (bestfacet) {
- qh_removefacet (bestfacet);
- qh_prependfacet (bestfacet, &qh facet_next);
- trace1((qh ferr, "qh_furthestnext: made f%d next facet (dist %.2g)\n",
- bestfacet->id, bestdist));
- }
-} /* furthestnext */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="furthestout">-</a>
-
- qh_furthestout( facet )
- make furthest outside point the last point of outsideset
-
- returns:
- updates facet->outsideset
- clears facet->notfurthest
- sets facet->furthestdist
-
- design:
- determine best point of outsideset
- make it the last point of outsideset
-*/
-void qh_furthestout (facetT *facet) {
- pointT *point, **pointp, *bestpoint= NULL;
- realT dist, bestdist= -REALmax;
-
- FOREACHpoint_(facet->outsideset) {
- qh_distplane (point, facet, &dist);
- zinc_(Zcomputefurthest);
- if (dist > bestdist) {
- bestpoint= point;
- bestdist= dist;
- }
- }
- if (bestpoint) {
- qh_setdel (facet->outsideset, point);
- qh_setappend (&facet->outsideset, point);
-#if !qh_COMPUTEfurthest
- facet->furthestdist= bestdist;
-#endif
- }
- facet->notfurthest= False;
- trace3((qh ferr, "qh_furthestout: p%d is furthest outside point of f%d\n",
- qh_pointid (point), facet->id));
-} /* furthestout */
-
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="infiniteloop">-</a>
-
- qh_infiniteloop( facet )
- report infinite loop error due to facet
-*/
-void qh_infiniteloop (facetT *facet) {
-
- fprintf (qh ferr, "qhull internal error (qh_infiniteloop): potential infinite loop detected\n");
- qh_errexit (qh_ERRqhull, facet, NULL);
-} /* qh_infiniteloop */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="initbuild">-</a>
-
- qh_initbuild()
- initialize hull and outside sets with point array
- qh.FIRSTpoint/qh.NUMpoints is point array
- if qh.GOODpoint
- adds qh.GOODpoint to initial hull
-
- returns:
- qh_facetlist with initial hull
- points partioned into outside sets, coplanar sets, or inside
- initializes qh.GOODpointp, qh.GOODvertexp,
-
- design:
- initialize global variables used during qh_buildhull
- determine precision constants and points with max/min coordinate values
- if qh.SCALElast, scale last coordinate (for 'd')
- build initial simplex
- partition input points into facets of initial simplex
- set up lists
- if qh.ONLYgood
- check consistency
- add qh.GOODvertex if defined
-*/
-void qh_initbuild( void) {
- setT *maxpoints, *vertices;
- facetT *facet;
- int i, numpart;
- realT dist;
- boolT isoutside;
-
- qh furthest_id= -1;
- qh lastreport= 0;
- qh facet_id= qh vertex_id= qh ridge_id= 0;
- qh visit_id= qh vertex_visit= 0;
- qh maxoutdone= False;
-
- if (qh GOODpoint > 0)
- qh GOODpointp= qh_point (qh GOODpoint-1);
- else if (qh GOODpoint < 0)
- qh GOODpointp= qh_point (-qh GOODpoint-1);
- if (qh GOODvertex > 0)
- qh GOODvertexp= qh_point (qh GOODvertex-1);
- else if (qh GOODvertex < 0)
- qh GOODvertexp= qh_point (-qh GOODvertex-1);
- if ((qh GOODpoint
- && (qh GOODpointp < qh first_point /* also catches !GOODpointp */
- || qh GOODpointp > qh_point (qh num_points-1)))
- || (qh GOODvertex
- && (qh GOODvertexp < qh first_point /* also catches !GOODvertexp */
- || qh GOODvertexp > qh_point (qh num_points-1)))) {
- fprintf (qh ferr, "qhull input error: either QGn or QVn point is > p%d\n",
- qh num_points-1);
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- maxpoints= qh_maxmin(qh first_point, qh num_points, qh hull_dim);
- if (qh SCALElast)
- qh_scalelast (qh first_point, qh num_points, qh hull_dim,
- qh MINlastcoord, qh MAXlastcoord, qh MAXwidth);
- qh_detroundoff();
- if (qh DELAUNAY && qh upper_threshold[qh hull_dim-1] > REALmax/2
- && qh lower_threshold[qh hull_dim-1] < -REALmax/2) {
- for (i= qh_PRINTEND; i--; ) {
- if (qh PRINTout[i] == qh_PRINTgeom && qh DROPdim < 0
- && !qh GOODthreshold && !qh SPLITthresholds)
- break; /* in this case, don't set upper_threshold */
- }
- if (i < 0) {
- if (qh UPPERdelaunay) { /* matches qh.upperdelaunay in qh_setfacetplane */
- qh lower_threshold[qh hull_dim-1]= qh ANGLEround * qh_ZEROdelaunay;
- qh GOODthreshold= True;
- }else {
- qh upper_threshold[qh hull_dim-1]= -qh ANGLEround * qh_ZEROdelaunay;
- if (!qh GOODthreshold)
- qh SPLITthresholds= True; /* build upper-convex hull even if Qg */
- /* qh_initqhull_globals errors if Qg without Pdk/etc. */
- }
- }
- }
- vertices= qh_initialvertices(qh hull_dim, maxpoints, qh first_point, qh num_points);
- qh_initialhull (vertices); /* initial qh facet_list */
- qh_partitionall (vertices, qh first_point, qh num_points);
- if (qh PRINToptions1st || qh TRACElevel || qh IStracing) {
- if (qh TRACElevel || qh IStracing)
- fprintf (qh ferr, "\nTrace level %d for %s | %s\n",
- qh IStracing ? qh IStracing : qh TRACElevel, qh rbox_command, qh qhull_command);
- fprintf (qh ferr, "Options selected for Qhull %s:\n%s\n", qh_version, qh qhull_options);
- }
- qh_resetlists (False, qh_RESETvisible /*qh visible_list newvertex_list newfacet_list */);
- qh facet_next= qh facet_list;
- qh_furthestnext (/* qh facet_list */);
- if (qh PREmerge) {
- qh cos_max= qh premerge_cos;
- qh centrum_radius= qh premerge_centrum;
- }
- if (qh ONLYgood) {
- if (qh GOODvertex > 0 && qh MERGING) {
- fprintf (qh ferr, "qhull input error: 'Qg QVn' (only good vertex) does not work with merging.\nUse 'QJ' to joggle the input or 'Q0' to turn off merging.\n");
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- if (!(qh GOODthreshold || qh GOODpoint
- || (!qh MERGEexact && !qh PREmerge && qh GOODvertexp))) {
- fprintf (qh ferr, "qhull input error: 'Qg' (ONLYgood) needs a good threshold ('Pd0D0'), a\n\
-good point (QGn or QG-n), or a good vertex with 'QJ' or 'Q0' (QVn).\n");
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- if (qh GOODvertex > 0 && !qh MERGING /* matches qh_partitionall */
- && !qh_isvertex (qh GOODvertexp, vertices)) {
- facet= qh_findbestnew (qh GOODvertexp, qh facet_list,
- &dist, !qh_ALL, &isoutside, &numpart);
- zadd_(Zdistgood, numpart);
- if (!isoutside) {
- fprintf (qh ferr, "qhull input error: point for QV%d is inside initial simplex. It can not be made a vertex.\n",
- qh_pointid(qh GOODvertexp));
- qh_errexit (qh_ERRinput, NULL, NULL);
- }
- if (!qh_addpoint (qh GOODvertexp, facet, False)) {
- qh_settempfree(&vertices);
- qh_settempfree(&maxpoints);
- return;
- }
- }
- qh_findgood (qh facet_list, 0);
- }
- qh_settempfree(&vertices);
- qh_settempfree(&maxpoints);
- trace1((qh ferr, "qh_initbuild: initial hull created and points partitioned\n"));
-} /* initbuild */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="initialhull">-</a>
-
- qh_initialhull( vertices )
- constructs the initial hull as a DIM3 simplex of vertices
-
- design:
- creates a simplex (initializes lists)
- determines orientation of simplex
- sets hyperplanes for facets
- doubles checks orientation (in case of axis-parallel facets with Gaussian elimination)
- checks for flipped facets and qh.NARROWhull
- checks the result
-*/
-void qh_initialhull(setT *vertices) {
- facetT *facet, *firstfacet, *neighbor, **neighborp;
- realT dist, angle, minangle= REALmax;
-#ifndef qh_NOtrace
- int k;
-#endif
-
- qh_createsimplex(vertices); /* qh facet_list */
- qh_resetlists (False, qh_RESETvisible);
- qh facet_next= qh facet_list; /* advance facet when processed */
- qh interior_point= qh_getcenter(vertices);
- firstfacet= qh facet_list;
- qh_setfacetplane(firstfacet);
- zinc_(Znumvisibility); /* needs to be in printsummary */
- qh_distplane(qh interior_point, firstfacet, &dist);
- if (dist > 0) {
- FORALLfacets
- facet->toporient ^= True;
- }
- FORALLfacets
- qh_setfacetplane(facet);
- FORALLfacets {
- if (!qh_checkflipped (facet, NULL, qh_ALL)) {/* due to axis-parallel facet */
- trace1((qh ferr, "qh_initialhull: initial orientation incorrect. Correct all facets\n"));
- facet->flipped= False;
- FORALLfacets {
- facet->toporient ^= True;
- qh_orientoutside (facet);
- }
- break;
- }
- }
- FORALLfacets {
- if (!qh_checkflipped (facet, NULL, !qh_ALL)) { /* can happen with 'R0.1' */
- qh_precision ("initial facet is coplanar with interior point");
- fprintf (qh ferr, "qhull precision error: initial facet %d is coplanar with the interior point\n",
- facet->id);
- qh_errexit (qh_ERRsingular, facet, NULL);
- }
- FOREACHneighbor_(facet) {
- angle= qh_getangle (facet->normal, neighbor->normal);
- minimize_( minangle, angle);
- }
- }
- if (minangle < qh_MAXnarrow && !qh NOnarrow) {
- realT diff= 1.0 + minangle;
-
- qh NARROWhull= True;
- qh_option ("_narrow-hull", NULL, &diff);
- if (minangle < qh_WARNnarrow && !qh RERUN && qh PRINTprecision)
- fprintf (qh ferr, "qhull precision warning: \n\
-The initial hull is narrow (cosine of min. angle is %.16f).\n\
-A coplanar point may lead to a wide facet. Options 'QbB' (scale to unit box)\n\
-or 'Qbb' (scale last coordinate) may remove this warning. Use 'Pp' to skip\n\
-this warning. See 'Limitations' in qh-impre.htm.\n",
- -minangle); /* convert from angle between normals to angle between facets */
- }
- zzval_(Zprocessed)= qh hull_dim+1;
- qh_checkpolygon (qh facet_list);
- qh_checkconvex(qh facet_list, qh_DATAfault);
-#ifndef qh_NOtrace
- if (qh IStracing >= 1) {
- fprintf(qh ferr, "qh_initialhull: simplex constructed, interior point:");
- for (k=0; k < qh hull_dim; k++)
- fprintf (qh ferr, " %6.4g", qh interior_point[k]);
- fprintf (qh ferr, "\n");
- }
-#endif
-} /* initialhull */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="initialvertices">-</a>
-
- qh_initialvertices( dim, maxpoints, points, numpoints )
- determines a non-singular set of initial vertices
- maxpoints may include duplicate points
-
- returns:
- temporary set of dim+1 vertices in descending order by vertex id
- if qh.RANDOMoutside && !qh.ALLpoints
- picks random points
- if dim >= qh_INITIALmax,
- uses min/max x and max points with non-zero determinants
-
- notes:
- unless qh.ALLpoints,
- uses maxpoints as long as determinate is non-zero
-*/
-setT *qh_initialvertices(int dim, setT *maxpoints, pointT *points, int numpoints) {
- pointT *point, **pointp;
- setT *vertices, *simplex, *tested;
- realT randr;
- int index, point_i, point_n, k;
- boolT nearzero= False;
-
- vertices= qh_settemp (dim + 1);
- simplex= qh_settemp (dim+1);
- if (qh ALLpoints)
- qh_maxsimplex (dim, NULL, points, numpoints, &simplex);
- else if (qh RANDOMoutside) {
- while (qh_setsize (simplex) != dim+1) {
- randr= qh_RANDOMint;
- randr= randr/(qh_RANDOMmax+1);
- index= (int)floor(qh num_points * randr);
- while (qh_setin (simplex, qh_point (index))) {
- index++; /* in case qh_RANDOMint always returns the same value */
- index= index < qh num_points ? index : 0;
- }
- qh_setappend (&simplex, qh_point (index));
- }
- }else if (qh hull_dim >= qh_INITIALmax) {
- tested= qh_settemp (dim+1);
- qh_setappend (&simplex, SETfirst_(maxpoints)); /* max and min X coord */
- qh_setappend (&simplex, SETsecond_(maxpoints));
- qh_maxsimplex (fmin_(qh_INITIALsearch, dim), maxpoints, points, numpoints, &simplex);
- k= qh_setsize (simplex);
- FOREACHpoint_i_(maxpoints) {
- if (point_i & 0x1) { /* first pick up max. coord. points */
- if (!qh_setin (simplex, point) && !qh_setin (tested, point)){
- qh_detsimplex(point, simplex, k, &nearzero);
- if (nearzero)
- qh_setappend (&tested, point);
- else {
- qh_setappend (&simplex, point);
- if (++k == dim) /* use search for last point */
- break;
- }
- }
- }
- }
- while (k != dim && (point= (pointT*)qh_setdellast (maxpoints))) {
- if (!qh_setin (simplex, point) && !qh_setin (tested, point)){
- qh_detsimplex (point, simplex, k, &nearzero);
- if (nearzero)
- qh_setappend (&tested, point);
- else {
- qh_setappend (&simplex, point);
- k++;
- }
- }
- }
- index= 0;
- while (k != dim && (point= qh_point (index++))) {
- if (!qh_setin (simplex, point) && !qh_setin (tested, point)){
- qh_detsimplex (point, simplex, k, &nearzero);
- if (!nearzero){
- qh_setappend (&simplex, point);
- k++;
- }
- }
- }
- qh_settempfree (&tested);
- qh_maxsimplex (dim, maxpoints, points, numpoints, &simplex);
- }else
- qh_maxsimplex (dim, maxpoints, points, numpoints, &simplex);
- FOREACHpoint_(simplex)
- qh_setaddnth (&vertices, 0, qh_newvertex(point)); /* descending order */
- qh_settempfree (&simplex);
- return vertices;
-} /* initialvertices */
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="isvertex">-</a>
-
- qh_isvertex( )
- returns vertex if point is in vertex set, else returns NULL
-
- notes:
- for qh.GOODvertex
-*/
-vertexT *qh_isvertex (pointT *point, setT *vertices) {
- vertexT *vertex, **vertexp;
-
- FOREACHvertex_(vertices) {
- if (vertex->point == point)
- return vertex;
- }
- return NULL;
-} /* isvertex */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="makenewfacets">-</a>
-
- qh_makenewfacets( point )
- make new facets from point and qh.visible_list
-
- returns:
- qh.newfacet_list= list of new facets with hyperplanes and ->newfacet
- qh.newvertex_list= list of vertices in new facets with ->newlist set
-
- if (qh.ONLYgood)
- newfacets reference horizon facets, but not vice versa
- ridges reference non-simplicial horizon ridges, but not vice versa
- does not change existing facets
- else
- sets qh.NEWfacets
- new facets attached to horizon facets and ridges
- for visible facets,
- visible->r.replace is corresponding new facet
-
- see also:
- qh_makenewplanes() -- make hyperplanes for facets
- qh_attachnewfacets() -- attachnewfacets if not done here (qh ONLYgood)
- qh_matchnewfacets() -- match up neighbors
- qh_updatevertices() -- update vertex neighbors and delvertices
- qh_deletevisible() -- delete visible facets
- qh_checkpolygon() --check the result
- qh_triangulate() -- triangulate a non-simplicial facet
-
- design:
- for each visible facet
- make new facets to its horizon facets
- update its f.replace
- clear its neighbor set
-*/
-vertexT *qh_makenewfacets (pointT *point /*visible_list*/) {
- facetT *visible, *newfacet= NULL, *newfacet2= NULL, *neighbor, **neighborp;
- vertexT *apex;
- int numnew=0;
-
- qh newfacet_list= qh facet_tail;
- qh newvertex_list= qh vertex_tail;
- apex= qh_newvertex(point);
- qh_appendvertex (apex);
- qh visit_id++;
- if (!qh ONLYgood)
- qh NEWfacets= True;
- FORALLvisible_facets {
- FOREACHneighbor_(visible)
- neighbor->seen= False;
- if (visible->ridges) {
- visible->visitid= qh visit_id;
- newfacet2= qh_makenew_nonsimplicial (visible, apex, &numnew);
- }
- if (visible->simplicial)
- newfacet= qh_makenew_simplicial (visible, apex, &numnew);
- if (!qh ONLYgood) {
- if (newfacet2) /* newfacet is null if all ridges defined */
- newfacet= newfacet2;
- if (newfacet)
- visible->f.replace= newfacet;
- else
- zinc_(Zinsidevisible);
- SETfirst_(visible->neighbors)= NULL;
- }
- }
- trace1((qh ferr, "qh_makenewfacets: created %d new facets from point p%d to horizon\n",
- numnew, qh_pointid(point)));
- if (qh IStracing >= 4)
- qh_printfacetlist (qh newfacet_list, NULL, qh_ALL);
- return apex;
-} /* makenewfacets */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="matchduplicates">-</a>
-
- qh_matchduplicates( atfacet, atskip, hashsize, hashcount )
- match duplicate ridges in qh.hash_table for atfacet/atskip
- duplicates marked with ->dupridge and qh_DUPLICATEridge
-
- returns:
- picks match with worst merge (min distance apart)
- updates hashcount
-
- see also:
- qh_matchneighbor
-
- notes:
-
- design:
- compute hash value for atfacet and atskip
- repeat twice -- once to make best matches, once to match the rest
- for each possible facet in qh.hash_table
- if it is a matching facet and pass 2
- make match
- unless tricoplanar, mark match for merging (qh_MERGEridge)
- [e.g., tricoplanar RBOX s 1000 t993602376 | QHULL C-1e-3 d Qbb FA Qt]
- if it is a matching facet and pass 1
- test if this is a better match
- if pass 1,
- make best match (it will not be merged)
-*/
-#ifndef qh_NOmerge
-void qh_matchduplicates (facetT *atfacet, int atskip, int hashsize, int *hashcount) {
- boolT same, ismatch;
- int hash, scan;
- facetT *facet, *newfacet, *maxmatch= NULL, *maxmatch2= NULL, *nextfacet;
- int skip, newskip, nextskip= 0, maxskip= 0, maxskip2= 0, makematch;
- realT maxdist= -REALmax, mindist, dist2, low, high;
-
- hash= (int)qh_gethash (hashsize, atfacet->vertices, qh hull_dim, 1,
- SETelem_(atfacet->vertices, atskip));
- trace2((qh ferr, "qh_matchduplicates: find duplicate matches for f%d skip %d hash %d hashcount %d\n",
- atfacet->id, atskip, hash, *hashcount));
- for (makematch= 0; makematch < 2; makematch++) {
- qh visit_id++;
- for (newfacet= atfacet, newskip= atskip; newfacet; newfacet= nextfacet, newskip= nextskip) {
- zinc_(Zhashlookup);
- nextfacet= NULL;
- newfacet->visitid= qh visit_id;
- for (scan= hash; (facet= SETelemt_(qh hash_table, scan, facetT));
- scan= (++scan >= hashsize ? 0 : scan)) {
- if (!facet->dupridge || facet->visitid == qh visit_id)
- continue;
- zinc_(Zhashtests);
- if (qh_matchvertices (1, newfacet->vertices, newskip, facet->vertices, &skip, &same)) {
- ismatch= (same == (newfacet->toporient ^ facet->toporient));
- if (SETelemt_(facet->neighbors, skip, facetT) != qh_DUPLICATEridge) {
- if (!makematch) {
- fprintf (qh ferr, "qhull internal error (qh_matchduplicates): missing dupridge at f%d skip %d for new f%d skip %d hash %d\n",
- facet->id, skip, newfacet->id, newskip, hash);
- qh_errexit2 (qh_ERRqhull, facet, newfacet);
- }
- }else if (ismatch && makematch) {
- if (SETelemt_(newfacet->neighbors, newskip, facetT) == qh_DUPLICATEridge) {
- SETelem_(facet->neighbors, skip)= newfacet;
- if (newfacet->tricoplanar)
- SETelem_(newfacet->neighbors, newskip)= facet;
- else
- SETelem_(newfacet->neighbors, newskip)= qh_MERGEridge;
- *hashcount -= 2; /* removed two unmatched facets */
- trace4((qh ferr, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d merge\n",
- facet->id, skip, newfacet->id, newskip));
- }
- }else if (ismatch) {
- mindist= qh_getdistance (facet, newfacet, &low, &high);
- dist2= qh_getdistance (newfacet, facet, &low, &high);
- minimize_(mindist, dist2);
- if (mindist > maxdist) {
- maxdist= mindist;
- maxmatch= facet;
- maxskip= skip;
- maxmatch2= newfacet;
- maxskip2= newskip;
- }
- trace3((qh ferr, "qh_matchduplicates: duplicate f%d skip %d new f%d skip %d at dist %2.2g, max is now f%d f%d\n",
- facet->id, skip, newfacet->id, newskip, mindist,
- maxmatch->id, maxmatch2->id));
- }else { /* !ismatch */
- nextfacet= facet;
- nextskip= skip;
- }
- }
- if (makematch && !facet
- && SETelemt_(facet->neighbors, skip, facetT) == qh_DUPLICATEridge) {
- fprintf (qh ferr, "qhull internal error (qh_matchduplicates): no MERGEridge match for duplicate f%d skip %d at hash %d\n",
- newfacet->id, newskip, hash);
- qh_errexit (qh_ERRqhull, newfacet, NULL);
- }
- }
- } /* end of for each new facet at hash */
- if (!makematch) {
- if (!maxmatch) {
- fprintf (qh ferr, "qhull internal error (qh_matchduplicates): no maximum match at duplicate f%d skip %d at hash %d\n",
- atfacet->id, atskip, hash);
- qh_errexit (qh_ERRqhull, atfacet, NULL);
- }
- SETelem_(maxmatch->neighbors, maxskip)= maxmatch2;
- SETelem_(maxmatch2->neighbors, maxskip2)= maxmatch;
- *hashcount -= 2; /* removed two unmatched facets */
- zzinc_(Zmultiridge);
- trace0((qh ferr, "qh_matchduplicates: duplicate f%d skip %d matched with new f%d skip %d keep\n",
- maxmatch->id, maxskip, maxmatch2->id, maxskip2));
- qh_precision ("ridge with multiple neighbors");
- if (qh IStracing >= 4)
- qh_errprint ("DUPLICATED/MATCH", maxmatch, maxmatch2, NULL, NULL);
- }
- }
-} /* matchduplicates */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="nearcoplanar">-</a>
-
- qh_nearcoplanar()
- for all facets, remove near-inside points from facet->coplanarset</li>
- coplanar points defined by innerplane from qh_outerinner()
-
- returns:
- if qh KEEPcoplanar && !qh KEEPinside
- facet->coplanarset only contains coplanar points
- if qh.JOGGLEmax
- drops inner plane by another qh.JOGGLEmax diagonal since a
- vertex could shift out while a coplanar point shifts in
-
- notes:
- used for qh.PREmerge and qh.JOGGLEmax
- must agree with computation of qh.NEARcoplanar in qh_detroundoff()
- design:
- if not keeping coplanar or inside points
- free all coplanar sets
- else if not keeping both coplanar and inside points
- remove !coplanar or !inside points from coplanar sets
-*/
-void qh_nearcoplanar ( void /* qh.facet_list */) {
- facetT *facet;
- pointT *point, **pointp;
- int numpart;
- realT dist, innerplane;
-
- if (!qh KEEPcoplanar && !qh KEEPinside) {
- FORALLfacets {
- if (facet->coplanarset)
- qh_setfree( &facet->coplanarset);
- }
- }else if (!qh KEEPcoplanar || !qh KEEPinside) {
- qh_outerinner (NULL, NULL, &innerplane);
- if (qh JOGGLEmax < REALmax/2)
- innerplane -= qh JOGGLEmax * sqrt (qh hull_dim);
- numpart= 0;
- FORALLfacets {
- if (facet->coplanarset) {
- FOREACHpoint_(facet->coplanarset) {
- numpart++;
- qh_distplane (point, facet, &dist);
- if (dist < innerplane) {
- if (!qh KEEPinside)
- SETref_(point)= NULL;
- }else if (!qh KEEPcoplanar)
- SETref_(point)= NULL;
- }
- qh_setcompact (facet->coplanarset);
- }
- }
- zzadd_(Zcheckpart, numpart);
- }
-} /* nearcoplanar */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="nearvertex">-</a>
-
- qh_nearvertex( facet, point, bestdist )
- return nearest vertex in facet to point
-
- returns:
- vertex and its distance
-
- notes:
- if qh.DELAUNAY
- distance is measured in the input set
- searches neighboring tricoplanar facets (requires vertexneighbors)
- Slow implementation. Recomputes vertex set for each point.
- The vertex set could be stored in the qh.keepcentrum facet.
-*/
-vertexT *qh_nearvertex (facetT *facet, pointT *point, realT *bestdistp) {
- realT bestdist= REALmax, dist;
- vertexT *bestvertex= NULL, *vertex, **vertexp, *apex;
- coordT *center;
- facetT *neighbor, **neighborp;
- setT *vertices;
- int dim= qh hull_dim;
-
- if (qh DELAUNAY)
- dim--;
- if (facet->tricoplanar) {
- if (!qh VERTEXneighbors || !facet->center) {
- fprintf(qh ferr, "qhull internal error (qh_nearvertex): qh.VERTEXneighbors and facet->center required for tricoplanar facets\n");
- qh_errexit(qh_ERRqhull, facet, NULL);
- }
- vertices= qh_settemp (qh TEMPsize);
- apex= SETfirst_(facet->vertices);
- center= facet->center;
- FOREACHneighbor_(apex) {
- if (neighbor->center == center) {
- FOREACHvertex_(neighbor->vertices)
- qh_setappend(&vertices, vertex);
- }
- }
- }else
- vertices= facet->vertices;
- FOREACHvertex_(vertices) {
- dist= qh_pointdist (vertex->point, point, -dim);
- if (dist < bestdist) {
- bestdist= dist;
- bestvertex= vertex;
- }
- }
- if (facet->tricoplanar)
- qh_settempfree (&vertices);
- *bestdistp= sqrt (bestdist);
- trace3((qh ferr, "qh_nearvertex: v%d dist %2.2g for f%d p%d\n",
- bestvertex->id, *bestdistp, facet->id, qh_pointid(point)));
- return bestvertex;
-} /* nearvertex */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="newhashtable">-</a>
-
- qh_newhashtable( newsize )
- returns size of qh.hash_table of at least newsize slots
-
- notes:
- assumes qh.hash_table is NULL
- qh_HASHfactor determines the number of extra slots
- size is not divisible by 2, 3, or 5
-*/
-int qh_newhashtable(int newsize) {
- int size;
-
- size= ((newsize+1)*qh_HASHfactor) | 0x1; /* odd number */
- while (True) {
- if ((size%3) && (size%5))
- break;
- size += 2;
- /* loop terminates because there is an infinite number of primes */
- }
- qh hash_table= qh_setnew (size);
- qh_setzero (qh hash_table, 0, size);
- return size;
-} /* newhashtable */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="newvertex">-</a>
-
- qh_newvertex( point )
- returns a new vertex for point
-*/
-vertexT *qh_newvertex(pointT *point) {
- vertexT *vertex;
-
- zinc_(Ztotvertices);
- vertex= (vertexT *)qh_memalloc(sizeof(vertexT));
- memset ((char *) vertex, 0, sizeof (vertexT));
- if (qh vertex_id == 0xFFFFFF) {
- fprintf(qh ferr, "qhull input error: more than %d vertices. ID field overflows and two vertices\n\
-may have the same identifier. Vertices not sorted correctly.\n", 0xFFFFFF);
- qh_errexit(qh_ERRinput, NULL, NULL);
- }
- if (qh vertex_id == qh tracevertex_id)
- qh tracevertex= vertex;
- vertex->id= qh vertex_id++;
- vertex->point= point;
- trace4((qh ferr, "qh_newvertex: vertex p%d (v%d) created\n", qh_pointid(vertex->point),
- vertex->id));
- return (vertex);
-} /* newvertex */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="nextridge3d">-</a>
-
- qh_nextridge3d( atridge, facet, vertex )
- return next ridge and vertex for a 3d facet
-
- notes:
- in qh_ORIENTclock order
- this is a O(n^2) implementation to trace all ridges
- be sure to stop on any 2nd visit
-
- design:
- for each ridge
- exit if it is the ridge after atridge
-*/
-ridgeT *qh_nextridge3d (ridgeT *atridge, facetT *facet, vertexT **vertexp) {
- vertexT *atvertex, *vertex, *othervertex;
- ridgeT *ridge, **ridgep;
-
- if ((atridge->top == facet) ^ qh_ORIENTclock)
- atvertex= SETsecondt_(atridge->vertices, vertexT);
- else
- atvertex= SETfirstt_(atridge->vertices, vertexT);
- FOREACHridge_(facet->ridges) {
- if (ridge == atridge)
- continue;
- if ((ridge->top == facet) ^ qh_ORIENTclock) {
- othervertex= SETsecondt_(ridge->vertices, vertexT);
- vertex= SETfirstt_(ridge->vertices, vertexT);
- }else {
- vertex= SETsecondt_(ridge->vertices, vertexT);
- othervertex= SETfirstt_(ridge->vertices, vertexT);
- }
- if (vertex == atvertex) {
- if (vertexp)
- *vertexp= othervertex;
- return ridge;
- }
- }
- return NULL;
-} /* nextridge3d */
-#else /* qh_NOmerge */
-void qh_matchduplicates (facetT *atfacet, int atskip, int hashsize, int *hashcount) {
-}
-ridgeT *qh_nextridge3d (ridgeT *atridge, facetT *facet, vertexT **vertexp) {
-
- return NULL;
-}
-#endif /* qh_NOmerge */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="outcoplanar">-</a>
-
- qh_outcoplanar()
- move points from all facets' outsidesets to their coplanarsets
-
- notes:
- for post-processing under qh.NARROWhull
-
- design:
- for each facet
- for each outside point for facet
- partition point into coplanar set
-*/
-void qh_outcoplanar (void /* facet_list */) {
- pointT *point, **pointp;
- facetT *facet;
- realT dist;
-
- trace1((qh ferr, "qh_outcoplanar: move outsideset to coplanarset for qh NARROWhull\n"));
- FORALLfacets {
- FOREACHpoint_(facet->outsideset) {
- qh num_outside--;
- if (qh KEEPcoplanar || qh KEEPnearinside) {
- qh_distplane (point, facet, &dist);
- zinc_(Zpartition);
- qh_partitioncoplanar (point, facet, &dist);
- }
- }
- qh_setfree (&facet->outsideset);
- }
-} /* outcoplanar */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="point">-</a>
-
- qh_point( id )
- return point for a point id, or NULL if unknown
-
- alternative code:
- return ((pointT *)((unsigned long)qh.first_point
- + (unsigned long)((id)*qh.normal_size)));
-*/
-pointT *qh_point (int id) {
-
- if (id < 0)
- return NULL;
- if (id < qh num_points)
- return qh first_point + id * qh hull_dim;
- id -= qh num_points;
- if (id < qh_setsize (qh other_points))
- return SETelemt_(qh other_points, id, pointT);
- return NULL;
-} /* point */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="point_add">-</a>
-
- qh_point_add( set, point, elem )
- stores elem at set[point.id]
-
- returns:
- access function for qh_pointfacet and qh_pointvertex
-
- notes:
- checks point.id
-*/
-void qh_point_add (setT *set, pointT *point, void *elem) {
- int id, size;
-
- SETreturnsize_(set, size);
- if ((id= qh_pointid(point)) < 0)
- fprintf (qh ferr, "qhull internal warning (point_add): unknown point %p id %d\n",
- point, id);
- else if (id >= size) {
- fprintf (qh ferr, "qhull internal errror (point_add): point p%d is out of bounds (%d)\n",
- id, size);
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }else
- SETelem_(set, id)= elem;
-} /* point_add */
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="pointfacet">-</a>
-
- qh_pointfacet()
- return temporary set of facet for each point
- the set is indexed by point id
-
- notes:
- vertices assigned to one of the facets
- coplanarset assigned to the facet
- outside set assigned to the facet
- NULL if no facet for point (inside)
- includes qh.GOODpointp
-
- access:
- FOREACHfacet_i_(facets) { ... }
- SETelem_(facets, i)
-
- design:
- for each facet
- add each vertex
- add each coplanar point
- add each outside point
-*/
-setT *qh_pointfacet (void /*qh facet_list*/) {
- int numpoints= qh num_points + qh_setsize (qh other_points);
- setT *facets;
- facetT *facet;
- vertexT *vertex, **vertexp;
- pointT *point, **pointp;
-
- facets= qh_settemp (numpoints);
- qh_setzero (facets, 0, numpoints);
- qh vertex_visit++;
- FORALLfacets {
- FOREACHvertex_(facet->vertices) {
- if (vertex->visitid != qh vertex_visit) {
- vertex->visitid= qh vertex_visit;
- qh_point_add (facets, vertex->point, facet);
- }
- }
- FOREACHpoint_(facet->coplanarset)
- qh_point_add (facets, point, facet);
- FOREACHpoint_(facet->outsideset)
- qh_point_add (facets, point, facet);
- }
- return facets;
-} /* pointfacet */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="pointvertex">-</a>
-
- qh_pointvertex( )
- return temporary set of vertices indexed by point id
- entry is NULL if no vertex for a point
- this will include qh.GOODpointp
-
- access:
- FOREACHvertex_i_(vertices) { ... }
- SETelem_(vertices, i)
-*/
-setT *qh_pointvertex (void /*qh facet_list*/) {
- int numpoints= qh num_points + qh_setsize (qh other_points);
- setT *vertices;
- vertexT *vertex;
-
- vertices= qh_settemp (numpoints);
- qh_setzero (vertices, 0, numpoints);
- FORALLvertices
- qh_point_add (vertices, vertex->point, vertex);
- return vertices;
-} /* pointvertex */
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="prependfacet">-</a>
-
- qh_prependfacet( facet, facetlist )
- prepend facet to the start of a facetlist
-
- returns:
- increments qh.numfacets
- updates facetlist, qh.facet_list, facet_next
-
- notes:
- be careful of prepending since it can lose a pointer.
- e.g., can lose _next by deleting and then prepending before _next
-*/
-void qh_prependfacet(facetT *facet, facetT **facetlist) {
- facetT *prevfacet, *list;
-
-
- trace4((qh ferr, "qh_prependfacet: prepend f%d before f%d\n",
- facet->id, getid_(*facetlist)));
- if (!*facetlist)
- (*facetlist)= qh facet_tail;
- list= *facetlist;
- prevfacet= list->previous;
- facet->previous= prevfacet;
- if (prevfacet)
- prevfacet->next= facet;
- list->previous= facet;
- facet->next= *facetlist;
- if (qh facet_list == list) /* this may change *facetlist */
- qh facet_list= facet;
- if (qh facet_next == list)
- qh facet_next= facet;
- *facetlist= facet;
- qh num_facets++;
-} /* prependfacet */
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="printhashtable">-</a>
-
- qh_printhashtable( fp )
- print hash table to fp
-
- notes:
- not in I/O to avoid bringing io.c in
-
- design:
- for each hash entry
- if defined
- if unmatched or will merge (NULL, qh_MERGEridge, qh_DUPLICATEridge)
- print entry and neighbors
-*/
-void qh_printhashtable(FILE *fp) {
- facetT *facet, *neighbor;
- int id, facet_i, facet_n, neighbor_i= 0, neighbor_n= 0;
- vertexT *vertex, **vertexp;
-
- FOREACHfacet_i_(qh hash_table) {
- if (facet) {
- FOREACHneighbor_i_(facet) {
- if (!neighbor || neighbor == qh_MERGEridge || neighbor == qh_DUPLICATEridge)
- break;
- }
- if (neighbor_i == neighbor_n)
- continue;
- fprintf (fp, "hash %d f%d ", facet_i, facet->id);
- FOREACHvertex_(facet->vertices)
- fprintf (fp, "v%d ", vertex->id);
- fprintf (fp, "\n neighbors:");
- FOREACHneighbor_i_(facet) {
- if (neighbor == qh_MERGEridge)
- id= -3;
- else if (neighbor == qh_DUPLICATEridge)
- id= -2;
- else
- id= getid_(neighbor);
- fprintf (fp, " %d", id);
- }
- fprintf (fp, "\n");
- }
- }
-} /* printhashtable */
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="printlists">-</a>
-
- qh_printlists( fp )
- print out facet and vertex list for debugging (without 'f/v' tags)
-*/
-void qh_printlists (void) {
- facetT *facet;
- vertexT *vertex;
- int count= 0;
-
- fprintf (qh ferr, "qh_printlists: facets:");
- FORALLfacets {
- if (++count % 100 == 0)
- fprintf (qh ferr, "\n ");
- fprintf (qh ferr, " %d", facet->id);
- }
- fprintf (qh ferr, "\n new facets %d visible facets %d next facet for qh_addpoint %d\n vertices (new %d):",
- getid_(qh newfacet_list), getid_(qh visible_list), getid_(qh facet_next),
- getid_(qh newvertex_list));
- count = 0;
- FORALLvertices {
- if (++count % 100 == 0)
- fprintf (qh ferr, "\n ");
- fprintf (qh ferr, " %d", vertex->id);
- }
- fprintf (qh ferr, "\n");
-} /* printlists */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="resetlists">-</a>
-
- qh_resetlists( stats, qh_RESETvisible )
- reset newvertex_list, newfacet_list, visible_list
- if stats,
- maintains statistics
-
- returns:
- visible_list is empty if qh_deletevisible was called
-*/
-void qh_resetlists (boolT stats, boolT resetVisible /*qh newvertex_list newfacet_list visible_list*/) {
- vertexT *vertex;
- facetT *newfacet, *visible;
- int totnew=0, totver=0;
-
- if (stats) {
- FORALLvertex_(qh newvertex_list)
- totver++;
- FORALLnew_facets
- totnew++;
- zadd_(Zvisvertextot, totver);
- zmax_(Zvisvertexmax, totver);
- zadd_(Znewfacettot, totnew);
- zmax_(Znewfacetmax, totnew);
- }
- FORALLvertex_(qh newvertex_list)
- vertex->newlist= False;
- qh newvertex_list= NULL;
- FORALLnew_facets
- newfacet->newfacet= False;
- qh newfacet_list= NULL;
- if (resetVisible) {
- FORALLvisible_facets {
- visible->f.replace= NULL;
- visible->visible= False;
- }
- qh num_visible= 0;
- }
- qh visible_list= NULL; /* may still have visible facets via qh_triangulate */
- qh NEWfacets= False;
-} /* resetlists */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="setvoronoi_all">-</a>
-
- qh_setvoronoi_all()
- compute Voronoi centers for all facets
- includes upperDelaunay facets if qh.UPPERdelaunay ('Qu')
-
- returns:
- facet->center is the Voronoi center
-
- notes:
- this is unused/untested code
- please email bradb@shore.net if this works ok for you
-
- use:
- FORALLvertices {...} to locate the vertex for a point.
- FOREACHneighbor_(vertex) {...} to visit the Voronoi centers for a Voronoi cell.
-*/
-void qh_setvoronoi_all (void) {
- facetT *facet;
-
- qh_clearcenters (qh_ASvoronoi);
- qh_vertexneighbors();
-
- FORALLfacets {
- if (!facet->normal || !facet->upperdelaunay || qh UPPERdelaunay) {
- if (!facet->center)
- facet->center= qh_facetcenter (facet->vertices);
- }
- }
-} /* setvoronoi_all */
-
-#ifndef qh_NOmerge
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="triangulate">-</a>
-
- qh_triangulate()
- triangulate non-simplicial facets on qh.facet_list,
- if qh.CENTERtype=qh_ASvoronoi, sets Voronoi centers of non-simplicial facets
-
- returns:
- all facets simplicial
- each tricoplanar facet has ->f.triowner == owner of ->center,normal,etc.
-
- notes:
- call after qh_check_output since may switch to Voronoi centers
- Output may overwrite ->f.triowner with ->f.area
-*/
-void qh_triangulate (void /*qh facet_list*/) {
- facetT *facet, *nextfacet, *owner;
- int onlygood= qh ONLYgood;
- facetT *neighbor, *visible= NULL, *facet1, *facet2, *new_facet_list= NULL;
- facetT *orig_neighbor= NULL, *otherfacet;
- vertexT *new_vertex_list= NULL;
- mergeT *merge;
- mergeType mergetype;
- int neighbor_i, neighbor_n;
-
- trace1((qh ferr, "qh_triangulate: triangulate non-simplicial facets\n"));
- if (qh hull_dim == 2)
- return;
- if (qh VORONOI) { /* otherwise lose Voronoi centers [could rebuild vertex set from tricoplanar] */
- qh_clearcenters (qh_ASvoronoi);
- qh_vertexneighbors();
- }
- qh ONLYgood= False; /* for makenew_nonsimplicial */
- qh visit_id++;
- qh NEWfacets= True;
- qh degen_mergeset= qh_settemp (qh TEMPsize);
- qh newvertex_list= qh vertex_tail;
- for (facet= qh facet_list; facet && facet->next; facet= nextfacet) { /* non-simplicial facets moved to end */
- nextfacet= facet->next;
- if (facet->visible || facet->simplicial)
- continue;
- /* triangulate all non-simplicial facets, otherwise merging does not work, e.g., RBOX c P-0.1 P+0.1 P+0.1 D3 | QHULL d Qt Tv */
- if (!new_facet_list)
- new_facet_list= facet; /* will be moved to end */
- qh_triangulate_facet (facet, &new_vertex_list);
- }
- trace2((qh ferr, "qh_triangulate: delete null facets from f%d -- apex same as second vertex\n", getid_(new_facet_list)));
- for (facet= new_facet_list; facet && facet->next; facet= nextfacet) { /* null facets moved to end */
- nextfacet= facet->next;
- if (facet->visible)
- continue;
- if (facet->ridges) {
- if (qh_setsize(facet->ridges) > 0) {
- fprintf( qh ferr, "qhull error (qh_triangulate): ridges still defined for f%d\n", facet->id);
- qh_errexit (qh_ERRqhull, facet, NULL);
- }
- qh_setfree (&facet->ridges);
- }
- if (SETfirst_(facet->vertices) == SETsecond_(facet->vertices)) {
- zinc_(Ztrinull);
- qh_triangulate_null (facet);
- }
- }
- trace2((qh ferr, "qh_triangulate: delete %d or more mirror facets -- same vertices and neighbors\n", qh_setsize(qh degen_mergeset)));
- qh visible_list= qh facet_tail;
- while ((merge= (mergeT*)qh_setdellast (qh degen_mergeset))) {
- facet1= merge->facet1;
- facet2= merge->facet2;
- mergetype= merge->type;
- qh_memfree (merge, sizeof(mergeT));
- if (mergetype == MRGmirror) {
- zinc_(Ztrimirror);
- qh_triangulate_mirror (facet1, facet2);
- }
- }
- qh_settempfree(&qh degen_mergeset);
- trace2((qh ferr, "qh_triangulate: update neighbor lists for vertices from v%d\n", getid_(new_vertex_list)));
- qh newvertex_list= new_vertex_list; /* all vertices of new facets */
- qh visible_list= NULL;
- qh_updatevertices(/*qh newvertex_list, empty newfacet_list and visible_list*/);
- qh_resetlists (False, !qh_RESETvisible /*qh newvertex_list, empty newfacet_list and visible_list*/);
-
- trace2((qh ferr, "qh_triangulate: identify degenerate tricoplanar facets from f%d\n", getid_(new_facet_list)));
- trace2((qh ferr, "qh_triangulate: and replace facet->f.triowner with tricoplanar facets that own center, normal, etc.\n"));
- FORALLfacet_(new_facet_list) {
- if (facet->tricoplanar && !facet->visible) {
- FOREACHneighbor_i_(facet) {
- if (neighbor_i == 0) { /* first iteration */
- if (neighbor->tricoplanar)
- orig_neighbor= neighbor->f.triowner;
- else
- orig_neighbor= neighbor;
- }else {
- if (neighbor->tricoplanar)
- otherfacet= neighbor->f.triowner;
- else
- otherfacet= neighbor;
- if (orig_neighbor == otherfacet) {
- zinc_(Ztridegen);
- facet->degenerate= True;
- break;
- }
- }
- }
- }
- }
-
- trace2((qh ferr, "qh_triangulate: delete visible facets -- non-simplicial, null, and mirrored facets\n"));
- owner= NULL;
- visible= NULL;
- for (facet= new_facet_list; facet && facet->next; facet= nextfacet) { /* may delete facet */
- nextfacet= facet->next;
- if (facet->visible) {
- if (facet->tricoplanar) { /* a null or mirrored facet */
- qh_delfacet(facet);
- qh num_visible--;
- }else { /* a non-simplicial facet followed by its tricoplanars */
- if (visible && !owner) {
- /* RBOX 200 s D5 t1001471447 | QHULL Qt C-0.01 Qx Qc Tv Qt -- f4483 had 6 vertices/neighbors and 8 ridges */
- trace2((qh ferr, "qh_triangulate: all tricoplanar facets degenerate for non-simplicial facet f%d\n",
- visible->id));
- qh_delfacet(visible);
- qh num_visible--;
- }
- visible= facet;
- owner= NULL;
- }
- }else if (facet->tricoplanar) {
- if (facet->f.triowner != visible) {
- fprintf( qh ferr, "qhull error (qh_triangulate): tricoplanar facet f%d not owned by its visible, non-simplicial facet f%d\n", facet->id, getid_(visible));
- qh_errexit2 (qh_ERRqhull, facet, visible);
- }
- if (owner)
- facet->f.triowner= owner;
- else if (!facet->degenerate) {
- owner= facet;
- nextfacet= visible->next; /* rescan tricoplanar facets with owner */
- facet->keepcentrum= True; /* one facet owns ->normal, etc. */
- facet->coplanarset= visible->coplanarset;
- facet->outsideset= visible->outsideset;
- visible->coplanarset= NULL;
- visible->outsideset= NULL;
- if (!qh TRInormals) { /* center and normal copied to tricoplanar facets */
- visible->center= NULL;
- visible->normal= NULL;
- }
- qh_delfacet(visible);
- qh num_visible--;
- }
- }
- }
- if (visible && !owner) {
- trace2((qh ferr, "qh_triangulate: all tricoplanar facets degenerate for last non-simplicial facet f%d\n",
- visible->id));
- qh_delfacet(visible);
- qh num_visible--;
- }
- qh NEWfacets= False;
- qh ONLYgood= onlygood; /* restore value */
- if (qh CHECKfrequently)
- qh_checkpolygon (qh facet_list);
-} /* triangulate */
-
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="triangulate_facet">-</a>
-
- qh_triangulate_facet (facetA)
- triangulate a non-simplicial facet
- if qh.CENTERtype=qh_ASvoronoi, sets its Voronoi center
- returns:
- qh.newfacet_list == simplicial facets
- facet->tricoplanar set and ->keepcentrum false
- facet->degenerate set if duplicated apex
- facet->f.trivisible set to facetA
- facet->center copied from facetA (created if qh_ASvoronoi)
- qh_eachvoronoi, qh_detvridge, qh_detvridge3 assume centers copied
- facet->normal,offset,maxoutside copied from facetA
-
- notes:
- qh_makenew_nonsimplicial uses neighbor->seen for the same
-
- see also:
- qh_addpoint() -- add a point
- qh_makenewfacets() -- construct a cone of facets for a new vertex
-
- design:
- if qh_ASvoronoi,
- compute Voronoi center (facet->center)
- select first vertex (highest ID to preserve ID ordering of ->vertices)
- triangulate from vertex to ridges
- copy facet->center, normal, offset
- update vertex neighbors
-*/
-void qh_triangulate_facet (facetT *facetA, vertexT **first_vertex) {
- facetT *newfacet;
- facetT *neighbor, **neighborp;
- vertexT *apex;
- int numnew=0;
-
- trace3((qh ferr, "qh_triangulate_facet: triangulate facet f%d\n", facetA->id));
-
- if (qh IStracing >= 4)
- qh_printfacet (qh ferr, facetA);
- FOREACHneighbor_(facetA) {
- neighbor->seen= False;
- neighbor->coplanar= False;
- }
- if (qh CENTERtype == qh_ASvoronoi && !facetA->center /* matches upperdelaunay in qh_setfacetplane() */
- && fabs_(facetA->normal[qh hull_dim -1]) >= qh ANGLEround * qh_ZEROdelaunay) {
- facetA->center= qh_facetcenter (facetA->vertices);
- }
- qh_willdelete (facetA, NULL);
- qh newfacet_list= qh facet_tail;
- facetA->visitid= qh visit_id;
- apex= SETfirst_(facetA->vertices);
- qh_makenew_nonsimplicial (facetA, apex, &numnew);
- SETfirst_(facetA->neighbors)= NULL;
- FORALLnew_facets {
- newfacet->tricoplanar= True;
- newfacet->f.trivisible= facetA;
- newfacet->degenerate= False;
- newfacet->upperdelaunay= facetA->upperdelaunay;
- newfacet->good= facetA->good;
- if (qh TRInormals) {
- newfacet->keepcentrum= True;
- newfacet->normal= qh_copypoints (facetA->normal, 1, qh hull_dim);
- if (qh CENTERtype == qh_AScentrum)
- newfacet->center= qh_getcentrum (newfacet);
- else
- newfacet->center= qh_copypoints (facetA->center, 1, qh hull_dim);
- }else {
- newfacet->keepcentrum= False;
- newfacet->normal= facetA->normal;
- newfacet->center= facetA->center;
- }
- newfacet->offset= facetA->offset;
-#if qh_MAXoutside
- newfacet->maxoutside= facetA->maxoutside;
-#endif
- }
- qh_matchnewfacets(/*qh newfacet_list*/);
- zinc_(Ztricoplanar);
- zadd_(Ztricoplanartot, numnew);
- zmax_(Ztricoplanarmax, numnew);
- qh visible_list= NULL;
- if (!(*first_vertex))
- (*first_vertex)= qh newvertex_list;
- qh newvertex_list= NULL;
- qh_updatevertices(/*qh newfacet_list, empty visible_list and newvertex_list*/);
- qh_resetlists (False, !qh_RESETvisible /*qh newfacet_list, empty visible_list and newvertex_list*/);
-} /* triangulate_facet */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="triangulate_link">-</a>
-
- qh_triangulate_link (oldfacetA, facetA, oldfacetB, facetB)
- relink facetA to facetB via oldfacets
- returns:
- adds mirror facets to qh degen_mergeset (4-d and up only)
- design:
- if they are already neighbors, the opposing neighbors become MRGmirror facets
-*/
-void qh_triangulate_link (facetT *oldfacetA, facetT *facetA, facetT *oldfacetB, facetT *facetB) {
- int errmirror= False;
-
- trace3((qh ferr, "qh_triangulate_link: relink old facets f%d and f%d between neighbors f%d and f%d\n",
- oldfacetA->id, oldfacetB->id, facetA->id, facetB->id));
- if (qh_setin (facetA->neighbors, facetB)) {
- if (!qh_setin (facetB->neighbors, facetA))
- errmirror= True;
- else
- qh_appendmergeset (facetA, facetB, MRGmirror, NULL);
- }else if (qh_setin (facetB->neighbors, facetA))
- errmirror= True;
- if (errmirror) {
- fprintf( qh ferr, "qhull error (qh_triangulate_link): mirror facets f%d and f%d do not match for old facets f%d and f%d\n",
- facetA->id, facetB->id, oldfacetA->id, oldfacetB->id);
- qh_errexit2 (qh_ERRqhull, facetA, facetB);
- }
- qh_setreplace (facetB->neighbors, oldfacetB, facetA);
- qh_setreplace (facetA->neighbors, oldfacetA, facetB);
-} /* triangulate_link */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="triangulate_mirror">-</a>
-
- qh_triangulate_mirror (facetA, facetB)
- delete mirrored facets from qh_triangulate_null() and qh_triangulate_mirror
- a mirrored facet shares the same vertices of a logical ridge
- design:
- since a null facet duplicates the first two vertices, the opposing neighbors absorb the null facet
- if they are already neighbors, the opposing neighbors become MRGmirror facets
-*/
-void qh_triangulate_mirror (facetT *facetA, facetT *facetB) {
- facetT *neighbor, *neighborB;
- int neighbor_i, neighbor_n;
-
- trace3((qh ferr, "qh_triangulate_mirror: delete mirrored facets f%d and f%d\n",
- facetA->id, facetB->id));
- FOREACHneighbor_i_(facetA) {
- neighborB= SETelemt_(facetB->neighbors, neighbor_i, facetT);
- if (neighbor == neighborB)
- continue; /* occurs twice */
- qh_triangulate_link (facetA, neighbor, facetB, neighborB);
- }
- qh_willdelete (facetA, NULL);
- qh_willdelete (facetB, NULL);
-} /* triangulate_mirror */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="triangulate_null">-</a>
-
- qh_triangulate_null (facetA)
- remove null facetA from qh_triangulate_facet()
- a null facet has vertex #1 (apex) == vertex #2
- returns:
- adds facetA to ->visible for deletion after qh_updatevertices
- qh degen_mergeset contains mirror facets (4-d and up only)
- design:
- since a null facet duplicates the first two vertices, the opposing neighbors absorb the null facet
- if they are already neighbors, the opposing neighbors become MRGmirror facets
-*/
-void qh_triangulate_null (facetT *facetA) {
- facetT *neighbor, *otherfacet;
-
- trace3((qh ferr, "qh_triangulate_null: delete null facet f%d\n", facetA->id));
- neighbor= SETfirst_(facetA->neighbors);
- otherfacet= SETsecond_(facetA->neighbors);
- qh_triangulate_link (facetA, neighbor, facetA, otherfacet);
- qh_willdelete (facetA, NULL);
-} /* triangulate_null */
-
-#else /* qh_NOmerge */
-void qh_triangulate (void) {
-}
-#endif /* qh_NOmerge */
-
- /*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="vertexintersect">-</a>
-
- qh_vertexintersect( vertexsetA, vertexsetB )
- intersects two vertex sets (inverse id ordered)
- vertexsetA is a temporary set at the top of qhmem.tempstack
-
- returns:
- replaces vertexsetA with the intersection
-
- notes:
- could overwrite vertexsetA if currently too slow
-*/
-void qh_vertexintersect(setT **vertexsetA,setT *vertexsetB) {
- setT *intersection;
-
- intersection= qh_vertexintersect_new (*vertexsetA, vertexsetB);
- qh_settempfree (vertexsetA);
- *vertexsetA= intersection;
- qh_settemppush (intersection);
-} /* vertexintersect */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="vertexintersect_new">-</a>
-
- qh_vertexintersect_new( )
- intersects two vertex sets (inverse id ordered)
-
- returns:
- a new set
-*/
-setT *qh_vertexintersect_new (setT *vertexsetA,setT *vertexsetB) {
- setT *intersection= qh_setnew (qh hull_dim - 1);
- vertexT **vertexA= SETaddr_(vertexsetA, vertexT);
- vertexT **vertexB= SETaddr_(vertexsetB, vertexT);
-
- while (*vertexA && *vertexB) {
- if (*vertexA == *vertexB) {
- qh_setappend(&intersection, *vertexA);
- vertexA++; vertexB++;
- }else {
- if ((*vertexA)->id > (*vertexB)->id)
- vertexA++;
- else
- vertexB++;
- }
- }
- return intersection;
-} /* vertexintersect_new */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="vertexneighbors">-</a>
-
- qh_vertexneighbors()
- for each vertex in qh.facet_list,
- determine its neighboring facets
-
- returns:
- sets qh.VERTEXneighbors
- nop if qh.VERTEXneighbors already set
- qh_addpoint() will maintain them
-
- notes:
- assumes all vertex->neighbors are NULL
-
- design:
- for each facet
- for each vertex
- append facet to vertex->neighbors
-*/
-void qh_vertexneighbors (void /*qh facet_list*/) {
- facetT *facet;
- vertexT *vertex, **vertexp;
-
- if (qh VERTEXneighbors)
- return;
- trace1((qh ferr, "qh_vertexneighbors: determing neighboring facets for each vertex\n"));
- qh vertex_visit++;
- FORALLfacets {
- if (facet->visible)
- continue;
- FOREACHvertex_(facet->vertices) {
- if (vertex->visitid != qh vertex_visit) {
- vertex->visitid= qh vertex_visit;
- vertex->neighbors= qh_setnew (qh hull_dim);
- }
- qh_setappend (&vertex->neighbors, facet);
- }
- }
- qh VERTEXneighbors= True;
-} /* vertexneighbors */
-
-/*-<a href="qh-poly.htm#TOC"
- >-------------------------------</a><a name="vertexsubset">-</a>
-
- qh_vertexsubset( vertexsetA, vertexsetB )
- returns True if vertexsetA is a subset of vertexsetB
- assumes vertexsets are sorted
-
- note:
- empty set is a subset of any other set
-*/
-boolT qh_vertexsubset(setT *vertexsetA, setT *vertexsetB) {
- vertexT **vertexA= (vertexT **) SETaddr_(vertexsetA, vertexT);
- vertexT **vertexB= (vertexT **) SETaddr_(vertexsetB, vertexT);
-
- while (True) {
- if (!*vertexA)
- return True;
- if (!*vertexB)
- return False;
- if ((*vertexA)->id > (*vertexB)->id)
- return False;
- if (*vertexA == *vertexB)
- vertexA++;
- vertexB++;
- }
- return False; /* avoid warnings */
-} /* vertexsubset */
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qh-geom.htm b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qh-geom.htm
deleted file mode 100644
index 0f16f4518e72054b2d99412fa660cca5eb5946ab..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qh-geom.htm
+++ /dev/null
@@ -1,291 +0,0 @@
-<!-- Do not edit with Front Page, it adds too many spaces -->
-<html>
-<head>
-<meta http-equiv="Content-Type"
-content="text/html; charset=iso-8859-1">
-<title>geom.c, geom2.c -- geometric and floating point routines</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<p><a name="TOP"><b>Up:</b></a> <a
-href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
-<b>Up:</b> <a href="../html/qh-quick.htm#programs">Programs</a>
-• <a href="../html/qh-quick.htm#options">Options</a>
-• <a href="../html/qh-opto.htm#output">Output</a>
-• <a href="../html/qh-optf.htm#format">Formats</a>
-• <a href="../html/qh-optg.htm#geomview">Geomview</a>
-• <a href="../html/qh-optp.htm#print">Print</a>
-• <a href="../html/qh-optq.htm#qhull">Qhull</a>
-• <a href="../html/qh-optc.htm#prec">Precision</a>
-• <a href="../html/qh-optt.htm#trace">Trace</a><br>
-<b>Up:</b> <a href="../html/qh-in.htm#TOC">Qhull internals: Table of Contents</a><br>
-<b>To:</b> <a href="../src/index.htm">Qhull functions</a>, macros, and data structures<br>
-<b>To:</b> <a href="qh-geom.htm#TOC">Geom</a> • <a href="qh-globa.htm">Global</a>
-• <a href="qh-io.htm">Io</a> • <a href="qh-mem.htm">Mem</a>
-• <a href="qh-merge.htm">Merge</a> • <a href="qh-poly.htm">Poly</a>
-• <a href="qh-qhull.htm">Qhull</a> • <a href="qh-set.htm">Set</a>
-• <a href="qh-stat.htm">Stat</a> • <a href="qh-user.htm">User</a>
-</p>
-
-<hr>
-<!-- Main text of document. -->
-
-<h2>geom.c, geom2.c -- geometric and floating point routines</h2>
-<blockquote>
-<p>Geometrically, a vertex is a point with <em>d</em> coordinates
-and a facet is a halfspace. A <em>halfspace</em> is defined by an
-oriented hyperplane through the facet's vertices. A <em>hyperplane</em>
-is defined by <em>d</em> normalized coefficients and an offset. A
-point is <em>above</em> a facet if its distance to the facet is
-positive.</p>
-
-<p>Qhull uses floating point coordinates for input points,
-vertices, halfspace equations, centrums, and an interior point.</p>
-
-<p>Qhull may be configured for single precision or double
-precision floating point arithmetic (see <a href="user.h#realT">realT</a>
-). </p>
-
-<p>Each floating point operation may incur round-off error (see
-<a href="qh-merge.htm#TOC">Merge</a>). The maximum error for distance
-computations is determined at initialization. The roundoff error
-in halfspace computation is accounted for by computing the
-distance from vertices to the halfspace. </p>
-</blockquote>
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-<hr>
-<p><a href="#TOP">»</a> <b>Geom</b>
-<a name="TOC">•</a> <a href="qh-globa.htm#TOC">Global</a> •
-<a href="qh-io.htm#TOC">Io</a> • <a href="qh-mem.htm#TOC">Mem</a> •
-<a href="qh-merge.htm#TOC">Merge</a> • <a href="qh-poly.htm#TOC">Poly</a> •
-<a href="qh-qhull.htm#TOC">Qhull</a> • <a href="qh-set.htm#TOC">Set</a> •
-<a href="qh-stat.htm#TOC">Stat</a> • <a href="qh-user.htm#TOC">User</a> </p>
-
-<h3>Index to <a href="geom.c">geom.c</a>,
-<a href="geom2.c">geom2.c</a>, and <a href="geom.h">geom.h</a></h3>
-
-<ul>
-<li><a href="#gtype">geometric data types and constants</a> </li>
-<li><a href="#gmacro">mathematical macros</a>
-</li>
-<li><a href="#gmath">mathematical functions</a> </li>
-<li><a href="#gcomp">computational geometry functions</a> </li>
-<li><a href="#gpoint">point array functions</a> </li>
-<li><a href="#gfacet">geometric facet functions</a> </li>
-<li><a href="#ground">geometric roundoff functions</a></li>
-</ul>
-
-<h3><a href="qh-geom.htm#TOC">»</a><a name="gtype">geometric data types
-and constants</a></h3>
-
-<ul>
-<li><a href="qhull.h#coordT">coordT</a> coordinates and
-coefficients are stored as realT</li>
-<li><a href="qhull.h#pointT">pointT</a> a point is an array
-of <tt>DIM3</tt> coordinates </li>
-</ul>
-
-<h3><a href="qh-geom.htm#TOC">»</a><a name="gmacro">mathematical macros</a></h3>
-
-<ul>
-<li><a href="geom.h#fabs_">fabs_</a> returns the absolute
-value of a </li>
-<li><a href="geom.h#fmax_">fmax_</a> returns the maximum
-value of a and b </li>
-<li><a href="geom.h#fmin_">fmin_</a> returns the minimum
-value of a and b </li>
-<li><a href="geom.h#maximize_">maximize_</a> maximize a value
-</li>
-<li><a href="geom.h#minimize_">minimize_</a> minimize a value
-</li>
-<li><a href="geom.h#det2_">det2_</a> compute a 2-d
-determinate </li>
-<li><a href="geom.h#det3_">det3_</a> compute a 3-d
-determinate </li>
-<li><a href="geom.h#dX">dX, dY, dZ</a> compute the difference
-between two coordinates </li>
-</ul>
-
-<h3><a href="qh-geom.htm#TOC">»</a><a name="gmath">mathematical functions</a></h3>
-
-<ul>
-<li><a href="geom.c#backnormal">qh_backnormal</a> solve for
-normal using back substitution </li>
-<li><a href="geom2.c#crossproduct">qh_crossproduct</a>
-compute the cross product of two 3-d vectors </li>
-<li><a href="geom2.c#determinant">qh_determinant</a> compute
-the determinant of a square matrix </li>
-<li><a href="geom.c#gausselim">qh_gausselim</a> Gaussian
-elimination with partial pivoting </li>
-<li><a href="geom2.c#gram_schmidt">qh_gram_schmidt</a>
-implements Gram-Schmidt orthogonalization by rows </li>
-<li><a href="geom2.c#maxabsval">qh_maxabsval</a> return max
-absolute value of a vector </li>
-<li><a href="geom2.c#minabsval">qh_minabsval</a> return min
-absolute value of a dim vector </li>
-<li><a href="geom2.c#mindiff">qh_mindiff</a> return index of
-min absolute difference of two vectors </li>
-<li><a href="geom.c#normalize">qh_normalize</a> normalize a
-vector </li>
-<li><a href="geom.c#normalize2">qh_normalize2</a> normalize a
-vector and report if too small </li>
-<li><a href="geom2.c#printmatrix">qh_printmatrix</a> print
-matrix given by row vectors </li>
-<li><a href="geom2.c#rand">qh_rand/srand</a> generate random
-numbers </li>
-<li><a href="geom2.c#randomfactor">qh_randomfactor</a> return
-a random factor near 1.0 </li>
-<li><a href="geom2.c#randommatrix">qh_randommatrix</a>
-generate a random dimXdim matrix in range (-1,1) </li>
-</ul>
-
-<h3><a href="qh-geom.htm#TOC">»</a><a name="gcomp">computational geometry functions</a></h3>
-
-<ul>
-<li><a href="geom2.c#detsimplex">qh_detsimplex</a> compute
-determinate of a simplex of points </li>
-<li><a href="io.c#detvnorm">qh_detvnorm</a> determine normal for Voronoi ridge </li>
-<li><a href="geom2.c#distnorm">qh_distnorm</a> compute
-distance from point to hyperplane as defined by normal and offset</li>
-<li><a href="geom2.c#facetarea_simplex">qh_facetarea_simplex</a>
-return area of a simplex</li>
-<li><a href="geom.c#getangle">qh_getangle</a> return cosine
-of angle (i.e., dot product) </li>
-<li><a href="geom.c#getcenter">qh_getcenter</a> return
-arithmetic center for a set of vertices </li>
-<li><a href="geom2.c#pointdist">qh_pointdist</a> return
-distance between two points </li>
-<li><a href="geom2.c#rotatepoints">qh_rotatepoints</a> rotate
-numpoints points by a row matrix </li>
-<li><a href="geom2.c#sethalfspace">qh_sethalfspace</a> set
-coords to dual of halfspace relative to an interior point </li>
-<li><a href="geom.c#sethyperplane_det">qh_sethyperplane_det</a>
-return hyperplane for oriented simplex using determinates
-</li>
-<li><a href="geom.c#sethyperplane_gauss">qh_sethyperplane_gauss</a>
-return hyperplane for oriented simplex using Gaussian
-elimination </li>
-<li><a href="geom2.c#voronoi_center">qh_voronoi_center</a>
-return Voronoi center for a set of points </li>
-</ul>
-
-<h3><a href="qh-geom.htm#TOC">»</a><a name="gpoint">point array functions</a></h3>
-<ul>
-<li><a href="geom2.c#copypoints">qh_copypoints</a> return
-malloc'd copy of points</li>
-<li><a href="geom2.c#joggleinput">qh_joggleinput</a> joggle
-input points by qh.JOGGLEmax </li>
-<li><a href="geom2.c#maxmin">qh_maxmin</a> return max/min
-points for each dimension</li>
-<li><a href="geom2.c#maxsimplex">qh_maxsimplex</a> determines
-maximum simplex for a set of points </li>
-<li><a href="geom2.c#printpoints">qh_printpoints</a> print ids for a
-set of points </li>
-<li><a href="geom2.c#projectinput">qh_projectinput</a> project
-input using qh DELAUNAY and qh low_bound/high_bound </li>
-<li><a href="geom2.c#projectpoints">qh_projectpoints</a>
-project points along one or more dimensions </li>
-<li><a href="geom2.c#rotateinput">qh_rotateinput</a> rotate
-input points using row matrix </li>
-<li><a href="geom2.c#scaleinput">qh_scaleinput</a> scale
-input points using qh low_bound/high_bound </li>
-<li><a href="geom2.c#scalelast">qh_scalelast</a> scale last
-coordinate to [0,m] for Delaunay triangulations </li>
-<li><a href="geom2.c#scalepoints">qh_scalepoints</a> scale
-points to new lowbound and highbound </li>
-<li><a href="geom2.c#setdelaunay">qh_setdelaunay</a> project
-points to paraboloid for Delaunay triangulation </li>
-<li><a href="geom2.c#sethalfspace_all">qh_sethalfspace_all</a>
-generate dual for halfspace intersection with interior
-point </li>
-</ul>
-
-<h3><a href="qh-geom.htm#TOC">»</a><a name="gfacet">geometric facet functions</a></h3>
-<ul>
-<li><a href="geom.c#distplane">qh_distplane</a> return
-distance from point to facet </li>
-<li><a href="geom2.c#facetarea">qh_facetarea</a> return area
-of a facet </li>
-<li><a href="geom2.c#facetcenter">qh_facetcenter</a> return
-Voronoi center for a facet's vertices </li>
-<li><a href="geom.c#findbest">qh_findbest</a> find visible
-facet or best facet for a point </li>
-<li><a href="geom.c#findbesthorizon">qh_findbesthorizon</a>
-update best new facet with horizon facets</li>
-<li><a href="geom.c#findbestnew">qh_findbestnew</a> find best
-new facet for point </li>
-<li><a href="geom2.c#getarea">qh_getarea</a> get area of all
-facets in facetlist, collect statistics </li>
-<li><a href="geom.c#getcentrum">qh_getcentrum</a> return
-centrum for a facet </li>
-<li><a href="geom.c#getdistance">qh_getdistance</a> returns
-the max and min distance of a facet's vertices to a
-neighboring facet</li>
-<li><a href="geom2.c#findgooddist">qh_findgooddist</a> find
-best good facet visible for point from facet </li>
-<li><a href="geom2.c#inthresholds">qh_inthresholds</a> return
-True if facet normal within 'Pdn' and 'PDn'</li>
-<li><a href="geom2.c#orientoutside">qh_orientoutside</a>
-orient facet so that <tt>qh.interior_point</tt> is inside</li>
-<li><a href="geom.c#projectpoint">qh_projectpoint</a> project
-point onto a facet </li>
-<li><a href="geom.c#setfacetplane">qh_setfacetplane</a> sets
-the hyperplane for a facet </li>
-<li><a href="geom2.c#sharpnewfacets">qh_sharpnewfacets</a> true
-if new facets contains a sharp corner</li>
-</ul>
-
-<h3><a href="qh-geom.htm#TOC">»</a><a name="ground">geometric roundoff functions</a></h3>
-<ul>
-<li><a href="geom2.c#detjoggle">qh_detjoggle</a> determine
-default joggle for points and distance roundoff error</li>
-<li><a href="geom2.c#detroundoff">qh_detroundoff</a>
-determine maximum roundoff error and other precision constants</li>
-<li><a href="geom2.c#distround">qh_distround</a> compute
-maximum roundoff error due to a distance computation to a
-normalized hyperplane</li>
-<li><a href="geom2.c#divzero">qh_divzero</a> divide by a
-number that is nearly zero </li>
-<li><a href="geom2.c#maxouter">qh_maxouter</a> return maximum outer
-plane</li>
-<li><a href="geom2.c#outerinner">qh_outerinner</a> return actual
-outer and inner planes
-</ul>
-
-<p><!-- Navigation links --> </p>
-<hr>
-<p><b>Up:</b>
-<a href="http://www.qhull.org">Home page for
-Qhull</a> <br>
-<b>Up:</b> <a href="index.htm#TOC">Qhull manual: Table of Contents</a> <br>
-<b>Up:</b> <a href="../html/qh-quick.htm#programs">Programs</a>
-• <a href="../html/qh-quick.htm#options">Options</a>
-• <a href="../html/qh-opto.htm#output">Output</a>
-• <a href="../html/qh-optf.htm#format">Formats</a>
-• <a href="../html/qh-optg.htm#geomview">Geomview</a>
-• <a href="../html/qh-optp.htm#print">Print</a>
-• <a href="../html/qh-optq.htm#qhull">Qhull</a>
-• <a href="../html/qh-optc.htm#prec">Precision</a>
-• <a href="../html/qh-optt.htm#trace">Trace</a><br>
-<b>Up:</b> <a href="../html/qh-in.htm#TOC">Qhull internals: Table of Contents</a> <br>
-<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
-<b>To:</b> <a href="qh-geom.htm">Geom</a> •
-<a href="qh-globa.htm">Global</a> • <a href="qh-io.htm">Io</a>
-• <a href="qh-mem.htm">Mem</a> • <a href="qh-merge.htm">Merge</a>
-• <a href="qh-poly.htm">Poly</a> • <a href="qh-qhull.htm#TOC">Qhull</a>
-• <a href="qh-set.htm">Set</a> • <a href="qh-stat.htm">Stat</a>
-• <a href="qh-user.htm">User</a><br>
-
-
-<p><!-- GC common information --> </p>
-<hr>
-<p><a href="http://www.geom.uiuc.edu/"><img
-src="../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
-Geometry Center Home Page </i></p>
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qh-globa.htm b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qh-globa.htm
deleted file mode 100644
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--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qh-globa.htm
+++ /dev/null
@@ -1,159 +0,0 @@
-<!-- Do not edit with Front Page, it adds too many spaces -->
-<html>
-<head>
-<meta http-equiv="Content-Type"
-content="text/html; charset=iso-8859-1">
-<title>global.c -- global variables and their functions</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<p><a name="TOP"><b>Up:</b></a> <a
-href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
-<b>Up:</b> <a href="../html/qh-quick.htm#programs">Programs</a>
-• <a href="../html/qh-quick.htm#options">Options</a>
-• <a href="../html/qh-opto.htm#output">Output</a>
-• <a href="../html/qh-optf.htm#format">Formats</a>
-• <a href="../html/qh-optg.htm#geomview">Geomview</a>
-• <a href="../html/qh-optp.htm#print">Print</a>
-• <a href="../html/qh-optq.htm#qhull">Qhull</a>
-• <a href="../html/qh-optc.htm#prec">Precision</a>
-• <a href="../html/qh-optt.htm#trace">Trace</a><br>
-<b>Up:</b> <a href="../html/qh-in.htm#TOC">Qhull internals: Table of Contents</a><br>
-<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
-<b>To:</b> <a href="qh-geom.htm">Geom</a> • <a href="qh-globa.htm#TOC">Global</a>
-• <a href="qh-io.htm">Io</a> • <a href="qh-mem.htm">Mem</a>
-• <a href="qh-merge.htm">Merge</a> • <a href="qh-poly.htm">Poly</a>
-• <a href="qh-qhull.htm">Qhull</a> • <a href="qh-set.htm">Set</a>
-• <a href="qh-stat.htm">Stat</a> • <a href="qh-user.htm">User</a>
-</p>
-
-<hr>
-<!-- Main text of document. -->
-
-<h2>global.c -- global variables and their functions</h2>
-<blockquote>
-<p>Qhull uses a global data structure, <tt>qh</tt>, to store
-globally defined constants, lists, sets, and variables. This
-allows multiple instances of Qhull to execute at the same time.
-The structure may be statically allocated or
-dynamically allocated with malloc(). See
-<a href="user.h#QHpointer">QHpointer</a>.
-</p>
-</blockquote>
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-<hr>
-<p><a href="#TOP">»</a> <a href="qh-geom.htm#TOC">Geom</a>
-<a name="TOC">•</a> <b>Global</b> •
-<a href="qh-io.htm#TOC">Io</a> • <a href="qh-mem.htm#TOC">Mem</a> •
-<a href="qh-merge.htm#TOC">Merge</a> • <a href="qh-poly.htm#TOC">Poly</a> •
-<a href="qh-qhull.htm#TOC">Qhull</a> • <a href="qh-set.htm#TOC">Set</a> •
-<a href="qh-stat.htm#TOC">Stat</a> • <a href="qh-user.htm#TOC">User</a> </p>
-
-<h3>Index to <a href="global.c">global.c</a> and
-<a href="qhull.h">qhull.h</a></h3>
-
-<ul>
-<li><a href="#ovar">Qhull's global variables</a> </li>
-<li><a href="#ofunc">Global variable and initialization
-routines</a> </li>
-</ul>
-
-<h3><a href="qh-globa.htm#TOC">»</a><a name="ovar">Qhull's global
-variables</a></h3>
-
-<ul>
-<li><a href=global.c#qh_version>qh_version</a> version string
-<li><a href="qhull.h#qh">qh</a> all global variables for
-qhull are in <tt>qh,qhmem</tt>, and <tt>qhstat</tt></li>
-<li><a href="qhull.h#qh-const">qh constants</a> configuration
-flags and constants for Qhull </li>
-<li><a href="qhull.h#qh-prec">qh precision constants</a>
-precision constants for Qhull </li>
-<li><a href="qhull.h#qh-intern">qh internal constants</a>
-internal constants for Qhull </li>
-<li><a href="qhull.h#qh-lists">qh facet and vertex lists</a>
-lists of facets and vertices </li>
-<li><a href="qhull.h#qh-var">qh global variables</a> minimum
-and maximum distances, next visit ids, several flags, and
-other global variables. </li>
-<li><a href="qhull.h#qh-set">qh global sets</a> global sets
-for merging, hashing, input, etc. </li>
-<li><a href="qhull.h#qh-buf">qh global buffers</a> buffers
-for matrix operations and input </li>
-<li><a href="qhull.h#qh-static">qh static variables</a>
-static variables for individual functions </li>
-</ul>
-
-<h3><a href="qh-globa.htm#TOC">»</a><a name="ofunc">Global variable and
-initialization routines</a></h3>
-
-<ul>
-<li><a href="global.c#appendprint">qh_appendprint</a> append
-output format to <tt>qh.PRINTout</tt> </li>
-<li><a href="global.c#freebuffers">qh_freebuffers</a> free
-global memory buffers </li>
-<li><a href="global.c#freeqhull">qh_freeqhull</a> free memory
-used by qhull </li>
-<li><a href="global.c#init_A">qh_init_A</a> called before
-error handling initialized </li>
-<li><a href="global.c#init_B">qh_init_B</a> called after
-points are defined </li>
-<li><a href="global.c#init_qhull_command">qh_init_qhull_command</a>
-build <tt>qh.qhull_command</tt> from <tt>argc/argv</tt></li>
-<li><a href="global.c#initflags">qh_initflags</a> set flags
-and constants from command line </li>
-<li><a href="global.c#initqhull_buffers">qh_initqhull_buffers</a>
-initialize global memory buffers </li>
-<li><a href="global.c#initqhull_globals">qh_initqhull_globals</a>
-initialize global variables </li>
-<li><a href="global.c#initqhull_mem">qh_initqhull_mem</a>
-initialize Qhull memory management </li>
-<li><a href="global.c#initqhull_start">qh_initqhull_start</a>
-initialize default values at Qhull startup </li>
-<li><a href="global.c#initthresholds">qh_initthresholds</a>
-initialize 'Pdn' and 'PDn' thresholds </li>
-<li><a href="global.c#option">qh_option</a> append option
-description to <tt>qh.global_options</tt> </li>
-<li><a href="global.c#restore_qhull">qh_restore_qhull</a>
-restores a previously saved qhull </li>
-<li><a href="global.c#save_qhull">qh_save_qhull</a> saves
-qhull for a later qh_restore_qhull() </li>
-<li><a href="global.c#strtol">qh_strtol</a> duplicates
-strtod() and strtol() </li>
-</ul>
-
-<p><!-- Navigation links --> </p>
-<hr>
-<p><b>Up:</b>
-<a href="http://www.qhull.org">Home page for
-Qhull</a> <br>
-<b>Up:</b> <a href="../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
-<b>Up:</b> <a href="../html/qh-quick.htm#programs">Programs</a>
-• <a href="../html/qh-quick.htm#options">Options</a>
-• <a href="../html/qh-opto.htm#output">Output</a>
-• <a href="../html/qh-optf.htm#format">Formats</a>
-• <a href="../html/qh-optg.htm#geomview">Geomview</a>
-• <a href="../html/qh-optp.htm#print">Print</a>
-• <a href="../html/qh-optq.htm#qhull">Qhull</a>
-• <a href="../html/qh-optc.htm#prec">Precision</a>
-• <a href="../html/qh-optt.htm#trace">Trace</a><br>
-<b>Up:</b> <a href="../html/qh-in.htm#TOC">Qhull internals: Table of Contents</a> <br>
-<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
-<b>To:</b> <a href="qh-geom.htm">Geom</a> •
-<a href="qh-globa.htm">Global</a> • <a href="qh-io.htm">Io</a>
-• <a href="qh-mem.htm">Mem</a> • <a href="qh-merge.htm">Merge</a>
-• <a href="qh-poly.htm">Poly</a> • <a href="qh-qhull.htm#TOC">Qhull</a>
-• <a href="qh-set.htm">Set</a> • <a href="qh-stat.htm">Stat</a>
-• <a href="qh-user.htm">User</a><br>
-<p><!-- GC common information --> </p>
-<hr>
-<p><a href="http://www.geom.uiuc.edu/"><img
-src="../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
-Geometry Center Home Page </i></p>
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qh-io.htm b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qh-io.htm
deleted file mode 100644
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--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qh-io.htm
+++ /dev/null
@@ -1,295 +0,0 @@
-<!-- Do not edit with Front Page, it adds too many spaces -->
-<html>
-<head>
-<meta http-equiv="Content-Type"
-content="text/html; charset=iso-8859-1">
-<title>io.c -- input and output operations</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<p><a name="TOP"><b>Up:</b></a> <a
-href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
-<b>Up:</b> <a href="../html/qh-quick.htm#programs">Programs</a>
-• <a href="../html/qh-quick.htm#options">Options</a>
-• <a href="../html/qh-opto.htm#output">Output</a>
-• <a href="../html/qh-optf.htm#format">Formats</a>
-• <a href="../html/qh-optg.htm#geomview">Geomview</a>
-• <a href="../html/qh-optp.htm#print">Print</a>
-• <a href="../html/qh-optq.htm#qhull">Qhull</a>
-• <a href="../html/qh-optc.htm#prec">Precision</a>
-• <a href="../html/qh-optt.htm#trace">Trace</a><br>
-<b>Up:</b> <a href="../html/qh-in.htm#TOC">Qhull internals: Table of Contents</a><br>
-<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
-<b>To:</b> <a href="qh-geom.htm">Geom</a> • <a href="qh-globa.htm">Global</a>
-• <a href="qh-io.htm#TOC">Io</a> • <a href="qh-mem.htm">Mem</a>
-• <a href="qh-merge.htm">Merge</a> • <a href="qh-poly.htm">Poly</a>
-• <a href="qh-qhull.htm">Qhull</a> • <a href="qh-set.htm">Set</a>
-• <a href="qh-stat.htm">Stat</a> • <a href="qh-user.htm">User</a>
-</p>
-<hr>
-
-<h2>io.c -- input and output operations</h2>
-<blockquote>
-
-<p>Qhull provides a wide range of input
-and output options. To organize the code, most output formats use
-the same driver: </p>
-
-<pre>
- qh_printbegin( fp, format, facetlist, facets, printall );
-
- FORALLfacet_( facetlist )
- qh_printafacet( fp, format, facet, printall );
-
- FOREACHfacet_( facets )
- qh_printafacet( fp, format, facet, printall );
-
- qh_printend( fp, format );
-</pre>
-
-<p>Note the 'printall' flag. It selects whether or not
-qh_skipfacet() is tested. </p>
-
-</blockquote>
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-<hr>
-<p><a href="#TOP">»</a> <a href="qh-geom.htm#TOC">Geom</a> <a name="TOC">•</a>
-<a href="qh-globa.htm#TOC">Global</a> • <b>Io</b> •
-<a href="qh-mem.htm#TOC">Mem</a> • <a href="qh-merge.htm#TOC">Merge</a> •
-<a href="qh-poly.htm#TOC">Poly</a> • <a href="qh-qhull.htm#TOC">Qhull</a> •
-<a href="qh-set.htm#TOC">Set</a> • <a href="qh-stat.htm#TOC">Stat</a> •
-<a href="qh-user.htm#TOC">User</a> </p>
-
-<h3>Index to <a href="io.c">io.c</a> and <a href="io.h">io.h</a></h3>
-
-<ul>
-<li><a href="#iconst">io.h constants and types</a> </li>
-<li><a href="#ilevel">User level functions</a> </li>
-<li><a href="#iprint">Print functions for all output formats</a></li>
-<li><a href="#itext">Text output functions</a> </li>
-<li><a href="#iutil">Text utility functions</a></li>
-<li><a href="#igeom">Geomview output functions</a> </li>
-<li><a href="#iview">Geomview utility functions</a></li>
-</ul>
-
-<h3><a href="qh-io.htm#TOC">»</a><a name="iconst">io.h constants and types</a></h3>
-
-<ul>
-<li><a href="io.h#qh_MAXfirst">qh_MAXfirst</a> maximum length
-of first two lines of stdin </li>
-<li><a href="io.h#qh_WHITESPACE">qh_WHITESPACE</a> possible
-values of white space </li>
-<li><a href="io.h#printvridgeT">printvridgeT</a> function to
-print results of qh_printvdiagram or qh_eachvoronoi</li>
-</ul>
-
-<h3><a href="qh-io.htm#TOC">»</a><a name="ilevel">User level functions</a></h3>
-
-<ul>
-<li><a href="io.c#eachvoronoi_all">qh_eachvoronoi_all</a>
-visit each Voronoi ridge of the Voronoi diagram
-<li><a href="io.c#printhelp_degenerate">qh_printhelp_degenerate</a>
-prints descriptive message for precision error </li>
-<li><a href="io.c#printhelp_singular">qh_printhelp_singular</a>
-print help message for singular data </li>
-<li><a href="qhull.c#printsummary">qh_printsummary</a> print
-summary ('s')</li>
-<li><a href="io.c#produce_output">qh_produce_output</a>
-prints out the result of qhull()</li>
-<li><a href="io.c#readfeasible">qh_readfeasible</a> read
-interior point from remainder and qh fin ('H')</li>
-<li><a href="io.c#readpoints">qh_readpoints</a> read input
-points </li>
-<li><a href="io.c#setfeasible">qh_setfeasible</a> set
-interior point from qh feasible_string ('Hn,n,n')</li>
-</ul>
-
-<h3><a href="qh-io.htm#TOC">»</a><a name="iprint">Print functions for all
-output formats</a></h3>
-
-<ul>
-<li><a href="io.c#countfacets">qh_countfacets</a> count good
-facets for printing and set visitid </li>
-<li><a href="io.c#markkeep">qh_markkeep</a> mark good facets
-that meet qh.KEEParea ('PAn'), qh.KEEPmerge ('PMn'), and qh.KEEPminArea ('PFn')</li>
-<li><a href="io.c#order_vertexneighbors">qh_order_vertexneighbors</a>
-order neighbors for a 3-d vertex by adjacency ('i', 'o')</li>
-<li><a href="io.c#printafacet">qh_printafacet</a> print facet
-in an output format </li>
-<li><a href="io.c#printbegin">qh_printbegin</a> print header
-for an output format </li>
-<li><a href="io.c#printend">qh_printend</a> print trailer for
-an output format </li>
-<li><a href="user.c#printfacetlist">qh_printfacetlist</a>
-print facets in a facetlist</li>
-<li><a href="io.c#printfacets">qh_printfacets</a> print
-facetlist and/or facet set in an output format </li>
-<li><a href="io.c#printneighborhood">qh_printneighborhood</a>
-print neighborhood of one or two facets ('Po')</li>
-<li><a href="io.c#produce_output">qh_produce_output</a>
-print the results of qh_qhull() </li>
-<li><a href="io.c#skipfacet">qh_skipfacet</a> True if not
-printing this facet ('Pdk:n', 'QVn', 'QGn')</li>
-<li><a href="io.c#facetvertices">qh_facetvertices</a> return
-vertices in a set of facets ('p')</li>
-</ul>
-
-<h3><a href="qh-io.htm#TOC">»</a><a name="itext">Text output functions</a></h3>
-<ul>
-<li><a href="io.c#eachvoronoi">qh_eachvoronoi</a>
-print or visit each Voronoi ridge for an input site of the Voronoi diagram
-<li><a href="io.c#printextremes">qh_printextremes</a> print
-extreme points by point ID (vertices of convex hull) ('Fx')</li>
-<li><a href="io.c#printextremes_2d">qh_printextremes_2d</a> print
-2-d extreme points by point ID ('Fx')</li>
-<li><a href="io.c#printextremes_d">qh_printextremes_d</a> print
-extreme points of input sites for Delaunay triangulations ('Fx')</li>
-<li><a href="io.c#printfacet">qh_printfacet</a> print all
-fields of a facet ('f')</li>
-<li><a href="io.c#printfacet2math">qh_printfacet2math</a> print
-2-d Maple or Mathematica output for a facet ('FM' or 'm')</li>
-<li><a href="io.c#printfacet3math">qh_printfacet3math</a>
-print 3-d Maple or Mathematica facet ('FM' or 'm')</li>
-<li><a href="io.c#printfacet3vertex">qh_printfacet3vertex</a>
-print vertices for a 3-d facet ('i', 'o')</li>
-<li><a href="io.c#printfacetheader">qh_printfacetheader</a>
-prints header fields of a facet ('f')</li>
-<li><a href="io.c#printfacetNvertex_nonsimplicial">qh_printfacetNvertex_nonsimplicial</a>
-print vertices for an N-d non-simplicial facet ('i', 'Ft')</li>
-<li><a href="io.c#printfacetNvertex_simplicial">qh_printfacetNvertex_simplicial</a>
-print vertices for an N-d simplicial facet ('i', 'o', 'Ft')</li>
-<li><a href="io.c#printfacetridges">qh_printfacetridges</a>
-prints ridges of a facet ('f')</li>
-<li><a href="io.c#printpoints_out">qh_printpoints_out</a> prints
-vertices for facets by their point coordinates ('p')</li>
-<li><a href="io.c#printridge">qh_printridge</a> print all
-fields for a ridge ('f')</li>
-<li><a href="io.c#printvdiagram">qh_printvdiagram</a> print
-voronoi diagram as Voronoi vertices for each input pair</li>
-<li><a href="io.c#printvertex">qh_printvertex</a> print all
-fields for a vertex ('f')</li>
-<li><a href="io.c#printvertexlist">qh_printvertexlist</a>
-print vertices used by a list or set of facets ('f')</li>
-<li><a href="io.c#printvertices">qh_printvertices</a> print a
-set of vertices ('f')</li>
-<li><a href="io.c#printvneighbors">qh_printvneighbors</a>
-print vertex neighbors of vertices ('FN')</li>
-<li><a href="io.c#printvoronoi">qh_printvoronoi</a> print
-voronoi diagram in 'o' or 'G' format</li>
-</ul>
-
-<h3><a href="qh-io.htm#TOC">»</a><a name="iutil">Text utility functions</a></h3>
-<ul>
-<li><a href="io.c#dfacet">dfacet</a> print facet by ID </li>
-<li><a href="io.c#dvertex">dvertex</a> print vertex by ID </li>
-<li><a href="io.c#compare_facetarea">qh_compare_facetarea</a>
-used by qsort() to order facets by area </li>
-<li><a href="io.c#compare_facetmerge">qh_compare_facetmerge</a>
-used by qsort() to order facets by number of merges </li>
-<li><a href="io.c#compare_facetvisit">qh_compare_facetvisit</a>
-used by qsort() to order facets by visit ID or ID </li>
-<li><a href="io.c#compare_vertexpoint">qh_compare_vertexpoint</a>
-used by qsort() to order vertices by point ID </li>
-<li><a href="io.c#detvnorm">qh_detvnorm</a> determine normal for Voronoi ridge </li>
-<li><a href="io.c#detvridge">qh_detvridge</a> determine Voronoi
-ridge for an input site
-<li><a href="io.c#detvridge3">qh_detvridge3</a> determine 3-d Voronoi
-ridge for an input site
-<li><a href="io.c#facet2point">qh_facet2point</a> return two
-projected temporary vertices for a 2-d facet ('m', 'G')</li>
-<li><a href="io.c#markvoronoi">qh_markvoronoi</a> mark Voronoi
-vertices for printing
-<li><a href="io.c#printcenter">qh_printcenter</a> print
-facet->center as centrum or Voronoi center ('Ft', 'v p', 'FC', 'f') </li>
-<li><a href="io.c#printpoint">qh_printpoint</a>, qh_printpointid, print
-coordinates of a point ('p', 'o', 'Fp', 'G', 'f')</li>
-<li><a href="io.c#printpoint3">qh_printpoint3</a> prints 2-d,
-3-d, or 4-d point as 3-d coordinates ('G')</li>
-<li><a href="io.c#printvdiagram2">qh_printvdiagram2</a> print
-voronoi diagram for each ridge of each vertex from qh_markvoronoi</li>
-<li><a href="io.c#printvnorm">qh_printvnorm</a> print
-separating plane of the Voronoi diagram for a pair of input sites</li>
-<li><a href="io.c#printvridge">qh_printvridge</a> print
-ridge of the Voronoi diagram for a pair of input sites</li>
-<li><a href="io.c#projectdim3">qh_projectdim3</a> project 2-d
-3-d or 4-d point to a 3-d point ('G')</li>
-</ul>
-
-<h3><a href="qh-io.htm#TOC">»</a><a name="igeom">Geomview output functions</a></h3>
-<ul>
-<li><a href="io.c#printfacet2geom">qh_printfacet2geom</a>
-print facet as a 2-d VECT object </li>
-<li><a href="io.c#printfacet2geom_points">qh_printfacet2geom_points</a>
-print points as a 2-d VECT object with offset </li>
-<li><a href="io.c#printfacet3geom_nonsimplicial">qh_printfacet3geom_nonsimplicial</a>
-print Geomview OFF for a 3-d nonsimplicial facet. </li>
-<li><a href="io.c#printfacet3geom_points">qh_printfacet3geom_points</a>
-prints a 3-d facet as OFF Geomview object. </li>
-<li><a href="io.c#printfacet3geom_simplicial">qh_printfacet3geom_simplicial</a>
-print Geomview OFF for a 3-d simplicial facet. </li>
-<li><a href="io.c#printfacet4geom_nonsimplicial">qh_printfacet4geom_nonsimplicial</a>
-print Geomview 4OFF file for a 4d nonsimplicial facet </li>
-<li><a href="io.c#printfacet4geom_simplicial">qh_printfacet4geom_simplicial</a>
-print Geomview 4OFF file for a 4d simplicial facet </li>
-<li><a href="io.c#printhyperplaneintersection">qh_printhyperplaneintersection</a>
-print hyperplane intersection as OFF or 4OFF </li>
-<li><a href="io.c#printvoronoi">qh_printvoronoi</a> print
-voronoi diagram in 'o' or 'G' format</li>
-</ul>
-<h3><a href="qh-io.htm#TOC">»</a><a name="iview">Geomview utility functions</a></h3>
-<ul>
-<li><a href="io.c#geomplanes">qh_geomplanes</a>
- return outer and inner planes for Geomview</li>
-<li><a href="io.c#printcentrum">qh_printcentrum</a> print
-centrum for a facet in OOGL format </li>
-<li><a href="io.c#printend4geom">qh_printend4geom</a> helper
-function for qh_printbegin/printend </li>
-<li><a href="io.c#printhyperplaneintersection">qh_printhyperplaneintersection</a>
-print Geomview OFF or 4OFF for the intersection of two
-hyperplanes in 3-d or 4-d </li>
-<li><a href="io.c#printline3geom">qh_printline3geom</a> prints a
-line as a VECT </li>
-<li><a href="io.c#printpointvect">qh_printpointvect</a>
-prints a 2-d or 3-d point as 3-d VECT's </li>
-<li><a href="io.c#printpointvect2">qh_printpointvect2</a>
-prints a 2-d or 3-d point as 2 3-d VECT's </li>
-<li><a href="io.c#printspheres">qh_printspheres</a> prints 3-d
-vertices as OFF spheres </li>
-</ul>
-<p>
-<p><!-- Navigation links --> </p>
-<hr>
-<p><b>Up:</b>
-<a href="http://www.qhull.org">Home page for
-Qhull</a> <br>
-<b>Up:</b> <a href="../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
-<b>Up:</b> <a href="../html/qh-quick.htm#programs">Programs</a>
-• <a href="../html/qh-quick.htm#options">Options</a>
-• <a href="../html/qh-opto.htm#output">Output</a>
-• <a href="../html/qh-optf.htm#format">Formats</a>
-• <a href="../html/qh-optg.htm#geomview">Geomview</a>
-• <a href="../html/qh-optp.htm#print">Print</a>
-• <a href="../html/qh-optq.htm#qhull">Qhull</a>
-• <a href="../html/qh-optc.htm#prec">Precision</a>
-• <a href="../html/qh-optt.htm#trace">Trace</a><br>
-<b>Up:</b> <a href="../html/qh-in.htm#TOC">Qhull internals: Table of Contents</a> <br>
-<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
-<b>To:</b> <a href="qh-geom.htm">Geom</a> •
-<a href="qh-globa.htm">Global</a> • <a href="qh-io.htm">Io</a>
-• <a href="qh-mem.htm">Mem</a> • <a href="qh-merge.htm">Merge</a>
-• <a href="qh-poly.htm">Poly</a> • <a href="qh-qhull.htm#TOC">Qhull</a>
-• <a href="qh-set.htm">Set</a> • <a href="qh-stat.htm">Stat</a>
-• <a href="qh-user.htm">User</a><br>
-</p>
-<p><!-- GC common information --> </p>
-<hr>
-<p><a href="http://www.geom.uiuc.edu/"><img
-src="../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
-Geometry Center Home Page </i></p>
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qh-mem.htm b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qh-mem.htm
deleted file mode 100644
index cfc414a7750f859eaf14e11e01910e5cae594d3f..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qh-mem.htm
+++ /dev/null
@@ -1,140 +0,0 @@
-<!-- Do not edit with Front Page, it adds too many spaces -->
-<html>
-<head>
-<meta http-equiv="Content-Type"
-content="text/html; charset=iso-8859-1">
-<title>mem.c -- memory operations</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<p><a name="TOP"><b>Up:</b></a> <a
-href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
-<b>Up:</b> <a href="../html/qh-quick.htm#programs">Programs</a>
-• <a href="../html/qh-quick.htm#options">Options</a>
-• <a href="../html/qh-opto.htm#output">Output</a>
-• <a href="../html/qh-optf.htm#format">Formats</a>
-• <a href="../html/qh-optg.htm#geomview">Geomview</a>
-• <a href="../html/qh-optp.htm#print">Print</a>
-• <a href="../html/qh-optq.htm#qhull">Qhull</a>
-• <a href="../html/qh-optc.htm#prec">Precision</a>
-• <a href="../html/qh-optt.htm#trace">Trace</a><br>
-<b>Up:</b> <a href="../html/qh-in.htm#TOC">Qhull internals: Table of Contents</a><br>
-<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
-<b>To:</b> <a href="qh-geom.htm">Geom</a> • <a href="qh-globa.htm">Global</a>
-• <a href="qh-io.htm">Io</a> • <a href="qh-mem.htm#TOC">Mem</a>
-• <a href="qh-merge.htm">Merge</a> • <a href="qh-poly.htm">Poly</a>
-• <a href="qh-qhull.htm">Qhull</a> • <a href="qh-set.htm">Set</a>
-• <a href="qh-stat.htm">Stat</a> • <a href="qh-user.htm">User</a>
-</p>
-<hr>
-
-<h2>mem.c -- memory operations</h2>
-<blockquote>
-<p>Qhull uses quick-fit memory allocation. It maintains a
-set of free lists for a variety of small allocations. A
-small request returns a block from the best fitting free
-list. If the free list is empty, Qhull allocates a block
-from a reserved buffer. </p>
-<p>Use 'T5' to trace memory allocations.</p>
-
-</blockquote>
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-<hr>
-<p><a href="#TOP">»</a> <a href="qh-geom.htm#TOC">Geom</a>
-<a name="TOC">•</a> <a href="qh-globa.htm#TOC">Global</a> •
-<a href="qh-io.htm#TOC">Io</a> • <b>Mem</b>
-• <a href="qh-merge.htm#TOC">Merge</a> • <a href="qh-poly.htm#TOC">Poly</a>
-• <a href="qh-qhull.htm#TOC">Qhull</a> • <a href="qh-set.htm#TOC">Set</a>
-• <a href="qh-stat.htm#TOC">Stat</a> • <a href="qh-user.htm#TOC">User</a>
-</p>
-<h3>Index to <a href="mem.c">mem.c</a> and
-<a href="mem.h">mem.h</a></h3>
-<ul>
-<li><a href="#etype">mem.h data types</a> </li>
-<li><a href="#emacro">mem.h macros</a> </li>
-<li><a href="#efunc">User level functions</a> </li>
-</ul>
-<h3><a href="qh-mem.htm#TOC">»</a><a name="etype">mem.h data types and constants</a></h3>
-<ul>
-<li><a href="mem.h#ptr_intT">ptr_intT</a> for casting
-a void* to an integer-type </li>
-<li><a href="mem.h#qhmemT">qhmemT</a> global memory
-structure for mem.c </li>
-<li><a href="mem.h#NOmem">qh_NOmem</a> disable memory allocation</li>
-</ul>
-<h3><a href="qh-mem.htm#TOC">»</a><a name="emacro">mem.h macros</a></h3>
-<ul>
-<li><a href="mem.h#memalloc_">qh_memalloc_</a>
-allocate memory</li>
-<li><a href="mem.h#memfree_">qh_memfree_</a> free
-memory</li>
-</ul>
-<h3><a href="qh-mem.htm#TOC">»</a><a name="efunc">User level
-functions</a></h3>
-<ul>
-<li><a href="mem.c#memalloc">qh_memalloc</a> allocate
-memory </li>
-<li><a href="mem.c#memfree">qh_memfree</a> free
-memory </li>
-<li><a href="mem.c#meminit">qh_meminit</a> initialize
-memory </li>
-<li><a href="mem.c#memstatistics">qh_memstatistics</a>
-print memory statistics </li>
-<li><a href="mem.c#NOmem">qh_NOmem</a> allocation routines with malloc() and free()
-</ul>
-
-<h3><a href="qh-mem.htm#TOC">»</a><a name="m">Initialization and
-termination functions</a></h3>
-<ul>
-<li><a href="mem.c#intcompare">qh_intcompare</a> used by
-qsort and bsearch to compare two integers </li>
-<li><a href="mem.c#memfreeshort">qh_memfreeshort</a>
-frees up all short and qhmem memory allocations </li>
-<li><a href="mem.c#meminit">qh_meminit</a> initialize
-memory </li>
-<li><a href="mem.c#meminitbuffers">qh_meminitbuffers</a>
-initialize qhmem </li>
-<li><a href="mem.c#memsetup">qh_memsetup</a> set up
-memory after running memsize() </li>
-<li><a href="mem.c#memsize">qh_memsize</a> define a free
-list for this size </li>
-<li><a href="mem.c#memstatistics">qh_memstatistics</a>
-print out memory statistics </li>
-</ul>
-
-<p><!-- Navigation links --> </p>
-<hr>
-<p><b>Up:</b>
-<a href="http://www.qhull.org">Home page for
-Qhull</a> <br>
-<b>Up:</b> <a href="../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
-<b>Up:</b> <a href="../html/qh-quick.htm#programs">Programs</a>
-• <a href="../html/qh-quick.htm#options">Options</a>
-• <a href="../html/qh-opto.htm#output">Output</a>
-• <a href="../html/qh-optf.htm#format">Formats</a>
-• <a href="../html/qh-optg.htm#geomview">Geomview</a>
-• <a href="../html/qh-optp.htm#print">Print</a>
-• <a href="../html/qh-optq.htm#qhull">Qhull</a>
-• <a href="../html/qh-optc.htm#prec">Precision</a>
-• <a href="../html/qh-optt.htm#trace">Trace</a><br>
-<b>Up:</b> <a href="../html/qh-in.htm#TOC">Qhull internals: Table of Contents</a> <br>
-<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
-<b>To:</b> <a href="qh-geom.htm">Geom</a> •
-<a href="qh-globa.htm">Global</a> • <a href="qh-io.htm">Io</a>
-• <a href="qh-mem.htm">Mem</a> • <a href="qh-merge.htm">Merge</a>
-• <a href="qh-poly.htm">Poly</a> • <a href="qh-qhull.htm#TOC">Qhull</a>
-• <a href="qh-set.htm">Set</a> • <a href="qh-stat.htm">Stat</a>
-• <a href="qh-user.htm">User</a><br>
-</p>
-<p><!-- GC common information --> </p>
-<hr>
-<p><a href="http://www.geom.uiuc.edu/"><img
-src="../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
-Geometry Center Home Page </i></p>
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qh-merge.htm b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qh-merge.htm
deleted file mode 100644
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--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qh-merge.htm
+++ /dev/null
@@ -1,364 +0,0 @@
-<!-- Do not edit with Front Page, it adds too many spaces -->
-<html>
-<head>
-<meta http-equiv="Content-Type"
-content="text/html; charset=iso-8859-1">
-<title>merge.c -- facet merge operations</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<p><a name="TOP"><b>Up:</b></a> <a
-href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
-<b>Up:</b> <a href="../html/qh-quick.htm#programs">Programs</a>
-• <a href="../html/qh-quick.htm#options">Options</a>
-• <a href="../html/qh-opto.htm#output">Output</a>
-• <a href="../html/qh-optf.htm#format">Formats</a>
-• <a href="../html/qh-optg.htm#geomview">Geomview</a>
-• <a href="../html/qh-optp.htm#print">Print</a>
-• <a href="../html/qh-optq.htm#qhull">Qhull</a>
-• <a href="../html/qh-optc.htm#prec">Precision</a>
-• <a href="../html/qh-optt.htm#trace">Trace</a><br>
-<b>Up:</b> <a href="../html/qh-in.htm#TOC">Qhull internals: Table of Contents</a><br>
-<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
-<b>To:</b> <a href="qh-geom.htm">Geom</a> • <a href="qh-globa.htm">Global</a>
-• <a href="qh-io.htm">Io</a> • <a href="qh-mem.htm">Mem</a>
-• <a href="qh-merge.htm#TOC">Merge</a> • <a href="qh-poly.htm">Poly</a>
-• <a href="qh-qhull.htm">Qhull</a> • <a href="qh-set.htm">Set</a>
-• <a href="qh-stat.htm">Stat</a> • <a href="qh-user.htm">User</a>
-</p>
-<hr>
-
-<h2>merge.c -- facet merge operations</h2>
-<blockquote>
-<p>Qhull handles precision problems by merged facets or joggled input.
-Except for redundant vertices, it corrects a problem by
-merging two facets. When done, all facets are clearly
-convex. See <a href="../html/qh-impre.htm">Imprecision in Qhull</a>
-for further information. </p>
-<p>Users may joggle the input ('<a href="../html/qh-optq.htm#QJn">QJn</a>')
-instead of merging facets. </p>
-<p>Qhull detects and corrects the following problems: </p>
-<ul>
-<li><b>More than two facets meeting at a ridge. </b>When
-Qhull creates facets, it creates an even number
-of facets for each ridge. A convex hull always
-has two facets for each ridge. More than two
-facets may be created if non-adjacent facets
-share a vertex. This is called a <em>duplicate
-ridge</em>. In 2-d, a duplicate ridge would
-create a loop of facets. </li>
-</ul>
-<ul>
-<li><b>A facet contained in another facet. </b>Facet
-merging may leave all vertices of one facet as a
-subset of the vertices of another facet. This is
-called a <em>redundant facet</em>. </li>
-</ul>
-<ul>
-<li><b>A facet with fewer than three neighbors. </b>Facet
-merging may leave a facet with one or two
-neighbors. This is called a <em>degenerate facet</em>.
-</li>
-</ul>
-<ul>
-<li><b>A facet with flipped orientation. </b>A
-facet's hyperplane may define a halfspace that
-does not include the interior point.This is
-called a <em>flipped facet</em>. </li>
-</ul>
-<ul>
-<li><strong>A coplanar horizon facet.</strong> A
-newly processed point may be coplanar with an
-horizon facet. Qhull creates a new facet without
-a hyperplane. It links new facets for the same
-horizon facet together. This is called a <em>samecycle</em>.
-The new facet or samecycle is merged into the
-horizon facet. </li>
-</ul>
-<ul>
-<li><b>Concave facets. </b>A facet's centrum may be
-above a neighboring facet. If so, the facets meet
-at a concave angle. </li>
-</ul>
-<ul>
-<li><b>Coplanar facets. </b>A facet's centrum may be
-coplanar with a neighboring facet (i.e., it is
-neither clearly below nor clearly above the
-facet's hyperplane). Qhull removes coplanar
-facets in independent sets sorted by angle.</li>
-</ul>
-<ul>
-<li><b>Redundant vertex. </b>A vertex may have fewer
-than three neighboring facets. If so, it is
-redundant and may be renamed to an adjacent
-vertex without changing the topological
-structure.This is called a <em>redundant vertex</em>.
-</li>
-</ul>
-</blockquote>
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-<hr>
-<p><a href="#TOP">»</a> <a href="qh-geom.htm#TOC">Geom</a>
-<a name="TOC">•</a> <a href="qh-globa.htm#TOC">Global</a>
-• <a href="qh-io.htm#TOC">Io</a> • <a href="qh-mem.htm#TOC">Mem</a>
-• <b>Merge</b> • <a href="qh-poly.htm#TOC">Poly</a>
-• <a href="qh-qhull.htm#TOC">Qhull</a> • <a href="qh-set.htm#TOC">Set</a>
-• <a href="qh-stat.htm#TOC">Stat</a> • <a href="qh-user.htm#TOC">User</a>
-</p>
-<h3>Index to <a href="merge.c">merge.c</a> and
-<a href="merge.h">merge.h</a></h3>
-<ul>
-<li><a href="#mtype">merge.h data types, macros, and
-global sets</a> </li>
-<li><a href="#mconst">merge.h constants</a> </li>
-</ul>
-<ul>
-<li><a href="#mtop">top-level merge functions</a> </li>
-<li><a href="#mset">functions for identifying merges</a></li>
-<li><a href="#mbest">functions for determining the
-best merge</a> </li>
-<li><a href="#mmerge">functions for merging facets</a>
-</li>
-<li><a href="#mcycle">functions for merging a cycle
-of facets</a> </li>
-<li><a href="#mrename">functions for renaming a
-vertex</a> </li>
-<li><a href="#mvertex">functions for identifying
-vertices for renaming</a> </li>
-<li><a href="#mcheck">functions for check and trace</a> </li>
-</ul>
-<h3><a href="qh-merge.htm#TOC">»</a><a name="mtype">merge.h data
-types, macros, and global sets</a></h3>
-<ul>
-<li><a href="merge.h#mergeT">mergeT</a> structure to
-identify a merge of two facets</li>
-<li><a href="merge.h#FOREACHmerge_">FOREACHmerge_</a>
-assign 'merge' to each merge in merges </li>
-<li><a href="qhull.h#qh-set">qh global sets</a>
-qh.facet_mergeset contains non-convex merges
-while qh.degen_mergeset contains degenerate and
-redundant facets</li>
-</ul>
-<h3><a href="qh-merge.htm#TOC">»</a><a name="mconst">merge.h
-constants</a></h3>
-<ul>
-<li><a href="qhull.h#qh-prec">qh precision constants</a>
-precision constants for Qhull </li>
-<li><a href="merge.h#MRG">MRG...</a> indicates the
-type of a merge (mergeT->type)</li>
-<li><a href="merge.h#qh_ANGLEredundant">qh_ANGLEredundant</a>
-indicates redundant merge in mergeT->angle </li>
-<li><a href="merge.h#qh_ANGLEdegen">qh_ANGLEdegen</a>
-indicates degenerate facet in mergeT->angle </li>
-<li><a href="merge.h#qh_ANGLEconcave">qh_ANGLEconcave</a>
-offset to indicate concave facets in
-mergeT->angle </li>
-<li><a href="merge.h#qh_MERGEapex">qh_MERGEapex</a>
-flag for qh_mergefacet() to indicate an apex
-merge </li>
-</ul>
-<h3><a href="qh-merge.htm#TOC">»</a><a name="mtop">top-level merge
-functions</a></h3>
-<ul>
-<li><a href="merge.c#all_merges">qh_all_merges</a>
-merge all non-convex facets </li>
-<li><a href="merge.c#checkzero">qh_checkzero</a>
-check that facets are clearly convex </li>
-<li><a href="merge.c#flippedmerges">qh_flippedmerges</a>
-merge flipped facets into best neighbor </li>
-<li><a href="merge.c#forcedmerges">qh_forcedmerges</a>
-merge all duplicate ridges </li>
-<li><a href="merge.c#merge_degenredundant">qh_merge_degenredundant</a>
-merge degenerate and redundant facets </li>
-<li><a href="merge.c#merge_nonconvex">qh_merge_nonconvex</a>
-merge a non-convex ridge </li>
-<li><a href="merge.c#premerge">qh_premerge</a>
-pre-merge non-convex facets </li>
-<li><a href="merge.c#postmerge">qh_postmerge</a>
-post-merge nonconvex facets as defined by
-maxcentrum/maxangle </li>
-</ul>
-
-<h3><a href="qh-merge.htm#TOC">»</a><a name="mset">functions for
-identifying merges</a></h3>
-<ul>
-<li><a href="merge.c#appendmergeset">qh_appendmergeset</a>
-appends an entry to qh.facet_mergeset</li>
-<li><a href="merge.c#compareangle">qh_compareangle</a>
-used by qsort() to order merges </li>
-<li><a href="merge.c#comparemerge">qh_comparemerge</a>
-used by qsort() to order merges </li>
-<li><a href="merge.c#degen_redundant_facet">qh_degen_redundant_facet</a>
-check for a degenerate and redundant facet</li>
-<li><a href="merge.c#degen_redundant_neighbors">qh_degen_redundant_neighbors</a>
-append degenerate and redundant neighbors to
-qh.degen_mergeset </li>
-<li><a href="merge.c#getmergeset_initial">qh_getmergeset_initial</a>
-build initial qh.facet_mergeset </li>
-<li><a href="merge.c#getmergeset">qh_getmergeset</a>
-update qh.facet_mergeset </li>
-<li><a href="merge.c#mark_dupridges">qh_mark_dupridges</a>
-add duplicated ridges to qh.facet_mergeset</li>
-<li><a href="merge.c#maydropneighbor">qh_maydropneighbor</a>
-drop neighbor relationship if no ridge between
-facet and neighbor </li>
-<li><a href="merge.c#test_appendmerge">qh_test_appendmerge</a>
-test a pair of facets for convexity and append to
-qh.facet_mergeset if non-convex </li>
-<li><a href="merge.c#test_vneighbors">qh_test_vneighbors</a>
-test vertex neighbors for convexity </li>
-</ul>
-
-<h3><a href="qh-merge.htm#TOC">»</a><a name="mbest">functions for
-determining the best merge</a></h3>
-<ul>
-<li><a href="merge.c#findbest_test">qh_findbest_test</a>
-test neighbor for best merge </li>
-<li><a href="merge.c#findbestneighbor">qh_findbestneighbor</a>
-finds best neighbor of a facet for merging (i.e.,
-closest hyperplane) </li>
-</ul>
-
-<h3><a href="qh-merge.htm#TOC">»</a><a name="mmerge">functions for
-merging facets</a></h3>
-<ul>
-<li><a href="merge.c#copynonconvex">qh_copynonconvex</a>
-copy non-convex flag to another ridge for the
-same neighbor </li>
-<li><a href="merge.c#makeridges">qh_makeridges</a>
-creates explicit ridges between simplicial facets
-</li>
-<li><a href="merge.c#mergefacet">qh_mergefacet</a>
-merges one facet into another facet</li>
-<li><a href="merge.c#mergeneighbors">qh_mergeneighbors</a>
-merges the neighbors of two facets </li>
-<li><a href="merge.c#mergeridges">qh_mergeridges</a>
-merges the ridge sets of two facets </li>
-<li><a href="merge.c#mergesimplex">qh_mergesimplex</a>
-merge a simplicial facet into another simplicial
-facet </li>
-<li><a href="merge.c#mergevertex_del">qh_mergevertex_del</a>
-delete a vertex due to merging one facet into
-another facet </li>
-<li><a href="merge.c#mergevertex_neighbors">qh_mergevertex_neighbors</a>
-merge the vertex neighbors of two facets </li>
-<li><a href="merge.c#mergevertices">qh_mergevertices</a>
-merge the vertex sets of two facets </li>
-<li><a href="merge.c#newvertices">qh_newvertices</a>
-register all vertices as new vertices </li>
-<li><a href="merge.c#updatetested">qh_updatetested</a>
-clear tested flags and centrums involved in a
-merge </li>
-<li><a href="merge.c#willdelete">qh_willdelete</a>
-moves facet to qh.visible_list; sets replacement
-or NULL </li>
-</ul>
-
-<h3><a href="qh-merge.htm#TOC">»</a><a name="mcycle">functions for
-merging a cycle of facets</a></h3>
-<p>If a point is coplanar with an horizon facet, the
-corresponding new facets are linked together (a <em>samecycle</em>)
-for merging.</p>
-<ul>
-<li><a href="merge.c#basevertices">qh_basevertices</a>
-return temporary set of base vertices for a
-samecycle </li>
-<li><a href="merge.c#mergecycle">qh_mergecycle</a>
-merge a samecycle into a horizon facet </li>
-<li><a href="merge.c#mergecycle_all">qh_mergecycle_all</a>
-merge all samecycles into horizon facets</li>
-<li><a href="merge.c#mergecycle_facets">qh_mergecycle_facets</a>
-finish merge of samecycle </li>
-<li><a href="merge.c#mergecycle_neighbors">qh_mergecycle_neighbors</a>
-merge neighbor sets for samecycle </li>
-<li><a href="merge.c#mergecycle_ridges">qh_mergecycle_ridges</a>
-merge ridge sets for samecycle </li>
-<li><a href="merge.c#mergecycle_vneighbors">qh_mergecycle_vneighbors</a>
-merge vertex neighbor sets for samecycle </li>
-</ul>
-<h3><a href="qh-merge.htm#TOC">»</a><a name="mrename">functions
-for renaming a vertex</a></h3>
-<ul>
-<li><a href="merge.c#comparevisit">qh_comparevisit</a>
-used by qsort() to order vertices by visitid</li>
-<li><a href="merge.c#reducevertices">qh_reducevertices</a>
-reduce vertex sets </li>
-<li><a href="merge.c#redundant_vertex">qh_redundant_vertex</a>
-returns true if detect and rename redundant
-vertex </li>
-<li><a href="merge.c#rename_sharedvertex">qh_rename_sharedvertex</a>
-detect and rename a shared vertex </li>
-<li><a href="merge.c#renameridgevertex">qh_renameridgevertex</a>
-rename oldvertex to newvertex in a ridge </li>
-<li><a href="merge.c#renamevertex">qh_renamevertex</a>
-rename oldvertex to newvertex in ridges </li>
-<li><a href="merge.c#remove_extravertices">qh_remove_extravertices</a>
-remove extra vertices in non-simplicial facets </li>
-</ul>
-
-<h3><a href="qh-merge.htm#TOC">»</a><a name="mvertex">functions
-for identifying vertices for renaming</a></h3>
-<ul>
-<li><a href="merge.c#find_newvertex">qh_find_newvertex</a>
-locate new vertex for renaming old vertex </li>
-<li><a href="merge.c#hashridge">qh_hashridge</a> add
-ridge to hashtable </li>
-<li><a href="merge.c#hashridge_find">qh_hashridge_find</a>
-returns matching ridge in hashtable</li>
-<li><a href="merge.c#neighbor_intersections">qh_neighbor_intersections</a>
-return intersection of vertex sets for
-neighboring facets </li>
-<li><a href="merge.c#vertexridges">qh_vertexridges</a>
-return temporary set of ridges adjacent to a
-vertex </li>
-<li><a href="merge.c#vertexridges_facet">qh_vertexridges_facet</a>
-add adjacent ridges for a vertex in facet </li>
-</ul>
-
-<h3><a href="qh-merge.htm#TOC">»</a><a name="mcheck">functions for check and
-trace</a></h3>
-<ul>
-<li><a href="merge.c#checkconnect">qh_checkconnect</a>
-check that new facets are connected </li>
-<li><a href="merge.c#tracemerge">qh_tracemerge</a>
-print trace message after merge </li>
-<li><a href="merge.c#tracemerging">qh_tracemerging</a>
-print trace message during post-merging </li>
-</ul>
-
-<p><!-- Navigation links --> </p>
-<hr>
-<p><b>Up:</b>
-<a href="http://www.qhull.org">Home page for
-Qhull</a> <br>
-<b>Up:</b> <a href="../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
-<b>Up:</b> <a href="../html/qh-quick.htm#programs">Programs</a>
-• <a href="../html/qh-quick.htm#options">Options</a>
-• <a href="../html/qh-opto.htm#output">Output</a>
-• <a href="../html/qh-optf.htm#format">Formats</a>
-• <a href="../html/qh-optg.htm#geomview">Geomview</a>
-• <a href="../html/qh-optp.htm#print">Print</a>
-• <a href="../html/qh-optq.htm#qhull">Qhull</a>
-• <a href="../html/qh-optc.htm#prec">Precision</a>
-• <a href="../html/qh-optt.htm#trace">Trace</a><br>
-<b>Up:</b> <a href="../html/qh-in.htm#TOC">Qhull internals: Table of Contents</a> <br>
-<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
-<b>To:</b> <a href="qh-geom.htm">Geom</a> •
-<a href="qh-globa.htm">Global</a> • <a href="qh-io.htm">Io</a>
-• <a href="qh-mem.htm">Mem</a> • <a href="qh-merge.htm">Merge</a>
-• <a href="qh-poly.htm">Poly</a> • <a href="qh-qhull.htm#TOC">Qhull</a>
-• <a href="qh-set.htm">Set</a> • <a href="qh-stat.htm">Stat</a>
-• <a href="qh-user.htm">User</a><br>
-</p>
-<p><!-- GC common information --> </p>
-<hr>
-<p><a href="http://www.geom.uiuc.edu/"><img
-src="../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
-Geometry Center Home Page </i></p>
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
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-<!-- Do not edit with Front Page, it adds too many spaces -->
-<html>
-<head>
-<meta http-equiv="Content-Type"
-content="text/html; charset=iso-8859-1">
-<title>poly.c, poly2.c -- polyhedron operations</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<p><a name="TOP"><b>Up:</b></a> <a
-href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
-<b>Up:</b> <a href="../html/qh-quick.htm#programs">Programs</a>
-• <a href="../html/qh-quick.htm#options">Options</a>
-• <a href="../html/qh-opto.htm#output">Output</a>
-• <a href="../html/qh-optf.htm#format">Formats</a>
-• <a href="../html/qh-optg.htm#geomview">Geomview</a>
-• <a href="../html/qh-optp.htm#print">Print</a>
-• <a href="../html/qh-optq.htm#qhull">Qhull</a>
-• <a href="../html/qh-optc.htm#prec">Precision</a>
-• <a href="../html/qh-optt.htm#trace">Trace</a><br>
-<b>Up:</b> <a href="../html/qh-in.htm#TOC">Qhull internals: Table of Contents</a><br>
-<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
-<b>To:</b> <a href="qh-geom.htm">Geom</a> • <a href="qh-globa.htm">Global</a>
-• <a href="qh-io.htm">Io</a> • <a href="qh-mem.htm">Mem</a>
-• <a href="qh-merge.htm">Merge</a> • <a href="qh-poly.htm#TOC">Poly</a>
-• <a href="qh-qhull.htm">Qhull</a> • <a href="qh-set.htm">Set</a>
-• <a href="qh-stat.htm">Stat</a> • <a href="qh-user.htm">User</a>
-</p>
-<hr>
-
-<h2>poly.c, poly2.c -- polyhedron operations</h2>
-<blockquote>
-
-<p>Qhull uses dimension-free terminology. Qhull builds a
-polyhedron in dimension <em>d. </em>A <em>polyhedron</em> is a
-simplicial complex of faces with geometric information for the
-top and bottom-level faces. A (<em>d-1</em>)-face is a <em>facet</em>,
-a (<em>d-2</em>)-face is a <em>ridge</em>, and a <em>0</em>-face
-is a <em>vertex</em>. For example in 3-d, a facet is a polygon
-and a ridge is an edge. A facet is built from a ridge (the <em>base</em>)
-and a vertex (the <em>apex</em>). See
-<a href="../html/index.htm#structure">Qhull's data structures</a>.</p>
-
-<p>Qhull's primary data structure is a polyhedron. A
-polyhedron is a list of facets. Each facet has a set of
-neighboring facets and a set of vertices. Each facet has a
-hyperplane. For example, a tetrahedron has four facets.
-If its vertices are <em>a, b, c, d</em>, and its facets
-are <em>1, 2, 3, 4,</em> the tetrahedron is </p>
-<blockquote>
-<ul>
-<li>facet 1 <ul>
- <li>vertices: b c d </li>
- <li>neighbors: 2 3 4 </li>
-</ul>
-</li>
-<li>facet 2 <ul>
- <li>vertices: a c d </li>
- <li>neighbors: 1 3 4 </li>
-</ul>
-</li>
-<li>facet 3 <ul>
- <li>vertices: a b d </li>
- <li>neighbors: 1 2 4 </li>
-</ul>
-</li>
-<li>facet 4 <ul>
- <li>vertices: a b c </li>
- <li>neighbors: 1 2 3 </li>
-</ul>
-</li>
-</ul>
-</blockquote>
-<p>A facet may be simplicial or non-simplicial. In 3-d, a
-<i>simplicial facet</i> has three vertices and three
-neighbors. A <i>nonsimplicial facet</i> has more than
-three vertices and more than three neighbors. A
-nonsimplicial facet has a set of ridges and a centrum. </p>
-<p>
-A simplicial facet has an orientation. An <i>orientation</i>
-is either <i>top</i> or <i>bottom</i>.
-The flag, <tt>facet->toporient,</tt>
-defines the orientation of the facet's vertices. For example in 3-d,
-'top' is left-handed orientation (i.e., the vertex order follows the direction
-of the left-hand fingers when the thumb is pointing away from the center).
-Except for axis-parallel facets in 5-d and higher, topological orientation
-determines the geometric orientation of the facet's hyperplane.
-
-<p>A nonsimplicial facet is due to merging two or more
-facets. The facet's ridge set determine a simplicial
-decomposition of the facet. Each ridge is a 1-face (i.e.,
-it has two vertices and two neighboring facets). The
-orientation of a ridge is determined by the order of the
-neighboring facets. The flag, <tt>facet->toporient,</tt>is
-ignored. </p>
-<p>A nonsimplicial facet has a centrum for testing
-convexity. A <i>centrum</i> is a point on the facet's
-hyperplane that is near the center of the facet. Except
-for large facets, it is the arithmetic average of the
-facet's vertices. </p>
-<p>A nonsimplicial facet is an approximation that is
-defined by offsets from the facet's hyperplane. When
-Qhull finishes, the <i>outer plane</i> is above all
-points while the <i>inner plane</i> is below the facet's
-vertices. This guarantees that any exact convex hull
-passes between the inner and outer planes. The outer
-plane is defined by <tt>facet->maxoutside</tt> while
-the inner plane is computed from the facet's vertices.</p>
-
-<p>Qhull 3.1 includes triangulation of non-simplicial facets
-('<A href="../html/qh-optq.htm#Qt">Qt</A>').
-These facets,
-called <i>tricoplanar</i>, share the same normal. centrum, and Voronoi center.
-One facet (keepcentrum) owns these data structures.
-While tricoplanar facets are more accurate than the simplicial facets from
-joggled input, they
-may have zero area or flipped orientation.
-
-</blockquote>
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-<hr>
-<p><a href="#TOP">»</a> <a href="qh-geom.htm#TOC">Geom</a>
-<a name="TOC">•</a> <a href="qh-globa.htm#TOC">Global</a>
-• <a href="qh-io.htm#TOC">Io</a> • <a href="qh-mem.htm#TOC">Mem</a>
-• <a href="qh-merge.htm#TOC">Merge</a> • <b>Poly</b>
-• <a href="qh-qhull.htm#TOC">Qhull</a> • <a href="qh-set.htm#TOC">Set</a>
-• <a href="qh-stat.htm#TOC">Stat</a> • <a href="qh-user.htm#TOC">User</a>
-</p>
-<h3>Index to <a href="poly.c">poly.c</a>,
-<a href="poly2.c">poly2.c</a>, <a href="poly.h">poly.h</a>,
-and <a href="qhull.h">qhull.h</a></h3>
-<ul>
-<li><a href="#ptype">Data types and global
-lists for polyhedrons</a> </li>
-<li><a href="#pconst">poly.h constants</a> </li>
-<li><a href="#pgall">Global FORALL macros</a> </li>
-<li><a href="#pall">FORALL macros</a> </li>
-<li><a href="#peach">FOREACH macros</a> </li>
-<li><a href="#pieach">Indexed FOREACH macros</a> </li>
-<li><a href="#pmacro">Other macros for polyhedrons</a><p> </li>
-<li><a href="#plist">Facetlist functions</a> </li>
-<li><a href="#pfacet">Facet functions</a> </li>
-<li><a href="#pvertex">Vertex, ridge, and point
-functions</a> </li>
-<li><a href="#phash">Hashtable functions</a> </li>
-<li><a href="#pnew">Allocation and deallocation
-functions</a> </li>
-<li><a href="#pcheck">Check functions</a> </li>
-</ul>
-<h3><a href="qh-poly.htm#TOC">»</a><a name="ptype">Data
-types and global lists for polyhedrons</a></h3>
-<ul>
-<li><a href="qhull.h#facetT">facetT</a> defines a
-facet </li>
-<li><a href="qhull.h#ridgeT">ridgeT</a> defines a
-ridge </li>
-<li><a href="qhull.h#vertexT">vertexT</a> defines a
-vertex </li>
-<li><a href="qhull.h#qh-lists">qh facet and vertex
-lists</a> lists of facets and vertices </li>
-<li><a href="qhull.h#qh-set">qh global sets</a>
-global sets for merging, hashing, input, etc. </li>
-</ul>
-<h3><a href="qh-poly.htm#TOC">»</a><a name="pconst">poly.h constants</a></h3>
-<ul>
-<li><a href="poly.h#ALGORITHMfault">ALGORITHMfault</a>
-flag to not report errors in qh_checkconvex() </li>
-<li><a href="poly.h#DATAfault">DATAfault</a> flag to
-report errors in qh_checkconvex() </li>
-<li><a href="poly.h#DUPLICATEridge">DUPLICATEridge</a>
-special value for facet->neighbor to indicate
-a duplicate ridge </li>
-<li><a href="poly.h#MERGEridge">MERGEridge</a>
-special value for facet->neighbor to indicate
-a merged ridge </li>
-</ul>
-<h3><a href="qh-poly.htm#TOC">»</a><a name="pgall">Global FORALL
-macros</a></h3>
-<ul>
-<li><a href="qhull.h#FORALLfacets">FORALLfacets</a>
-assign 'facet' to each facet in qh.facet_list </li>
-<li><a href="poly.h#FORALLnew_facets">FORALLnew_facets</a>
-assign 'facet' to each facet in qh.newfacet_list </li>
-<li><a href="poly.h#FORALLvisible_facets">FORALLvisible_facets</a>
-assign 'visible' to each visible facet in
-qh.visible_list </li>
-<li><a href="qhull.h#FORALLpoints">FORALLpoints</a>
-assign 'point' to each point in qh.first_point,
-qh.num_points </li>
-<li><a href="qhull.h#FORALLvertices">FORALLvertices</a>
-assign 'vertex' to each vertex in qh.vertex_list </li>
-</ul>
-<h3><a href="qh-poly.htm#TOC">»</a><a name="pall">FORALL macros</a></h3>
-<ul>
-<li><a href="poly.h#FORALLfacet_">FORALLfacet_</a>
-assign 'facet' to each facet in facetlist </li>
-<li><a href="qhull.h#FORALLpoint_">FORALLpoint_</a>
-assign 'point' to each point in points array</li>
-<li><a href="poly.h#FORALLsame_">FORALLsame_</a>
-assign 'same' to each facet in samecycle</li>
-<li><a href="poly.h#FORALLsame_cycle_">FORALLsame_cycle_</a>
-assign 'same' to each facet in samecycle</li>
-<li><a href="poly.h#FORALLvertex_">FORALLvertex_</a>
-assign 'vertex' to each vertex in vertexlist </li>
-</ul>
-<h3><a href="qh-poly.htm#TOC">»</a><a name="peach">FOREACH macros</a></h3>
-<ul>
-<li><a href="qhull.h#FOREACHfacet_">FOREACHfacet_</a>
-assign 'facet' to each facet in facets </li>
-<li><a href="qhull.h#FOREACHneighbor_">FOREACHneighbor_</a>
-assign 'neighbor' to each facet in
-facet->neighbors or vertex->neighbors</li>
-<li><a href="poly.h#FOREACHnewfacet_">FOREACHnewfacet_</a>
-assign 'newfacet' to each facet in facet set </li>
-<li><a href="qhull.h#FOREACHpoint_">FOREACHpoint_</a>
-assign 'point' to each point in points set </li>
-<li><a href="qhull.h#FOREACHridge_">FOREACHridge_</a>
-assign 'ridge' to each ridge in ridge set </li>
-<li><a href="qhull.h#FOREACHvertex_">FOREACHvertex_</a>
-assign 'vertex' to each vertex in vertex set </li>
-<li><a href="poly.h#FOREACHvertexA_">FOREACHvertexA_</a>
-assign 'vertexA' to each vertex in vertex set</li>
-<li><a href="poly.h#FOREACHvisible_">FOREACHvisible_</a>
-assign 'visible' to each facet in facet set </li>
-</ul>
-<h3><a href="qh-poly.htm#TOC">»</a><a name="pieach">Indexed
-FOREACH macros</a></h3>
-<ul>
-<li><a href="qhull.h#FOREACHfacet_i_">FOREACHfacet_i_</a>
-assign 'facet' and 'facet_i' to each facet in
-facet set </li>
-<li><a href="qhull.h#FOREACHneighbor_i_">FOREACHneighbor_i_</a>
-assign 'neighbor' and 'neighbor_i' to each facet
-in facet->neighbors or vertex->neighbors</li>
-<li><a href="qhull.h#FOREACHpoint_i_">FOREACHpoint_i_</a>
-assign 'point' and 'point_i' to each point in
-points set </li>
-<li><a href="qhull.h#FOREACHridge_i_">FOREACHridge_i_</a>
-assign 'ridge' and 'ridge_i' to each ridge in
-ridges set </li>
-<li><a href="qhull.h#FOREACHvertex_i_">FOREACHvertex_i_</a>
-assign 'vertex' and 'vertex_i' to each vertex in
-vertices set </li>
-<li><a href="poly.h#FOREACHvertexreverse12_">FOREACHvertexreverse12_</a>
-assign 'vertex' to each vertex in vertex set;
-reverse the order of first two vertices </li>
-</ul>
-<h3><a href="qh-poly.htm#TOC">»</a><a name="pmacro">Other macros for polyhedrons</a></h3>
-<ul>
-<li><a href="qhull.h#getid_">getid_</a> return ID for
-a facet, ridge, or vertex </li>
-<li><a href="qhull.h#otherfacet_">otherfacet_</a>
-return neighboring facet for a ridge in a facet </li>
-</ul>
-<h3><a href="qh-poly.htm#TOC">»</a><a name="plist">Facetlist
-functions</a></h3>
-<ul>
-<li><a href="poly.c#appendfacet">qh_appendfacet</a>
-appends facet to end of qh.facet_list</li>
-<li><a href="poly.c#attachnewfacets">qh_attachnewfacets</a>
-attach new facets in qh.newfacet_list to the
-horizon </li>
-<li><a href="poly2.c#findgood">qh_findgood</a>
-identify good facets for qh.PRINTgood </li>
-<li><a href="poly2.c#findgood_all">qh_findgood_all</a>
-identify more good facets for qh.PRINTgood </li>
-<li><a href="poly2.c#furthestnext">qh_furthestnext</a>
-move facet with furthest of furthest points to
-facet_next </li>
-<li><a href="poly2.c#initialhull">qh_initialhull</a>
-construct the initial hull as a simplex of
-vertices </li>
-<li><a href="poly2.c#nearcoplanar">qh_nearcoplanar</a>
- remove near-inside points from coplanar sets</li>
-<li><a href="poly2.c#prependfacet">qh_prependfacet</a>
-prepends facet to start of facetlist </li>
-<li><a href="user.c#printfacetlist">qh_printfacetlist</a>
-print facets in a facetlist</li>
-<li><a href="poly2.c#printlists">qh_printlists</a>
-print out facet list for debugging </li>
-<li><a href="poly.c#removefacet">qh_removefacet</a>
-unlinks facet from qh.facet_list</li>
-<li><a href="poly2.c#resetlists">qh_resetlists</a>
-reset qh.newvertex_list, qh.newfacet_list, and
-qh.visible_list </li>
-</ul>
-<h3><a href="qh-poly.htm#TOC">»</a><a name="pfacet">Facet
-functions</a></h3>
-<ul>
-<li><a href="poly2.c#createsimplex">qh_createsimplex</a>
-create a simplex of facets from a set of vertices
-</li>
-<li><a href="poly2.c#findbestlower">qh_findbestlower</a> find best
-non-upper, non-flipped facet for point at upperfacet</li>
-<li><a href="poly2.c#furthestout">qh_furthestout</a>
-make furthest outside point the last point of a
-facet's outside set </li>
-<li><a href="poly.c#makenew_nonsimplicial">qh_makenew_nonsimplicial</a>
-make new facets from ridges of visible facets </li>
-<li><a href="poly.c#makenew_simplicial">qh_makenew_simplicial</a>
-make new facets for horizon neighbors </li>
-<li><a href="poly.c#makenewfacet">qh_makenewfacet</a>
-create a facet from vertices and apex </li>
-<li><a href="poly2.c#makenewfacets">qh_makenewfacets</a>
-make new facets from vertex, horizon facets, and
-visible facets </li>
-<li><a href="poly.c#makenewplanes">qh_makenewplanes</a>
-make new hyperplanes for facets </li>
-<li><a href="poly2.c#outcoplanar">qh_outcoplanar</a>
-move points from outside set to coplanar set </li>
-<li><a href="poly2.c#setvoronoi_all">qh_setvoronoi_all</a>
-compute Voronoi centers for all facets </li>
-<li><a href="poly2.c#triangulate">qh_triangulate</a>
-triangulate non-simplicial facets</li>
-<li><a href="poly2.c#triangulate_facet">qh_triangulate_facet</a>
-triangulate a non-simplicial facet</li>
-<li><a href="poly2.c#triangulate_link">qh_triangulate_link</a>
-link facets together from qh_triangulate</li>
-<li><a href="poly2.c#triangulate_mirror">qh_triangulate_mirror</a>
-delete mirrored facets from qh_triangulate</li>
-<li><a href="poly2.c#triangulate_null">qh_triangulate_null</a>
-delete null facet from qh_triangulate</li>
-</ul>
-<h3><a href="qh-poly.htm#TOC">»</a><a name="pvertex">Vertex,
-ridge, and point functions</a></h3>
-<ul>
-<li><a href="poly.c#appendvertex">qh_appendvertex</a>
-append vertex to end of qh.vertex_list, </li>
-<li><a href="io.c#detvridge">qh_detvridge</a> determine Voronoi
-ridge for an input site
-<li><a href="io.c#detvridge3">qh_detvridge3</a> determine 3-d Voronoi
-ridge for an input site
-<li><a href="poly2.c#facet3vertex">qh_facet3vertex</a>
-return an oriented vertex set for a 3-d facet </li>
-<li><a href="poly.c#facetintersect">qh_facetintersect</a>
-return intersection of simplicial facets </li>
-<li><a href="poly2.c#initialvertices">qh_initialvertices</a>
-return non-singular set of initial vertices </li>
-<li><a href="poly2.c#isvertex">qh_isvertex</a> true
-if point is in a vertex set </li>
-<li><a href="poly2.c#nearvertex">qh_nearvertex</a>
-return nearest vertex to point </li>
-<li><a href="poly2.c#nextridge3d">qh_nextridge3d</a>
-iterate over each ridge and vertex for a 3-d
-facet </li>
-<li><a href="poly2.c#point">qh_point</a> return point
-for a point ID </li>
-<li><a href="poly2.c#pointfacet">qh_pointfacet</a>
-return temporary set of facets indexed by point
-ID </li>
-<li><a href="poly.c#pointid">qh_pointid</a> return ID
-for a point</li>
-<li><a href="poly2.c#pointvertex">qh_pointvertex</a>
-return temporary set of vertices indexed by point
-ID </li>
-<li><a href="poly.c#removevertex">qh_removevertex</a>
-unlink vertex from qh.vertex_list, </li>
-<li><a href="poly.c#updatevertices">qh_updatevertices</a>
-update vertex neighbors and delete interior
-vertices </li>
-<li><a href="poly2.c#vertexintersect">qh_vertexintersect</a>
-intersect two vertex sets </li>
-<li><a href="poly2.c#vertexintersect_new">qh_vertexintersect_new</a>
-return intersection of two vertex sets </li>
-<li><a href="poly2.c#vertexneighbors">qh_vertexneighbors</a>
-for each vertex in hull, determine facet
-neighbors </li>
-<li><a href="poly2.c#vertexsubset">qh_vertexsubset</a>
-returns True if vertexsetA is a subset of
-vertexsetB </li>
-</ul>
-<h3><a href="qh-poly.htm#TOC">»</a><a name="phash">Hashtable functions</a></h3>
-<ul>
-<li><a href="poly2.c#addhash">qh_addhash</a> add hash
-element to linear hash table</li>
-<li><a href="poly.c#gethash">qh_gethash</a> return
-hash value for a set</li>
-<li><a href="poly2.c#matchduplicates">qh_matchduplicates</a>
-match duplicate ridges in hash table </li>
-<li><a href="poly.c#matchneighbor">qh_matchneighbor</a>
-try to match subridge of new facet with a
-neighbor </li>
-<li><a href="poly.c#matchnewfacets">qh_matchnewfacets</a>
-match new facets with their new facet neighbors </li>
-<li><a href="poly.c#matchvertices">qh_matchvertices</a>
-tests whether a facet and hash entry match at a
-ridge </li>
-<li><a href="poly2.c#newhashtable">qh_newhashtable</a>
-allocate a new qh.hash_table </li>
-<li><a href="poly2.c#printhashtable">qh_printhashtable</a>
-print hash table </li>
-</ul>
-<h3><a href="qh-poly.htm#TOC">»</a><a name="pnew">Allocation and
-deallocation functions</a></h3>
-<ul>
-<li><a href="poly2.c#clearcenters">qh_clearcenters</a>
-clear old data from facet->center </li>
-<li><a href="poly.c#deletevisible">qh_deletevisible</a>
-delete visible facets and vertices </li>
-<li><a href="poly.c#delfacet">qh_delfacet</a> free up
-the memory occupied by a facet </li>
-<li><a href="poly2.c#delridge">qh_delridge</a> delete
-ridge</li>
-<li><a href="poly2.c#delvertex">qh_delvertex</a>
-delete vertex </li>
-<li><a href="poly.c#newfacet">qh_newfacet</a> create
-and allocate space for a facet </li>
-<li><a href="poly.c#newridge">qh_newridge</a> create
-and allocate space for a ridge </li>
-<li><a href="poly2.c#newvertex">qh_newvertex</a>
-create and allocate space for a vertex </li>
-</ul>
-<h3><a href="qh-poly.htm#TOC">»</a><a name="pcheck">Check
-functions</a></h3>
-<ul>
-<li><a href="poly2.c#check_bestdist">qh_check_bestdist</a>
-check that points are not outside of facets </li>
-<li><a href="poly2.c#check_maxout">qh_check_maxout</a>
-updates qh.max_outside and checks all points
-against bestfacet </li>
-<li><a href="poly2.c#check_output">qh_check_output</a>
-check topological and geometric output</li>
-<li><a href="poly2.c#check_point">qh_check_point</a>
-check that point is not outside of facet </li>
-<li><a href="poly2.c#check_points">qh_check_points</a>
-check that all points are inside all facets </li>
-<li><a href="poly2.c#checkconvex">qh_checkconvex</a>
-check that each ridge in facetlist is convex </li>
-<li><a href="poly2.c#checkfacet">qh_checkfacet</a>
-check for consistency errors in facet </li>
-<li><a href="poly.c#checkflipped">qh_checkflipped</a>
-check facet orientation to the interior point </li>
-<li><a href="poly2.c#checkflipped_all">qh_checkflipped_all</a>
-check facet orientation for a facet list </li>
-<li><a href="poly2.c#checkpolygon">qh_checkpolygon</a>
-check topological structure </li>
-<li><a href="poly2.c#checkvertex">qh_checkvertex</a>
-check vertex for consistency </li>
-<li><a href="poly2.c#infiniteloop">qh_infiniteloop</a>
-report error for a loop of facets </li>
-<li><a href="poly2.c#printlists">qh_printlists</a>
-print out facet list for debugging </li>
-</ul>
-
-
-<p><!-- Navigation links --> </p>
-<hr>
-<p><b>Up:</b>
-<a href="http://www.qhull.org">Home page for
-Qhull</a> <br>
-<b>Up:</b> <a href="../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
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-</p>
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-<hr>
-<p><a href="http://www.geom.uiuc.edu/"><img
-src="../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
-Geometry Center Home Page </i></p>
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
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-</p>
-<hr>
-
-<h2>qhull.c -- top-level functions and basic data types</h2>
-<blockquote>
-<p>Qhull implements the Quickhull algorithm for computing
-the convex hull. The Quickhull algorithm combines two
-well-known algorithms: the 2-d quickhull algorithm and
-the n-d beneath-beyond algorithm. See
-<a href="../html/index.htm#description">Description of Qhull</a>. </p>
-<p>This section provides an index to the top-level
-functions and base data types. The top-level header file, <tt>qhull.h</tt>,
-contains prototypes for these functions.</p>
-</blockquote>
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-<hr>
-<p><a href="#TOP">»</a> <a href="qh-geom.htm#TOC">Geom</a>
-<a name="TOC">•</a> <a href="qh-globa.htm#TOC">Global</a>
-• <a href="qh-io.htm#TOC">Io</a> • <a href="qh-mem.htm#TOC">Mem</a>
-• <a href="qh-merge.htm#TOC">Merge</a> • <a href="qh-poly.htm#TOC">Poly</a>
-• <b>Qhull</b> • <a href="qh-set.htm#TOC">Set</a>
-• <a href="qh-stat.htm#TOC">Stat</a> • <a href="qh-user.htm#TOC">User</a>
-</p>
-<h3>Index to <a href="qhull.c">qhull.c</a>,
-<a href="qhull.h">qhull.h</a>, and
-<a href="unix.c">unix.c</a></h3>
-<ul>
-<li><a href="#qtype">qhull.h and unix.c data types and
-constants</a> </li>
-<li><a href="#qmacro">qhull.h other macros</a> </li>
-<li><a href="#qfunc">Quickhull routines in call order</a> </li>
-<li><a href="#qinit">Top-level routines for initializing and terminating Qhull</a></li>
-<li><a href="#qin">Top-level routines for reading and modifying the input</a></li>
-<li><a href="#qcall">Top-level routines for calling Qhull</a></li>
-<li><a href="#qout">Top-level routines for returning results</a></li>
-<li><a href="#qtest">Top-level routines for testing and debugging</a></li>
-</ul>
-
-<h3><a href="qh-qhull.htm#TOC">»</a><a name="qtype">qhull.h and unix.c
-data types and constants</a></h3>
-<ul>
-<li><a href="qhull.h#flagT">flagT</a> Boolean flag as
-a bit </li>
-<li><a href="qhull.h#boolT">boolT</a> boolean value,
-either True or False </li>
-<li><a href="qhull.h#CENTERtype">CENTERtype</a> to
-distinguish facet->center </li>
-<li><a href="qhull.h#qh_PRINT">qh_PRINT</a> output
-formats for printing (qh.PRINTout) </li>
-<li><a href="qhull.h#qh_ALL">qh_ALL</a> argument flag
-for selecting everything </li>
-<li><a href="qhull.h#qh_ERR">qh_ERR</a> Qhull exit
-codes for indicating errors </li>
-<li><a href="unix.c#prompt">qh_prompt</a> version and long prompt for Qhull</li>
-<li><a href="unix.c#prompt2">qh_prompt2</a> synopsis for Qhull</li>
-<li><a href="unix.c#prompt3">qh_prompt3</a> concise prompt for Qhull</li>
-<li><a href="global.c#qh_version">qh_version</a> version stamp</li>
-</ul>
-
-<h3><a href="qh-qhull.htm#TOC">»</a><a name="qmacro">qhull.h other
-macros</a></h3>
-<ul>
-<li><a href="qhull_a.h#traceN">traceN</a> print trace
-message if <em>qh.IStracing >= N</em>. </li>
-</ul>
-
-<h3><a href="qh-qhull.htm#TOC">»</a><a name="qfunc">Quickhull
-routines in call order</a></h3>
-<ul>
-<li><a href="unix.c#main">main</a> processes the
-command line, calls qhull() to do the work, and
-exits </li>
-<li><a href="qhull.c#qhull">qh_qhull</a> construct
-the convex hull of a set of points </li>
-<li><a href="qhull.c#build_withrestart">qh_build_withrestart</a>
-allow restarts while calling qh_buildhull</li>
-<li><a href="poly2.c#initbuild">qh_initbuild</a>
-initialize hull and outside sets with point array</li>
-<li><a href="qhull.c#partitionall">qh_partitionall</a>
-partition all points into outside sets </li>
-<li><a href="qhull.c#buildhull">qh_buildhull</a>
-construct a convex hull by adding points one at a
-time </li>
-<li><a href="qhull.c#nextfurthest">qh_nextfurthest</a>
-return next furthest point for processing </li>
-<li><a href="qhull.c#buildtracing">qh_buildtracing</a>
-trace an iteration of buildhull </li>
-<li><a href="qhull.c#addpoint">qh_addpoint</a> add a
-point to the convex hull </li>
-<li><a href="qhull.c#findhorizon">qh_findhorizon</a>
-find the horizon and visible facets for a point </li>
-<li><a href="qhull.c#partitionvisible">qh_partitionvisible</a>
-partition points from facets in qh.visible_list
-to facets in qh.newfacet_list </li>
-<li><a href="qhull.c#partitionpoint">qh_partitionpoint</a>
-partition a point as inside, coplanar with, or
-outside a facet </li>
-<li><a href="qhull.c#partitioncoplanar">qh_partitioncoplanar</a>
-partition coplanar point into a facet </li>
-<li><a href="qhull.c#precision">qh_precision</a> restart on precision errors if not merging and if 'QJn'</li>
-</ul>
-
-<h3><a href="qh-qhull.htm#TOC">»</a><a name="qinit">Top-level routines for initializing and terminating Qhull (in other modules)</a></h3>
-<ul>
-<li><a href="global.c#freebuild">qh_freebuild</a>
-free memory used by qh_initbuild and qh_buildhull
-</li>
-<li><a href="global.c#checkflags">qh_checkflags</a>
-check flags for multiple frontends to qhull
-<li><a href="global.c#freeqhull">qh_freeqhull</a>
-free memory used by qhull </li>
-<li><a href="global.c#init_A">qh_init_A</a> called
-before error handling initialized </li>
-<li><a href="global.c#init_B">qh_init_B</a> called
-after points are defined </li>
-<li><a href="global.c#initflags">qh_initflags</a> set
-flags and constants from command line </li>
-<li><a href="global.c#restore_qhull">qh_restore_qhull</a>
-restores a saved qhull </li>
-<li><a href="global.c#save_qhull">qh_save_qhull</a>
-saves qhull for later restoring </li>
-<li><a href="user.c#user_memsizes">qh_user_memsizes</a>
-define additional quick allocation sizes
-</li>
-</ul>
-
-<h3><a href="qh-qhull.htm#TOC">»</a><a name="qin">Top-level routines for reading and modifying the input (in other modules)</a></h3>
-<ul>
-<li><a href="geom2.c#gram_schmidt">qh_gram_schmidt</a>
-implements Gram-Schmidt orthogonalization by rows </li>
-<li><a href="geom2.c#projectinput">qh_projectinput</a>
-project input along one or more dimensions +
-Delaunay projection </li>
-<li><a href="geom2.c#randommatrix">qh_randommatrix</a>
-generate a random dimXdim matrix in range (-1,1) </li>
-<li><a href="io.c#readpoints">qh_readpoints</a> read
-points from input </li>
-<li><a href="geom2.c#rotateinput">qh_rotateinput</a> rotate
-input points using row matrix </li>
-<li><a href="geom2.c#scaleinput">qh_scaleinput</a> scale
-input points using qh low_bound/high_bound </li>
-<li><a href="geom2.c#setdelaunay">qh_setdelaunay</a> project
-points to paraboloid for Delaunay triangulation </li>
-<li><a href="geom2.c#sethalfspace_all">qh_sethalfspace_all</a>
-generate dual for halfspace intersection with interior
-point </li>
-</ul>
-
-<h3><a href="qh-qhull.htm#TOC">»</a><a name="qcall">Top-level routines for calling Qhull (in other modules)</a></h3>
-<ul>
-<li><a href="qhull.c#addpoint">qh_addpoint</a> add
-point to convex hull </li>
-<li><a href="poly2.c#findbestfacet">qh_findbestfacet</a>
-find facet that is furthest below a point </li>
-<li><a href="poly2.c#findfacet_all">qh_findfacet_all</a>
-exhaustive search for facet below a point </li>
-<li><a href="qhull.c#qhull">qh_qhull</a> construct
-the convex hull of a set of points </li>
-</ul>
-
-<h3><a href="qh-qhull.htm#TOC">»</a><a name="qout">Top-level routines for returning results (in other modules)</a></h3>
-<ul>
-<li><a href="stat.c#collectstatistics">qh_collectstatistics</a>
-collect statistics for qh.facet_list </li>
-<li><a href="poly2.c#nearvertex">qh_nearvertex</a>
-return nearest vertex to point </li>
-<li><a href="poly2.c#point">qh_point</a> return point
-for a point ID </li>
-<li><a href="poly2.c#pointfacet">qh_pointfacet</a>
-return temporary set of facets indexed by point
-ID </li>
-<li><a href="poly.c#pointid">qh_pointid</a> return ID
-for a point</li>
-<li><a href="poly2.c#pointvertex">qh_pointvertex</a>
-return vertices (if any) for all points</li>
-<li><a href="stat.c#printallstatistics">qh_printallstatistics</a>
-print all statistics </li>
-<li><a href="io.c#printneighborhood">qh_printneighborhood</a>
-print neighborhood of one or two facets </li>
-<li><a href="qhull.c#printsummary">qh_printsummary</a>
-print summary </li>
-<li><a href="io.c#produce_output">qh_produce_output</a>
-print the results of qh_qhull() </li>
-<li><a href="poly2.c#setvoronoi_all">qh_setvoronoi_all</a>
-compute Voronoi centers for all facets </li>
-</ul>
-
-<h3><a href="qh-qhull.htm#TOC">»</a><a name="qtest">Top-level routines for testing and debugging (in other modules)</a></h3>
-<ul>
-<li><a href="io.c#dfacet">dfacet</a> print facet by
-ID from debugger </li>
-<li><a href="io.c#dvertex">dvertex</a> print vertex
-by ID from debugger </li>
-<li><a href="poly2.c#check_output">qh_check_output</a>
-check output </li>
-<li><a href="poly2.c#check_points">qh_check_points</a>
-verify that all points are inside the convex hull
-</li>
-<li><a href="user.c#errexit">qh_errexit</a> report
-error with a facet and a ridge</li>
-<li><a href="qhull.c#errexit2">qh_errexit2</a> report
-error with two facets </li>
-<li><a href="user.c#errprint">qh_errprint</a> print
-erroneous facets, ridge, and vertex </li>
-<li><a href="user.c#printfacetlist">qh_printfacetlist</a>
-print all fields for a list of facets </li>
-</ul>
-
-<p><!-- Navigation links --> </p>
-<hr>
-<p><b>Up:</b>
-<a href="http://www.qhull.org">Home page for
-Qhull</a> <br>
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-</p>
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-src="../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
-Geometry Center Home Page </i></p>
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
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@@ -1,304 +0,0 @@
-<!-- Do not edit with Front Page, it adds too many spaces -->
-<html>
-<head>
-<meta http-equiv="Content-Type"
-content="text/html; charset=iso-8859-1">
-<title>qset.c -- set data type and operations</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<p><a name="TOP"><b>Up:</b></a> <a
-href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
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-• <a href="qh-qhull.htm">Qhull</a> • <a href="qh-set.htm#TOC">Set</a>
-• <a href="qh-stat.htm">Stat</a> • <a href="qh-user.htm">User</a>
-</p>
-<hr>
-
-<h2>qset.c -- set data type and operations</h2>
-<blockquote>
-<p>Qhull's data structures are constructed from sets. The
-functions and macros in qset.c construct, iterate, and
-modify these sets. They are the most frequently called
-functions in Qhull. For this reason, efficiency is the
-primary concern. </p>
-<p>In Qhull, a <i>set</i> is represented by an unordered
-array of pointers with a maximum size and a NULL
-terminator (<a href="qset.h#setT">setT</a>).
-Most sets correspond to mathematical sets
-(i.e., the pointers are unique). Some sets are sorted to
-enforce uniqueness. Some sets are ordered. For example,
-the order of vertices in a ridge determine the ridge's
-orientation. If you reverse the order of adjacent
-vertices, the orientation reverses. Some sets are not
-mathematical sets. They may be indexed as an array and
-they may include NULL pointers. </p>
-<p>The most common operation on a set is to iterate its
-members. This is done with a 'FOREACH...' macro. Each set
-has a custom macro. For example, 'FOREACHvertex_'
-iterates over a set of vertices. Each vertex is assigned
-to the variable 'vertex' from the pointer 'vertexp'. </p>
-<p>Most sets are constructed by appending elements to the
-set. The last element of a set is either NULL or the
-index of the terminating NULL for a partially full set.
-If a set is full, appending an element copies the set to
-a larger array. </p>
-
-</blockquote>
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-<hr>
-<p><a href="#TOP">»</a> <a href="qh-geom.htm#TOC">Geom</a>
-<a name="TOC">•</a> <a href="qh-globa.htm#TOC">Global</a> •
-<a href="qh-io.htm#TOC">Io</a> • <a href="qh-mem.htm#TOC">Mem</a> •
-<a href="qh-merge.htm#TOC">Merge</a> • <a href="qh-poly.htm#TOC">Poly</a>
-• <a href="qh-qhull.htm#TOC">Qhull</a> • <b>Set</b>
-• <a href="qh-stat.htm#TOC">Stat</a> • <a href="qh-user.htm#TOC">User</a>
-</p>
-<h3>Index to <a href="qset.c">qset.c</a> and
-<a href="qset.h">qset.h</a></h3>
-<ul>
-<li><a href="#stype">Data types and constants</a> </li>
-<li><a href="#seach">FOREACH macros</a> </li>
-<li><a href="#saccess">access and size macros</a> </li>
-<li><a href="#sint">internal macros</a> </li>
-<li><a href="#saddr">address macros</a><p> </li>
-
-<li><a href="#snew">Allocation and deallocation functions</a> </li>
-<li><a href="#spred">Access and predicate functions</a>
-</li>
-<li><a href="#sadd">Add functions</a> </li>
-<li><a href="#scheck">Check and print functions</a></li>
-<li><a href="#scopy">Copy, compact, and zero functions</a></li>
-<li><a href="#sdel">Delete functions</a> </li>
-<li><a href="#stemp">Temporary set functions</a> </li>
-</ul>
-<h3><a href="qh-set.htm#TOC">»</a><a name="stype">Data types and
-constants</a></h3>
-<ul>
-<li><a href="qset.h#SETelemsize">SETelemsize</a> size
-of a set element in bytes </li>
-<li><a href="qset.h#setT">setT</a> a set with a
-maximum size and a current size</li>
-<li><a href="qhull.h#qh-set">qh global sets</a>
-global sets for temporary sets, etc. </li>
-</ul>
-<h3><a href="qh-set.htm#TOC">»</a><a name="seach">FOREACH macros</a></h3>
-<ul>
-<li><a href="qset.h#FOREACHelem_">FOREACHelem_</a>
-assign 'elem' to each element in a set </li>
-<li><a href="qset.h#FOREACHset_">FOREACHset_</a>
-assign 'set' to each set in a set of sets </li>
-<li><a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
-define a FOREACH iterator </li>
-<li><a href="qset.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
-define an indexed FOREACH iterator </li>
-<li><a href="qset.h#FOREACHsetelementreverse_">FOREACHsetelementreverse_</a>
-define a reversed FOREACH iterator </li>
-<li><a href="qset.h#FOREACHsetelementreverse12_">FOREACHsetelementreverse12_</a>
-define a FOREACH iterator with e[1] and e[0]
-reversed </li>
-</ul>
-<h3><a href="qh-set.htm#TOC">»</a><a name="saccess">Access and
-size macros</a></h3>
-<ul>
-<li><a href="qset.h#SETelem_">SETelem_</a> return the
-n'th element of set </li>
-<li><a href="qset.h#SETelemt_">SETelemt_</a> return
-the n'th element of set as a type</li>
-<li><a href="qset.h#SETempty_">SETempty_</a> return
-true (1) if set is empty </li>
-<li><a href="qset.h#SETfirst_">SETfirst_</a> return
-first element of set </li>
-<li><a href="qset.h#SETfirstt_">SETfirstt_</a> return
-first element of set as a type</li>
-<li><a href="qset.h#SETindex_">SETindex_</a> return
-index of elem in set </li>
-<li><a href="qset.h#SETreturnsize_">SETreturnsize_</a>
-return size of a set (normally use <a href="qset.c#setsize">qh_setsize</a>) </li>
-<li><a href="qset.h#SETsecond_">SETsecond_</a> return
-second element of set </li>
-<li><a href="qset.h#SETsecondt_">SETsecondt_</a>
-return second element of set as a type</li>
-<li><a href="qset.h#SETtruncate_">SETtruncate_</a>
-truncate set to size, i.e., qh_settruncate()</li>
-</ul>
-<h3><a href="qh-set.htm#TOC">»</a><a name="sint">Internal macros</a></h3>
-<ul>
-<li><a href="qset.c#SETsizeaddr_">SETsizeaddr_</a>
-return pointer to end element of a set (indicates
-current size) </li>
-</ul>
-
-<h3><a href="qh-set.htm#TOC">»</a><a name="saddr">address macros</a></h3>
-<ul>
-<li><a href="qset.h#SETaddr_">SETaddr_</a> return
-address of a set's elements </li>
-<li><a href="qset.h#SETelemaddr_">SETelemaddr_</a>
-return address of the n'th element of a set </li>
-<li><a href="qset.h#SETref_">SETref_</a> l.h.s. for
-modifying the current element in a FOREACH
-iteration </li>
-</ul>
-
-<h3><a href="qh-set.htm#TOC">»</a><a name="snew">Allocation and
-deallocation functions</a></h3>
-<ul>
-<li><a href="qset.c#setfree">qh_setfree</a> free the
-space occupied by a set </li>
-<li><a href="qset.c#setfree2">qh_setfree2</a> free a
-set and its elements </li>
-<li><a href="qset.c#setfreelong">qh_setfreelong</a>
-free a set only if it is in long memory </li>
-<li><a href="qset.c#setnew">qh_setnew</a> create a new
-set </li>
-</ul>
-
-<h3><a href="qh-set.htm#TOC">»</a><a name="spred">Access and
-predicate functions </a></h3>
-<ul>
-<li><a href="qset.c#setequal">qh_setequal</a> return 1
-if two sorted sets are equal </li>
-<li><a href="qset.c#setequal_except">qh_setequal_except</a>
-return 1 if two sorted sets are equal except for
-an element </li>
-<li><a href="qset.c#setequal_skip">qh_setequal_skip</a>
-return 1 if two sorted sets are equal except for
-a pair of skipped elements </li>
-<li><a href="qset.c#setequal_skip">qh_setequal_skip</a>
-return 1 if two sorted sets are equal except for
-a pair of skipped elements </li>
-<li><a href="qset.c#setin">qh_setin</a> return 1 if an
-element is in a set </li>
-<li><a href="qset.c#setindex">qh_setindex</a> return
-the index of an element in a set </li>
-<li><a href="qset.c#setlast">qh_setlast</a> return
-last element of a set</li>
-<li><a href="qset.c#setsize">qh_setsize</a> returns
-the size of a set </li>
-</ul>
-
-<h3><a href="qh-set.htm#TOC">»</a><a name="sadd">Add functions</a></h3>
-<ul>
-<li><a href="qset.c#setaddnth">qh_setaddnth</a> add a
-element as n'th element of sorted or unsorted set
-</li>
-<li><a href="qset.c#setaddsorted">qh_setaddsorted</a>
-add an element to a sorted set </li>
-<li><a href="qset.c#setappend">qh_setappend</a> append
-an element to a set </li>
-<li><a href="qset.c#setappend_set">qh_setappend_set</a>
-append a set of elements to a set </li>
-<li><a href="qset.c#setappend2ndlast">qh_setappend2ndlast</a>
-add an element as the next to the last element in
-a set </li>
-<li><a href="qset.c#setlarger">qh_setlarger</a> return
-a larger set with the same elements</li>
-<li><a href="qset.c#setreplace">qh_setreplace</a>
-replace one element with another in a set</li>
-<li><a href="qset.c#setunique">qh_setunique</a> add an
-element if it is not already in a set </li>
-</ul>
-
-<h3><a href="qh-set.htm#TOC">»</a><a name="scheck">Check and print functions</a></h3>
-<ul>
-<li><a href="qset.c#setcheck">qh_setcheck</a> check a
-set for validity </li>
-<li><a href="qset.c#setprint">qh_setprint</a> print a
-set's elements to fp </li>
-</ul>
-
-<h3><a href="qh-set.htm#TOC">»</a><a name="scopy">Copy, compact, and zero functions</a></h3>
-<ul>
-<li><a href="qset.c#setcompact">qh_setcompact</a>
-compact NULLs from an unsorted set </li>
-<li><a href="qset.c#setcopy">qh_setcopy</a> make a
-copy of a sorted or unsorted set </li>
-<li><a href="qset.c#setduplicate">qh_setduplicate</a>
-duplicate a set and its elements </li>
-<li><a href="qset.c#settruncate">qh_settruncate</a>
-truncate a set to size elements </li>
-<li><a href="qset.c#setzero">qh_setzero</a> zero the
-remainder of a set </li>
-</ul>
-
-<h3><a href="qh-set.htm#TOC">»</a><a name="sdel">Delete functions</a></h3>
-<ul>
-<li><a href="qset.c#setdel">qh_setdel</a> delete an
-element from an unsorted set. </li>
-<li><a href="qset.c#setdellast">qh_setdellast</a>
-delete and return last element from a set</li>
-<li><a href="qset.c#setdelnth">qh_setdelnth</a> delete
-and return nth element from an unsorted set </li>
-<li><a href="qset.c#setdelnthsorted">qh_setdelnthsorted</a>
-delete and return nth element from a sorted set </li>
-<li><a href="qset.c#setdelsorted">qh_setdelsorted</a>
-delete an element from a sorted set </li>
-<li><a href="qset.c#setnew_delnthsorted">qh_setnew_delnthsorted</a>
-create a sorted set not containing the nth
-element </li>
-</ul>
-
-<h3><a href="qh-set.htm#TOC">»</a><a name="stemp">Temporary set functions</a></h3>
-<ul>
-<li><a href="qset.c#settemp">qh_settemp</a> return a
-temporary set and append it qhmem.tempstack</li>
-<li><a href="qset.c#settempfree">qh_settempfree</a>
-free and pop a set from qhmem.tempstack</li>
-<li><a href="qset.c#settempfree_all">qh_settempfree_all</a>
-free all sets in qhmem.tempstack </li>
-<li><a href="qset.c#settemppop">qh_settemppop</a> pop
-a set from qhmem.tempstack (makes it permanent) </li>
-<li><a href="qset.c#settemppush">qh_settemppush</a>
-push a set unto qhmem.tempstack (makes it
-temporary) </li>
-</ul>
-
-<p><!-- Navigation links --> </p>
-<hr>
-<p><b>Up:</b>
-<a href="http://www.qhull.org">Home page for
-Qhull</a> <br>
-<b>Up:</b> <a href="../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
-<b>Up:</b> <a href="../html/qh-quick.htm#programs">Programs</a>
-• <a href="../html/qh-quick.htm#options">Options</a>
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-• <a href="../html/qh-optf.htm#format">Formats</a>
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-• <a href="../html/qh-optp.htm#print">Print</a>
-• <a href="../html/qh-optq.htm#qhull">Qhull</a>
-• <a href="../html/qh-optc.htm#prec">Precision</a>
-• <a href="../html/qh-optt.htm#trace">Trace</a><br>
-<b>Up:</b> <a href="../html/qh-in.htm#TOC">Qhull internals: Table of Contents</a> <br>
-<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
-<b>To:</b> <a href="qh-geom.htm">Geom</a> •
-<a href="qh-globa.htm">Global</a> • <a href="qh-io.htm">Io</a>
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-• <a href="qh-poly.htm">Poly</a> • <a href="qh-qhull.htm#TOC">Qhull</a>
-• <a href="qh-set.htm">Set</a> • <a href="qh-stat.htm">Stat</a>
-• <a href="qh-user.htm">User</a><br>
-</p>
-<p><!-- GC common information --> </p>
-<hr>
-<p><a href="http://www.geom.uiuc.edu/"><img
-src="../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
-Geometry Center Home Page </i></p>
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qh-stat.htm b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qh-stat.htm
deleted file mode 100644
index ec5fb115a6465eec02e755db22c063888a504bbd..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qh-stat.htm
+++ /dev/null
@@ -1,161 +0,0 @@
-<!-- Do not edit with Front Page, it adds too many spaces -->
-<html>
-<head>
-<meta http-equiv="Content-Type"
-content="text/html; charset=iso-8859-1">
-<title>stat.c -- statistical operations</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<p><a name="TOP"><b>Up:</b></a> <a
-href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
-<b>Up:</b> <a href="../html/qh-quick.htm#programs">Programs</a>
-• <a href="../html/qh-quick.htm#options">Options</a>
-• <a href="../html/qh-opto.htm#output">Output</a>
-• <a href="../html/qh-optf.htm#format">Formats</a>
-• <a href="../html/qh-optg.htm#geomview">Geomview</a>
-• <a href="../html/qh-optp.htm#print">Print</a>
-• <a href="../html/qh-optq.htm#qhull">Qhull</a>
-• <a href="../html/qh-optc.htm#prec">Precision</a>
-• <a href="../html/qh-optt.htm#trace">Trace</a><br>
-<b>Up:</b> <a href="../html/qh-in.htm#TOC">Qhull internals: Table of Contents</a><br>
-<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
-<b>To:</b> <a href="qh-geom.htm">Geom</a> • <a href="qh-globa.htm">Global</a>
-• <a href="qh-io.htm">Io</a> • <a href="qh-mem.htm">Mem</a>
-• <a href="qh-merge.htm">Merge</a> • <a href="qh-poly.htm">Poly</a>
-• <a href="qh-qhull.htm">Qhull</a> • <a href="qh-set.htm">Set</a>
-• <a href="qh-stat.htm#TOC">Stat</a> • <a href="qh-user.htm">User</a>
-</p>
-<hr>
-
-<h2>stat.c -- statistical operations</h2>
-<blockquote>
-<p>Qhull records many statistics. These functions and
-macros make it inexpensive to add a statistic.
-<p>As with Qhull's global variables, the statistics data structure is
-accessed by a macro, 'qhstat'. If qh_QHpointer is defined, the macro
-is 'qh_qhstat->', otherwise the macro is 'qh_qhstat.'.
-Statistics
-may be turned off in user.h. If so, all but the 'zz'
-statistics are ignored.</p>
-</blockquote>
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-<hr>
-<p><a href="#TOP">»</a> <a href="qh-geom.htm#TOC">Geom</a>
-<a name="TOC">•</a> <a href="qh-globa.htm#TOC">Global</a>
-• <a href="qh-io.htm#TOC">Io</a> • <a href="qh-mem.htm#TOC">Mem</a>
-• <a href="qh-merge.htm#TOC">Merge</a> • <a href="qh-poly.htm#TOC">Poly</a>
-• <a href="qh-qhull.htm#TOC">Qhull</a> • <a href="qh-set.htm#TOC">Set</a>
-• <b>Stat</b> • <a href="qh-user.htm#TOC">User</a>
-</p>
-<h3>Index to <a href="stat.c">stat.c</a> and
-<a href="stat.h">stat.h</a></h3>
-<ul>
-<li><a href="#ttype">stat.h types</a> </li>
-<li><a href="#tconst">stat.h constants</a> </li>
-<li><a href="#tmacro">stat.h macros</a> </li>
-<li><a href="#tfunc">stat.c functions</a> </li>
-</ul>
-
-<h3><a href="qh-stat.htm#TOC">»</a><a name="ttype">stat.h types</a></h3>
-<ul>
-<li><a href="stat.h#intrealT">intrealT</a> union of
-integer and real</li>
-<li><a href="stat.h#qhstat">qhstat</a> global data
-structure for statistics </li>
-</ul>
-<h3><a href="qh-stat.htm#TOC">»</a><a name="tconst">stat.h
-constants</a></h3>
-<ul>
-<li><a href="stat.h#KEEPstatistics">qh_KEEPstatistics</a> 0 turns off most statistics</li>
-<li><a href="stat.h#statistics">Z..., W...</a> integer (Z) and real (W) statistics
-</li>
-<li><a href="stat.h#ZZstat">ZZstat</a> Z.../W... statistics that
-remain defined if qh_KEEPstatistics=0
-</li>
-<li><a href="stat.h#ztype">ztype</a> zdoc, zinc, etc.
-for definining statistics </li>
-</ul>
-<h3><a href="qh-stat.htm#TOC">»</a><a name="tmacro">stat.h macros</a></h3>
-<ul>
-<li><a href="stat.h#MAYdebugx">MAYdebugx</a> called
-frequently for error trapping </li>
-<li><a href="stat.h#zadd_">zadd_/wadd_</a> add value
-to an integer or real statistic </li>
-<li><a href="stat.h#zdef_">zdef_</a> define a
-statistic </li>
-<li><a href="stat.h#zinc_">zinc_</a> increment an
-integer statistic </li>
-<li><a href="stat.h#zmax_">zmax_/wmax_</a> update
-integer or real maximum statistic </li>
-<li><a href="stat.h#zmin_">zmin_/wmin_</a> update
-integer or real minimum statistic </li>
-<li><a href="stat.h#zval_">zval_/wval_</a> set or
-return value of a statistic </li>
-</ul>
-
-<h3><a href="qh-stat.htm#TOC">»</a><a name="tfunc">stat.c
-functions</a></h3>
-<ul>
-<li><a href="stat.c#allstatA">qh_allstatA</a> define
-statistics in groups of 20 </li>
-<li><a href="stat.c#allstatistics">qh_allstatistics</a>
-reset printed flag for all statistics </li>
-<li><a href="stat.c#collectstatistics">qh_collectstatistics</a>
-collect statistics for qh.facet_list </li>
-<li><a href="stat.c#freestatistics">qh_freestatistics</a>
-free memory used for statistics </li>
-<li><a href="stat.c#initstatistics">qh_initstatistics</a>
-allocate and initialize statistics </li>
-<li><a href="stat.c#newstats">qh_newstats</a> returns
-True if statistics for zdoc </li>
-<li><a href="stat.c#nostatistic">qh_nostatistic</a>
-true if no statistic to print </li>
-<li><a href="stat.c#printallstatistics">qh_printallstatistics</a>
-print all statistics </li>
-<li><a href="stat.c#printstatistics">qh_printstatistics</a>
-print statistics to a file </li>
-<li><a href="stat.c#printstatlevel">qh_printstatlevel</a>
-print level information for a statistic </li>
-<li><a href="stat.c#printstats">qh_printstats</a>
-print statistics for a zdoc group </li>
-<li><a href="stat.c#stddev">qh_stddev</a> compute the
-standard deviation and average from statistics </li>
-</ul>
-
-<p><!-- Navigation links --> </p>
-<hr>
-<p><b>Up:</b>
-<a href="http://www.qhull.org">Home page for
-Qhull</a> <br>
-<b>Up:</b> <a href="../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
-<b>Up:</b> <a href="../html/qh-quick.htm#programs">Programs</a>
-• <a href="../html/qh-quick.htm#options">Options</a>
-• <a href="../html/qh-opto.htm#output">Output</a>
-• <a href="../html/qh-optf.htm#format">Formats</a>
-• <a href="../html/qh-optg.htm#geomview">Geomview</a>
-• <a href="../html/qh-optp.htm#print">Print</a>
-• <a href="../html/qh-optq.htm#qhull">Qhull</a>
-• <a href="../html/qh-optc.htm#prec">Precision</a>
-• <a href="../html/qh-optt.htm#trace">Trace</a><br>
-<b>Up:</b> <a href="../html/qh-in.htm#TOC">Qhull internals: Table of Contents</a> <br>
-<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
-<b>To:</b> <a href="qh-geom.htm">Geom</a> •
-<a href="qh-globa.htm">Global</a> • <a href="qh-io.htm">Io</a>
-• <a href="qh-mem.htm">Mem</a> • <a href="qh-merge.htm">Merge</a>
-• <a href="qh-poly.htm">Poly</a> • <a href="qh-qhull.htm#TOC">Qhull</a>
-• <a href="qh-set.htm">Set</a> • <a href="qh-stat.htm">Stat</a>
-• <a href="qh-user.htm">User</a><br>
-</p>
-<p><!-- GC common information --> </p>
-<hr>
-<p><a href="http://www.geom.uiuc.edu/"><img
-src="../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
-Geometry Center Home Page </i></p>
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qh-user.htm b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qh-user.htm
deleted file mode 100644
index 4c92321719957adc0b0c508fd3cccc076e95c86c..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qh-user.htm
+++ /dev/null
@@ -1,234 +0,0 @@
-<!-- Do not edit with Front Page, it adds too many spaces -->
-<html>
-<head>
-<meta http-equiv="Content-Type"
-content="text/html; charset=iso-8859-1">
-<title>user.c -- user-definable operations</title>
-</head>
-
-<body>
-<!-- Navigation links -->
-<p><a name="TOP"><b>Up:</b></a> <a
-href="http://www.qhull.org">Home page</a> for Qhull<br>
-<b>Up:</b> <a href="../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br>
-<b>Up:</b> <a href="../html/qh-quick.htm#programs">Programs</a>
-• <a href="../html/qh-quick.htm#options">Options</a>
-• <a href="../html/qh-opto.htm#output">Output</a>
-• <a href="../html/qh-optf.htm#format">Formats</a>
-• <a href="../html/qh-optg.htm#geomview">Geomview</a>
-• <a href="../html/qh-optp.htm#print">Print</a>
-• <a href="../html/qh-optq.htm#qhull">Qhull</a>
-• <a href="../html/qh-optc.htm#prec">Precision</a>
-• <a href="../html/qh-optt.htm#trace">Trace</a><br>
-<b>Up:</b> <a href="../html/qh-in.htm#TOC">Qhull internals: Table of Contents</a><br>
-<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
-<b>To:</b> <a href="qh-geom.htm">Geom</a> • <a href="qh-globa.htm">Global</a>
-• <a href="qh-io.htm">Io</a> • <a href="qh-mem.htm">Mem</a>
-• <a href="qh-merge.htm">Merge</a> • <a href="qh-poly.htm">Poly</a>
-• <a href="qh-qhull.htm">Qhull</a> • <a href="qh-set.htm">Set</a>
-• <a href="qh-stat.htm">Stat</a> • <a href="qh-user.htm#TOC">User</a>
-</p>
-<hr>
-<h2>user.c -- user-definable operations</h2>
-<blockquote>
-<p>This section contains functions and constants that the
-user may want to change. </p>
-
-</blockquote>
-<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
-<hr>
-<p><a href="#TOP">»</a> <a href="qh-geom.htm#TOC">Geom</a>
-<a name="TOC">•</a> <a href="qh-globa.htm#TOC">Global</a>
-• <a href="qh-io.htm#TOC">Io</a> • <a href="qh-mem.htm#TOC">Mem</a>
-• <a href="qh-merge.htm#TOC">Merge</a> • <a href="qh-poly.htm#TOC">Poly</a>
-• <a href="qh-qhull.htm#TOC">Qhull</a> • <a href="qh-set.htm#TOC">Set</a>
-• <a href="qh-stat.htm#TOC">Stat</a> • <b>User</b>
-</p>
-<h3>Index to <a href="user.c">user.c</a> and
-<a href="user.h">user.h</a></h3>
-<ul>
-<li><a href="#utype">user.h data types and
-configuration macros</a> </li>
-<li><a href="#ujoggle">joggle constants</a></li>
-<li><a href="#uperform">performance related constants</a></li>
-<li><a href="#umemory">memory constants</a></li>
-<li><a href="#ucond">conditional compilation</a></li>
-<li><a href="#umerge">merge constants</a> </li>
-<li><a href="#ufunc">user.c functions</a> </li>
-</ul>
-<h3><a href="qh-user.htm#TOC">»</a><a name="utype">user.h data
-types and configuration macros</a></h3>
-<ul>
-<li><a href="user.h#realT">realT, qh_REAL...</a> size
-of floating point numbers </li>
-<li><a href="user.h#CPUclock">qh_CPUclock</a> clock()
-function for reporting the total time spent by
-Qhull </li>
-<li><a href="user.h#RANDOM">qh_RANDOM...</a> random
-number generator </li>
-</ul>
-
-<h3><a href="qh-user.htm#TOC">»</a><a name="udef">definition constants</a></h3>
-<ul>
-<li><a href="user.h#DEFAULTbox">qh_DEFAULTbox</a>
-define default box size for rbox, 'Qbb', and 'QbB' (Geomview expects 0.5) </li>
-<li><a href="user.h#INFINITE">qh_INFINITE</a> on
-output, indicates Voronoi center at infinity </li>
-<li><a href="user.h#ORIENTclock">qh_ORIENTclock</a>
-define convention for orienting facets</li>
-<li><a href="user.h#ZEROdelaunay">qh_ZEROdelaunay</a>
-define facets that are ignored in Delaunay triangulations</li>
-</ul>
-
-<h3><a href="qh-user.htm#TOC">»</a><a name="ujoggle">joggle constants</a></h3>
-<ul>
-<li><a href="user.h#JOGGLEagain">qh_JOGGLEagain</a>
-how often to retry before using qh_JOGGLEmaxincrease
-again </li>
-<li><a href="user.h#JOGGLEdefault">qh_JOGGLEdefault</a>
-default value for qh.JOGGLEmax for 'QP' </li>
-<li><a href="user.h#JOGGLEincrease">qh_JOGGLEincrease</a>
-factor to increase qh.JOGGLEmax on retrys for
-'QPn' </li>
-<li><a href="user.h#JOGGLEmaxincrease">qh_JOGGLEmaxincrease</a> max
-for increasing qh.JOGGLEmax relative to
-qh.MAXwidth </li>
-<li><a href="user.h#JOGGLEretry">qh_JOGGLEmaxretry</a>
-report error if this many retries </li>
-<li><a href="user.h#JOGGLEretry">qh_JOGGLEretry</a>
-how often to retry before using qh_JOGGLEmax </li>
-</ul>
-
-<h3><a href="qh-user.htm#TOC">»</a><a name="uperform">performance
-related constants</a></h3>
-<ul>
-<li><a href="user.h#HASHfactor">qh_HASHfactor</a>
-total/used hash slots </li>
-<li><a href="user.h#INITIALmax">qh_INITIALmax</a> if
-dim >= qh_INITIALmax, use min/max coordinate
-points for initial simplex </li>
-<li><a href="user.h#INITIALsearch">qh_INITIALsearch</a>
-if qh.INITIALmax, search points up to this
-dimension </li>
-<li><a href="user.h#NOtrace">qh_NOtrace</a> disallow
-tracing </li>
-<li><a href="user.h#VERIFYdirect">qh_VERIFYdirect</a>
-'Tv' verifies all <em>points X facets</em> if op
-count is smaller </li>
-</ul>
-
-<h3><a href="qh-user.htm#TOC">»</a><a name="umemory">memory constants</a></h3>
-<ul>
-<li><a href="user.h#MEMalign">qh_MEMalign</a> memory
-alignment for qh_meminitbuffers() in global.c </li>
-<li><a href="user.h#MEMbufsize">qh_MEMbufsize</a>
-size of additional memory buffers </li>
-<li><a href="user.h#MEMinitbuf">qh_MEMinitbuf</a>
-size of initial memory buffer </li>
-</ul>
-
-<h3><a href="qh-user.htm#TOC">»</a><a name="ucond">conditional compilation</a></h3>
-<ul>
-<li><a href="user.h#compiler">compiler</a> defined symbols,
-e.g., _STDC_ and _cplusplus
-
-<li><a href="user.h#COMPUTEfurthest">qh_COMPUTEfurthest</a>
- compute furthest distance to an outside point instead of storing it with the facet
-<li><a href="user.h#KEEPstatistics">qh_KEEPstatistics</a>
- enable statistic gathering and reporting with option 'Ts'
-<li><a href="user.h#MAXoutside">qh_MAXoutside</a>
-record outer plane for each facet
-<li><a href="user.h#NOmerge">qh_NOmerge</a>
-disable facet merging
-<li><a href="user.h#NOtrace">qh_NOtrace</a>
-disable tracing with option 'T4'
-<li><a href="user.h#QHpointer">qh_QHpointer</a>
-access global data with pointer or static structure
-<li><a href="user.h#QUICKhelp">qh_QUICKhelp</a>
-use abbreviated help messages, e.g., for degenerate inputs
-</ul>
-
-<h3><a href="qh-user.htm#TOC">»</a><a name="umerge">merge
-constants</a></h3>
-<ul>
-<li><a href="user.h#BESTcentrum">qh_BESTcentrum</a>
-when does qh_findbestneighbor() test centrums? </li>
-<li><a href="user.h#BESTnonconvex">qh_BESTnonconvex</a>
-when does qh_findbestneighbor() test nonconvex
-ridges only? </li>
-<li><a href="user.h#COPLANARratio">qh_COPLANARratio</a>
-what is qh.MINvisible? </li>
-<li><a href="user.h#DIMreduceBuild">qh_DIMreduceBuild</a>
-max dimension for vertex reduction </li>
-<li><a href="user.h#DIMmergeVertex">qh_DIMmergeVertex</a>
-max dimension for vertex merging </li>
-<li><a href="user.h#DISToutside">qh_DISToutside</a>
-when is a point clearly outside of a facet for qh_findbestnew and qh_partitionall</li>
-<li><a href="user.h#MAXnarrow">qh_MAXnarrow</a> max.
-cosine for qh.NARROWhull </li>
-<li><a href="user.h#MAXnewcentrum">qh_MAXnewcentrum</a>
-when does qh_reducevertices_centrum() reset the
-centrum? </li>
-<li><a href="user.h#MAXnewmerges">qh_MAXnewmerges</a>
-when does qh_merge_nonconvex() call
-qh_reducevertices_centrums? </li>
-<li><a href="user.h#RATIOnearinside">qh_RATIOnearinside</a>
-ratio for retaining inside points for
-qh_check_maxout() </li>
-<li><a href="user.h#SEARCHdist">qh_SEARCHdist</a>
-when is facet coplanar with the best facet for qh_findbesthorizon</li>
-<li><a href="user.h#USEfindbestnew">qh_USEfindbestnew</a>
-when to use qh_findbestnew for qh_partitionpoint()</li>
-<li><a href="user.h#WIDEcoplanar">qh_WIDEcoplanar</a>
-what is a WIDEfacet? </li>
-<li><a href="user.h#WARNnarrow">qh_WARNnarrow</a>
-max. cosine to warn about qh.NARROWhull </li>
-</ul>
-
-<h3><a href="qh-user.htm#TOC">»</a><a name="ufunc">user.c
-functions</a></h3>
-<ul>
-<li><a href="user.c#errexit">qh_errexit</a> report
-error and exit qhull()</li>
-<li><a href="user.c#errprint">qh_errprint</a> print
-information about facets and ridges </li>
-<li><a href="user.c#new_qhull">qh_new_qhull</a> call qhull on an array
-of points</li>
-<li><a href="user.c#printfacetlist">qh_printfacetlist</a>
-print all fields of all facets </li>
-</ul>
-
-<p><!-- Navigation links --> </p>
-<hr>
-<p><b>Up:</b>
-<a href="http://www.qhull.org">Home page for
-Qhull</a> <br>
-<b>Up:</b> <a href="../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br>
-<b>Up:</b> <a href="../html/qh-quick.htm#programs">Programs</a>
-• <a href="../html/qh-quick.htm#options">Options</a>
-• <a href="../html/qh-opto.htm#output">Output</a>
-• <a href="../html/qh-optf.htm#format">Formats</a>
-• <a href="../html/qh-optg.htm#geomview">Geomview</a>
-• <a href="../html/qh-optp.htm#print">Print</a>
-• <a href="../html/qh-optq.htm#qhull">Qhull</a>
-• <a href="../html/qh-optc.htm#prec">Precision</a>
-• <a href="../html/qh-optt.htm#trace">Trace</a><br>
-<b>Up:</b> <a href="../html/qh-in.htm#TOC">Qhull internals: Table of Contents</a> <br>
-<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br>
-<b>To:</b> <a href="qh-geom.htm">Geom</a> •
-<a href="qh-globa.htm">Global</a> • <a href="qh-io.htm">Io</a>
-• <a href="qh-mem.htm">Mem</a> • <a href="qh-merge.htm">Merge</a>
-• <a href="qh-poly.htm">Poly</a> • <a href="qh-qhull.htm#TOC">Qhull</a>
-• <a href="qh-set.htm">Set</a> • <a href="qh-stat.htm">Stat</a>
-• <a href="qh-user.htm">User</a><br>
-</p>
-<p><!-- GC common information --> </p>
-<hr>
-<p><a href="http://www.geom.uiuc.edu/"><img
-src="../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The
-Geometry Center Home Page </i></p>
-<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a>
-</a><br>
-Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
-</body>
-</html>
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qhull.c b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qhull.c
deleted file mode 100644
index 55a152103227f4827db814905e7275f68ae0b92d..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qhull.c
+++ /dev/null
@@ -1,1396 +0,0 @@
-/*<html><pre> -<a href="qh-qhull.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- qhull.c
- Quickhull algorithm for convex hulls
-
- qhull() and top-level routines
-
- see qh-qhull.htm, qhull.h, unix.c
-
- see qhull_a.h for internal functions
-
- copyright (c) 1993-2003 The Geometry Center
-*/
-
-#include "qhull_a.h"
-
-/*============= functions in alphabetic order after qhull() =======*/
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="qhull">-</a>
-
- qh_qhull()
- compute DIM3 convex hull of qh.num_points starting at qh.first_point
- qh contains all global options and variables
-
- returns:
- returns polyhedron
- qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices,
-
- returns global variables
- qh.hulltime, qh.max_outside, qh.interior_point, qh.max_vertex, qh.min_vertex
-
- returns precision constants
- qh.ANGLEround, centrum_radius, cos_max, DISTround, MAXabs_coord, ONEmerge
-
- notes:
- unless needed for output
- qh.max_vertex and qh.min_vertex are max/min due to merges
-
- see:
- to add individual points to either qh.num_points
- use qh_addpoint()
-
- if qh.GETarea
- qh_produceoutput() returns qh.totarea and qh.totvol via qh_getarea()
-
- design:
- record starting time
- initialize hull and partition points
- build convex hull
- unless early termination
- update facet->maxoutside for vertices, coplanar, and near-inside points
- error if temporary sets exist
- record end time
-*/
-
-void qh_qhull (void) {
- int numoutside;
-
- qh hulltime= qh_CPUclock;
- if (qh RERUN || qh JOGGLEmax < REALmax/2)
- qh_build_withrestart();
- else {
- qh_initbuild();
- qh_buildhull();
- }
- if (!qh STOPpoint && !qh STOPcone) {
- if (qh ZEROall_ok && !qh TESTvneighbors && qh MERGEexact)
- qh_checkzero( qh_ALL);
- if (qh ZEROall_ok && !qh TESTvneighbors && !qh WAScoplanar) {
- trace2((qh ferr, "qh_qhull: all facets are clearly convex and no coplanar points. Post-merging and check of maxout not needed.\n"));
- qh DOcheckmax= False;
- }else {
- if (qh MERGEexact || (qh hull_dim > qh_DIMreduceBuild && qh PREmerge))
- qh_postmerge ("First post-merge", qh premerge_centrum, qh premerge_cos,
- (qh POSTmerge ? False : qh TESTvneighbors));
- else if (!qh POSTmerge && qh TESTvneighbors)
- qh_postmerge ("For testing vertex neighbors", qh premerge_centrum,
- qh premerge_cos, True);
- if (qh POSTmerge)
- qh_postmerge ("For post-merging", qh postmerge_centrum,
- qh postmerge_cos, qh TESTvneighbors);
- if (qh visible_list == qh facet_list) { /* i.e., merging done */
- qh findbestnew= True;
- qh_partitionvisible (/*visible_list, newfacet_list*/ !qh_ALL, &numoutside);
- qh findbestnew= False;
- qh_deletevisible (/*qh visible_list*/);
- qh_resetlists (False, qh_RESETvisible /*qh visible_list newvertex_list newfacet_list */);
- }
- }
- if (qh DOcheckmax){
- if (qh REPORTfreq) {
- qh_buildtracing (NULL, NULL);
- fprintf (qh ferr, "\nTesting all coplanar points.\n");
- }
- qh_check_maxout();
- }
- if (qh KEEPnearinside && !qh maxoutdone)
- qh_nearcoplanar();
- }
- if (qh_setsize ((setT*)qhmem.tempstack) != 0) {
- fprintf (qh ferr, "qhull internal error (qh_qhull): temporary sets not empty (%d)\n",
- qh_setsize ((setT*)qhmem.tempstack));
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- qh hulltime= qh_CPUclock - qh hulltime;
- qh QHULLfinished= True;
- trace1((qh ferr, "qh_qhull: algorithm completed\n"));
-} /* qhull */
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="addpoint">-</a>
-
- qh_addpoint( furthest, facet, checkdist )
- add point (usually furthest point) above facet to hull
- if checkdist,
- check that point is above facet.
- if point is not outside of the hull, uses qh_partitioncoplanar()
- assumes that facet is defined by qh_findbestfacet()
- else if facet specified,
- assumes that point is above facet (major damage if below)
- for Delaunay triangulations,
- Use qh_setdelaunay() to lift point to paraboloid and scale by 'Qbb' if needed
- Do not use options 'Qbk', 'QBk', or 'QbB' since they scale the coordinates.
-
- returns:
- returns False if user requested an early termination
- qh.visible_list, newfacet_list, delvertex_list, NEWfacets may be defined
- updates qh.facet_list, qh.num_facets, qh.vertex_list, qh.num_vertices
- clear qh.maxoutdone (will need to call qh_check_maxout() for facet->maxoutside)
- if unknown point, adds a pointer to qh.other_points
- do not deallocate the point's coordinates
-
- notes:
- assumes point is near its best facet and not at a local minimum of a lens
- distributions. Use qh_findbestfacet to avoid this case.
- uses qh.visible_list, qh.newfacet_list, qh.delvertex_list, qh.NEWfacets
-
- see also:
- qh_triangulate() -- triangulate non-simplicial facets
-
- design:
- check point in qh.first_point/.num_points
- if checkdist
- if point not above facet
- partition coplanar point
- exit
- exit if pre STOPpoint requested
- find horizon and visible facets for point
- make new facets for point to horizon
- make hyperplanes for point
- compute balance statistics
- match neighboring new facets
- update vertex neighbors and delete interior vertices
- exit if STOPcone requested
- merge non-convex new facets
- if merge found, many merges, or 'Qf'
- use qh_findbestnew() instead of qh_findbest()
- partition outside points from visible facets
- delete visible facets
- check polyhedron if requested
- exit if post STOPpoint requested
- reset working lists of facets and vertices
-*/
-boolT qh_addpoint (pointT *furthest, facetT *facet, boolT checkdist) {
- int goodvisible, goodhorizon;
- vertexT *vertex;
- facetT *newfacet;
- realT dist, newbalance, pbalance;
- boolT isoutside= False;
- int numpart, numpoints, numnew, firstnew;
-
- qh maxoutdone= False;
- if (qh_pointid (furthest) == -1)
- qh_setappend (&qh other_points, furthest);
- if (!facet) {
- fprintf (qh ferr, "qh_addpoint: NULL facet. Need to call qh_findbestfacet first\n");
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- if (checkdist) {
- facet= qh_findbest (furthest, facet, !qh_ALL, !qh_ISnewfacets, !qh_NOupper,
- &dist, &isoutside, &numpart);
- zzadd_(Zpartition, numpart);
- if (!isoutside) {
- zinc_(Znotmax); /* last point of outsideset is no longer furthest. */
- facet->notfurthest= True;
- qh_partitioncoplanar (furthest, facet, &dist);
- return True;
- }
- }
- qh_buildtracing (furthest, facet);
- if (qh STOPpoint < 0 && qh furthest_id == -qh STOPpoint-1) {
- facet->notfurthest= True;
- return False;
- }
- qh_findhorizon (furthest, facet, &goodvisible, &goodhorizon);
- if (qh ONLYgood && !(goodvisible+goodhorizon) && !qh GOODclosest) {
- zinc_(Znotgood);
- facet->notfurthest= True;
- /* last point of outsideset is no longer furthest. This is ok
- since all points of the outside are likely to be bad */
- qh_resetlists (False, qh_RESETvisible /*qh visible_list newvertex_list newfacet_list */);
- return True;
- }
- zzinc_(Zprocessed);
- firstnew= qh facet_id;
- vertex= qh_makenewfacets (furthest /*visible_list, attaches if !ONLYgood */);
- qh_makenewplanes (/* newfacet_list */);
- numnew= qh facet_id - firstnew;
- newbalance= numnew - (realT) (qh num_facets-qh num_visible)
- * qh hull_dim/qh num_vertices;
- wadd_(Wnewbalance, newbalance);
- wadd_(Wnewbalance2, newbalance * newbalance);
- if (qh ONLYgood
- && !qh_findgood (qh newfacet_list, goodhorizon) && !qh GOODclosest) {
- FORALLnew_facets
- qh_delfacet (newfacet);
- qh_delvertex (vertex);
- qh_resetlists (True, qh_RESETvisible /*qh visible_list newvertex_list newfacet_list */);
- zinc_(Znotgoodnew);
- facet->notfurthest= True;
- return True;
- }
- if (qh ONLYgood)
- qh_attachnewfacets(/*visible_list*/);
- qh_matchnewfacets();
- qh_updatevertices();
- if (qh STOPcone && qh furthest_id == qh STOPcone-1) {
- facet->notfurthest= True;
- return False; /* visible_list etc. still defined */
- }
- qh findbestnew= False;
- if (qh PREmerge || qh MERGEexact) {
- qh_premerge (vertex, qh premerge_centrum, qh premerge_cos);
- if (qh_USEfindbestnew)
- qh findbestnew= True;
- else {
- FORALLnew_facets {
- if (!newfacet->simplicial) {
- qh findbestnew= True; /* use qh_findbestnew instead of qh_findbest*/
- break;
- }
- }
- }
- }else if (qh BESToutside)
- qh findbestnew= True;
- qh_partitionvisible (/*visible_list, newfacet_list*/ !qh_ALL, &numpoints);
- qh findbestnew= False;
- qh findbest_notsharp= False;
- zinc_(Zpbalance);
- pbalance= numpoints - (realT) qh hull_dim /* assumes all points extreme */
- * (qh num_points - qh num_vertices)/qh num_vertices;
- wadd_(Wpbalance, pbalance);
- wadd_(Wpbalance2, pbalance * pbalance);
- qh_deletevisible (/*qh visible_list*/);
- zmax_(Zmaxvertex, qh num_vertices);
- qh NEWfacets= False;
- if (qh IStracing >= 4) {
- if (qh num_facets < 2000)
- qh_printlists();
- qh_printfacetlist (qh newfacet_list, NULL, True);
- qh_checkpolygon (qh facet_list);
- }else if (qh CHECKfrequently) {
- if (qh num_facets < 50)
- qh_checkpolygon (qh facet_list);
- else
- qh_checkpolygon (qh newfacet_list);
- }
- if (qh STOPpoint > 0 && qh furthest_id == qh STOPpoint-1)
- return False;
- qh_resetlists (True, qh_RESETvisible /*qh visible_list newvertex_list newfacet_list */);
- /* qh_triangulate(); to test qh.TRInormals */
- trace2((qh ferr, "qh_addpoint: added p%d new facets %d new balance %2.2g point balance %2.2g\n",
- qh_pointid (furthest), numnew, newbalance, pbalance));
- return True;
-} /* addpoint */
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="build_withrestart">-</a>
-
- qh_build_withrestart()
- allow restarts due to qh.JOGGLEmax while calling qh_buildhull()
- qh.FIRSTpoint/qh.NUMpoints is point array
- it may be moved by qh_joggleinput()
-*/
-void qh_build_withrestart (void) {
- int restart;
-
- qh ALLOWrestart= True;
- while (True) {
- restart= setjmp (qh restartexit); /* simple statement for CRAY J916 */
- if (restart) { /* only from qh_precision() */
- zzinc_(Zretry);
- wmax_(Wretrymax, qh JOGGLEmax);
- qh ERREXITcalled= False;
- qh STOPcone= True; /* if break, prevents normal output */
- }
- if (!qh RERUN && qh JOGGLEmax < REALmax/2) {
- if (qh build_cnt > qh_JOGGLEmaxretry) {
- fprintf(qh ferr, "\n\
-qhull precision error: %d attempts to construct a convex hull\n\
- with joggled input. Increase joggle above 'QJ%2.2g'\n\
- or modify qh_JOGGLE... parameters in user.h\n",
- qh build_cnt, qh JOGGLEmax);
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- if (qh build_cnt && !restart)
- break;
- }else if (qh build_cnt && qh build_cnt >= qh RERUN)
- break;
- qh STOPcone= False;
- qh_freebuild (True); /* first call is a nop */
- qh build_cnt++;
- if (!qh qhull_optionsiz)
- qh qhull_optionsiz= strlen (qh qhull_options);
- else {
- qh qhull_options [qh qhull_optionsiz]= '\0';
- qh qhull_optionlen= 80;
- }
- qh_option("_run", &qh build_cnt, NULL);
- if (qh build_cnt == qh RERUN) {
- qh IStracing= qh TRACElastrun; /* duplicated from qh_initqhull_globals */
- if (qh TRACEpoint != -1 || qh TRACEdist < REALmax/2 || qh TRACEmerge) {
- qh TRACElevel= (qh IStracing? qh IStracing : 3);
- qh IStracing= 0;
- }
- qhmem.IStracing= qh IStracing;
- }
- if (qh JOGGLEmax < REALmax/2)
- qh_joggleinput();
- qh_initbuild();
- qh_buildhull();
- if (qh JOGGLEmax < REALmax/2 && !qh MERGING)
- qh_checkconvex (qh facet_list, qh_ALGORITHMfault);
- }
- qh ALLOWrestart= False;
-} /* qh_build_withrestart */
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="buildhull">-</a>
-
- qh_buildhull()
- construct a convex hull by adding outside points one at a time
-
- returns:
-
- notes:
- may be called multiple times
- checks facet and vertex lists for incorrect flags
- to recover from STOPcone, call qh_deletevisible and qh_resetlists
-
- design:
- check visible facet and newfacet flags
- check newlist vertex flags and qh.STOPcone/STOPpoint
- for each facet with a furthest outside point
- add point to facet
- exit if qh.STOPcone or qh.STOPpoint requested
- if qh.NARROWhull for initial simplex
- partition remaining outside points to coplanar sets
-*/
-void qh_buildhull(void) {
- facetT *facet;
- pointT *furthest;
- vertexT *vertex;
- int id;
-
- trace1((qh ferr, "qh_buildhull: start build hull\n"));
- FORALLfacets {
- if (facet->visible || facet->newfacet) {
- fprintf (qh ferr, "qhull internal error (qh_buildhull): visible or new facet f%d in facet list\n",
- facet->id);
- qh_errexit (qh_ERRqhull, facet, NULL);
- }
- }
- FORALLvertices {
- if (vertex->newlist) {
- fprintf (qh ferr, "qhull internal error (qh_buildhull): new vertex f%d in vertex list\n",
- vertex->id);
- qh_errprint ("ERRONEOUS", NULL, NULL, NULL, vertex);
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- id= qh_pointid (vertex->point);
- if ((qh STOPpoint>0 && id == qh STOPpoint-1) ||
- (qh STOPpoint<0 && id == -qh STOPpoint-1) ||
- (qh STOPcone>0 && id == qh STOPcone-1)) {
- trace1((qh ferr,"qh_buildhull: stop point or cone P%d in initial hull\n", id));
- return;
- }
- }
- qh facet_next= qh facet_list; /* advance facet when processed */
- while ((furthest= qh_nextfurthest (&facet))) {
- qh num_outside--; /* if ONLYmax, furthest may not be outside */
- if (!qh_addpoint (furthest, facet, qh ONLYmax))
- break;
- }
- if (qh NARROWhull) /* move points from outsideset to coplanarset */
- qh_outcoplanar( /* facet_list */ );
- if (qh num_outside && !furthest) {
- fprintf (qh ferr, "qhull internal error (qh_buildhull): %d outside points were never processed.\n", qh num_outside);
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }
- trace1((qh ferr, "qh_buildhull: completed the hull construction\n"));
-} /* buildhull */
-
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="buildtracing">-</a>
-
- qh_buildtracing( furthest, facet )
- trace an iteration of qh_buildhull() for furthest point and facet
- if !furthest, prints progress message
-
- returns:
- tracks progress with qh.lastreport
- updates qh.furthest_id (-3 if furthest is NULL)
- also resets visit_id, vertext_visit on wrap around
-
- see:
- qh_tracemerging()
-
- design:
- if !furthest
- print progress message
- exit
- if 'TFn' iteration
- print progress message
- else if tracing
- trace furthest point and facet
- reset qh.visit_id and qh.vertex_visit if overflow may occur
- set qh.furthest_id for tracing
-*/
-void qh_buildtracing (pointT *furthest, facetT *facet) {
- realT dist= 0;
- float cpu;
- int total, furthestid;
- time_t timedata;
- struct tm *tp;
- vertexT *vertex;
-
- qh old_randomdist= qh RANDOMdist;
- qh RANDOMdist= False;
- if (!furthest) {
- time (&timedata);
- tp= localtime (&timedata);
- cpu= qh_CPUclock - qh hulltime;
- cpu /= qh_SECticks;
- total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
- fprintf (qh ferr, "\n\
-At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\
- The current hull contains %d facets and %d vertices. Last point was p%d\n",
- tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh facet_id -1,
- total, qh num_facets, qh num_vertices, qh furthest_id);
- return;
- }
- furthestid= qh_pointid (furthest);
- if (qh TRACEpoint == furthestid) {
- qh IStracing= qh TRACElevel;
- qhmem.IStracing= qh TRACElevel;
- }else if (qh TRACEpoint != -1 && qh TRACEdist < REALmax/2) {
- qh IStracing= 0;
- qhmem.IStracing= 0;
- }
- if (qh REPORTfreq && (qh facet_id-1 > qh lastreport+qh REPORTfreq)) {
- qh lastreport= qh facet_id-1;
- time (&timedata);
- tp= localtime (&timedata);
- cpu= qh_CPUclock - qh hulltime;
- cpu /= qh_SECticks;
- total= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
- zinc_(Zdistio);
- qh_distplane (furthest, facet, &dist);
- fprintf (qh ferr, "\n\
-At %02d:%02d:%02d & %2.5g CPU secs, qhull has created %d facets and merged %d.\n\
- The current hull contains %d facets and %d vertices. There are %d\n\
- outside points. Next is point p%d (v%d), %2.2g above f%d.\n",
- tp->tm_hour, tp->tm_min, tp->tm_sec, cpu, qh facet_id -1,
- total, qh num_facets, qh num_vertices, qh num_outside+1,
- furthestid, qh vertex_id, dist, getid_(facet));
- }else if (qh IStracing >=1) {
- cpu= qh_CPUclock - qh hulltime;
- cpu /= qh_SECticks;
- qh_distplane (furthest, facet, &dist);
- fprintf (qh ferr, "qh_addpoint: add p%d (v%d) to hull of %d facets (%2.2g above f%d) and %d outside at %4.4g CPU secs. Previous was p%d.\n",
- furthestid, qh vertex_id, qh num_facets, dist,
- getid_(facet), qh num_outside+1, cpu, qh furthest_id);
- }
- if (qh visit_id > (unsigned) INT_MAX) {
- qh visit_id= 0;
- FORALLfacets
- facet->visitid= qh visit_id;
- }
- if (qh vertex_visit > (unsigned) INT_MAX) {
- qh vertex_visit= 0;
- FORALLvertices
- vertex->visitid= qh vertex_visit;
- }
- qh furthest_id= furthestid;
- qh RANDOMdist= qh old_randomdist;
-} /* buildtracing */
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="errexit2">-</a>
-
- qh_errexit2( exitcode, facet, otherfacet )
- return exitcode to system after an error
- report two facets
-
- returns:
- assumes exitcode non-zero
-
- see:
- normally use qh_errexit() in user.c (reports a facet and a ridge)
-*/
-void qh_errexit2(int exitcode, facetT *facet, facetT *otherfacet) {
-
- qh_errprint("ERRONEOUS", facet, otherfacet, NULL, NULL);
- qh_errexit (exitcode, NULL, NULL);
-} /* errexit2 */
-
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="findhorizon">-</a>
-
- qh_findhorizon( point, facet, goodvisible, goodhorizon )
- given a visible facet, find the point's horizon and visible facets
- for all facets, !facet-visible
-
- returns:
- returns qh.visible_list/num_visible with all visible facets
- marks visible facets with ->visible
- updates count of good visible and good horizon facets
- updates qh.max_outside, qh.max_vertex, facet->maxoutside
-
- see:
- similar to qh_delpoint()
-
- design:
- move facet to qh.visible_list at end of qh.facet_list
- for all visible facets
- for each unvisited neighbor of a visible facet
- compute distance of point to neighbor
- if point above neighbor
- move neighbor to end of qh.visible_list
- else if point is coplanar with neighbor
- update qh.max_outside, qh.max_vertex, neighbor->maxoutside
- mark neighbor coplanar (will create a samecycle later)
- update horizon statistics
-*/
-void qh_findhorizon(pointT *point, facetT *facet, int *goodvisible, int *goodhorizon) {
- facetT *neighbor, **neighborp, *visible;
- int numhorizon= 0, coplanar= 0;
- realT dist;
-
- trace1((qh ferr,"qh_findhorizon: find horizon for point p%d facet f%d\n",qh_pointid(point),facet->id));
- *goodvisible= *goodhorizon= 0;
- zinc_(Ztotvisible);
- qh_removefacet(facet); /* visible_list at end of qh facet_list */
- qh_appendfacet(facet);
- qh num_visible= 1;
- if (facet->good)
- (*goodvisible)++;
- qh visible_list= facet;
- facet->visible= True;
- facet->f.replace= NULL;
- if (qh IStracing >=4)
- qh_errprint ("visible", facet, NULL, NULL, NULL);
- qh visit_id++;
- FORALLvisible_facets {
- if (visible->tricoplanar && !qh TRInormals) {
- fprintf (qh ferr, "qh_findhorizon: does not work for tricoplanar facets. Use option 'Q11'\n");
- qh_errexit (qh_ERRqhull, visible, NULL);
- }
- visible->visitid= qh visit_id;
- FOREACHneighbor_(visible) {
- if (neighbor->visitid == qh visit_id)
- continue;
- neighbor->visitid= qh visit_id;
- zzinc_(Znumvisibility);
- qh_distplane(point, neighbor, &dist);
- if (dist > qh MINvisible) {
- zinc_(Ztotvisible);
- qh_removefacet(neighbor); /* append to end of qh visible_list */
- qh_appendfacet(neighbor);
- neighbor->visible= True;
- neighbor->f.replace= NULL;
- qh num_visible++;
- if (neighbor->good)
- (*goodvisible)++;
- if (qh IStracing >=4)
- qh_errprint ("visible", neighbor, NULL, NULL, NULL);
- }else {
- if (dist > - qh MAXcoplanar) {
- neighbor->coplanar= True;
- zzinc_(Zcoplanarhorizon);
- qh_precision ("coplanar horizon");
- coplanar++;
- if (qh MERGING) {
- if (dist > 0) {
- maximize_(qh max_outside, dist);
- maximize_(qh max_vertex, dist);
-#if qh_MAXoutside
- maximize_(neighbor->maxoutside, dist);
-#endif
- }else
- minimize_(qh min_vertex, dist); /* due to merge later */
- }
- trace2((qh ferr, "qh_findhorizon: point p%d is coplanar to horizon f%d, dist=%2.7g < qh MINvisible (%2.7g)\n",
- qh_pointid(point), neighbor->id, dist, qh MINvisible));
- }else
- neighbor->coplanar= False;
- zinc_(Ztothorizon);
- numhorizon++;
- if (neighbor->good)
- (*goodhorizon)++;
- if (qh IStracing >=4)
- qh_errprint ("horizon", neighbor, NULL, NULL, NULL);
- }
- }
- }
- if (!numhorizon) {
- qh_precision ("empty horizon");
- fprintf(qh ferr, "qhull precision error (qh_findhorizon): empty horizon\n\
-Point p%d was above all facets.\n", qh_pointid(point));
- qh_printfacetlist (qh facet_list, NULL, True);
- qh_errexit(qh_ERRprec, NULL, NULL);
- }
- trace1((qh ferr, "qh_findhorizon: %d horizon facets (good %d), %d visible (good %d), %d coplanar\n",
- numhorizon, *goodhorizon, qh num_visible, *goodvisible, coplanar));
- if (qh IStracing >= 4 && qh num_facets < 50)
- qh_printlists ();
-} /* findhorizon */
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="nextfurthest">-</a>
-
- qh_nextfurthest( visible )
- returns next furthest point and visible facet for qh_addpoint()
- starts search at qh.facet_next
-
- returns:
- removes furthest point from outside set
- NULL if none available
- advances qh.facet_next over facets with empty outside sets
-
- design:
- for each facet from qh.facet_next
- if empty outside set
- advance qh.facet_next
- else if qh.NARROWhull
- determine furthest outside point
- if furthest point is not outside
- advance qh.facet_next (point will be coplanar)
- remove furthest point from outside set
-*/
-pointT *qh_nextfurthest (facetT **visible) {
- facetT *facet;
- int size, index;
- realT randr, dist;
- pointT *furthest;
-
- while ((facet= qh facet_next) != qh facet_tail) {
- if (!facet->outsideset) {
- qh facet_next= facet->next;
- continue;
- }
- SETreturnsize_(facet->outsideset, size);
- if (!size) {
- qh_setfree (&facet->outsideset);
- qh facet_next= facet->next;
- continue;
- }
- if (qh NARROWhull) {
- if (facet->notfurthest)
- qh_furthestout (facet);
- furthest= (pointT*)qh_setlast (facet->outsideset);
-#if qh_COMPUTEfurthest
- qh_distplane (furthest, facet, &dist);
- zinc_(Zcomputefurthest);
-#else
- dist= facet->furthestdist;
-#endif
- if (dist < qh MINoutside) { /* remainder of outside set is coplanar for qh_outcoplanar */
- qh facet_next= facet->next;
- continue;
- }
- }
- if (!qh RANDOMoutside && !qh VIRTUALmemory) {
- if (qh PICKfurthest) {
- qh_furthestnext (/* qh facet_list */);
- facet= qh facet_next;
- }
- *visible= facet;
- return ((pointT*)qh_setdellast (facet->outsideset));
- }
- if (qh RANDOMoutside) {
- int outcoplanar = 0;
- if (qh NARROWhull) {
- FORALLfacets {
- if (facet == qh facet_next)
- break;
- if (facet->outsideset)
- outcoplanar += qh_setsize( facet->outsideset);
- }
- }
- randr= qh_RANDOMint;
- randr= randr/(qh_RANDOMmax+1);
- index= (int)floor((qh num_outside - outcoplanar) * randr);
- FORALLfacet_(qh facet_next) {
- if (facet->outsideset) {
- SETreturnsize_(facet->outsideset, size);
- if (!size)
- qh_setfree (&facet->outsideset);
- else if (size > index) {
- *visible= facet;
- return ((pointT*)qh_setdelnth (facet->outsideset, index));
- }else
- index -= size;
- }
- }
- fprintf (qh ferr, "qhull internal error (qh_nextfurthest): num_outside %d is too low\nby at least %d, or a random real %g >= 1.0\n",
- qh num_outside, index+1, randr);
- qh_errexit (qh_ERRqhull, NULL, NULL);
- }else { /* VIRTUALmemory */
- facet= qh facet_tail->previous;
- if (!(furthest= (pointT*)qh_setdellast(facet->outsideset))) {
- if (facet->outsideset)
- qh_setfree (&facet->outsideset);
- qh_removefacet (facet);
- qh_prependfacet (facet, &qh facet_list);
- continue;
- }
- *visible= facet;
- return furthest;
- }
- }
- return NULL;
-} /* nextfurthest */
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="partitionall">-</a>
-
- qh_partitionall( vertices, points, numpoints )
- partitions all points in points/numpoints to the outsidesets of facets
- vertices= vertices in qh.facet_list (not partitioned)
-
- returns:
- builds facet->outsideset
- does not partition qh.GOODpoint
- if qh.ONLYgood && !qh.MERGING,
- does not partition qh.GOODvertex
-
- notes:
- faster if qh.facet_list sorted by anticipated size of outside set
-
- design:
- initialize pointset with all points
- remove vertices from pointset
- remove qh.GOODpointp from pointset (unless it's qh.STOPcone or qh.STOPpoint)
- for all facets
- for all remaining points in pointset
- compute distance from point to facet
- if point is outside facet
- remove point from pointset (by not reappending)
- update bestpoint
- append point or old bestpoint to facet's outside set
- append bestpoint to facet's outside set (furthest)
- for all points remaining in pointset
- partition point into facets' outside sets and coplanar sets
-*/
-void qh_partitionall(setT *vertices, pointT *points, int numpoints){
- setT *pointset;
- vertexT *vertex, **vertexp;
- pointT *point, **pointp, *bestpoint;
- int size, point_i, point_n, point_end, remaining, i, id;
- facetT *facet;
- realT bestdist= -REALmax, dist, distoutside;
-
- trace1((qh ferr, "qh_partitionall: partition all points into outside sets\n"));
- pointset= qh_settemp (numpoints);
- qh num_outside= 0;
- pointp= SETaddr_(pointset, pointT);
- for (i=numpoints, point= points; i--; point += qh hull_dim)
- *(pointp++)= point;
- qh_settruncate (pointset, numpoints);
- FOREACHvertex_(vertices) {
- if ((id= qh_pointid(vertex->point)) >= 0)
- SETelem_(pointset, id)= NULL;
- }
- id= qh_pointid (qh GOODpointp);
- if (id >=0 && qh STOPcone-1 != id && -qh STOPpoint-1 != id)
- SETelem_(pointset, id)= NULL;
- if (qh GOODvertexp && qh ONLYgood && !qh MERGING) { /* matches qhull()*/
- if ((id= qh_pointid(qh GOODvertexp)) >= 0)
- SETelem_(pointset, id)= NULL;
- }
- if (!qh BESToutside) { /* matches conditional for qh_partitionpoint below */
- distoutside= qh_DISToutside; /* multiple of qh.MINoutside & qh.max_outside, see user.h */
- zval_(Ztotpartition)= qh num_points - qh hull_dim - 1; /*misses GOOD... */
- remaining= qh num_facets;
- point_end= numpoints;
- FORALLfacets {
- size= point_end/(remaining--) + 100;
- facet->outsideset= qh_setnew (size);
- bestpoint= NULL;
- point_end= 0;
- FOREACHpoint_i_(pointset) {
- if (point) {
- zzinc_(Zpartitionall);
- qh_distplane (point, facet, &dist);
- if (dist < distoutside)
- SETelem_(pointset, point_end++)= point;
- else {
- qh num_outside++;
- if (!bestpoint) {
- bestpoint= point;
- bestdist= dist;
- }else if (dist > bestdist) {
- qh_setappend (&facet->outsideset, bestpoint);
- bestpoint= point;
- bestdist= dist;
- }else
- qh_setappend (&facet->outsideset, point);
- }
- }
- }
- if (bestpoint) {
- qh_setappend (&facet->outsideset, bestpoint);
-#if !qh_COMPUTEfurthest
- facet->furthestdist= bestdist;
-#endif
- }else
- qh_setfree (&facet->outsideset);
- qh_settruncate (pointset, point_end);
- }
- }
- /* if !qh BESToutside, pointset contains points not assigned to outsideset */
- if (qh BESToutside || qh MERGING || qh KEEPcoplanar || qh KEEPinside) {
- qh findbestnew= True;
- FOREACHpoint_i_(pointset) {
- if (point)
- qh_partitionpoint(point, qh facet_list);
- }
- qh findbestnew= False;
- }
- zzadd_(Zpartitionall, zzval_(Zpartition));
- zzval_(Zpartition)= 0;
- qh_settempfree(&pointset);
- if (qh IStracing >= 4)
- qh_printfacetlist (qh facet_list, NULL, True);
-} /* partitionall */
-
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="partitioncoplanar">-</a>
-
- qh_partitioncoplanar( point, facet, dist )
- partition coplanar point to a facet
- dist is distance from point to facet
- if dist NULL,
- searches for bestfacet and does nothing if inside
- if qh.findbestnew set,
- searches new facets instead of using qh_findbest()
-
- returns:
- qh.max_ouside updated
- if qh.KEEPcoplanar or qh.KEEPinside
- point assigned to best coplanarset
-
- notes:
- facet->maxoutside is updated at end by qh_check_maxout
-
- design:
- if dist undefined
- find best facet for point
- if point sufficiently below facet (depends on qh.NEARinside and qh.KEEPinside)
- exit
- if keeping coplanar/nearinside/inside points
- if point is above furthest coplanar point
- append point to coplanar set (it is the new furthest)
- update qh.max_outside
- else
- append point one before end of coplanar set
- else if point is clearly outside of qh.max_outside and bestfacet->coplanarset
- and bestfacet is more than perpendicular to facet
- repartition the point using qh_findbest() -- it may be put on an outsideset
- else
- update qh.max_outside
-*/
-void qh_partitioncoplanar (pointT *point, facetT *facet, realT *dist) {
- facetT *bestfacet;
- pointT *oldfurthest;
- realT bestdist, dist2, angle;
- int numpart= 0, oldfindbest;
- boolT isoutside;
-
- qh WAScoplanar= True;
- if (!dist) {
- if (qh findbestnew)
- bestfacet= qh_findbestnew (point, facet, &bestdist, qh_ALL, &isoutside, &numpart);
- else
- bestfacet= qh_findbest (point, facet, qh_ALL, !qh_ISnewfacets, qh DELAUNAY,
- &bestdist, &isoutside, &numpart);
- zinc_(Ztotpartcoplanar);
- zzadd_(Zpartcoplanar, numpart);
- if (!qh DELAUNAY && !qh KEEPinside) { /* for 'd', bestdist skips upperDelaunay facets */
- if (qh KEEPnearinside) {
- if (bestdist < -qh NEARinside) {
- zinc_(Zcoplanarinside);
- trace4((qh ferr, "qh_partitioncoplanar: point p%d is more than near-inside facet f%d dist %2.2g findbestnew %d\n",
- qh_pointid(point), bestfacet->id, bestdist, qh findbestnew));
- return;
- }
- }else if (bestdist < -qh MAXcoplanar) {
- trace4((qh ferr, "qh_partitioncoplanar: point p%d is inside facet f%d dist %2.2g findbestnew %d\n",
- qh_pointid(point), bestfacet->id, bestdist, qh findbestnew));
- zinc_(Zcoplanarinside);
- return;
- }
- }
- }else {
- bestfacet= facet;
- bestdist= *dist;
- }
- if (bestdist > qh max_outside) {
- if (!dist && facet != bestfacet) {
- zinc_(Zpartangle);
- angle= qh_getangle(facet->normal, bestfacet->normal);
- if (angle < 0) {
- /* typically due to deleted vertex and coplanar facets, e.g.,
- RBOX 1000 s Z1 G1e-13 t1001185205 | QHULL Tv */
- zinc_(Zpartflip);
- trace2((qh ferr, "qh_partitioncoplanar: repartition point p%d from f%d. It is above flipped facet f%d dist %2.2g\n",
- qh_pointid(point), facet->id, bestfacet->id, bestdist));
- oldfindbest= qh findbestnew;
- qh findbestnew= False;
- qh_partitionpoint(point, bestfacet);
- qh findbestnew= oldfindbest;
- return;
- }
- }
- qh max_outside= bestdist;
- if (bestdist > qh TRACEdist) {
- fprintf (qh ferr, "qh_partitioncoplanar: ====== p%d from f%d increases max_outside to %2.2g of f%d last p%d\n",
- qh_pointid(point), facet->id, bestdist, bestfacet->id, qh furthest_id);
- qh_errprint ("DISTANT", facet, bestfacet, NULL, NULL);
- }
- }
- if (qh KEEPcoplanar + qh KEEPinside + qh KEEPnearinside) {
- oldfurthest= (pointT*)qh_setlast (bestfacet->coplanarset);
- if (oldfurthest) {
- zinc_(Zcomputefurthest);
- qh_distplane (oldfurthest, bestfacet, &dist2);
- }
- if (!oldfurthest || dist2 < bestdist)
- qh_setappend(&bestfacet->coplanarset, point);
- else
- qh_setappend2ndlast(&bestfacet->coplanarset, point);
- }
- trace4((qh ferr, "qh_partitioncoplanar: point p%d is coplanar with facet f%d (or inside) dist %2.2g\n",
- qh_pointid(point), bestfacet->id, bestdist));
-} /* partitioncoplanar */
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="partitionpoint">-</a>
-
- qh_partitionpoint( point, facet )
- assigns point to an outside set, coplanar set, or inside set (i.e., dropt)
- if qh.findbestnew
- uses qh_findbestnew() to search all new facets
- else
- uses qh_findbest()
-
- notes:
- after qh_distplane(), this and qh_findbest() are most expensive in 3-d
-
- design:
- find best facet for point
- (either exhaustive search of new facets or directed search from facet)
- if qh.NARROWhull
- retain coplanar and nearinside points as outside points
- if point is outside bestfacet
- if point above furthest point for bestfacet
- append point to outside set (it becomes the new furthest)
- if outside set was empty
- move bestfacet to end of qh.facet_list (i.e., after qh.facet_next)
- update bestfacet->furthestdist
- else
- append point one before end of outside set
- else if point is coplanar to bestfacet
- if keeping coplanar points or need to update qh.max_outside
- partition coplanar point into bestfacet
- else if near-inside point
- partition as coplanar point into bestfacet
- else is an inside point
- if keeping inside points
- partition as coplanar point into bestfacet
-*/
-void qh_partitionpoint (pointT *point, facetT *facet) {
- realT bestdist;
- boolT isoutside;
- facetT *bestfacet;
- int numpart;
-#if qh_COMPUTEfurthest
- realT dist;
-#endif
-
- if (qh findbestnew)
- bestfacet= qh_findbestnew (point, facet, &bestdist, qh BESToutside, &isoutside, &numpart);
- else
- bestfacet= qh_findbest (point, facet, qh BESToutside, qh_ISnewfacets, !qh_NOupper,
- &bestdist, &isoutside, &numpart);
- zinc_(Ztotpartition);
- zzadd_(Zpartition, numpart);
- if (qh NARROWhull) {
- if (qh DELAUNAY && !isoutside && bestdist >= -qh MAXcoplanar)
- qh_precision ("nearly incident point (narrow hull)");
- if (qh KEEPnearinside) {
- if (bestdist >= -qh NEARinside)
- isoutside= True;
- }else if (bestdist >= -qh MAXcoplanar)
- isoutside= True;
- }
-
- if (isoutside) {
- if (!bestfacet->outsideset
- || !qh_setlast (bestfacet->outsideset)) {
- qh_setappend(&(bestfacet->outsideset), point);
- if (!bestfacet->newfacet) {
- qh_removefacet (bestfacet); /* make sure it's after qh facet_next */
- qh_appendfacet (bestfacet);
- }
-#if !qh_COMPUTEfurthest
- bestfacet->furthestdist= bestdist;
-#endif
- }else {
-#if qh_COMPUTEfurthest
- zinc_(Zcomputefurthest);
- qh_distplane (oldfurthest, bestfacet, &dist);
- if (dist < bestdist)
- qh_setappend(&(bestfacet->outsideset), point);
- else
- qh_setappend2ndlast(&(bestfacet->outsideset), point);
-#else
- if (bestfacet->furthestdist < bestdist) {
- qh_setappend(&(bestfacet->outsideset), point);
- bestfacet->furthestdist= bestdist;
- }else
- qh_setappend2ndlast(&(bestfacet->outsideset), point);
-#endif
- }
- qh num_outside++;
- trace4((qh ferr, "qh_partitionpoint: point p%d is outside facet f%d new? %d(or narrowhull)\n",
- qh_pointid(point), bestfacet->id, bestfacet->newfacet));
- }else if (qh DELAUNAY || bestdist >= -qh MAXcoplanar) { /* for 'd', bestdist skips upperDelaunay facets */
- zzinc_(Zcoplanarpart);
- if (qh DELAUNAY)
- qh_precision ("nearly incident point");
- if ((qh KEEPcoplanar + qh KEEPnearinside) || bestdist > qh max_outside)
- qh_partitioncoplanar (point, bestfacet, &bestdist);
- else {
- trace4((qh ferr, "qh_partitionpoint: point p%d is coplanar to facet f%d (dropped)\n",
- qh_pointid(point), bestfacet->id));
- }
- }else if (qh KEEPnearinside && bestdist > -qh NEARinside) {
- zinc_(Zpartnear);
- qh_partitioncoplanar (point, bestfacet, &bestdist);
- }else {
- zinc_(Zpartinside);
- trace4((qh ferr, "qh_partitionpoint: point p%d is inside all facets, closest to f%d dist %2.2g\n",
- qh_pointid(point), bestfacet->id, bestdist));
- if (qh KEEPinside)
- qh_partitioncoplanar (point, bestfacet, &bestdist);
- }
-} /* partitionpoint */
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="partitionvisible">-</a>
-
- qh_partitionvisible( allpoints, numoutside )
- partitions points in visible facets to qh.newfacet_list
- qh.visible_list= visible facets
- for visible facets
- 1st neighbor (if any) points to a horizon facet or a new facet
- if allpoints (not used),
- repartitions coplanar points
-
- returns:
- updates outside sets and coplanar sets of qh.newfacet_list
- updates qh.num_outside (count of outside points)
-
- notes:
- qh.findbest_notsharp should be clear (extra work if set)
-
- design:
- for all visible facets with outside set or coplanar set
- select a newfacet for visible facet
- if outside set
- partition outside set into new facets
- if coplanar set and keeping coplanar/near-inside/inside points
- if allpoints
- partition coplanar set into new facets, may be assigned outside
- else
- partition coplanar set into coplanar sets of new facets
- for each deleted vertex
- if allpoints
- partition vertex into new facets, may be assigned outside
- else
- partition vertex into coplanar sets of new facets
-*/
-void qh_partitionvisible(/*visible_list*/ boolT allpoints, int *numoutside) {
- facetT *visible, *newfacet;
- pointT *point, **pointp;
- int coplanar=0, size;
- unsigned count;
- vertexT *vertex, **vertexp;
-
- if (qh ONLYmax)
- maximize_(qh MINoutside, qh max_vertex);
- *numoutside= 0;
- FORALLvisible_facets {
- if (!visible->outsideset && !visible->coplanarset)
- continue;
- newfacet= visible->f.replace;
- count= 0;
- while (newfacet && newfacet->visible) {
- newfacet= newfacet->f.replace;
- if (count++ > qh facet_id)
- qh_infiniteloop (visible);
- }
- if (!newfacet)
- newfacet= qh newfacet_list;
- if (newfacet == qh facet_tail) {
- fprintf (qh ferr, "qhull precision error (qh_partitionvisible): all new facets deleted as\n degenerate facets. Can not continue.\n");
- qh_errexit (qh_ERRprec, NULL, NULL);
- }
- if (visible->outsideset) {
- size= qh_setsize (visible->outsideset);
- *numoutside += size;
- qh num_outside -= size;
- FOREACHpoint_(visible->outsideset)
- qh_partitionpoint (point, newfacet);
- }
- if (visible->coplanarset && (qh KEEPcoplanar + qh KEEPinside + qh KEEPnearinside)) {
- size= qh_setsize (visible->coplanarset);
- coplanar += size;
- FOREACHpoint_(visible->coplanarset) {
- if (allpoints) /* not used */
- qh_partitionpoint (point, newfacet);
- else
- qh_partitioncoplanar (point, newfacet, NULL);
- }
- }
- }
- FOREACHvertex_(qh del_vertices) {
- if (vertex->point) {
- if (allpoints) /* not used */
- qh_partitionpoint (vertex->point, qh newfacet_list);
- else
- qh_partitioncoplanar (vertex->point, qh newfacet_list, NULL);
- }
- }
- trace1((qh ferr,"qh_partitionvisible: partitioned %d points from outsidesets and %d points from coplanarsets\n", *numoutside, coplanar));
-} /* partitionvisible */
-
-
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="precision">-</a>
-
- qh_precision( reason )
- restart on precision errors if not merging and if 'QJn'
-*/
-void qh_precision (char *reason) {
-
- if (qh ALLOWrestart && !qh PREmerge && !qh MERGEexact) {
- if (qh JOGGLEmax < REALmax/2) {
- trace0((qh ferr, "qh_precision: qhull restart because of %s\n", reason));
- longjmp(qh restartexit, qh_ERRprec);
- }
- }
-} /* qh_precision */
-
-/*-<a href="qh-qhull.htm#TOC"
- >-------------------------------</a><a name="printsummary">-</a>
-
- qh_printsummary( fp )
- prints summary to fp
-
- notes:
- not in io.c so that user_eg.c can prevent io.c from loading
- qh_printsummary and qh_countfacets must match counts
-
- design:
- determine number of points, vertices, and coplanar points
- print summary
-*/
-void qh_printsummary(FILE *fp) {
- realT ratio, outerplane, innerplane;
- float cpu;
- int size, id, nummerged, numvertices, numcoplanars= 0, nonsimplicial=0;
- int goodused;
- facetT *facet;
- char *s;
- int numdel= zzval_(Zdelvertextot);
- int numtricoplanars= 0;
-
- size= qh num_points + qh_setsize (qh other_points);
- numvertices= qh num_vertices - qh_setsize (qh del_vertices);
- id= qh_pointid (qh GOODpointp);
- FORALLfacets {
- if (facet->coplanarset)
- numcoplanars += qh_setsize( facet->coplanarset);
- if (facet->good) {
- if (facet->simplicial) {
- if (facet->keepcentrum && facet->tricoplanar)
- numtricoplanars++;
- }else if (qh_setsize(facet->vertices) != qh hull_dim)
- nonsimplicial++;
- }
- }
- if (id >=0 && qh STOPcone-1 != id && -qh STOPpoint-1 != id)
- size--;
- if (qh STOPcone || qh STOPpoint)
- fprintf (fp, "\nAt a premature exit due to 'TVn', 'TCn', 'TRn', or precision error.");
- if (qh UPPERdelaunay)
- goodused= qh GOODvertex + qh GOODpoint + qh SPLITthresholds;
- else if (qh DELAUNAY)
- goodused= qh GOODvertex + qh GOODpoint + qh GOODthreshold;
- else
- goodused= qh num_good;
- nummerged= zzval_(Ztotmerge) - zzval_(Zcyclehorizon) + zzval_(Zcyclefacettot);
- if (qh VORONOI) {
- if (qh UPPERdelaunay)
- fprintf (fp, "\n\
-Furthest-site Voronoi vertices by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
- else
- fprintf (fp, "\n\
-Voronoi diagram by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
- fprintf(fp, " Number of Voronoi regions%s: %d\n",
- qh ATinfinity ? " and at-infinity" : "", numvertices);
- if (numdel)
- fprintf(fp, " Total number of deleted points due to merging: %d\n", numdel);
- if (numcoplanars - numdel > 0)
- fprintf(fp, " Number of nearly incident points: %d\n", numcoplanars - numdel);
- else if (size - numvertices - numdel > 0)
- fprintf(fp, " Total number of nearly incident points: %d\n", size - numvertices - numdel);
- fprintf(fp, " Number of%s Voronoi vertices: %d\n",
- goodused ? " 'good'" : "", qh num_good);
- if (nonsimplicial)
- fprintf(fp, " Number of%s non-simplicial Voronoi vertices: %d\n",
- goodused ? " 'good'" : "", nonsimplicial);
- }else if (qh DELAUNAY) {
- if (qh UPPERdelaunay)
- fprintf (fp, "\n\
-Furthest-site Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
- else
- fprintf (fp, "\n\
-Delaunay triangulation by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
- fprintf(fp, " Number of input sites%s: %d\n",
- qh ATinfinity ? " and at-infinity" : "", numvertices);
- if (numdel)
- fprintf(fp, " Total number of deleted points due to merging: %d\n", numdel);
- if (numcoplanars - numdel > 0)
- fprintf(fp, " Number of nearly incident points: %d\n", numcoplanars - numdel);
- else if (size - numvertices - numdel > 0)
- fprintf(fp, " Total number of nearly incident points: %d\n", size - numvertices - numdel);
- fprintf(fp, " Number of%s Delaunay regions: %d\n",
- goodused ? " 'good'" : "", qh num_good);
- if (nonsimplicial)
- fprintf(fp, " Number of%s non-simplicial Delaunay regions: %d\n",
- goodused ? " 'good'" : "", nonsimplicial);
- }else if (qh HALFspace) {
- fprintf (fp, "\n\
-Halfspace intersection by the convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
- fprintf(fp, " Number of halfspaces: %d\n", size);
- fprintf(fp, " Number of non-redundant halfspaces: %d\n", numvertices);
- if (numcoplanars) {
- if (qh KEEPinside && qh KEEPcoplanar)
- s= "similar and redundant";
- else if (qh KEEPinside)
- s= "redundant";
- else
- s= "similar";
- fprintf(fp, " Number of %s halfspaces: %d\n", s, numcoplanars);
- }
- fprintf(fp, " Number of intersection points: %d\n", qh num_facets - qh num_visible);
- if (goodused)
- fprintf(fp, " Number of 'good' intersection points: %d\n", qh num_good);
- if (nonsimplicial)
- fprintf(fp, " Number of%s non-simplicial intersection points: %d\n",
- goodused ? " 'good'" : "", nonsimplicial);
- }else {
- fprintf (fp, "\n\
-Convex hull of %d points in %d-d:\n\n", size, qh hull_dim);
- fprintf(fp, " Number of vertices: %d\n", numvertices);
- if (numcoplanars) {
- if (qh KEEPinside && qh KEEPcoplanar)
- s= "coplanar and interior";
- else if (qh KEEPinside)
- s= "interior";
- else
- s= "coplanar";
- fprintf(fp, " Number of %s points: %d\n", s, numcoplanars);
- }
- fprintf(fp, " Number of facets: %d\n", qh num_facets - qh num_visible);
- if (goodused)
- fprintf(fp, " Number of 'good' facets: %d\n", qh num_good);
- if (nonsimplicial)
- fprintf(fp, " Number of%s non-simplicial facets: %d\n",
- goodused ? " 'good'" : "", nonsimplicial);
- }
- if (numtricoplanars)
- fprintf(fp, " Number of triangulated facets: %d\n", numtricoplanars);
- fprintf(fp, "\nStatistics for: %s | %s",
- qh rbox_command, qh qhull_command);
- if (qh ROTATErandom != INT_MIN)
- fprintf(fp, " QR%d\n\n", qh ROTATErandom);
- else
- fprintf(fp, "\n\n");
- fprintf(fp, " Number of points processed: %d\n", zzval_(Zprocessed));
- fprintf(fp, " Number of hyperplanes created: %d\n", zzval_(Zsetplane));
- if (qh DELAUNAY)
- fprintf(fp, " Number of facets in hull: %d\n", qh num_facets - qh num_visible);
- fprintf(fp, " Number of distance tests for qhull: %d\n", zzval_(Zpartition)+
- zzval_(Zpartitionall)+zzval_(Znumvisibility)+zzval_(Zpartcoplanar));
-#if 0 /* NOTE: must print before printstatistics() */
- {realT stddev, ave;
- fprintf(fp, " average new facet balance: %2.2g\n",
- wval_(Wnewbalance)/zval_(Zprocessed));
- stddev= qh_stddev (zval_(Zprocessed), wval_(Wnewbalance),
- wval_(Wnewbalance2), &ave);
- fprintf(fp, " new facet standard deviation: %2.2g\n", stddev);
- fprintf(fp, " average partition balance: %2.2g\n",
- wval_(Wpbalance)/zval_(Zpbalance));
- stddev= qh_stddev (zval_(Zpbalance), wval_(Wpbalance),
- wval_(Wpbalance2), &ave);
- fprintf(fp, " partition standard deviation: %2.2g\n", stddev);
- }
-#endif
- if (nummerged) {
- fprintf(fp," Number of distance tests for merging: %d\n",zzval_(Zbestdist)+
- zzval_(Zcentrumtests)+zzval_(Zdistconvex)+zzval_(Zdistcheck)+
- zzval_(Zdistzero));
- fprintf(fp," Number of distance tests for checking: %d\n",zzval_(Zcheckpart));
- fprintf(fp," Number of merged facets: %d\n", nummerged);
- }
- if (!qh RANDOMoutside && qh QHULLfinished) {
- cpu= qh hulltime;
- cpu /= qh_SECticks;
- wval_(Wcpu)= cpu;
- fprintf (fp, " CPU seconds to compute hull (after input): %2.4g\n", cpu);
- }
- if (qh RERUN) {
- if (!qh PREmerge && !qh MERGEexact)
- fprintf(fp, " Percentage of runs with precision errors: %4.1f\n",
- zzval_(Zretry)*100.0/qh build_cnt); /* careful of order */
- }else if (qh JOGGLEmax < REALmax/2) {
- if (zzval_(Zretry))
- fprintf(fp, " After %d retries, input joggled by: %2.2g\n",
- zzval_(Zretry), qh JOGGLEmax);
- else
- fprintf(fp, " Input joggled by: %2.2g\n", qh JOGGLEmax);
- }
- if (qh totarea != 0.0)
- fprintf(fp, " %s facet area: %2.8g\n",
- zzval_(Ztotmerge) ? "Approximate" : "Total", qh totarea);
- if (qh totvol != 0.0)
- fprintf(fp, " %s volume: %2.8g\n",
- zzval_(Ztotmerge) ? "Approximate" : "Total", qh totvol);
- if (qh MERGING) {
- qh_outerinner (NULL, &outerplane, &innerplane);
- if (outerplane > 2 * qh DISTround) {
- fprintf(fp, " Maximum distance of %spoint above facet: %2.2g",
- (qh QHULLfinished ? "" : "merged "), outerplane);
- ratio= outerplane/(qh ONEmerge + qh DISTround);
- /* don't report ratio if MINoutside is large */
- if (ratio > 0.05 && 2* qh ONEmerge > qh MINoutside && qh JOGGLEmax > REALmax/2)
- fprintf (fp, " (%.1fx)\n", ratio);
- else
- fprintf (fp, "\n");
- }
- if (innerplane < -2 * qh DISTround) {
- fprintf(fp, " Maximum distance of %svertex below facet: %2.2g",
- (qh QHULLfinished ? "" : "merged "), innerplane);
- ratio= -innerplane/(qh ONEmerge+qh DISTround);
- if (ratio > 0.05 && qh JOGGLEmax > REALmax/2)
- fprintf (fp, " (%.1fx)\n", ratio);
- else
- fprintf (fp, "\n");
- }
- }
- fprintf(fp, "\n");
-} /* printsummary */
-
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qhull.h b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qhull.h
deleted file mode 100644
index ebc0d2becc309ea76adbd9f2d194c29b609b45df..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qhull.h
+++ /dev/null
@@ -1,1036 +0,0 @@
-/*<html><pre> -<a href="qh-qhull.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- qhull.h
- user-level header file for using qhull.a library
-
- see qh-qhull.htm, qhull_a.h
-
- copyright (c) 1993-2003, The Geometry Center
-
- NOTE: access to qh_qh is via the 'qh' macro. This allows
- qh_qh to be either a pointer or a structure. An example
- of using qh is "qh DROPdim" which accesses the DROPdim
- field of qh_qh. Similarly, access to qh_qhstat is via
- the 'qhstat' macro.
-
- includes function prototypes for qhull.c, geom.c, global.c, io.c, user.c
-
- use mem.h for mem.c
- use qset.h for qset.c
-
- see unix.c for an example of using qhull.h
-
- recompile qhull if you change this file
-*/
-
-#ifndef qhDEFqhull
-#define qhDEFqhull 1
-
-/*=========================== -included files ==============*/
-
-#include <setjmp.h>
-#include <float.h>
-#include <time.h>
-
-#if __MWERKS__ && __POWERPC__
-#include <SIOUX.h>
-#include <Files.h>
-#include <Desk.h>
-#endif
-
-#ifndef __STDC__
-#ifndef __cplusplus
-#if !_MSC_VER
-#error Neither __STDC__ nor __cplusplus is defined. Please use strict ANSI C or C++ to compile
-#error Qhull. You may need to turn off compiler extensions in your project configuration. If
-#error your compiler is a standard C compiler, you can delete this warning from qhull.h
-#endif
-#endif
-#endif
-
-#include "user.h" /* user defineable constants */
-
-/*============ constants and basic types ====================*/
-
-extern char* qh_version; /* defined in global.c */
-
-/*-<a href="qh-geom.htm#TOC"
- >--------------------------------</a><a name="coordT">-</a>
-
- coordT
- coordinates and coefficients are stored as realT (i.e., double)
-
- notes:
- could use 'float' for data and 'double' for calculations (realT vs. coordT)
- This requires many type casts, and adjusted error bounds.
- Also C compilers may do expressions in double anyway.
-*/
-#define coordT realT
-
-/*-<a href="qh-geom.htm#TOC"
- >--------------------------------</a><a name="pointT">-</a>
-
- pointT
- a point is an array of DIM3 coordinates
-*/
-#define pointT coordT
-
-/*-<a href="qh-qhull.htm#TOC"
- >--------------------------------</a><a name="flagT">-</a>
-
- flagT
- Boolean flag as a bit
-*/
-#define flagT unsigned int
-
-/*-<a href="qh-qhull.htm#TOC"
- >--------------------------------</a><a name="boolT">-</a>
-
- boolT
- boolean value, either True or False
-
- notes:
- needed for portability
-*/
-#define boolT unsigned int
-#ifdef False
-#undef False
-#endif
-#ifdef True
-#undef True
-#endif
-#define False 0
-#define True 1
-
-/*-<a href="qh-qhull.htm#TOC"
- >--------------------------------</a><a name="CENTERtype">-</a>
-
- qh_CENTER
- to distinguish facet->center
-*/
-typedef enum
-{
- qh_ASnone = 0, qh_ASvoronoi, qh_AScentrum
-}
-qh_CENTER;
-
-/*-<a href="qh-qhull.htm#TOC"
- >--------------------------------</a><a name="qh_PRINT">-</a>
-
- qh_PRINT
- output formats for printing (qh.PRINTout).
- 'Fa' 'FV' 'Fc' 'FC'
-
-
- notes:
- some of these names are similar to qh names. The similar names are only
- used in switch statements in qh_printbegin() etc.
-*/
-typedef enum {qh_PRINTnone = 0,
- qh_PRINTarea, qh_PRINTaverage, /* 'Fa' 'FV' 'Fc' 'FC' */
- qh_PRINTcoplanars, qh_PRINTcentrums,
- qh_PRINTfacets, qh_PRINTfacets_xridge, /* 'f' 'FF' 'G' 'FI' 'Fi' 'Fn' */
- qh_PRINTgeom, qh_PRINTids, qh_PRINTinner, qh_PRINTneighbors,
- qh_PRINTnormals, qh_PRINTouter, qh_PRINTmaple, /* 'n' 'Fo' 'i' 'm' 'Fm' 'FM', 'o' */
- qh_PRINTincidences, qh_PRINTmathematica, qh_PRINTmerges, qh_PRINToff,
- qh_PRINToptions, qh_PRINTpointintersect, /* 'FO' 'Fp' 'FP' 'p' 'FQ' 'FS' */
- qh_PRINTpointnearest, qh_PRINTpoints, qh_PRINTqhull, qh_PRINTsize,
- qh_PRINTsummary, qh_PRINTtriangles, /* 'Fs' 'Ft' 'Fv' 'FN' 'Fx' */
- qh_PRINTvertices, qh_PRINTvneighbors, qh_PRINTextremes,
- qh_PRINTEND
- } qh_PRINT;
-
-/*-<a href="qh-qhull.htm#TOC"
- >--------------------------------</a><a name="qh_ALL">-</a>
-
- qh_ALL
- argument flag for selecting everything
-*/
-#define qh_ALL True
-#define qh_NOupper True /* argument for qh_findbest */
-#define qh_IScheckmax True /* argument for qh_findbesthorizon */
-#define qh_ISnewfacets True /* argument for qh_findbest */
-#define qh_RESETvisible True /* argument for qh_resetlists */
-
-/*-<a href="qh-qhull.htm#TOC"
- >--------------------------------</a><a name="qh_ERR">-</a>
-
- qh_ERR
- Qhull exit codes, for indicating errors
-*/
-#define qh_ERRnone 0 /* no error occurred during qhull */
-#define qh_ERRinput 1 /* input inconsistency */
-#define qh_ERRsingular 2 /* singular input data */
-#define qh_ERRprec 3 /* precision error */
-#define qh_ERRmem 4 /* insufficient memory, matches mem.h */
-#define qh_ERRqhull 5 /* internal error detected, matches mem.h */
-
-/* ============ -structures- ====================
- each of the following structures is defined by a typedef
- all realT and coordT fields occur at the beginning of a structure
- (otherwise space may be wasted due to alignment)
- define all flags together and pack into 32-bit number
-*/
-
-typedef struct vertexT vertexT;
-typedef struct ridgeT ridgeT;
-typedef struct facetT facetT;
-#ifndef DEFsetT
-#define DEFsetT 1
-typedef struct setT setT; /* defined in qset.h */
-#endif
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="facetT">-</a>
-
- facetT
- defines a facet
-
- notes:
- qhull() generates the hull as a list of facets.
-
- topological information:
- f.previous,next doubly-linked list of facets
- f.vertices set of vertices
- f.ridges set of ridges
- f.neighbors set of neighbors
- f.toporient True if facet has top-orientation (else bottom)
-
- geometric information:
- f.offset,normal hyperplane equation
- f.maxoutside offset to outer plane -- all points inside
- f.center centrum for testing convexity
- f.simplicial True if facet is simplicial
- f.flipped True if facet does not include qh.interior_point
-
- for constructing hull:
- f.visible True if facet on list of visible facets (will be deleted)
- f.newfacet True if facet on list of newly created facets
- f.coplanarset set of points coplanar with this facet
- (includes near-inside points for later testing)
- f.outsideset set of points outside of this facet
- f.furthestdist distance to furthest point of outside set
- f.visitid marks visited facets during a loop
- f.replace replacement facet for to-be-deleted, visible facets
- f.samecycle,newcycle cycle of facets for merging into horizon facet
-
- see below for other flags and fields
-*/
-struct facetT
-{
-#if !qh_COMPUTEfurthest
- coordT furthestdist;/* distance to furthest point of outsideset */
-#endif
-#if qh_MAXoutside
- coordT maxoutside; /* max computed distance of point to facet
- Before QHULLfinished this is an approximation
- since maxdist not always set for mergefacet
- Actual outer plane is +DISTround and
- computed outer plane is +2*DISTround */
-#endif
- coordT offset; /* exact offset of hyperplane from origin */
- coordT* normal; /* normal of hyperplane, hull_dim coefficients */
- /* if tricoplanar, shared with a neighbor */
- union /* in order of testing */
- {
- realT area; /* area of facet, only in io.c if ->isarea */
- facetT* replace; /* replacement facet if ->visible and NEWfacets
- is NULL only if qh_mergedegen_redundant or interior */
- facetT* samecycle; /* cycle of facets from the same visible/horizon intersection,
- if ->newfacet */
- facetT* newcycle; /* in horizon facet, current samecycle of new facets */
- facetT* trivisible; /* visible facet for ->tricoplanar facets during qh_triangulate() */
- facetT* triowner; /* owner facet for ->tricoplanar, !isarea facets w/ ->keepcentrum */
- } f;
- coordT* center; /* centrum for convexity, qh CENTERtype == qh_AScentrum */
- /* Voronoi center, qh CENTERtype == qh_ASvoronoi */
- /* if tricoplanar, shared with a neighbor */
- facetT* previous; /* previous facet in the facet_list */
- facetT* next; /* next facet in the facet_list */
- setT* vertices; /* vertices for this facet, inverse sorted by ID
- if simplicial, 1st vertex was apex/furthest */
- setT* ridges; /* explicit ridges for nonsimplicial facets.
- for simplicial facets, neighbors defines ridge */
- setT* neighbors; /* neighbors of the facet. If simplicial, the kth
- neighbor is opposite the kth vertex, and the first
- neighbor is the horizon facet for the first vertex*/
- setT* outsideset; /* set of points outside this facet
- if non-empty, last point is furthest
- if NARROWhull, includes coplanars for partitioning*/
- setT* coplanarset; /* set of points coplanar with this facet
- > qh.min_vertex and <= facet->max_outside
- a point is assigned to the furthest facet
- if non-empty, last point is furthest away */
- unsigned visitid; /* visit_id, for visiting all neighbors,
- all uses are independent */
- unsigned id; /* unique identifier from qh facet_id */
- unsigned nummerge: 9; /* number of merges */
-#define qh_MAXnummerge 511 /* 2^9-1, 32 flags total, see "flags:" in io.c */
- flagT tricoplanar: 1; /* True if TRIangulate and simplicial and coplanar with a neighbor */
- /* all tricoplanars share the same ->center, ->normal, ->offset, ->maxoutside */
- /* all tricoplanars share the same apex */
- /* if ->degenerate, does not span facet (one logical ridge) */
- /* one tricoplanar has ->keepcentrum and ->coplanarset */
- /* during qh_triangulate, f.trivisible points to original facet */
- flagT newfacet: 1; /* True if facet on qh newfacet_list (new or merged) */
- flagT visible: 1; /* True if visible facet (will be deleted) */
- flagT toporient: 1; /* True if created with top orientation
- after merging, use ridge orientation */
- flagT simplicial: 1; /* True if simplicial facet, ->ridges may be implicit */
- flagT seen: 1; /* used to perform operations only once, like visitid */
- flagT seen2: 1; /* used to perform operations only once, like visitid */
- flagT flipped: 1; /* True if facet is flipped */
- flagT upperdelaunay: 1; /* True if facet is upper envelope of Delaunay triangulation */
- flagT notfurthest: 1; /* True if last point of outsideset is not furthest*/
-
- /*-------- flags primarily for output ---------*/
- flagT good: 1; /* True if a facet marked good for output */
- flagT isarea: 1; /* True if facet->f.area is defined */
-
- /*-------- flags for merging ------------------*/
- flagT dupridge: 1; /* True if duplicate ridge in facet */
- flagT mergeridge: 1; /* True if facet or neighbor contains a qh_MERGEridge
- ->normal defined (also defined for mergeridge2) */
- flagT mergeridge2: 1; /* True if neighbor contains a qh_MERGEridge (mark_dupridges */
- flagT coplanar: 1; /* True if horizon facet is coplanar at last use */
- flagT mergehorizon: 1; /* True if will merge into horizon (->coplanar) */
- flagT cycledone: 1; /* True if mergecycle_all already done */
- flagT tested: 1; /* True if facet convexity has been tested (false after merge */
- flagT keepcentrum: 1; /* True if keep old centrum after a merge, or marks owner for ->tricoplanar */
- flagT newmerge: 1; /* True if facet is newly merged for reducevertices */
- flagT degenerate: 1; /* True if facet is degenerate (degen_mergeset or ->tricoplanar) */
- flagT redundant: 1; /* True if facet is redundant (degen_mergeset) */
-};
-
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="ridgeT">-</a>
-
- ridgeT
- defines a ridge
-
- notes:
- a ridge is DIM3-1 simplex between two neighboring facets. If the
- facets are non-simplicial, there may be more than one ridge between
- two facets. E.G. a 4-d hypercube has two triangles between each pair
- of neighboring facets.
-
- topological information:
- vertices a set of vertices
- top,bottom neighboring facets with orientation
-
- geometric information:
- tested True if ridge is clearly convex
- nonconvex True if ridge is non-convex
-*/
-struct ridgeT
-{
- setT* vertices; /* vertices belonging to this ridge, inverse sorted by ID
- NULL if a degen ridge (matchsame) */
- facetT* top; /* top facet this ridge is part of */
- facetT* bottom; /* bottom facet this ridge is part of */
- unsigned id: 24; /* unique identifier, =>room for 8 flags */
- flagT seen: 1; /* used to perform operations only once */
- flagT tested: 1; /* True when ridge is tested for convexity */
- flagT nonconvex: 1; /* True if getmergeset detected a non-convex neighbor
- only one ridge between neighbors may have nonconvex */
-};
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="vertexT">-</a>
-
- vertexT
- defines a vertex
-
- topological information:
- next,previous doubly-linked list of all vertices
- neighbors set of adjacent facets (only if qh.VERTEXneighbors)
-
- geometric information:
- point array of DIM3 coordinates
-*/
-struct vertexT
-{
- vertexT* next; /* next vertex in vertex_list */
- vertexT* previous; /* previous vertex in vertex_list */
- pointT* point; /* hull_dim coordinates (coordT) */
- setT* neighbors; /* neighboring facets of vertex, qh_vertexneighbors()
- inits in io.c or after first merge */
- unsigned visitid; /* for use with qh vertex_visit */
- unsigned id: 24; /* unique identifier, =>room for 8 flags */
- flagT seen: 1; /* used to perform operations only once */
- flagT seen2: 1; /* another seen flag */
- flagT delridge: 1; /* vertex was part of a deleted ridge */
- flagT deleted: 1; /* true if vertex on qh del_vertices */
- flagT newlist: 1; /* true if vertex on qh newvertex_list */
-};
-
-/*======= -global variables -qh ============================*/
-
-/*-<a href="qh-globa.htm#TOC"
- >--------------------------------</a><a name="qh">-</a>
-
- qh
- all global variables for qhull are in qh, qhmem, and qhstat
-
- notes:
- qhmem is defined in mem.h and qhstat is defined in stat.h
- Access to qh_qh is via the "qh" macro. See qh_QHpointer in user.h
-*/
-typedef struct qhT qhT;
-#if qh_QHpointer
-#define qh qh_qh->
-extern qhT* qh_qh; /* allocated in global.c */
-#else
-#define qh qh_qh.
-extern qhT qh_qh;
-#endif
-
-struct qhT
-{
-
- /*-<a href="qh-globa.htm#TOC"
- >--------------------------------</a><a name="qh-const">-</a>
-
- qh constants
- configuration flags and constants for Qhull
-
- notes:
- The user configures Qhull by defining flags. They are
- copied into qh by qh_setflags(). qh-quick.htm#options defines the flags.
- */
- boolT ALLpoints; /* true 'Qs' if search all points for initial simplex */
- boolT ANGLEmerge; /* true 'Qa' if sort potential merges by angle */
- boolT APPROXhull; /* true 'Wn' if MINoutside set */
- realT MINoutside; /* 'Wn' min. distance for an outside point */
- boolT ATinfinity; /* true 'Qz' if point num_points-1 is "at-infinity"
- for improving precision in Delaunay triangulations */
- boolT AVOIDold; /* true 'Q4' if avoid old->new merges */
- boolT BESToutside; /* true 'Qf' if partition points into best outsideset */
- boolT CDDinput; /* true 'Pc' if input uses CDD format (1.0/offset first) */
- boolT CDDoutput; /* true 'PC' if print normals in CDD format (offset first) */
- boolT CHECKfrequently; /* true 'Tc' if checking frequently */
- realT premerge_cos; /* 'A-n' cos_max when pre merging */
- realT postmerge_cos; /* 'An' cos_max when post merging */
- boolT DELAUNAY; /* true 'd' if computing DELAUNAY triangulation */
- boolT DOintersections; /* true 'Gh' if print hyperplane intersections */
- int DROPdim; /* drops dim 'GDn' for 4-d -> 3-d output */
- boolT FORCEoutput; /* true 'Po' if forcing output despite degeneracies */
- int GOODpoint; /* 1+n for 'QGn', good facet if visible/not(-) from point n*/
- pointT* GOODpointp; /* the actual point */
- boolT GOODthreshold; /* true if qh lower_threshold/upper_threshold defined
- false if qh SPLITthreshold */
- int GOODvertex; /* 1+n, good facet if vertex for point n */
- pointT* GOODvertexp; /* the actual point */
- boolT HALFspace; /* true 'Hn,n,n' if halfspace intersection */
- int IStracing; /* trace execution, 0=none, 1=least, 4=most, -1=events */
- int KEEParea; /* 'PAn' number of largest facets to keep */
- boolT KEEPcoplanar; /* true 'Qc' if keeping nearest facet for coplanar points */
- boolT KEEPinside; /* true 'Qi' if keeping nearest facet for inside points
- set automatically if 'd Qc' */
- int KEEPmerge; /* 'PMn' number of facets to keep with most merges */
- realT KEEPminArea; /* 'PFn' minimum facet area to keep */
- realT MAXcoplanar; /* 'Un' max distance below a facet to be coplanar*/
- boolT MERGEexact; /* true 'Qx' if exact merges (coplanar, degen, dupridge, flipped) */
- boolT MERGEindependent; /* true 'Q2' if merging independent sets */
- boolT MERGING; /* true if exact-, pre- or post-merging, with angle and centrum tests */
- realT premerge_centrum; /* 'C-n' centrum_radius when pre merging. Default is round-off */
- realT postmerge_centrum; /* 'Cn' centrum_radius when post merging. Default is round-off */
- boolT MERGEvertices; /* true 'Q3' if merging redundant vertices */
- realT MINvisible; /* 'Vn' min. distance for a facet to be visible */
- boolT NOnarrow; /* true 'Q10' if no special processing for narrow distributions */
- boolT NOnearinside; /* true 'Q8' if ignore near-inside points when partitioning */
- boolT NOpremerge; /* true 'Q0' if no defaults for C-0 or Qx */
- boolT ONLYgood; /* true 'Qg' if process points with good visible or horizon facets */
- boolT ONLYmax; /* true 'Qm' if only process points that increase max_outside */
- boolT PICKfurthest; /* true 'Q9' if process furthest of furthest points*/
- boolT POSTmerge; /* true if merging after buildhull (Cn or An) */
- boolT PREmerge; /* true if merging during buildhull (C-n or A-n) */
- /* NOTE: some of these names are similar to qh_PRINT names */
- boolT PRINTcentrums; /* true 'Gc' if printing centrums */
- boolT PRINTcoplanar; /* true 'Gp' if printing coplanar points */
- int PRINTdim; /* print dimension for Geomview output */
- boolT PRINTdots; /* true 'Ga' if printing all points as dots */
- boolT PRINTgood; /* true 'Pg' if printing good facets */
- boolT PRINTinner; /* true 'Gi' if printing inner planes */
- boolT PRINTneighbors; /* true 'PG' if printing neighbors of good facets */
- boolT PRINTnoplanes; /* true 'Gn' if printing no planes */
- boolT PRINToptions1st; /* true 'FO' if printing options to stderr */
- boolT PRINTouter; /* true 'Go' if printing outer planes */
- boolT PRINTprecision; /* false 'Pp' if not reporting precision problems */
- qh_PRINT PRINTout[qh_PRINTEND]; /* list of output formats to print */
- boolT PRINTridges; /* true 'Gr' if print ridges */
- boolT PRINTspheres; /* true 'Gv' if print vertices as spheres */
- boolT PRINTstatistics; /* true 'Ts' if printing statistics to stderr */
- boolT PRINTsummary; /* true 's' if printing summary to stderr */
- boolT PRINTtransparent; /* true 'Gt' if print transparent outer ridges */
- boolT PROJECTdelaunay; /* true if DELAUNAY, no readpoints() and
- need projectinput() for Delaunay in qh_init_B */
- int PROJECTinput; /* number of projected dimensions 'bn:0Bn:0' */
- boolT QUICKhelp; /* true if quick help message for degen input */
- boolT RANDOMdist; /* true if randomly change distplane and setfacetplane */
- realT RANDOMfactor; /* maximum random perturbation */
- realT RANDOMa; /* qh_randomfactor is randr * RANDOMa + RANDOMb */
- realT RANDOMb;
- boolT RANDOMoutside; /* true if select a random outside point */
- int REPORTfreq; /* buildtracing reports every n facets */
- int REPORTfreq2; /* tracemerging reports every REPORTfreq/2 facets */
- int RERUN; /* 'TRn' rerun qhull n times (qh.build_cnt) */
- int ROTATErandom; /* 'QRn' seed, 0 time, >= rotate input */
- boolT SCALEinput; /* true 'Qbk' if scaling input */
- boolT SCALElast; /* true 'Qbb' if scale last coord to max prev coord */
- boolT SETroundoff; /* true 'E' if qh DISTround is predefined */
- boolT SKIPcheckmax; /* true 'Q5' if skip qh_check_maxout */
- boolT SKIPconvex; /* true 'Q6' if skip convexity testing during pre-merge */
- boolT SPLITthresholds; /* true if upper_/lower_threshold defines a region
- used only for printing (not for qh ONLYgood) */
- int STOPcone; /* 'TCn' 1+n for stopping after cone for point n*/
- /* also used by qh_build_withresart for err exit*/
- int STOPpoint; /* 'TVn' 'TV-n' 1+n for stopping after/before(-)
- adding point n */
- int TESTpoints; /* 'QTn' num of test points after qh.num_points. Test points always coplanar. */
- boolT TESTvneighbors; /* true 'Qv' if test vertex neighbors at end */
- int TRACElevel; /* 'Tn' conditional IStracing level */
- int TRACElastrun; /* qh.TRACElevel applies to last qh.RERUN */
- int TRACEpoint; /* 'TPn' start tracing when point n is a vertex */
- realT TRACEdist; /* 'TWn' start tracing when merge distance too big */
- int TRACEmerge; /* 'TMn' start tracing before this merge */
- boolT TRIangulate; /* true 'Qt' if triangulate non-simplicial facets */
- boolT TRInormals; /* true 'Q11' if triangulate duplicates normals (sets Qt) */
- boolT UPPERdelaunay; /* true 'Qu' if computing furthest-site Delaunay */
- boolT VERIFYoutput; /* true 'Tv' if verify output at end of qhull */
- boolT VIRTUALmemory; /* true 'Q7' if depth-first processing in buildhull */
- boolT VORONOI; /* true 'v' if computing Voronoi diagram */
-
- /*--------input constants ---------*/
- realT AREAfactor; /* 1/(hull_dim-1)! for converting det's to area */
- boolT DOcheckmax; /* true if calling qh_check_maxout (qh_initqhull_globals) */
- char* feasible_string; /* feasible point 'Hn,n,n' for halfspace intersection */
- coordT* feasible_point; /* as coordinates, both malloc'd */
- boolT GETarea; /* true 'Fa', 'FA', 'FS', 'PAn', 'PFn' if compute facet area/Voronoi volume in io.c */
- boolT KEEPnearinside; /* true if near-inside points in coplanarset */
- int hull_dim; /* dimension of hull, set by initbuffers */
- int input_dim; /* dimension of input, set by initbuffers */
- int num_points; /* number of input points */
- pointT* first_point; /* array of input points, see POINTSmalloc */
- boolT POINTSmalloc; /* true if qh first_point/num_points allocated */
- pointT* input_points; /* copy of original qh.first_point for input points for qh_joggleinput */
- boolT input_malloc; /* true if qh input_points malloc'd */
- char qhull_command[256];/* command line that invoked this program */
- char rbox_command[256]; /* command line that produced the input points */
- char qhull_options[512];/* descriptive list of options */
- int qhull_optionlen; /* length of last line */
- int qhull_optionsiz; /* size of qhull_options before qh_initbuild */
- boolT VERTEXneighbors; /* true if maintaining vertex neighbors */
- boolT ZEROcentrum; /* true if 'C-0' or 'C-0 Qx'. sets ZEROall_ok */
- realT* upper_threshold; /* don't print if facet->normal[k]>=upper_threshold[k]
- must set either GOODthreshold or SPLITthreshold
- if Delaunay, default is 0.0 for upper envelope */
- realT* lower_threshold; /* don't print if facet->normal[k] <=lower_threshold[k] */
- realT* upper_bound; /* scale point[k] to new upper bound */
- realT* lower_bound; /* scale point[k] to new lower bound
- project if both upper_ and lower_bound == 0 */
-
- /*-<a href="qh-globa.htm#TOC"
- >--------------------------------</a><a name="qh-prec">-</a>
-
- qh precision constants
- precision constants for Qhull
-
- notes:
- qh_detroundoff() computes the maximum roundoff error for distance
- and other computations. It also sets default values for the
- qh constants above.
- */
- realT ANGLEround; /* max round off error for angles */
- realT centrum_radius; /* max centrum radius for convexity (roundoff added) */
- realT cos_max; /* max cosine for convexity (roundoff added) */
- realT DISTround; /* max round off error for distances, 'E' overrides */
- realT MAXabs_coord; /* max absolute coordinate */
- realT MAXlastcoord; /* max last coordinate for qh_scalelast */
- realT MAXsumcoord; /* max sum of coordinates */
- realT MAXwidth; /* max rectilinear width of point coordinates */
- realT MINdenom_1; /* min. abs. value for 1/x */
- realT MINdenom; /* use divzero if denominator < MINdenom */
- realT MINdenom_1_2; /* min. abs. val for 1/x that allows normalization */
- realT MINdenom_2; /* use divzero if denominator < MINdenom_2 */
- realT MINlastcoord; /* min. last coordinate for qh_scalelast */
- boolT NARROWhull; /* set in qh_initialhull if angle < qh_MAXnarrow */
- realT* NEARzero; /* hull_dim array for near zero in gausselim */
- realT NEARinside; /* keep points for qh_check_maxout if close to facet */
- realT ONEmerge; /* max distance for merging simplicial facets */
- realT outside_err; /* application's epsilon for coplanar points
- qh_check_bestdist() qh_check_points() reports error if point outside */
- realT WIDEfacet; /* size of wide facet for skipping ridge in
- area computation and locking centrum */
-
- /*-<a href="qh-globa.htm#TOC"
- >--------------------------------</a><a name="qh-intern">-</a>
-
- qh internal constants
- internal constants for Qhull
- */
- char qhull[sizeof("qhull")]; /* for checking ownership */
- void* old_stat; /* pointer to saved qh_qhstat, qh_save_qhull */
- jmp_buf errexit; /* exit label for qh_errexit, defined by setjmp() */
- char jmpXtra[40]; /* extra bytes in case jmp_buf is defined wrong by compiler */
- jmp_buf restartexit; /* restart label for qh_errexit, defined by setjmp() */
- char jmpXtra2[40]; /* extra bytes in case jmp_buf is defined wrong by compiler*/
- FILE* fin; /* pointer to input file, init by qh_meminit */
- FILE* fout; /* pointer to output file */
- FILE* ferr; /* pointer to error file */
- pointT* interior_point; /* center point of the initial simplex*/
- int normal_size; /* size in bytes for facet normals and point coords*/
- int center_size; /* size in bytes for Voronoi centers */
- int TEMPsize; /* size for small, temporary sets (in quick mem) */
-
- /*-<a href="qh-globa.htm#TOC"
- >--------------------------------</a><a name="qh-lists">-</a>
-
- qh facet and vertex lists
- defines lists of facets, new facets, visible facets, vertices, and
- new vertices. Includes counts, next ids, and trace ids.
- see:
- qh_resetlists()
- */
- facetT* facet_list; /* first facet */
- facetT* facet_tail; /* end of facet_list (dummy facet) */
- facetT* facet_next; /* next facet for buildhull()
- previous facets do not have outside sets
- NARROWhull: previous facets may have coplanar outside sets for qh_outcoplanar */
- facetT* newfacet_list; /* list of new facets to end of facet_list */
- facetT* visible_list; /* list of visible facets preceeding newfacet_list,
- facet->visible set */
- int num_visible; /* current number of visible facets */
- unsigned tracefacet_id; /* set at init, then can print whenever */
- facetT* tracefacet; /* set in newfacet/mergefacet, undone in delfacet*/
- unsigned tracevertex_id; /* set at buildtracing, can print whenever */
- vertexT* tracevertex; /* set in newvertex, undone in delvertex*/
- vertexT* vertex_list; /* list of all vertices, to vertex_tail */
- vertexT* vertex_tail; /* end of vertex_list (dummy vertex) */
- vertexT* newvertex_list; /* list of vertices in newfacet_list, to vertex_tail
- all vertices have 'newlist' set */
- int num_facets; /* number of facets in facet_list
- includes visble faces (num_visible) */
- int num_vertices; /* number of vertices in facet_list */
- int num_outside; /* number of points in outsidesets (for tracing and RANDOMoutside)
- includes coplanar outsideset points for NARROWhull/qh_outcoplanar() */
- int num_good; /* number of good facets (after findgood_all) */
- unsigned facet_id; /* ID of next, new facet from newfacet() */
- unsigned ridge_id; /* ID of next, new ridge from newridge() */
- unsigned vertex_id; /* ID of next, new vertex from newvertex() */
-
- /*-<a href="qh-globa.htm#TOC"
- >--------------------------------</a><a name="qh-var">-</a>
-
- qh global variables
- defines minimum and maximum distances, next visit ids, several flags,
- and other global variables.
- initialize in qh_initbuild or qh_maxmin if used in qh_buildhull
- */
- unsigned long hulltime; /* ignore time to set up input and randomize */
- /* use unsigned to avoid wrap-around errors */
- boolT ALLOWrestart; /* true if qh_precision can use qh.restartexit */
- int build_cnt; /* number of calls to qh_initbuild */
- qh_CENTER CENTERtype; /* current type of facet->center, qh_CENTER */
- int furthest_id; /* pointid of furthest point, for tracing */
- facetT* GOODclosest; /* closest facet to GOODthreshold in qh_findgood */
- realT JOGGLEmax; /* set 'QJn' if randomly joggle input */
- boolT maxoutdone; /* set qh_check_maxout(), cleared by qh_addpoint() */
- realT max_outside; /* maximum distance from a point to a facet,
- before roundoff, not simplicial vertices
- actual outer plane is +DISTround and
- computed outer plane is +2*DISTround */
- realT max_vertex; /* maximum distance (>0) from vertex to a facet,
- before roundoff, due to a merge */
- realT min_vertex; /* minimum distance (<0) from vertex to a facet,
- before roundoff, due to a merge
- if qh.JOGGLEmax, qh_makenewplanes sets it
- recomputed if qh.DOcheckmax, default -qh.DISTround */
- boolT NEWfacets; /* true while visible facets invalid due to new or merge
- from makecone/attachnewfacets to deletevisible */
- boolT findbestnew; /* true if partitioning calls qh_findbestnew */
- boolT findbest_notsharp; /* true if new facets are at least 90 degrees */
- boolT NOerrexit; /* true if qh.errexit is not available */
- realT PRINTcradius; /* radius for printing centrums */
- realT PRINTradius; /* radius for printing vertex spheres and points */
- boolT POSTmerging; /* true when post merging */
- int printoutvar; /* temporary variable for qh_printbegin, etc. */
- int printoutnum; /* number of facets printed */
- boolT QHULLfinished; /* True after qhull() is finished */
- realT totarea; /* 'FA': total facet area computed by qh_getarea */
- realT totvol; /* 'FA': total volume computed by qh_getarea */
- unsigned int visit_id; /* unique ID for searching neighborhoods, */
- unsigned int vertex_visit; /* unique ID for searching vertices */
- boolT ZEROall_ok; /* True if qh_checkzero always succeeds */
- boolT WAScoplanar; /* True if qh_partitioncoplanar (qh_check_maxout) */
-
- /*-<a href="qh-globa.htm#TOC"
- >--------------------------------</a><a name="qh-set">-</a>
-
- qh global sets
- defines sets for merging, initial simplex, hashing, extra input points,
- and deleted vertices
- */
- setT* facet_mergeset; /* temporary set of merges to be done */
- setT* degen_mergeset; /* temporary set of degenerate and redundant merges */
- setT* hash_table; /* hash table for matching ridges in qh_matchfacets
- size is setsize() */
- setT* other_points; /* additional points (first is qh interior_point) */
- setT* del_vertices; /* vertices to partition and delete with visible
- facets. Have deleted set for checkfacet */
-
- /*-<a href="qh-globa.htm#TOC"
- >--------------------------------</a><a name="qh-buf">-</a>
-
- qh global buffers
- defines buffers for maxtrix operations, input, and error messages
- */
- coordT* gm_matrix; /* (dim+1)Xdim matrix for geom.c */
- coordT** gm_row; /* array of gm_matrix rows */
- char* line; /* malloc'd input line of maxline+1 chars */
- int maxline;
- coordT* half_space; /* malloc'd input array for halfspace (qh normal_size+coordT) */
- coordT* temp_malloc; /* malloc'd input array for points */
-
- /*-<a href="qh-globa.htm#TOC"
- >--------------------------------</a><a name="qh-static">-</a>
-
- qh static variables
- defines static variables for individual functions
-
- notes:
- do not use 'static' within a function. Multiple instances of qhull
- may exist.
-
- do not assume zero initialization, 'QPn' may cause a restart
- */
- boolT ERREXITcalled; /* true during errexit (prevents duplicate calls */
- boolT firstcentrum; /* for qh_printcentrum */
- realT last_low; /* qh_scalelast parameters for qh_setdelaunay */
- realT last_high;
- realT last_newhigh;
- unsigned lastreport; /* for qh_buildtracing */
- int mergereport; /* for qh_tracemerging */
- boolT old_randomdist; /* save RANDOMdist when io, tracing, or statistics */
- int ridgeoutnum; /* number of ridges in 4OFF output */
- void* old_qhstat; /* for saving qh_qhstat in save_qhull() */
- setT* old_tempstack; /* for saving qhmem.tempstack in save_qhull */
- setT* coplanarset; /* set of coplanar facets for searching qh_findbesthorizon() */
-};
-
-/*=========== -macros- =========================*/
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="otherfacet_">-</a>
-
- otherfacet_(ridge, facet)
- return neighboring facet for a ridge in facet
-*/
-#define otherfacet_(ridge, facet) \
- (((ridge)->top == (facet)) ? (ridge)->bottom : (ridge)->top)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="getid_">-</a>
-
- getid_(p)
- return ID for facet, ridge, or vertex
- return MAXINT if NULL (-1 causes type conversion error )
-*/
-#define getid_(p) ((p) ? (p)->id : -1)
-
-/*============== FORALL macros ===================*/
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FORALLfacets">-</a>
-
- FORALLfacets { ... }
- assign 'facet' to each facet in qh.facet_list
-
- notes:
- uses 'facetT *facet;'
- assumes last facet is a sentinel
-
- see:
- FORALLfacet_( facetlist )
-*/
-#define FORALLfacets for (facet=qh facet_list;facet && facet->next;facet=facet->next)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FORALLpoints">-</a>
-
- FORALLpoints { ... }
- assign 'point' to each point in qh.first_point, qh.num_points
-
- declare:
- coordT *point, *pointtemp;
-*/
-#define FORALLpoints FORALLpoint_(qh first_point, qh num_points)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FORALLpoint_">-</a>
-
- FORALLpoint_( points, num) { ... }
- assign 'point' to each point in points array of num points
-
- declare:
- coordT *point, *pointtemp;
-*/
-#define FORALLpoint_(points, num) for(point= (points), \
- pointtemp= (points)+qh hull_dim*(num); point < pointtemp; point += qh hull_dim)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FORALLvertices">-</a>
-
- FORALLvertices { ... }
- assign 'vertex' to each vertex in qh.vertex_list
-
- declare:
- vertexT *vertex;
-
- notes:
- assumes qh.vertex_list terminated with a sentinel
-*/
-#define FORALLvertices for (vertex=qh vertex_list;vertex && vertex->next;vertex= vertex->next)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHfacet_">-</a>
-
- FOREACHfacet_( facets ) { ... }
- assign 'facet' to each facet in facets
-
- declare:
- facetT *facet, **facetp;
-
- see:
- <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
-*/
-#define FOREACHfacet_(facets) FOREACHsetelement_(facetT, facets, facet)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHneighbor_">-</a>
-
- FOREACHneighbor_( facet ) { ... }
- assign 'neighbor' to each neighbor in facet->neighbors
-
- FOREACHneighbor_( vertex ) { ... }
- assign 'neighbor' to each neighbor in vertex->neighbors
-
- declare:
- facetT *neighbor, **neighborp;
-
- see:
- <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
-*/
-#define FOREACHneighbor_(facet) FOREACHsetelement_(facetT, facet->neighbors, neighbor)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHpoint_">-</a>
-
- FOREACHpoint_( points ) { ... }
- assign 'point' to each point in points set
-
- declare:
- pointT *point, **pointp;
-
- see:
- <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
-*/
-#define FOREACHpoint_(points) FOREACHsetelement_(pointT, points, point)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHridge_">-</a>
-
- FOREACHridge_( ridges ) { ... }
- assign 'ridge' to each ridge in ridges set
-
- declare:
- ridgeT *ridge, **ridgep;
-
- see:
- <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
-*/
-#define FOREACHridge_(ridges) FOREACHsetelement_(ridgeT, ridges, ridge)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHvertex_">-</a>
-
- FOREACHvertex_( vertices ) { ... }
- assign 'vertex' to each vertex in vertices set
-
- declare:
- vertexT *vertex, **vertexp;
-
- see:
- <a href="qset.h#FOREACHsetelement_">FOREACHsetelement_</a>
-*/
-#define FOREACHvertex_(vertices) FOREACHsetelement_(vertexT, vertices,vertex)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHfacet_i_">-</a>
-
- FOREACHfacet_i_( facets ) { ... }
- assign 'facet' and 'facet_i' for each facet in facets set
-
- declare:
- facetT *facet;
- int facet_n, facet_i;
-
- see:
- <a href="qset.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
-*/
-#define FOREACHfacet_i_(facets) FOREACHsetelement_i_(facetT, facets, facet)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHneighbor_i_">-</a>
-
- FOREACHneighbor_i_( facet ) { ... }
- assign 'neighbor' and 'neighbor_i' for each neighbor in facet->neighbors
-
- FOREACHneighbor_i_( vertex ) { ... }
- assign 'neighbor' and 'neighbor_i' for each neighbor in vertex->neighbors
-
- declare:
- facetT *neighbor;
- int neighbor_n, neighbor_i;
-
- see:
- <a href="qset.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
-*/
-#define FOREACHneighbor_i_(facet) FOREACHsetelement_i_(facetT, facet->neighbors, neighbor)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHpoint_i_">-</a>
-
- FOREACHpoint_i_( points ) { ... }
- assign 'point' and 'point_i' for each point in points set
-
- declare:
- pointT *point;
- int point_n, point_i;
-
- see:
- <a href="qset.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
-*/
-#define FOREACHpoint_i_(points) FOREACHsetelement_i_(pointT, points, point)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHridge_i_">-</a>
-
- FOREACHridge_i_( ridges ) { ... }
- assign 'ridge' and 'ridge_i' for each ridge in ridges set
-
- declare:
- ridgeT *ridge;
- int ridge_n, ridge_i;
-
- see:
- <a href="qset.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
-*/
-#define FOREACHridge_i_(ridges) FOREACHsetelement_i_(ridgeT, ridges, ridge)
-
-/*-<a href="qh-poly.htm#TOC"
- >--------------------------------</a><a name="FOREACHvertex_i_">-</a>
-
- FOREACHvertex_i_( vertices ) { ... }
- assign 'vertex' and 'vertex_i' for each vertex in vertices set
-
- declare:
- vertexT *vertex;
- int vertex_n, vertex_i;
-
- see:
- <a href="qset.h#FOREACHsetelement_i_">FOREACHsetelement_i_</a>
- */
-#define FOREACHvertex_i_(vertices) FOREACHsetelement_i_(vertexT, vertices,vertex)
-
-/********* -qhull.c prototypes (duplicated from qhull_a.h) **********************/
-
-void qh_qhull(void);
-boolT qh_addpoint(pointT* furthest, facetT* facet, boolT checkdist);
-void qh_printsummary(FILE* fp);
-
-/********* -user.c prototypes (alphabetical) **********************/
-
-void qh_errexit(int exitcode, facetT* facet, ridgeT* ridge);
-void qh_errprint(char* string, facetT* atfacet, facetT* otherfacet, ridgeT* atridge, vertexT* atvertex);
-int qh_new_qhull(int dim, int numpoints, coordT* points, boolT ismalloc,
- char* qhull_cmd, FILE* outfile, FILE* errfile);
-void qh_printfacetlist(facetT* facetlist, setT* facets, boolT printall);
-void qh_user_memsizes(void);
-
-/***** -geom.c/geom2.c prototypes (duplicated from geom.h) ****************/
-
-facetT* qh_findbest(pointT* point, facetT* startfacet,
- boolT bestoutside, boolT newfacets, boolT noupper,
- realT* dist, boolT* isoutside, int* numpart);
-facetT* qh_findbestnew(pointT* point, facetT* startfacet,
- realT* dist, boolT bestoutside, boolT* isoutside, int* numpart);
-boolT qh_gram_schmidt(int dim, realT** rows);
-void qh_outerinner(facetT* facet, realT* outerplane, realT* innerplane);
-void qh_printsummary(FILE* fp);
-void qh_projectinput(void);
-void qh_randommatrix(realT* buffer, int dim, realT** row);
-void qh_rotateinput(realT** rows);
-void qh_scaleinput(void);
-void qh_setdelaunay(int dim, int count, pointT* points);
-coordT* qh_sethalfspace_all(int dim, int count, coordT* halfspaces, pointT* feasible);
-
-/***** -global.c prototypes (alphabetical) ***********************/
-
-unsigned long qh_clock(void);
-void qh_checkflags(char* command, char* hiddenflags);
-void qh_freebuffers(void);
-void qh_freeqhull(boolT allmem);
-void qh_init_A(FILE* infile, FILE* outfile, FILE* errfile, int argc, char* argv[]);
-void qh_init_B(coordT* points, int numpoints, int dim, boolT ismalloc);
-void qh_init_qhull_command(int argc, char* argv[]);
-void qh_initbuffers(coordT* points, int numpoints, int dim, boolT ismalloc);
-void qh_initflags(char* command);
-void qh_initqhull_buffers(void);
-void qh_initqhull_globals(coordT* points, int numpoints, int dim, boolT ismalloc);
-void qh_initqhull_mem(void);
-void qh_initqhull_start(FILE* infile, FILE* outfile, FILE* errfile);
-void qh_initthresholds(char* command);
-void qh_option(char* option, int* i, realT* r);
-#if qh_QHpointer
-void qh_restore_qhull(qhT** oldqh);
-qhT* qh_save_qhull(void);
-#endif
-
-/***** -io.c prototypes (duplicated from io.h) ***********************/
-
-void dfacet(unsigned id);
-void dvertex(unsigned id);
-void qh_printneighborhood(FILE* fp, int format, facetT* facetA, facetT* facetB, boolT printall);
-void qh_produce_output(void);
-coordT* qh_readpoints(int* numpoints, int* dimension, boolT* ismalloc);
-
-
-/********* -mem.c prototypes (duplicated from mem.h) **********************/
-
-void qh_meminit(FILE* ferr);
-void qh_memfreeshort(int* curlong, int* totlong);
-
-/********* -poly.c/poly2.c prototypes (duplicated from poly.h) **********************/
-
-void qh_check_output(void);
-void qh_check_points(void);
-setT* qh_facetvertices(facetT* facetlist, setT* facets, boolT allfacets);
-facetT* qh_findbestfacet(pointT* point, boolT bestoutside,
- realT* bestdist, boolT* isoutside);
-vertexT* qh_nearvertex(facetT* facet, pointT* point, realT* bestdistp);
-pointT* qh_point(int id);
-setT* qh_pointfacet(void /*qh.facet_list*/);
-int qh_pointid(pointT* point);
-setT* qh_pointvertex(void /*qh.facet_list*/);
-void qh_setvoronoi_all(void);
-void qh_triangulate(void /*qh facet_list*/);
-
-/********* -stat.c prototypes (duplicated from stat.h) **********************/
-
-void qh_collectstatistics(void);
-void qh_printallstatistics(FILE* fp, char* string);
-
-#endif /* qhDEFqhull */
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qhull_a.h b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qhull_a.h
deleted file mode 100644
index 5d985a084ab6fd201a6864692d249972ab5cb2f7..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qhull_a.h
+++ /dev/null
@@ -1,125 +0,0 @@
-/*<html><pre> -<a href="qh-qhull.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- qhull_a.h
- all header files for compiling qhull
-
- see qh-qhull.htm
-
- see qhull.h for user-level definitions
-
- see user.h for user-defineable constants
-
- defines internal functions for qhull.c global.c
-
- copyright (c) 1993-2003, The Geometry Center
-
- Notes: grep for ((" and (" to catch fprintf("lkasdjf");
- full parens around (x?y:z)
- use '#include qhull/qhull_a.h' to avoid name clashes
-*/
-
-#pragma once
-
-#include <stdio.h>
-#include <stdlib.h>
-#include <setjmp.h>
-#include <string.h>
-#include <math.h>
-#include <float.h> /* some compilers will not need float.h */
-#include <limits.h>
-#include <time.h>
-#include <ctype.h>
-/*** uncomment here and qset.c
- if string.h does not define memcpy()
-#include <memory.h>
-*/
-#include "qhull.h"
-#include "mem.h"
-#include "qset.h"
-#include "geom.h"
-#include "merge.h"
-#include "poly.h"
-#include "io.h"
-#include "stat.h"
-
-#if qh_CLOCKtype == 2 /* defined in user.h from qhull.h */
-#include <sys/types.h>
-#include <sys/times.h>
-#include <unistd.h>
-#endif
-
-#ifdef _MSC_VER /* Microsoft Visual C++ */
-#pragma warning( disable : 4056) /* float constant expression. Looks like a compiler bug */
-#pragma warning( disable : 4146) /* unary minus applied to unsigned type */
-#pragma warning( disable : 4244) /* conversion from 'unsigned long' to 'real' */
-#pragma warning( disable : 4305) /* conversion from 'const double' to 'float' */
-#endif
-
-/* ======= -macros- =========== */
-
-/*-<a href="qh-qhull.htm#TOC"
- >--------------------------------</a><a name="traceN">-</a>
-
- traceN((fp.ferr, "format\n", vars));
- calls fprintf if qh.IStracing >= N
-
- notes:
- removing tracing reduces code size but doesn't change execution speed
-*/
-#ifndef qh_NOtrace
-#define trace0(args) {if (qh IStracing) fprintf args;}
-#define trace1(args) {if (qh IStracing >= 1) fprintf args;}
-#define trace2(args) {if (qh IStracing >= 2) fprintf args;}
-#define trace3(args) {if (qh IStracing >= 3) fprintf args;}
-#define trace4(args) {if (qh IStracing >= 4) fprintf args;}
-#define trace5(args) {if (qh IStracing >= 5) fprintf args;}
-#else /* qh_NOtrace */
-#define trace0(args) {}
-#define trace1(args) {}
-#define trace2(args) {}
-#define trace3(args) {}
-#define trace4(args) {}
-#define trace5(args) {}
-#endif /* qh_NOtrace */
-
-/***** -qhull.c prototypes (alphabetical after qhull) ********************/
-
-void qh_qhull(void);
-boolT qh_addpoint(pointT* furthest, facetT* facet, boolT checkdist);
-void qh_buildhull(void);
-void qh_buildtracing(pointT* furthest, facetT* facet);
-void qh_build_withrestart(void);
-void qh_errexit2(int exitcode, facetT* facet, facetT* otherfacet);
-void qh_findhorizon(pointT* point, facetT* facet, int* goodvisible, int* goodhorizon);
-pointT* qh_nextfurthest(facetT** visible);
-void qh_partitionall(setT* vertices, pointT* points, int npoints);
-void qh_partitioncoplanar(pointT* point, facetT* facet, realT* dist);
-void qh_partitionpoint(pointT* point, facetT* facet);
-void qh_partitionvisible(boolT allpoints, int* numpoints);
-void qh_precision(char* reason);
-void qh_printsummary(FILE* fp);
-
-/***** -global.c internal prototypes (alphabetical) ***********************/
-
-void qh_appendprint(qh_PRINT format);
-void qh_freebuild(boolT allmem);
-void qh_freebuffers(void);
-void qh_initbuffers(coordT* points, int numpoints, int dim, boolT ismalloc);
-int qh_strtol(const char* s, char** endp);
-double qh_strtod(const char* s, char** endp);
-
-/***** -stat.c internal prototypes (alphabetical) ***********************/
-
-void qh_allstatA(void);
-void qh_allstatB(void);
-void qh_allstatC(void);
-void qh_allstatD(void);
-void qh_allstatE(void);
-void qh_allstatE2(void);
-void qh_allstatF(void);
-void qh_allstatG(void);
-void qh_allstatH(void);
-void qh_freebuffers(void);
-void qh_initbuffers(coordT* points, int numpoints, int dim, boolT ismalloc);
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qhull_interface.cpp b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qhull_interface.cpp
deleted file mode 100644
index b4a420a736930a2042c8e9741ec2f251f28abc41..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qhull_interface.cpp
+++ /dev/null
@@ -1,101 +0,0 @@
-/*<html><pre> -<a href="qh-user.htm"
- >-------------------------------</a><a name="TOP">-</a>
-*/
-
-#include <iostream.h>
-#include <conio.h>
-
-//--- Include qhull, so it works from with in a C++ source file
-//---
-//--- In MVC one cannot just do:
-//---
-//--- extern "C"
-//--- {
-//--- #include "qhull_a.h"
-//--- }
-//---
-//--- Because qhull_a.h includes math.h, which can not appear
-//--- inside a extern "C" declaration.
-//---
-//--- Maybe that why Numerical recipes in C avoid this problem, by removing
-//--- standard include headers from its header files and add them in the
-//--- respective source files instead.
-//---
-//--- [K. Erleben]
-
-#if defined(__cplusplus)
-extern "C"
-{
-#endif
-#include <stdio.h>
-#include <stdlib.h>
-#include <qhull/qhull.h>
-#include <qhull/mem.h>
-#include <qhull/qset.h>
-#include <qhull/geom.h>
-#include <qhull/merge.h>
-#include <qhull/poly.h>
-#include <qhull/io.h>
-#include <qhull/stat.h>
-#if defined(__cplusplus)
-}
-#endif
-
-/*********************************************************************/
-/* */
-/* */
-/* */
-/* */
-/*********************************************************************/
-
-void compute_convex_hull(void)
-{
- int dim; /* dimension of points */
- int numpoints; /* number of points */
- coordT* points; /* array of coordinates for each point */
- boolT ismalloc; /* True if qhull should free points in qh_freeqhull() or reallocation */
- char flags[] = "qhull Tv"; /* option flags for qhull, see qh_opt.htm */
- FILE* outfile = stdout; /* output from qh_produce_output()
- use NULL to skip qh_produce_output() */
- FILE* errfile = stderr; /* error messages from qhull code */
- int exitcode; /* 0 if no error from qhull */
- facetT* facet; /* set by FORALLfacets */
- int curlong, totlong; /* memory remaining after qh_memfreeshort */
-
- /* initialize dim, numpoints, points[], ismalloc here */
- exitcode = qh_new_qhull(dim, numpoints, points, ismalloc,
- flags, outfile, errfile);
-
- if (!exitcode) /* if no error */
- {
- /* 'qh facet_list' contains the convex hull */
- FORALLfacets
- {
- /* ... your code ... */
- }
- }
-
- qh_freeqhull(!qh_ALL);
- qh_memfreeshort(&curlong, &totlong);
-
- if (curlong || totlong)
- fprintf(errfile, "qhull internal warning (main): did not free %d bytes of long memory (%d pieces)\n",
- totlong, curlong);
-};
-
-/*********************************************************************/
-/* */
-/* */
-/* */
-/* */
-/*********************************************************************/
-
-void main()
-{
- cout << "Hello world" << endl;
-
- cout << "Press any key..." << endl;
-
- while (!_kbhit());
-
-};
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qset.c b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qset.c
deleted file mode 100644
index f902ea7a6cc7cf0c3f064471d9d83564f9008f6c..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qset.c
+++ /dev/null
@@ -1,1301 +0,0 @@
-/*<html><pre> -<a href="qh-set.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- qset.c
- implements set manipulations needed for quickhull
-
- see qh-set.htm and qset.h
-
- copyright (c) 1993-2003 The Geometry Center
-*/
-
-#include <stdio.h>
-#include <string.h>
-/*** uncomment here and qhull_a.h
- if string.h does not define memcpy()
-#include <memory.h>
-*/
-#include "qset.h"
-#include "mem.h"
-
-#ifndef qhDEFqhull
-typedef struct ridgeT ridgeT;
-typedef struct facetT facetT;
-void qh_errexit(int exitcode, facetT *, ridgeT *);
-#endif
-
-/*=============== internal macros ===========================*/
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="SETsizeaddr_">-</a>
-
- SETsizeaddr_(set)
- return pointer to actual size+1 of set (set CANNOT be NULL!!)
-
- notes:
- *SETsizeaddr==NULL or e[*SETsizeaddr-1].p==NULL
-*/
-#define SETsizeaddr_(set) (&((set)->e[(set)->maxsize].i))
-
-/*============ functions in alphabetical order ===================*/
-
-/*-<a href="qh-set.htm#TOC"
- >--------------------------------<a name="setaddnth">-</a>
-
- qh_setaddnth( setp, nth, newelem)
- adds newelem as n'th element of sorted or unsorted *setp
-
- notes:
- *setp and newelem must be defined
- *setp may be a temp set
- nth=0 is first element
- errors if nth is out of bounds
-
- design:
- expand *setp if empty or full
- move tail of *setp up one
- insert newelem
-*/
-void qh_setaddnth(setT **setp, int nth, void *newelem) {
- int *sizep, oldsize, i;
- void **oldp, **newp;
-
- if (!*setp || !*(sizep= SETsizeaddr_(*setp))) {
- qh_setlarger(setp);
- sizep= SETsizeaddr_(*setp);
- }
- oldsize= *sizep - 1;
- if (nth < 0 || nth > oldsize) {
- fprintf (qhmem.ferr, "qhull internal error (qh_setaddnth): nth %d is out-of-bounds for set:\n", nth);
- qh_setprint (qhmem.ferr, "", *setp);
- qh_errexit (qhmem_ERRqhull, NULL, NULL);
- }
- (*sizep)++;
- oldp= SETelemaddr_(*setp, oldsize, void); /* NULL */
- newp= oldp+1;
- for (i= oldsize-nth+1; i--; ) /* move at least NULL */
- *(newp--)= *(oldp--); /* may overwrite *sizep */
- *newp= newelem;
-} /* setaddnth */
-
-
-/*-<a href="qh-set.htm#TOC"
- >--------------------------------<a name="setaddsorted">-</a>
-
- setaddsorted( setp, newelem )
- adds an newelem into sorted *setp
-
- notes:
- *setp and newelem must be defined
- *setp may be a temp set
- nop if newelem already in set
-
- design:
- find newelem's position in *setp
- insert newelem
-*/
-void qh_setaddsorted(setT **setp, void *newelem) {
- int newindex=0;
- void *elem, **elemp;
-
- FOREACHelem_(*setp) { /* could use binary search instead */
- if (elem < newelem)
- newindex++;
- else if (elem == newelem)
- return;
- else
- break;
- }
- qh_setaddnth(setp, newindex, newelem);
-} /* setaddsorted */
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setappend">-</a>
-
- qh_setappend( setp, newelem)
- append newelem to *setp
-
- notes:
- *setp may be a temp set
- *setp and newelem may be NULL
-
- design:
- expand *setp if empty or full
- append newelem to *setp
-
-*/
-void qh_setappend(setT **setp, void *newelem) {
- int *sizep;
- void **endp;
-
- if (!newelem)
- return;
- if (!*setp || !*(sizep= SETsizeaddr_(*setp))) {
- qh_setlarger(setp);
- sizep= SETsizeaddr_(*setp);
- }
- *(endp= &((*setp)->e[(*sizep)++ - 1].p))= newelem;
- *(++endp)= NULL;
-} /* setappend */
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setappend_set">-</a>
-
- qh_setappend_set( setp, setA)
- appends setA to *setp
-
- notes:
- *setp can not be a temp set
- *setp and setA may be NULL
-
- design:
- setup for copy
- expand *setp if it is too small
- append all elements of setA to *setp
-*/
-void qh_setappend_set(setT **setp, setT *setA) {
- int *sizep, sizeA, size;
- setT *oldset;
-
- if (!setA)
- return;
- SETreturnsize_(setA, sizeA);
- if (!*setp)
- *setp= qh_setnew (sizeA);
- sizep= SETsizeaddr_(*setp);
- if (!(size= *sizep))
- size= (*setp)->maxsize;
- else
- size--;
- if (size + sizeA > (*setp)->maxsize) {
- oldset= *setp;
- *setp= qh_setcopy (oldset, sizeA);
- qh_setfree (&oldset);
- sizep= SETsizeaddr_(*setp);
- }
- *sizep= size+sizeA+1; /* memcpy may overwrite */
- if (sizeA > 0)
- memcpy((char *)&((*setp)->e[size].p), (char *)&(setA->e[0].p), SETelemsize *(sizeA+1));
-} /* setappend_set */
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setappend2ndlast">-</a>
-
- qh_setappend2ndlast( setp, newelem )
- makes newelem the next to the last element in *setp
-
- notes:
- *setp must have at least one element
- newelem must be defined
- *setp may be a temp set
-
- design:
- expand *setp if empty or full
- move last element of *setp up one
- insert newelem
-*/
-void qh_setappend2ndlast(setT **setp, void *newelem) {
- int *sizep;
- void **endp, **lastp;
-
- if (!*setp || !*(sizep= SETsizeaddr_(*setp))) {
- qh_setlarger(setp);
- sizep= SETsizeaddr_(*setp);
- }
- endp= SETelemaddr_(*setp, (*sizep)++ -1, void); /* NULL */
- lastp= endp-1;
- *(endp++)= *lastp;
- *endp= NULL; /* may overwrite *sizep */
- *lastp= newelem;
-} /* setappend2ndlast */
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setcheck">-</a>
-
- qh_setcheck( set, typename, id )
- check set for validity
- report errors with typename and id
-
- design:
- checks that maxsize, actual size, and NULL terminator agree
-*/
-void qh_setcheck(setT *set, char *tname, int id) {
- int maxsize, size;
- int waserr= 0;
-
- if (!set)
- return;
- SETreturnsize_(set, size);
- maxsize= set->maxsize;
- if (size > maxsize || !maxsize) {
- fprintf (qhmem.ferr, "qhull internal error (qh_setcheck): actual size %d of %s%d is greater than max size %d\n",
- size, tname, id, maxsize);
- waserr= 1;
- }else if (set->e[size].p) {
- fprintf (qhmem.ferr, "qhull internal error (qh_setcheck): %s%d (size %d max %d) is not null terminated.\n",
- tname, id, maxsize, size-1);
- waserr= 1;
- }
- if (waserr) {
- qh_setprint (qhmem.ferr, "ERRONEOUS", set);
- qh_errexit (qhmem_ERRqhull, NULL, NULL);
- }
-} /* setcheck */
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setcompact">-</a>
-
- qh_setcompact( set )
- remove internal NULLs from an unsorted set
-
- returns:
- updated set
-
- notes:
- set may be NULL
- it would be faster to swap tail of set into holes, like qh_setdel
-
- design:
- setup pointers into set
- skip NULLs while copying elements to start of set
- update the actual size
-*/
-void qh_setcompact(setT *set) {
- int size;
- void **destp, **elemp, **endp, **firstp;
-
- if (!set)
- return;
- SETreturnsize_(set, size);
- destp= elemp= firstp= SETaddr_(set, void);
- endp= destp + size;
- while (1) {
- if (!(*destp++ = *elemp++)) {
- destp--;
- if (elemp > endp)
- break;
- }
- }
- qh_settruncate (set, destp-firstp);
-} /* setcompact */
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setcopy">-</a>
-
- qh_setcopy( set, extra )
- make a copy of a sorted or unsorted set with extra slots
-
- returns:
- new set
-
- design:
- create a newset with extra slots
- copy the elements to the newset
-
-*/
-setT *qh_setcopy(setT *set, int extra) {
- setT *newset;
- int size;
-
- if (extra < 0)
- extra= 0;
- SETreturnsize_(set, size);
- newset= qh_setnew(size+extra);
- *SETsizeaddr_(newset)= size+1; /* memcpy may overwrite */
- memcpy((char *)&(newset->e[0].p), (char *)&(set->e[0].p), SETelemsize *(size+1));
- return (newset);
-} /* setcopy */
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setdel">-</a>
-
- qh_setdel( set, oldelem )
- delete oldelem from an unsorted set
-
- returns:
- returns oldelem if found
- returns NULL otherwise
-
- notes:
- set may be NULL
- oldelem must not be NULL;
- only deletes one copy of oldelem in set
-
- design:
- locate oldelem
- update actual size if it was full
- move the last element to the oldelem's location
-*/
-void *qh_setdel(setT *set, void *oldelem) {
- void **elemp, **lastp;
- int *sizep;
-
- if (!set)
- return NULL;
- elemp= SETaddr_(set, void);
- while (*elemp != oldelem && *elemp)
- elemp++;
- if (*elemp) {
- sizep= SETsizeaddr_(set);
- if (!(*sizep)--) /* if was a full set */
- *sizep= set->maxsize; /* *sizep= (maxsize-1)+ 1 */
- lastp= SETelemaddr_(set, *sizep-1, void);
- *elemp= *lastp; /* may overwrite itself */
- *lastp= NULL;
- return oldelem;
- }
- return NULL;
-} /* setdel */
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setdellast">-</a>
-
- qh_setdellast( set)
- return last element of set or NULL
-
- notes:
- deletes element from set
- set may be NULL
-
- design:
- return NULL if empty
- if full set
- delete last element and set actual size
- else
- delete last element and update actual size
-*/
-void *qh_setdellast(setT *set) {
- int setsize; /* actually, actual_size + 1 */
- int maxsize;
- int *sizep;
- void *returnvalue;
-
- if (!set || !(set->e[0].p))
- return NULL;
- sizep= SETsizeaddr_(set);
- if ((setsize= *sizep)) {
- returnvalue= set->e[setsize - 2].p;
- set->e[setsize - 2].p= NULL;
- (*sizep)--;
- }else {
- maxsize= set->maxsize;
- returnvalue= set->e[maxsize - 1].p;
- set->e[maxsize - 1].p= NULL;
- *sizep= maxsize;
- }
- return returnvalue;
-} /* setdellast */
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setdelnth">-</a>
-
- qh_setdelnth( set, nth )
- deletes nth element from unsorted set
- 0 is first element
-
- returns:
- returns the element (needs type conversion)
-
- notes:
- errors if nth invalid
-
- design:
- setup points and check nth
- delete nth element and overwrite with last element
-*/
-void *qh_setdelnth(setT *set, int nth) {
- void **elemp, **lastp, *elem;
- int *sizep;
-
-
- elemp= SETelemaddr_(set, nth, void);
- sizep= SETsizeaddr_(set);
- if (!(*sizep)--) /* if was a full set */
- *sizep= set->maxsize; /* *sizep= (maxsize-1)+ 1 */
- if (nth < 0 || nth >= *sizep) {
- fprintf (qhmem.ferr, "qhull internal error (qh_setaddnth): nth %d is out-of-bounds for set:\n", nth);
- qh_setprint (qhmem.ferr, "", set);
- qh_errexit (qhmem_ERRqhull, NULL, NULL);
- }
- lastp= SETelemaddr_(set, *sizep-1, void);
- elem= *elemp;
- *elemp= *lastp; /* may overwrite itself */
- *lastp= NULL;
- return elem;
-} /* setdelnth */
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setdelnthsorted">-</a>
-
- qh_setdelnthsorted( set, nth )
- deletes nth element from sorted set
-
- returns:
- returns the element (use type conversion)
-
- notes:
- errors if nth invalid
-
- see also:
- setnew_delnthsorted
-
- design:
- setup points and check nth
- copy remaining elements down one
- update actual size
-*/
-void *qh_setdelnthsorted(setT *set, int nth) {
- void **newp, **oldp, *elem;
- int *sizep;
-
- sizep= SETsizeaddr_(set);
- if (nth < 0 || (*sizep && nth >= *sizep-1) || nth >= set->maxsize) {
- fprintf (qhmem.ferr, "qhull internal error (qh_setaddnth): nth %d is out-of-bounds for set:\n", nth);
- qh_setprint (qhmem.ferr, "", set);
- qh_errexit (qhmem_ERRqhull, NULL, NULL);
- }
- newp= SETelemaddr_(set, nth, void);
- elem= *newp;
- oldp= newp+1;
- while ((*(newp++)= *(oldp++)))
- ; /* copy remaining elements and NULL */
- if (!(*sizep)--) /* if was a full set */
- *sizep= set->maxsize; /* *sizep= (max size-1)+ 1 */
- return elem;
-} /* setdelnthsorted */
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setdelsorted">-</a>
-
- qh_setdelsorted( set, oldelem )
- deletes oldelem from sorted set
-
- returns:
- returns oldelem if it was deleted
-
- notes:
- set may be NULL
-
- design:
- locate oldelem in set
- copy remaining elements down one
- update actual size
-*/
-void *qh_setdelsorted(setT *set, void *oldelem) {
- void **newp, **oldp;
- int *sizep;
-
- if (!set)
- return NULL;
- newp= SETaddr_(set, void);
- while(*newp != oldelem && *newp)
- newp++;
- if (*newp) {
- oldp= newp+1;
- while ((*(newp++)= *(oldp++)))
- ; /* copy remaining elements */
- sizep= SETsizeaddr_(set);
- if (!(*sizep)--) /* if was a full set */
- *sizep= set->maxsize; /* *sizep= (max size-1)+ 1 */
- return oldelem;
- }
- return NULL;
-} /* setdelsorted */
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setduplicate">-</a>
-
- qh_setduplicate( set, elemsize )
- duplicate a set of elemsize elements
-
- notes:
- use setcopy if retaining old elements
-
- design:
- create a new set
- for each elem of the old set
- create a newelem
- append newelem to newset
-*/
-setT *qh_setduplicate (setT *set, int elemsize) {
- void *elem, **elemp, *newElem;
- setT *newSet;
- int size;
-
- if (!(size= qh_setsize (set)))
- return NULL;
- newSet= qh_setnew (size);
- FOREACHelem_(set) {
- newElem= qh_memalloc (elemsize);
- memcpy (newElem, elem, elemsize);
- qh_setappend (&newSet, newElem);
- }
- return newSet;
-} /* setduplicate */
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setequal">-</a>
-
- qh_setequal( )
- returns 1 if two sorted sets are equal, otherwise returns 0
-
- notes:
- either set may be NULL
-
- design:
- check size of each set
- setup pointers
- compare elements of each set
-*/
-int qh_setequal(setT *setA, setT *setB) {
- void **elemAp, **elemBp;
- int sizeA, sizeB;
-
- SETreturnsize_(setA, sizeA);
- SETreturnsize_(setB, sizeB);
- if (sizeA != sizeB)
- return 0;
- if (!sizeA)
- return 1;
- elemAp= SETaddr_(setA, void);
- elemBp= SETaddr_(setB, void);
- if (!memcmp((char *)elemAp, (char *)elemBp, sizeA*SETelemsize))
- return 1;
- return 0;
-} /* setequal */
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setequal_except">-</a>
-
- qh_setequal_except( setA, skipelemA, setB, skipelemB )
- returns 1 if sorted setA and setB are equal except for skipelemA & B
-
- returns:
- false if either skipelemA or skipelemB are missing
-
- notes:
- neither set may be NULL
-
- if skipelemB is NULL,
- can skip any one element of setB
-
- design:
- setup pointers
- search for skipelemA, skipelemB, and mismatches
- check results
-*/
-int qh_setequal_except (setT *setA, void *skipelemA, setT *setB, void *skipelemB) {
- void **elemA, **elemB;
- int skip=0;
-
- elemA= SETaddr_(setA, void);
- elemB= SETaddr_(setB, void);
- while (1) {
- if (*elemA == skipelemA) {
- skip++;
- elemA++;
- }
- if (skipelemB) {
- if (*elemB == skipelemB) {
- skip++;
- elemB++;
- }
- }else if (*elemA != *elemB) {
- skip++;
- if (!(skipelemB= *elemB++))
- return 0;
- }
- if (!*elemA)
- break;
- if (*elemA++ != *elemB++)
- return 0;
- }
- if (skip != 2 || *elemB)
- return 0;
- return 1;
-} /* setequal_except */
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setequal_skip">-</a>
-
- qh_setequal_skip( setA, skipA, setB, skipB )
- returns 1 if sorted setA and setB are equal except for elements skipA & B
-
- returns:
- false if different size
-
- notes:
- neither set may be NULL
-
- design:
- setup pointers
- search for mismatches while skipping skipA and skipB
-*/
-int qh_setequal_skip (setT *setA, int skipA, setT *setB, int skipB) {
- void **elemA, **elemB, **skipAp, **skipBp;
-
- elemA= SETaddr_(setA, void);
- elemB= SETaddr_(setB, void);
- skipAp= SETelemaddr_(setA, skipA, void);
- skipBp= SETelemaddr_(setB, skipB, void);
- while (1) {
- if (elemA == skipAp)
- elemA++;
- if (elemB == skipBp)
- elemB++;
- if (!*elemA)
- break;
- if (*elemA++ != *elemB++)
- return 0;
- }
- if (*elemB)
- return 0;
- return 1;
-} /* setequal_skip */
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setfree">-</a>
-
- qh_setfree( setp )
- frees the space occupied by a sorted or unsorted set
-
- returns:
- sets setp to NULL
-
- notes:
- set may be NULL
-
- design:
- free array
- free set
-*/
-void qh_setfree(setT **setp) {
- int size;
- void **freelistp; /* used !qh_NOmem */
-
- if (*setp) {
- size= sizeof(setT) + ((*setp)->maxsize)*SETelemsize;
- if (size <= qhmem.LASTsize) {
- qh_memfree_(*setp, size, freelistp);
- }else
- qh_memfree (*setp, size);
- *setp= NULL;
- }
-} /* setfree */
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setfree2">-</a>
-
- qh_setfree2( setp, elemsize )
- frees the space occupied by a set and its elements
-
- notes:
- set may be NULL
-
- design:
- free each element
- free set
-*/
-void qh_setfree2 (setT **setp, int elemsize) {
- void *elem, **elemp;
-
- FOREACHelem_(*setp)
- qh_memfree (elem, elemsize);
- qh_setfree (setp);
-} /* setfree2 */
-
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setfreelong">-</a>
-
- qh_setfreelong( setp )
- frees a set only if it's in long memory
-
- returns:
- sets setp to NULL if it is freed
-
- notes:
- set may be NULL
-
- design:
- if set is large
- free it
-*/
-void qh_setfreelong(setT **setp) {
- int size;
-
- if (*setp) {
- size= sizeof(setT) + ((*setp)->maxsize)*SETelemsize;
- if (size > qhmem.LASTsize) {
- qh_memfree (*setp, size);
- *setp= NULL;
- }
- }
-} /* setfreelong */
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setin">-</a>
-
- qh_setin( set, setelem )
- returns 1 if setelem is in a set, 0 otherwise
-
- notes:
- set may be NULL or unsorted
-
- design:
- scans set for setelem
-*/
-int qh_setin(setT *set, void *setelem) {
- void *elem, **elemp;
-
- FOREACHelem_(set) {
- if (elem == setelem)
- return 1;
- }
- return 0;
-} /* setin */
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setindex">-</a>
-
- qh_setindex( set, atelem )
- returns the index of atelem in set.
- returns -1, if not in set or maxsize wrong
-
- notes:
- set may be NULL and may contain nulls.
-
- design:
- checks maxsize
- scans set for atelem
-*/
-int qh_setindex(setT *set, void *atelem) {
- void **elem;
- int size, i;
-
- SETreturnsize_(set, size);
- if (size > set->maxsize)
- return -1;
- elem= SETaddr_(set, void);
- for (i=0; i < size; i++) {
- if (*elem++ == atelem)
- return i;
- }
- return -1;
-} /* setindex */
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setlarger">-</a>
-
- qh_setlarger( oldsetp )
- returns a larger set that contains all elements of *oldsetp
-
- notes:
- the set is at least twice as large
- if temp set, updates qhmem.tempstack
-
- design:
- creates a new set
- copies the old set to the new set
- updates pointers in tempstack
- deletes the old set
-*/
-void qh_setlarger(setT **oldsetp) {
- int size= 1, *sizep;
- setT *newset, *set, **setp, *oldset;
- void **oldp, **newp;
-
- if (*oldsetp) {
- oldset= *oldsetp;
- SETreturnsize_(oldset, size);
- qhmem.cntlarger++;
- qhmem.totlarger += size+1;
- newset= qh_setnew(2 * size);
- oldp= SETaddr_(oldset, void);
- newp= SETaddr_(newset, void);
- memcpy((char *)newp, (char *)oldp, (size+1) * SETelemsize);
- sizep= SETsizeaddr_(newset);
- *sizep= size+1;
- FOREACHset_((setT *)qhmem.tempstack) {
- if (set == oldset)
- *(setp-1)= newset;
- }
- qh_setfree(oldsetp);
- }else
- newset= qh_setnew(3);
- *oldsetp= newset;
-} /* setlarger */
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setlast">-</a>
-
- qh_setlast( )
- return last element of set or NULL (use type conversion)
-
- notes:
- set may be NULL
-
- design:
- return last element
-*/
-void *qh_setlast(setT *set) {
- int size;
-
- if (set) {
- size= *SETsizeaddr_(set);
- if (!size)
- return SETelem_(set, set->maxsize - 1);
- else if (size > 1)
- return SETelem_(set, size - 2);
- }
- return NULL;
-} /* setlast */
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setnew">-</a>
-
- qh_setnew( setsize )
- creates and allocates space for a set
-
- notes:
- setsize means the number of elements (NOT including the NULL terminator)
- use qh_settemp/qh_setfreetemp if set is temporary
-
- design:
- allocate memory for set
- roundup memory if small set
- initialize as empty set
-*/
-setT *qh_setnew(int setsize) {
- setT *set;
- int sizereceived; /* used !qh_NOmem */
- int size;
- void **freelistp; /* used !qh_NOmem */
-
- if (!setsize)
- setsize++;
- size= sizeof(setT) + setsize * SETelemsize;
- if ((unsigned) size <= (unsigned) qhmem.LASTsize) {
- qh_memalloc_(size, freelistp, set, setT);
-#ifndef qh_NOmem
- sizereceived= qhmem.sizetable[ qhmem.indextable[size]];
- if (sizereceived > size)
- setsize += (sizereceived - size)/SETelemsize;
-#endif
- }else
- set= (setT*)qh_memalloc (size);
- set->maxsize= setsize;
- set->e[setsize].i= 1;
- set->e[0].p= NULL;
- return (set);
-} /* setnew */
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setnew_delnthsorted">-</a>
-
- qh_setnew_delnthsorted( set, size, nth, prepend )
- creates a sorted set not containing nth element
- if prepend, the first prepend elements are undefined
-
- notes:
- set must be defined
- checks nth
- see also: setdelnthsorted
-
- design:
- create new set
- setup pointers and allocate room for prepend'ed entries
- append head of old set to new set
- append tail of old set to new set
-*/
-setT *qh_setnew_delnthsorted(setT *set, int size, int nth, int prepend) {
- setT *newset;
- void **oldp, **newp;
- int tailsize= size - nth -1, newsize;
-
- if (tailsize < 0) {
- fprintf (qhmem.ferr, "qhull internal error (qh_setaddnth): nth %d is out-of-bounds for set:\n", nth);
- qh_setprint (qhmem.ferr, "", set);
- qh_errexit (qhmem_ERRqhull, NULL, NULL);
- }
- newsize= size-1 + prepend;
- newset= qh_setnew(newsize);
- newset->e[newset->maxsize].i= newsize+1; /* may be overwritten */
- oldp= SETaddr_(set, void);
- newp= SETaddr_(newset, void) + prepend;
- switch (nth) {
- case 0:
- break;
- case 1:
- *(newp++)= *oldp++;
- break;
- case 2:
- *(newp++)= *oldp++;
- *(newp++)= *oldp++;
- break;
- case 3:
- *(newp++)= *oldp++;
- *(newp++)= *oldp++;
- *(newp++)= *oldp++;
- break;
- case 4:
- *(newp++)= *oldp++;
- *(newp++)= *oldp++;
- *(newp++)= *oldp++;
- *(newp++)= *oldp++;
- break;
- default:
- memcpy((char *)newp, (char *)oldp, nth * SETelemsize);
- newp += nth;
- oldp += nth;
- break;
- }
- oldp++;
- switch (tailsize) {
- case 0:
- break;
- case 1:
- *(newp++)= *oldp++;
- break;
- case 2:
- *(newp++)= *oldp++;
- *(newp++)= *oldp++;
- break;
- case 3:
- *(newp++)= *oldp++;
- *(newp++)= *oldp++;
- *(newp++)= *oldp++;
- break;
- case 4:
- *(newp++)= *oldp++;
- *(newp++)= *oldp++;
- *(newp++)= *oldp++;
- *(newp++)= *oldp++;
- break;
- default:
- memcpy((char *)newp, (char *)oldp, tailsize * SETelemsize);
- newp += tailsize;
- }
- *newp= NULL;
- return(newset);
-} /* setnew_delnthsorted */
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setprint">-</a>
-
- qh_setprint( fp, string, set )
- print set elements to fp with identifying string
-
- notes:
- never errors
-*/
-void qh_setprint(FILE *fp, char* string, setT *set) {
- int size, k;
-
- if (!set)
- fprintf (fp, "%s set is null\n", string);
- else {
- SETreturnsize_(set, size);
- fprintf (fp, "%s set=%p maxsize=%d size=%d elems=",
- string, set, set->maxsize, size);
- if (size > set->maxsize)
- size= set->maxsize+1;
- for (k=0; k < size; k++)
- fprintf(fp, " %p", set->e[k].p);
- fprintf(fp, "\n");
- }
-} /* setprint */
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setreplace">-</a>
-
- qh_setreplace( set, oldelem, newelem )
- replaces oldelem in set with newelem
-
- notes:
- errors if oldelem not in the set
- newelem may be NULL, but it turns the set into an indexed set (no FOREACH)
-
- design:
- find oldelem
- replace with newelem
-*/
-void qh_setreplace(setT *set, void *oldelem, void *newelem) {
- void **elemp;
-
- elemp= SETaddr_(set, void);
- while(*elemp != oldelem && *elemp)
- elemp++;
- if (*elemp)
- *elemp= newelem;
- else {
- fprintf (qhmem.ferr, "qhull internal error (qh_setreplace): elem %p not found in set\n",
- oldelem);
- qh_setprint (qhmem.ferr, "", set);
- qh_errexit (qhmem_ERRqhull, NULL, NULL);
- }
-} /* setreplace */
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setsize">-</a>
-
- qh_setsize( set )
- returns the size of a set
-
- notes:
- errors if set's maxsize is incorrect
- same as SETreturnsize_(set)
-
- design:
- determine actual size of set from maxsize
-*/
-int qh_setsize(setT *set) {
- int size, *sizep;
-
- if (!set)
- return (0);
- sizep= SETsizeaddr_(set);
- if ((size= *sizep)) {
- size--;
- if (size > set->maxsize) {
- fprintf (qhmem.ferr, "qhull internal error (qh_setsize): current set size %d is greater than maximum size %d\n",
- size, set->maxsize);
- qh_setprint (qhmem.ferr, "set: ", set);
- qh_errexit (qhmem_ERRqhull, NULL, NULL);
- }
- }else
- size= set->maxsize;
- return size;
-} /* setsize */
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="settemp">-</a>
-
- qh_settemp( setsize )
- return a stacked, temporary set of upto setsize elements
-
- notes:
- use settempfree or settempfree_all to release from qhmem.tempstack
- see also qh_setnew
-
- design:
- allocate set
- append to qhmem.tempstack
-
-*/
-setT *qh_settemp(int setsize) {
- setT *newset;
-
- newset= qh_setnew (setsize);
- qh_setappend ((setT **)&qhmem.tempstack, newset);
- if (qhmem.IStracing >= 5)
- fprintf (qhmem.ferr, "qh_settemp: temp set %p of %d elements, depth %d\n",
- newset, newset->maxsize, qh_setsize ((setT*)qhmem.tempstack));
- return newset;
-} /* settemp */
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="settempfree">-</a>
-
- qh_settempfree( set )
- free temporary set at top of qhmem.tempstack
-
- notes:
- nop if set is NULL
- errors if set not from previous qh_settemp
-
- to locate errors:
- use 'T2' to find source and then find mis-matching qh_settemp
-
- design:
- check top of qhmem.tempstack
- free it
-*/
-void qh_settempfree(setT **set) {
- setT *stackedset;
-
- if (!*set)
- return;
- stackedset= qh_settemppop ();
- if (stackedset != *set) {
- qh_settemppush(stackedset);
- fprintf (qhmem.ferr, "qhull internal error (qh_settempfree): set %p (size %d) was not last temporary allocated (depth %d, set %p, size %d)\n",
- *set, qh_setsize(*set), qh_setsize((setT*)qhmem.tempstack)+1,
- stackedset, qh_setsize(stackedset));
- qh_errexit (qhmem_ERRqhull, NULL, NULL);
- }
- qh_setfree (set);
-} /* settempfree */
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="settempfree_all">-</a>
-
- qh_settempfree_all( )
- free all temporary sets in qhmem.tempstack
-
- design:
- for each set in tempstack
- free set
- free qhmem.tempstack
-*/
-void qh_settempfree_all(void) {
- setT *set, **setp;
-
- FOREACHset_((setT *)qhmem.tempstack)
- qh_setfree(&set);
- qh_setfree((setT **)&qhmem.tempstack);
-} /* settempfree_all */
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="settemppop">-</a>
-
- qh_settemppop( )
- pop and return temporary set from qhmem.tempstack
-
- notes:
- the returned set is permanent
-
- design:
- pop and check top of qhmem.tempstack
-*/
-setT *qh_settemppop(void) {
- setT *stackedset;
-
- stackedset= (setT*)qh_setdellast((setT *)qhmem.tempstack);
- if (!stackedset) {
- fprintf (qhmem.ferr, "qhull internal error (qh_settemppop): pop from empty temporary stack\n");
- qh_errexit (qhmem_ERRqhull, NULL, NULL);
- }
- if (qhmem.IStracing >= 5)
- fprintf (qhmem.ferr, "qh_settemppop: depth %d temp set %p of %d elements\n",
- qh_setsize((setT*)qhmem.tempstack)+1, stackedset, qh_setsize(stackedset));
- return stackedset;
-} /* settemppop */
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="settemppush">-</a>
-
- qh_settemppush( set )
- push temporary set unto qhmem.tempstack (makes it temporary)
-
- notes:
- duplicates settemp() for tracing
-
- design:
- append set to tempstack
-*/
-void qh_settemppush(setT *set) {
-
- qh_setappend ((setT**)&qhmem.tempstack, set);
- if (qhmem.IStracing >= 5)
- fprintf (qhmem.ferr, "qh_settemppush: depth %d temp set %p of %d elements\n",
- qh_setsize((setT*)qhmem.tempstack), set, qh_setsize(set));
-} /* settemppush */
-
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="settruncate">-</a>
-
- qh_settruncate( set, size )
- truncate set to size elements
-
- notes:
- set must be defined
-
- see:
- SETtruncate_
-
- design:
- check size
- update actual size of set
-*/
-void qh_settruncate (setT *set, int size) {
-
- if (size < 0 || size > set->maxsize) {
- fprintf (qhmem.ferr, "qhull internal error (qh_settruncate): size %d out of bounds for set:\n", size);
- qh_setprint (qhmem.ferr, "", set);
- qh_errexit (qhmem_ERRqhull, NULL, NULL);
- }
- set->e[set->maxsize].i= size+1; /* maybe overwritten */
- set->e[size].p= NULL;
-} /* settruncate */
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setunique">-</a>
-
- qh_setunique( set, elem )
- add elem to unsorted set unless it is already in set
-
- notes:
- returns 1 if it is appended
-
- design:
- if elem not in set
- append elem to set
-*/
-int qh_setunique (setT **set, void *elem) {
-
- if (!qh_setin (*set, elem)) {
- qh_setappend (set, elem);
- return 1;
- }
- return 0;
-} /* setunique */
-
-/*-<a href="qh-set.htm#TOC"
- >-------------------------------<a name="setzero">-</a>
-
- qh_setzero( set, index, size )
- zero elements from index on
- set actual size of set to size
-
- notes:
- set must be defined
- the set becomes an indexed set (can not use FOREACH...)
-
- see also:
- qh_settruncate
-
- design:
- check index and size
- update actual size
- zero elements starting at e[index]
-*/
-void qh_setzero (setT *set, int index, int size) {
- int count;
-
- if (index < 0 || index >= size || size > set->maxsize) {
- fprintf (qhmem.ferr, "qhull internal error (qh_setzero): index %d or size %d out of bounds for set:\n", index, size);
- qh_setprint (qhmem.ferr, "", set);
- qh_errexit (qhmem_ERRqhull, NULL, NULL);
- }
- set->e[set->maxsize].i= size+1; /* may be overwritten */
- count= size - index + 1; /* +1 for NULL terminator */
- memset ((char *)SETelemaddr_(set, index, void), 0, count * SETelemsize);
-} /* setzero */
-
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qset.h b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qset.h
deleted file mode 100644
index 165a84c3b361527d8478a66c829d29e49420816a..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/qset.h
+++ /dev/null
@@ -1,470 +0,0 @@
-/*<html><pre> -<a href="qh-set.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- qset.h
- header file for qset.c that implements set
-
- see qh-set.htm and qset.c
-
- only uses mem.c, malloc/free
-
- for error handling, writes message and calls
- qh_errexit (qhmem_ERRqhull, NULL, NULL);
-
- set operations satisfy the following properties:
- - sets have a max size, the actual size (if different) is stored at the end
- - every set is NULL terminated
- - sets may be sorted or unsorted, the caller must distinguish this
-
- copyright (c) 1993-2003, The Geometry Center
-*/
-
-#ifndef qhDEFset
-#define qhDEFset 1
-
-/*================= -structures- ===============*/
-
-#ifndef DEFsetT
-#define DEFsetT 1
-typedef struct setT setT; /* a set is a sorted or unsorted array of pointers */
-#endif
-
-/*-<a href="qh-set.htm#TOC"
->----------------------------------------</a><a name="setT">-</a>
-
-setT
- a set or list of pointers with maximum size and actual size.
-
-variations:
- unsorted, unique -- a list of unique pointers with NULL terminator
- user guarantees uniqueness
- sorted -- a sorted list of unique pointers with NULL terminator
- qset.c guarantees uniqueness
- unsorted -- a list of pointers terminated with NULL
- indexed -- an array of pointers with NULL elements
-
-structure for set of n elements:
-
- --------------
- | maxsize
- --------------
- | e[0] - a pointer, may be NULL for indexed sets
- --------------
- | e[1]
-
- --------------
- | ...
- --------------
- | e[n-1]
- --------------
- | e[n] = NULL
- --------------
- | ...
- --------------
- | e[maxsize] - n+1 or NULL (determines actual size of set)
- --------------
-
-*/
-
-/*-- setelemT -- internal type to allow both pointers and indices
-*/
-typedef union setelemT setelemT;
-union setelemT
-{
- void* p;
- int i; /* integer used for e[maxSize] */
-};
-
-struct setT
-{
- int maxsize; /* maximum number of elements (except NULL) */
- setelemT e[1]; /* array of pointers, tail is NULL */
- /* last slot (unless NULL) is actual size+1
- e[maxsize]==NULL or e[e[maxsize]-1]==NULL */
- /* this may generate a warning since e[] contains
- maxsize elements */
-};
-
-/*=========== -constants- =========================*/
-
-/*-<a href="qh-set.htm#TOC"
- >-----------------------------------</a><a name="SETelemsize">-</a>
-
- SETelemsize
- size of a set element in bytes
-*/
-#define SETelemsize sizeof(setelemT)
-
-
-/*=========== -macros- =========================*/
-
-/*-<a href="qh-set.htm#TOC"
- >-----------------------------------</a><a name="FOREACHsetelement_">-</a>
-
- FOREACHsetelement_(type, set, variable)
- define FOREACH iterator
-
- declare:
- assumes *variable and **variablep are declared
- no space in "variable)" [DEC Alpha cc compiler]
-
- each iteration:
- variable is set element
- variablep is one beyond variable.
-
- to repeat an element:
- variablep--; / *repeat* /
-
- at exit:
- variable is NULL at end of loop
-
- example:
- #define FOREACHfacet_( facets ) FOREACHsetelement_( facetT, facets, facet )
-
- notes:
- use FOREACHsetelement_i_() if need index or include NULLs
-
- WARNING:
- nested loops can't use the same variable (define another FOREACH)
-
- needs braces if nested inside another FOREACH
- this includes intervening blocks, e.g. FOREACH...{ if () FOREACH...} )
-*/
-#define FOREACHsetelement_(type, set, variable) \
- if (((variable= NULL), set)) for(\
- variable##p= (type **)&((set)->e[0].p); \
- (variable= *variable##p++);)
-
-/*-<a href="qh-set.htm#TOC"
- >----------------------------------------</a><a name="FOREACHsetelement_i_">-</a>
-
- FOREACHsetelement_i_(type, set, variable)
- define indexed FOREACH iterator
-
- declare:
- type *variable, variable_n, variable_i;
-
- each iteration:
- variable is set element, may be NULL
- variable_i is index, variable_n is qh_setsize()
-
- to repeat an element:
- variable_i--; variable_n-- repeats for deleted element
-
- at exit:
- variable==NULL and variable_i==variable_n
-
- example:
- #define FOREACHfacet_i_( facets ) FOREACHsetelement_i_( facetT, facets, facet )
-
- WARNING:
- nested loops can't use the same variable (define another FOREACH)
-
- needs braces if nested inside another FOREACH
- this includes intervening blocks, e.g. FOREACH...{ if () FOREACH...} )
-*/
-#define FOREACHsetelement_i_(type, set, variable) \
- if (((variable= NULL), set)) for (\
- variable##_i= 0, variable= (type *)((set)->e[0].p), \
- variable##_n= qh_setsize(set);\
- variable##_i < variable##_n;\
- variable= (type *)((set)->e[++variable##_i].p) )
-
-/*-<a href="qh-set.htm#TOC"
- >--------------------------------------</a><a name="FOREACHsetelementreverse_">-</a>
-
- FOREACHsetelementreverse_(type, set, variable)-
- define FOREACH iterator in reverse order
-
- declare:
- assumes *variable and **variablep are declared
- also declare 'int variabletemp'
-
- each iteration:
- variable is set element
-
- to repeat an element:
- variabletemp++; / *repeat* /
-
- at exit:
- variable is NULL
-
- example:
- #define FOREACHvertexreverse_( vertices ) FOREACHsetelementreverse_( vertexT, vertices, vertex )
-
- notes:
- use FOREACHsetelementreverse12_() to reverse first two elements
- WARNING: needs braces if nested inside another FOREACH
-*/
-#define FOREACHsetelementreverse_(type, set, variable) \
- if (((variable= NULL), set)) for(\
- variable##temp= qh_setsize(set)-1, variable= qh_setlast(set);\
- variable; variable= \
- ((--variable##temp >= 0) ? SETelemt_(set, variable##temp, type) : NULL))
-
-/*-<a href="qh-set.htm#TOC"
- >-----------------------------------</a><a name="FOREACHsetelementreverse12_">-</a>
-
- FOREACHsetelementreverse12_(type, set, variable)-
- define FOREACH iterator with e[1] and e[0] reversed
-
- declare:
- assumes *variable and **variablep are declared
-
- each iteration:
- variable is set element
- variablep is one after variable.
-
- to repeat an element:
- variablep--; / *repeat* /
-
- at exit:
- variable is NULL at end of loop
-
- example
- #define FOREACHvertexreverse12_( vertices ) FOREACHsetelementreverse12_( vertexT, vertices, vertex )
-
- notes:
- WARNING: needs braces if nested inside another FOREACH
-*/
-#define FOREACHsetelementreverse12_(type, set, variable) \
- if (((variable= NULL), set)) for(\
- variable##p= (type **)&((set)->e[1].p); \
- (variable= *variable##p); \
- variable##p == ((type **)&((set)->e[0].p))?variable##p += 2: \
- (variable##p == ((type **)&((set)->e[1].p))?variable##p--:variable##p++))
-
-/*-<a href="qh-set.htm#TOC"
- >-----------------------------------</a><a name="FOREACHelem_">-</a>
-
- FOREACHelem_( set )-
- iterate elements in a set
-
- declare:
- void *elem, *elemp;
-
- each iteration:
- elem is set element
- elemp is one beyond
-
- to repeat an element:
- elemp--; / *repeat* /
-
- at exit:
- elem == NULL at end of loop
-
- example:
- FOREACHelem_(set) {
-
- notes:
- WARNING: needs braces if nested inside another FOREACH
-*/
-#define FOREACHelem_(set) FOREACHsetelement_(void, set, elem)
-
-/*-<a href="qh-set.htm#TOC"
- >-----------------------------------</a><a name="FOREACHset_">-</a>
-
- FOREACHset_( set )-
- iterate a set of sets
-
- declare:
- setT *set, **setp;
-
- each iteration:
- set is set element
- setp is one beyond
-
- to repeat an element:
- setp--; / *repeat* /
-
- at exit:
- set == NULL at end of loop
-
- example
- FOREACHset_(sets) {
-
- notes:
- WARNING: needs braces if nested inside another FOREACH
-*/
-#define FOREACHset_(sets) FOREACHsetelement_(setT, sets, set)
-
-/*-<a href="qh-set.htm#TOC"
- >-----------------------------------------</a><a name="SETindex_">-</a>
-
- SETindex_( set, elem )
- return index of elem in set
-
- notes:
- for use with FOREACH iteration
-
- example:
- i= SETindex_(ridges, ridge)
-*/
-#define SETindex_(set, elem) ((void **)elem##p - (void **)&(set)->e[1].p)
-
-/*-<a href="qh-set.htm#TOC"
- >---------------------------------------</a><a name="SETref_">-</a>
-
- SETref_( elem )
- l.h.s. for modifying the current element in a FOREACH iteration
-
- example:
- SETref_(ridge)= anotherridge;
-*/
-#define SETref_(elem) (elem##p[-1])
-
-/*-<a href="qh-set.htm#TOC"
- >---------------------------------------</a><a name="SETelem_">-</a>
-
- SETelem_(set, n)
- return the n'th element of set
-
- notes:
- assumes that n is valid [0..size] and that set is defined
- use SETelemt_() for type cast
-*/
-#define SETelem_(set, n) ((set)->e[n].p)
-
-/*-<a href="qh-set.htm#TOC"
- >---------------------------------------</a><a name="SETelemt_">-</a>
-
- SETelemt_(set, n, type)
- return the n'th element of set as a type
-
- notes:
- assumes that n is valid [0..size] and that set is defined
-*/
-#define SETelemt_(set, n, type) ((type*)((set)->e[n].p))
-
-/*-<a href="qh-set.htm#TOC"
- >---------------------------------------</a><a name="SETelemaddr_">-</a>
-
- SETelemaddr_(set, n, type)
- return address of the n'th element of a set
-
- notes:
- assumes that n is valid [0..size] and set is defined
-*/
-#define SETelemaddr_(set, n, type) ((type **)(&((set)->e[n].p)))
-
-/*-<a href="qh-set.htm#TOC"
- >---------------------------------------</a><a name="SETfirst_">-</a>
-
- SETfirst_(set)
- return first element of set
-
-*/
-#define SETfirst_(set) ((set)->e[0].p)
-
-/*-<a href="qh-set.htm#TOC"
- >---------------------------------------</a><a name="SETfirstt_">-</a>
-
- SETfirstt_(set, type)
- return first element of set as a type
-
-*/
-#define SETfirstt_(set, type) ((type*)((set)->e[0].p))
-
-/*-<a href="qh-set.htm#TOC"
- >---------------------------------------</a><a name="SETsecond_">-</a>
-
- SETsecond_(set)
- return second element of set
-
-*/
-#define SETsecond_(set) ((set)->e[1].p)
-
-/*-<a href="qh-set.htm#TOC"
- >---------------------------------------</a><a name="SETsecondt_">-</a>
-
- SETsecondt_(set, type)
- return second element of set as a type
-*/
-#define SETsecondt_(set, type) ((type*)((set)->e[1].p))
-
-/*-<a href="qh-set.htm#TOC"
- >---------------------------------------</a><a name="SETaddr_">-</a>
-
- SETaddr_(set, type)
- return address of set's elements
-*/
-#define SETaddr_(set,type) ((type **)(&((set)->e[0].p)))
-
-/*-<a href="qh-set.htm#TOC"
- >---------------------------------------</a><a name="SETreturnsize_">-</a>
-
- SETreturnsize_(set, size)
- return size of a set
-
- notes:
- set must be defined
- use qh_setsize(set) unless speed is critical
-*/
-#define SETreturnsize_(set, size) (((size)= ((set)->e[(set)->maxsize].i))?(--(size)):((size)= (set)->maxsize))
-
-/*-<a href="qh-set.htm#TOC"
- >---------------------------------------</a><a name="SETempty_">-</a>
-
- SETempty_(set)
- return true (1) if set is empty
-
- notes:
- set may be NULL
-*/
-#define SETempty_(set) (!set || (SETfirst_(set) ? 0:1))
-
-/*-<a href="qh-set.htm#TOC"
- >---------------------------------------</a><a name="SETtruncate_">-</a>
-
- SETtruncate_(set)
- return first element of set
-
- see:
- qh_settruncate()
-
-*/
-#define SETtruncate_(set, size) {set->e[set->maxsize].i= size+1; /* maybe overwritten */ \
- set->e[size].p= NULL;}
-
-/*======= prototypes in alphabetical order ============*/
-
-void qh_setaddsorted(setT** setp, void* elem);
-void qh_setaddnth(setT** setp, int nth, void* newelem);
-void qh_setappend(setT** setp, void* elem);
-void qh_setappend_set(setT** setp, setT* setA);
-void qh_setappend2ndlast(setT** setp, void* elem);
-void qh_setcheck(setT* set, char* tname, int id);
-void qh_setcompact(setT* set);
-setT* qh_setcopy(setT* set, int extra);
-void* qh_setdel(setT* set, void* elem);
-void* qh_setdellast(setT* set);
-void* qh_setdelnth(setT* set, int nth);
-void* qh_setdelnthsorted(setT* set, int nth);
-void* qh_setdelsorted(setT* set, void* newelem);
-setT* qh_setduplicate(setT* set, int elemsize);
-int qh_setequal(setT* setA, setT* setB);
-int qh_setequal_except(setT* setA, void* skipelemA, setT* setB, void* skipelemB);
-int qh_setequal_skip(setT* setA, int skipA, setT* setB, int skipB);
-void qh_setfree(setT** set);
-void qh_setfree2(setT** setp, int elemsize);
-void qh_setfreelong(setT** set);
-int qh_setin(setT* set, void* setelem);
-int qh_setindex(setT* set, void* setelem);
-void qh_setlarger(setT** setp);
-void* qh_setlast(setT* set);
-setT* qh_setnew(int size);
-setT* qh_setnew_delnthsorted(setT* set, int size, int nth, int prepend);
-void qh_setprint(FILE* fp, char* string, setT* set);
-void qh_setreplace(setT* set, void* oldelem, void* newelem);
-int qh_setsize(setT* set);
-setT* qh_settemp(int setsize);
-void qh_settempfree(setT** set);
-void qh_settempfree_all(void);
-setT* qh_settemppop(void);
-void qh_settemppush(setT* set);
-void qh_settruncate(setT* set, int size);
-int qh_setunique(setT** set, void* elem);
-void qh_setzero(setT* set, int index, int size);
-
-
-#endif /* qhDEFset */
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/stat.c b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/stat.c
deleted file mode 100644
index 9ac3b0e74312f7e9ebe731d614ad4507d7f99ec8..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/stat.c
+++ /dev/null
@@ -1,702 +0,0 @@
-/*<html><pre> -<a href="qh-stat.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- stat.c
- contains all statistics that are collected for qhull
-
- see qh-stat.htm and stat.h
-
- copyright (c) 1993-2003, The Geometry Center
-*/
-
-#include "qhull_a.h"
-
-/*============ global data structure ==========*/
-
-#if qh_QHpointer
-qhstatT *qh_qhstat=NULL; /* global data structure */
-#else
-qhstatT qh_qhstat; /* add "={0}" if this causes a compiler error */
-#endif
-
-/*========== functions in alphabetic order ================*/
-
-/*-<a href="qh-stat.htm#TOC"
- >-------------------------------</a><a name="allstatA">-</a>
-
- qh_allstatA()
- define statistics in groups of 20
-
- notes:
- (otherwise, 'gcc -O2' uses too much memory)
- uses qhstat.next
-*/
-void qh_allstatA (void) {
-
- /* zdef_(type,name,doc,average) */
- zzdef_(zdoc, Zdoc2, "precision statistics", -1);
- zdef_(zinc, Znewvertex, NULL, -1);
- zdef_(wadd, Wnewvertex, "ave. distance of a new vertex to a facet (not 0s)", Znewvertex);
- zzdef_(wmax, Wnewvertexmax, "max. distance of a new vertex to a facet", -1);
- zdef_(wmax, Wvertexmax, "max. distance of an output vertex to a facet", -1);
- zdef_(wmin, Wvertexmin, "min. distance of an output vertex to a facet", -1);
- zdef_(wmin, Wmindenom, "min. denominator in hyperplane computation", -1);
-
- qhstat precision= qhstat next; /* call qh_precision for each of these */
- zzdef_(zdoc, Zdoc3, "precision problems (corrected unless 'Q0' or an error)", -1);
- zzdef_(zinc, Zcoplanarridges, "coplanar half ridges in output", -1);
- zzdef_(zinc, Zconcaveridges, "concave half ridges in output", -1);
- zzdef_(zinc, Zflippedfacets, "flipped facets", -1);
- zzdef_(zinc, Zcoplanarhorizon, "coplanar horizon facets for new vertices", -1);
- zzdef_(zinc, Zcoplanarpart, "coplanar points during partitioning", -1);
- zzdef_(zinc, Zminnorm, "degenerate hyperplanes recomputed with gaussian elimination", -1);
- zzdef_(zinc, Znearlysingular, "nearly singular or axis-parallel hyperplanes", -1);
- zzdef_(zinc, Zback0, "zero divisors during back substitute", -1);
- zzdef_(zinc, Zgauss0, "zero divisors during gaussian elimination", -1);
- zzdef_(zinc, Zmultiridge, "ridges with multiple neighbors", -1);
-}
-void qh_allstatB (void) {
- zzdef_(zdoc, Zdoc1, "summary information", -1);
- zdef_(zinc, Zvertices, "number of vertices in output", -1);
- zdef_(zinc, Znumfacets, "number of facets in output", -1);
- zdef_(zinc, Znonsimplicial, "number of non-simplicial facets in output", -1);
- zdef_(zinc, Znowsimplicial, "number of simplicial facets that were merged", -1);
- zdef_(zinc, Znumridges, "number of ridges in output", -1);
- zdef_(zadd, Znumridges, "average number of ridges per facet", Znumfacets);
- zdef_(zmax, Zmaxridges, "maximum number of ridges", -1);
- zdef_(zadd, Znumneighbors, "average number of neighbors per facet", Znumfacets);
- zdef_(zmax, Zmaxneighbors, "maximum number of neighbors", -1);
- zdef_(zadd, Znumvertices, "average number of vertices per facet", Znumfacets);
- zdef_(zmax, Zmaxvertices, "maximum number of vertices", -1);
- zdef_(zadd, Znumvneighbors, "average number of neighbors per vertex", Zvertices);
- zdef_(zmax, Zmaxvneighbors, "maximum number of neighbors", -1);
- zdef_(wadd, Wcpu, "cpu seconds for qhull after input", -1);
- zdef_(zinc, Ztotvertices, "vertices created altogether", -1);
- zzdef_(zinc, Zsetplane, "facets created altogether", -1);
- zdef_(zinc, Ztotridges, "ridges created altogether", -1);
- zdef_(zinc, Zpostfacets, "facets before post merge", -1);
- zdef_(zadd, Znummergetot, "average merges per facet (at most 511)", Znumfacets);
- zdef_(zmax, Znummergemax, " maximum merges for a facet (at most 511)", -1);
- zdef_(zinc, Zangle, NULL, -1);
- zdef_(wadd, Wangle, "average angle (cosine) of facet normals for all ridges", Zangle);
- zdef_(wmax, Wanglemax, " maximum angle (cosine) of facet normals across a ridge", -1);
- zdef_(wmin, Wanglemin, " minimum angle (cosine) of facet normals across a ridge", -1);
- zdef_(wadd, Wareatot, "total area of facets", -1);
- zdef_(wmax, Wareamax, " maximum facet area", -1);
- zdef_(wmin, Wareamin, " minimum facet area", -1);
-}
-void qh_allstatC (void) {
- zdef_(zdoc, Zdoc9, "build hull statistics", -1);
- zzdef_(zinc, Zprocessed, "points processed", -1);
- zzdef_(zinc, Zretry, "retries due to precision problems", -1);
- zdef_(wmax, Wretrymax, " max. random joggle", -1);
- zdef_(zmax, Zmaxvertex, "max. vertices at any one time", -1);
- zdef_(zinc, Ztotvisible, "ave. visible facets per iteration", Zprocessed);
- zdef_(zinc, Zinsidevisible, " ave. visible facets without an horizon neighbor", Zprocessed);
- zdef_(zadd, Zvisfacettot, " ave. facets deleted per iteration", Zprocessed);
- zdef_(zmax, Zvisfacetmax, " maximum", -1);
- zdef_(zadd, Zvisvertextot, "ave. visible vertices per iteration", Zprocessed);
- zdef_(zmax, Zvisvertexmax, " maximum", -1);
- zdef_(zinc, Ztothorizon, "ave. horizon facets per iteration", Zprocessed);
- zdef_(zadd, Znewfacettot, "ave. new or merged facets per iteration", Zprocessed);
- zdef_(zmax, Znewfacetmax, " maximum (includes initial simplex)", -1);
- zdef_(wadd, Wnewbalance, "average new facet balance", Zprocessed);
- zdef_(wadd, Wnewbalance2, " standard deviation", -1);
- zdef_(wadd, Wpbalance, "average partition balance", Zpbalance);
- zdef_(wadd, Wpbalance2, " standard deviation", -1);
- zdef_(zinc, Zpbalance, " number of trials", -1);
- zdef_(zinc, Zsearchpoints, "searches of all points for initial simplex", -1);
- zdef_(zinc, Zdetsimplex, "determinants computed (area & initial hull)", -1);
- zdef_(zinc, Znoarea, "determinants not computed because vertex too low", -1);
- zdef_(zinc, Znotmax, "points ignored (not above max_outside)", -1);
- zdef_(zinc, Znotgood, "points ignored (not above a good facet)", -1);
- zdef_(zinc, Znotgoodnew, "points ignored (didn't create a good new facet)", -1);
- zdef_(zinc, Zgoodfacet, "good facets found", -1);
- zzdef_(zinc, Znumvisibility, "distance tests for facet visibility", -1);
- zdef_(zinc, Zdistvertex, "distance tests to report minimum vertex", -1);
- zdef_(zinc, Ztotcheck, "points checked for facets' outer planes", -1);
- zzdef_(zinc, Zcheckpart, " ave. distance tests per check", Ztotcheck);
-}
-void qh_allstatD(void) {
- zdef_(zdoc, Zdoc4, "partitioning statistics (see previous for outer planes)", -1);
- zzdef_(zadd, Zdelvertextot, "total vertices deleted", -1);
- zdef_(zmax, Zdelvertexmax, " maximum vertices deleted per iteration", -1);
- zdef_(zinc, Zfindbest, "calls to findbest", -1);
- zdef_(zadd, Zfindbesttot, " ave. facets tested", Zfindbest);
- zdef_(zmax, Zfindbestmax, " max. facets tested", -1);
- zdef_(zadd, Zfindcoplanar, " ave. coplanar search", Zfindbest);
- zdef_(zinc, Zfindnew, "calls to findbestnew", -1);
- zdef_(zadd, Zfindnewtot, " ave. facets tested", Zfindnew);
- zdef_(zmax, Zfindnewmax, " max. facets tested", -1);
- zdef_(zinc, Zfindnewjump, " ave. clearly better", Zfindnew);
- zdef_(zinc, Zfindnewsharp, " calls due to qh_sharpnewfacets", -1);
- zdef_(zinc, Zfindhorizon, "calls to findhorizon", -1);
- zdef_(zadd, Zfindhorizontot, " ave. facets tested", Zfindhorizon);
- zdef_(zmax, Zfindhorizonmax, " max. facets tested", -1);
- zdef_(zinc, Zfindjump, " ave. clearly better", Zfindhorizon);
- zdef_(zinc, Zparthorizon, " horizon facets better than bestfacet", -1);
- zdef_(zinc, Zpartangle, "angle tests for repartitioned coplanar points", -1);
- zdef_(zinc, Zpartflip, " repartitioned coplanar points for flipped orientation", -1);
-}
-void qh_allstatE(void) {
- zdef_(zinc, Zpartinside, "inside points", -1);
- zdef_(zinc, Zpartnear, " inside points kept with a facet", -1);
- zdef_(zinc, Zcoplanarinside, " inside points that were coplanar with a facet", -1);
- zdef_(zinc, Zbestlower, "calls to findbestlower", -1);
- zdef_(zinc, Zbestlowerv, " with search of vertex neighbors", -1);
- zdef_(wadd, Wmaxout, "difference in max_outside at final check", -1);
- zzdef_(zinc, Zpartitionall, "distance tests for initial partition", -1);
- zdef_(zinc, Ztotpartition, "partitions of a point", -1);
- zzdef_(zinc, Zpartition, "distance tests for partitioning", -1);
- zzdef_(zinc, Zdistcheck, "distance tests for checking flipped facets", -1);
- zzdef_(zinc, Zdistconvex, "distance tests for checking convexity", -1);
- zdef_(zinc, Zdistgood, "distance tests for checking good point", -1);
- zdef_(zinc, Zdistio, "distance tests for output", -1);
- zdef_(zinc, Zdiststat, "distance tests for statistics", -1);
- zdef_(zinc, Zdistplane, "total number of distance tests", -1);
- zdef_(zinc, Ztotpartcoplanar, "partitions of coplanar points or deleted vertices", -1);
- zzdef_(zinc, Zpartcoplanar, " distance tests for these partitions", -1);
- zdef_(zinc, Zcomputefurthest, "distance tests for computing furthest", -1);
-}
-void qh_allstatE2(void) {
- zdef_(zdoc, Zdoc5, "statistics for matching ridges", -1);
- zdef_(zinc, Zhashlookup, "total lookups for matching ridges of new facets", -1);
- zdef_(zinc, Zhashtests, "average number of tests to match a ridge", Zhashlookup);
- zdef_(zinc, Zhashridge, "total lookups of subridges (duplicates and boundary)", -1);
- zdef_(zinc, Zhashridgetest, "average number of tests per subridge", Zhashridge);
- zdef_(zinc, Zdupsame, "duplicated ridges in same merge cycle", -1);
- zdef_(zinc, Zdupflip, "duplicated ridges with flipped facets", -1);
-
- zdef_(zdoc, Zdoc6, "statistics for determining merges", -1);
- zdef_(zinc, Zangletests, "angles computed for ridge convexity", -1);
- zdef_(zinc, Zbestcentrum, "best merges used centrum instead of vertices",-1);
- zzdef_(zinc, Zbestdist, "distance tests for best merge", -1);
- zzdef_(zinc, Zcentrumtests, "distance tests for centrum convexity", -1);
- zzdef_(zinc, Zdistzero, "distance tests for checking simplicial convexity", -1);
- zdef_(zinc, Zcoplanarangle, "coplanar angles in getmergeset", -1);
- zdef_(zinc, Zcoplanarcentrum, "coplanar centrums in getmergeset", -1);
- zdef_(zinc, Zconcaveridge, "concave ridges in getmergeset", -1);
-}
-void qh_allstatF(void) {
- zdef_(zdoc, Zdoc7, "statistics for merging", -1);
- zdef_(zinc, Zpremergetot, "merge iterations", -1);
- zdef_(zadd, Zmergeinittot, "ave. initial non-convex ridges per iteration", Zpremergetot);
- zdef_(zadd, Zmergeinitmax, " maximum", -1);
- zdef_(zadd, Zmergesettot, " ave. additional non-convex ridges per iteration", Zpremergetot);
- zdef_(zadd, Zmergesetmax, " maximum additional in one pass", -1);
- zdef_(zadd, Zmergeinittot2, "initial non-convex ridges for post merging", -1);
- zdef_(zadd, Zmergesettot2, " additional non-convex ridges", -1);
- zdef_(wmax, Wmaxoutside, "max distance of vertex or coplanar point above facet (w/roundoff)", -1);
- zdef_(wmin, Wminvertex, "max distance of merged vertex below facet (or roundoff)", -1);
- zdef_(zinc, Zwidefacet, "centrums frozen due to a wide merge", -1);
- zdef_(zinc, Zwidevertices, "centrums frozen due to extra vertices", -1);
- zzdef_(zinc, Ztotmerge, "total number of facets or cycles of facets merged", -1);
- zdef_(zinc, Zmergesimplex, "merged a simplex", -1);
- zdef_(zinc, Zonehorizon, "simplices merged into coplanar horizon", -1);
- zzdef_(zinc, Zcyclehorizon, "cycles of facets merged into coplanar horizon", -1);
- zzdef_(zadd, Zcyclefacettot, " ave. facets per cycle", Zcyclehorizon);
- zdef_(zmax, Zcyclefacetmax, " max. facets", -1);
- zdef_(zinc, Zmergeintohorizon, "new facets merged into horizon", -1);
- zdef_(zinc, Zmergenew, "new facets merged", -1);
- zdef_(zinc, Zmergehorizon, "horizon facets merged into new facets", -1);
- zdef_(zinc, Zmergevertex, "vertices deleted by merging", -1);
- zdef_(zinc, Zcyclevertex, "vertices deleted by merging into coplanar horizon", -1);
- zdef_(zinc, Zdegenvertex, "vertices deleted by degenerate facet", -1);
- zdef_(zinc, Zmergeflipdup, "merges due to flipped facets in duplicated ridge", -1);
- zdef_(zinc, Zneighbor, "merges due to redundant neighbors", -1);
- zdef_(zadd, Ztestvneighbor, "non-convex vertex neighbors", -1);
-}
-void qh_allstatG(void) {
- zdef_(zinc, Zacoplanar, "merges due to angle coplanar facets", -1);
- zdef_(wadd, Wacoplanartot, " average merge distance", Zacoplanar);
- zdef_(wmax, Wacoplanarmax, " maximum merge distance", -1);
- zdef_(zinc, Zcoplanar, "merges due to coplanar facets", -1);
- zdef_(wadd, Wcoplanartot, " average merge distance", Zcoplanar);
- zdef_(wmax, Wcoplanarmax, " maximum merge distance", -1);
- zdef_(zinc, Zconcave, "merges due to concave facets", -1);
- zdef_(wadd, Wconcavetot, " average merge distance", Zconcave);
- zdef_(wmax, Wconcavemax, " maximum merge distance", -1);
- zdef_(zinc, Zavoidold, "coplanar/concave merges due to avoiding old merge", -1);
- zdef_(wadd, Wavoidoldtot, " average merge distance", Zavoidold);
- zdef_(wmax, Wavoidoldmax, " maximum merge distance", -1);
- zdef_(zinc, Zdegen, "merges due to degenerate facets", -1);
- zdef_(wadd, Wdegentot, " average merge distance", Zdegen);
- zdef_(wmax, Wdegenmax, " maximum merge distance", -1);
- zdef_(zinc, Zflipped, "merges due to removing flipped facets", -1);
- zdef_(wadd, Wflippedtot, " average merge distance", Zflipped);
- zdef_(wmax, Wflippedmax, " maximum merge distance", -1);
- zdef_(zinc, Zduplicate, "merges due to duplicated ridges", -1);
- zdef_(wadd, Wduplicatetot, " average merge distance", Zduplicate);
- zdef_(wmax, Wduplicatemax, " maximum merge distance", -1);
-}
-void qh_allstatH(void) {
- zdef_(zdoc, Zdoc8, "renamed vertex statistics", -1);
- zdef_(zinc, Zrenameshare, "renamed vertices shared by two facets", -1);
- zdef_(zinc, Zrenamepinch, "renamed vertices in a pinched facet", -1);
- zdef_(zinc, Zrenameall, "renamed vertices shared by multiple facets", -1);
- zdef_(zinc, Zfindfail, "rename failures due to duplicated ridges", -1);
- zdef_(zinc, Zdupridge, " duplicate ridges detected", -1);
- zdef_(zinc, Zdelridge, "deleted ridges due to renamed vertices", -1);
- zdef_(zinc, Zdropneighbor, "dropped neighbors due to renamed vertices", -1);
- zdef_(zinc, Zdropdegen, "degenerate facets due to dropped neighbors", -1);
- zdef_(zinc, Zdelfacetdup, " facets deleted because of no neighbors", -1);
- zdef_(zinc, Zremvertex, "vertices removed from facets due to no ridges", -1);
- zdef_(zinc, Zremvertexdel, " deleted", -1);
- zdef_(zinc, Zintersectnum, "vertex intersections for locating redundant vertices", -1);
- zdef_(zinc, Zintersectfail, "intersections failed to find a redundant vertex", -1);
- zdef_(zinc, Zintersect, "intersections found redundant vertices", -1);
- zdef_(zadd, Zintersecttot, " ave. number found per vertex", Zintersect);
- zdef_(zmax, Zintersectmax, " max. found for a vertex", -1);
- zdef_(zinc, Zvertexridge, NULL, -1);
- zdef_(zadd, Zvertexridgetot, " ave. number of ridges per tested vertex", Zvertexridge);
- zdef_(zmax, Zvertexridgemax, " max. number of ridges per tested vertex", -1);
-
- zdef_(zdoc, Zdoc10, "memory usage statistics (in bytes)", -1);
- zdef_(zadd, Zmemfacets, "for facets and their normals, neighbor and vertex sets", -1);
- zdef_(zadd, Zmemvertices, "for vertices and their neighbor sets", -1);
- zdef_(zadd, Zmempoints, "for input points and outside and coplanar sets",-1);
- zdef_(zadd, Zmemridges, "for ridges and their vertex sets", -1);
-} /* allstat */
-
-void qh_allstatI(void) {
- qhstat vridges= qhstat next;
- zzdef_(zdoc, Zdoc11, "Voronoi ridge statistics", -1);
- zzdef_(zinc, Zridge, "non-simplicial Voronoi vertices for all ridges", -1);
- zzdef_(wadd, Wridge, " ave. distance to ridge", Zridge);
- zzdef_(wmax, Wridgemax, " max. distance to ridge", -1);
- zzdef_(zinc, Zridgemid, "bounded ridges", -1);
- zzdef_(wadd, Wridgemid, " ave. distance of midpoint to ridge", Zridgemid);
- zzdef_(wmax, Wridgemidmax, " max. distance of midpoint to ridge", -1);
- zzdef_(zinc, Zridgeok, "bounded ridges with ok normal", -1);
- zzdef_(wadd, Wridgeok, " ave. angle to ridge", Zridgeok);
- zzdef_(wmax, Wridgeokmax, " max. angle to ridge", -1);
- zzdef_(zinc, Zridge0, "bounded ridges with near-zero normal", -1);
- zzdef_(wadd, Wridge0, " ave. angle to ridge", Zridge0);
- zzdef_(wmax, Wridge0max, " max. angle to ridge", -1);
-
- zdef_(zdoc, Zdoc12, "Triangulation statistics (Qt)", -1);
- zdef_(zinc, Ztricoplanar, "non-simplicial facets triangulated", -1);
- zdef_(zadd, Ztricoplanartot, " ave. new facets created (may be deleted)", Ztricoplanar);
- zdef_(zmax, Ztricoplanarmax, " max. new facets created", -1);
- zdef_(zinc, Ztrinull, "null new facets deleted (duplicated vertex)", -1);
- zdef_(zinc, Ztrimirror, "mirrored pairs of new facets deleted (same vertices)", -1);
- zdef_(zinc, Ztridegen, "degenerate new facets in output (same ridge)", -1);
-} /* allstat */
-
-/*-<a href="qh-stat.htm#TOC"
- >-------------------------------</a><a name="allstatistics">-</a>
-
- qh_allstatistics()
- reset printed flag for all statistics
-*/
-void qh_allstatistics (void) {
- int i;
-
- for (i=ZEND; i--; )
- qhstat printed[i]= False;
-} /* allstatistics */
-
-#if qh_KEEPstatistics
-/*-<a href="qh-stat.htm#TOC"
- >-------------------------------</a><a name="collectstatistics">-</a>
-
- qh_collectstatistics()
- collect statistics for qh.facet_list
-
-*/
-void qh_collectstatistics (void) {
- facetT *facet, *neighbor, **neighborp;
- vertexT *vertex, **vertexp;
- realT dotproduct, dist;
- int sizneighbors, sizridges, sizvertices, i;
-
- qh old_randomdist= qh RANDOMdist;
- qh RANDOMdist= False;
- zval_(Zmempoints)= qh num_points * qh normal_size +
- sizeof (qhT) + sizeof (qhstatT);
- zval_(Zmemfacets)= 0;
- zval_(Zmemridges)= 0;
- zval_(Zmemvertices)= 0;
- zval_(Zangle)= 0;
- wval_(Wangle)= 0.0;
- zval_(Znumridges)= 0;
- zval_(Znumfacets)= 0;
- zval_(Znumneighbors)= 0;
- zval_(Znumvertices)= 0;
- zval_(Znumvneighbors)= 0;
- zval_(Znummergetot)= 0;
- zval_(Znummergemax)= 0;
- zval_(Zvertices)= qh num_vertices - qh_setsize (qh del_vertices);
- if (qh MERGING || qh APPROXhull || qh JOGGLEmax < REALmax/2)
- wmax_(Wmaxoutside, qh max_outside);
- if (qh MERGING)
- wmin_(Wminvertex, qh min_vertex);
- FORALLfacets
- facet->seen= False;
- if (qh DELAUNAY) {
- FORALLfacets {
- if (facet->upperdelaunay != qh UPPERdelaunay)
- facet->seen= True; /* remove from angle statistics */
- }
- }
- FORALLfacets {
- if (facet->visible && qh NEWfacets)
- continue;
- sizvertices= qh_setsize (facet->vertices);
- sizneighbors= qh_setsize (facet->neighbors);
- sizridges= qh_setsize (facet->ridges);
- zinc_(Znumfacets);
- zadd_(Znumvertices, sizvertices);
- zmax_(Zmaxvertices, sizvertices);
- zadd_(Znumneighbors, sizneighbors);
- zmax_(Zmaxneighbors, sizneighbors);
- zadd_(Znummergetot, facet->nummerge);
- i= facet->nummerge; /* avoid warnings */
- zmax_(Znummergemax, i);
- if (!facet->simplicial) {
- if (sizvertices == qh hull_dim) {
- zinc_(Znowsimplicial);
- }else {
- zinc_(Znonsimplicial);
- }
- }
- if (sizridges) {
- zadd_(Znumridges, sizridges);
- zmax_(Zmaxridges, sizridges);
- }
- zadd_(Zmemfacets, sizeof (facetT) + qh normal_size + 2*sizeof (setT)
- + SETelemsize * (sizneighbors + sizvertices));
- if (facet->ridges) {
- zadd_(Zmemridges,
- sizeof (setT) + SETelemsize * sizridges + sizridges *
- (sizeof (ridgeT) + sizeof (setT) + SETelemsize * (qh hull_dim-1))/2);
- }
- if (facet->outsideset)
- zadd_(Zmempoints, sizeof (setT) + SETelemsize * qh_setsize (facet->outsideset));
- if (facet->coplanarset)
- zadd_(Zmempoints, sizeof (setT) + SETelemsize * qh_setsize (facet->coplanarset));
- if (facet->seen) /* Delaunay upper envelope */
- continue;
- facet->seen= True;
- FOREACHneighbor_(facet) {
- if (neighbor == qh_DUPLICATEridge || neighbor == qh_MERGEridge
- || neighbor->seen || !facet->normal || !neighbor->normal)
- continue;
- dotproduct= qh_getangle(facet->normal, neighbor->normal);
- zinc_(Zangle);
- wadd_(Wangle, dotproduct);
- wmax_(Wanglemax, dotproduct)
- wmin_(Wanglemin, dotproduct)
- }
- if (facet->normal) {
- FOREACHvertex_(facet->vertices) {
- zinc_(Zdiststat);
- qh_distplane(vertex->point, facet, &dist);
- wmax_(Wvertexmax, dist);
- wmin_(Wvertexmin, dist);
- }
- }
- }
- FORALLvertices {
- if (vertex->deleted)
- continue;
- zadd_(Zmemvertices, sizeof (vertexT));
- if (vertex->neighbors) {
- sizneighbors= qh_setsize (vertex->neighbors);
- zadd_(Znumvneighbors, sizneighbors);
- zmax_(Zmaxvneighbors, sizneighbors);
- zadd_(Zmemvertices, sizeof (vertexT) + SETelemsize * sizneighbors);
- }
- }
- qh RANDOMdist= qh old_randomdist;
-} /* collectstatistics */
-#endif /* qh_KEEPstatistics */
-
-/*-<a href="qh-stat.htm#TOC"
- >-------------------------------</a><a name="freestatistics">-</a>
-
- qh_freestatistics( )
- free memory used for statistics
-*/
-void qh_freestatistics (void) {
-
-#if qh_QHpointer
- free (qh_qhstat);
- qh_qhstat= NULL;
-#endif
-} /* freestatistics */
-
-/*-<a href="qh-stat.htm#TOC"
- >-------------------------------</a><a name="initstatistics">-</a>
-
- qh_initstatistics( )
- allocate and initialize statistics
-
- notes:
- uses malloc() instead of qh_memalloc() since mem.c not set up yet
-*/
-void qh_initstatistics (void) {
- int i;
- realT realx;
- int intx;
-
-#if qh_QHpointer
- if (!(qh_qhstat= (qhstatT *)malloc (sizeof(qhstatT)))) {
- fprintf (qhmem.ferr, "qhull error (qh_initstatistics): insufficient memory\n");
- exit (1); /* can not use qh_errexit() */
- }
-#endif
-
- qhstat next= 0;
- qh_allstatA();
- qh_allstatB();
- qh_allstatC();
- qh_allstatD();
- qh_allstatE();
- qh_allstatE2();
- qh_allstatF();
- qh_allstatG();
- qh_allstatH();
- qh_allstatI();
- if (qhstat next > sizeof(qhstat id)) {
- fprintf (qhmem.ferr, "qhull error (qh_initstatistics): increase size of qhstat.id[].\n\
- qhstat.next %d should be <= sizeof(qhstat id) %lu\n", qhstat next, sizeof(qhstat id));
-#if 0 /* for locating error, Znumridges should be duplicated */
- for (i=0; i < ZEND; i++) {
- int j;
- for (j=i+1; j < ZEND; j++) {
- if (qhstat id[i] == qhstat id[j]) {
- fprintf (qhmem.ferr, "qhull error (qh_initstatistics): duplicated statistic %d at indices %d and %d\n",
- qhstat id[i], i, j);
- }
- }
- }
-#endif
- exit (1); /* can not use qh_errexit() */
- }
- qhstat init[zinc].i= 0;
- qhstat init[zadd].i= 0;
- qhstat init[zmin].i= INT_MAX;
- qhstat init[zmax].i= INT_MIN;
- qhstat init[wadd].r= 0;
- qhstat init[wmin].r= REALmax;
- qhstat init[wmax].r= -REALmax;
- for (i=0; i < ZEND; i++) {
- if (qhstat type[i] > ZTYPEreal) {
- realx= qhstat init[(unsigned char)(qhstat type[i])].r;
- qhstat stats[i].r= realx;
- }else if (qhstat type[i] != zdoc) {
- intx= qhstat init[(unsigned char)(qhstat type[i])].i;
- qhstat stats[i].i= intx;
- }
- }
-} /* initstatistics */
-
-/*-<a href="qh-stat.htm#TOC"
- >-------------------------------</a><a name="newstats">-</a>
-
- qh_newstats( )
- returns True if statistics for zdoc
-
- returns:
- next zdoc
-*/
-boolT qh_newstats (int index, int *nextindex) {
- boolT isnew= False;
- int start, i;
-
- if (qhstat type[qhstat id[index]] == zdoc)
- start= index+1;
- else
- start= index;
- for (i= start; i < qhstat next && qhstat type[qhstat id[i]] != zdoc; i++) {
- if (!qh_nostatistic(qhstat id[i]) && !qhstat printed[qhstat id[i]])
- isnew= True;
- }
- *nextindex= i;
- return isnew;
-} /* newstats */
-
-/*-<a href="qh-stat.htm#TOC"
- >-------------------------------</a><a name="nostatistic">-</a>
-
- qh_nostatistic( index )
- true if no statistic to print
-*/
-boolT qh_nostatistic (int i) {
-
- if ((qhstat type[i] > ZTYPEreal
- &&qhstat stats[i].r == qhstat init[(unsigned char)(qhstat type[i])].r)
- || (qhstat type[i] < ZTYPEreal
- &&qhstat stats[i].i == qhstat init[(unsigned char)(qhstat type[i])].i))
- return True;
- return False;
-} /* nostatistic */
-
-#if qh_KEEPstatistics
-/*-<a href="qh-stat.htm#TOC"
- >-------------------------------</a><a name="printallstatistics">-</a>
-
- qh_printallstatistics( fp, string )
- print all statistics with header 'string'
-*/
-void qh_printallstatistics (FILE *fp, char *string) {
-
- qh_allstatistics();
- qh_collectstatistics();
- qh_printstatistics (fp, string);
- qh_memstatistics (fp);
-}
-
-
-/*-<a href="qh-stat.htm#TOC"
- >-------------------------------</a><a name="printstatistics">-</a>
-
- qh_printstatistics( fp, string )
- print statistics to a file with header 'string'
- skips statistics with qhstat.printed[] (reset with qh_allstatistics)
-
- see:
- qh_printallstatistics()
-*/
-void qh_printstatistics (FILE *fp, char *string) {
- int i, k;
- realT ave;
-
- if (qh num_points != qh num_vertices) {
- wval_(Wpbalance)= 0;
- wval_(Wpbalance2)= 0;
- }else
- wval_(Wpbalance2)= qh_stddev (zval_(Zpbalance), wval_(Wpbalance),
- wval_(Wpbalance2), &ave);
- wval_(Wnewbalance2)= qh_stddev (zval_(Zprocessed), wval_(Wnewbalance),
- wval_(Wnewbalance2), &ave);
- fprintf (fp, "\n\
-%s\n\
- qhull invoked by: %s | %s\n%s with options:\n%s\n", string, qh rbox_command,
- qh qhull_command, qh_version, qh qhull_options);
- fprintf (fp, "\nprecision constants:\n\
- %6.2g max. abs. coordinate in the (transformed) input ('Qbd:n')\n\
- %6.2g max. roundoff error for distance computation ('En')\n\
- %6.2g max. roundoff error for angle computations\n\
- %6.2g min. distance for outside points ('Wn')\n\
- %6.2g min. distance for visible facets ('Vn')\n\
- %6.2g max. distance for coplanar facets ('Un')\n\
- %6.2g max. facet width for recomputing centrum and area\n\
-",
- qh MAXabs_coord, qh DISTround, qh ANGLEround, qh MINoutside,
- qh MINvisible, qh MAXcoplanar, qh WIDEfacet);
- if (qh KEEPnearinside)
- fprintf(fp, "\
- %6.2g max. distance for near-inside points\n", qh NEARinside);
- if (qh premerge_cos < REALmax/2) fprintf (fp, "\
- %6.2g max. cosine for pre-merge angle\n", qh premerge_cos);
- if (qh PREmerge) fprintf (fp, "\
- %6.2g radius of pre-merge centrum\n", qh premerge_centrum);
- if (qh postmerge_cos < REALmax/2) fprintf (fp, "\
- %6.2g max. cosine for post-merge angle\n", qh postmerge_cos);
- if (qh POSTmerge) fprintf (fp, "\
- %6.2g radius of post-merge centrum\n", qh postmerge_centrum);
- fprintf (fp, "\
- %6.2g max. distance for merging two simplicial facets\n\
- %6.2g max. roundoff error for arithmetic operations\n\
- %6.2g min. denominator for divisions\n\
- zero diagonal for Gauss: ", qh ONEmerge, REALepsilon, qh MINdenom);
- for (k=0; k < qh hull_dim; k++)
- fprintf (fp, "%6.2e ", qh NEARzero[k]);
- fprintf (fp, "\n\n");
- for (i=0 ; i < qhstat next; )
- qh_printstats (fp, i, &i);
-} /* printstatistics */
-#endif /* qh_KEEPstatistics */
-
-/*-<a href="qh-stat.htm#TOC"
- >-------------------------------</a><a name="printstatlevel">-</a>
-
- qh_printstatlevel( fp, id )
- print level information for a statistic
-
- notes:
- nop if id >= ZEND, printed, or same as initial value
-*/
-void qh_printstatlevel (FILE *fp, int id, int start) {
-#define NULLfield " "
-
- if (id >= ZEND || qhstat printed[id])
- return;
- if (qhstat type[id] == zdoc) {
- fprintf (fp, "%s\n", qhstat doc[id]);
- return;
- }
- start= 0; /* not used */
- if (qh_nostatistic(id) || !qhstat doc[id])
- return;
- qhstat printed[id]= True;
- if (qhstat count[id] != -1
- && qhstat stats[(unsigned char)(qhstat count[id])].i == 0)
- fprintf (fp, " *0 cnt*");
- else if (qhstat type[id] >= ZTYPEreal && qhstat count[id] == -1)
- fprintf (fp, "%7.2g", qhstat stats[id].r);
- else if (qhstat type[id] >= ZTYPEreal && qhstat count[id] != -1)
- fprintf (fp, "%7.2g", qhstat stats[id].r/ qhstat stats[(unsigned char)(qhstat count[id])].i);
- else if (qhstat type[id] < ZTYPEreal && qhstat count[id] == -1)
- fprintf (fp, "%7d", qhstat stats[id].i);
- else if (qhstat type[id] < ZTYPEreal && qhstat count[id] != -1)
- fprintf (fp, "%7.3g", (realT) qhstat stats[id].i / qhstat stats[(unsigned char)(qhstat count[id])].i);
- fprintf (fp, " %s\n", qhstat doc[id]);
-} /* printstatlevel */
-
-
-/*-<a href="qh-stat.htm#TOC"
- >-------------------------------</a><a name="printstats">-</a>
-
- qh_printstats( fp, index, nextindex )
- print statistics for a zdoc group
-
- returns:
- next zdoc if non-null
-*/
-void qh_printstats (FILE *fp, int index, int *nextindex) {
- int j, nexti;
-
- if (qh_newstats (index, &nexti)) {
- fprintf (fp, "\n");
- for (j=index; j<nexti; j++)
- qh_printstatlevel (fp, qhstat id[j], 0);
- }
- if (nextindex)
- *nextindex= nexti;
-} /* printstats */
-
-#if qh_KEEPstatistics
-
-/*-<a href="qh-stat.htm#TOC"
- >-------------------------------</a><a name="stddev">-</a>
-
- qh_stddev( num, tot, tot2, ave )
- compute the standard deviation and average from statistics
-
- tot2 is the sum of the squares
- notes:
- computes r.m.s.:
- (x-ave)^2
- == x^2 - 2x tot/num + (tot/num)^2
- == tot2 - 2 tot tot/num + tot tot/num
- == tot2 - tot ave
-*/
-realT qh_stddev (int num, realT tot, realT tot2, realT *ave) {
- realT stddev;
-
- *ave= tot/num;
- stddev= sqrt (tot2/num - *ave * *ave);
- return stddev;
-} /* stddev */
-
-#endif /* qh_KEEPstatistics */
-
-#if !qh_KEEPstatistics
-void qh_collectstatistics (void) {}
-void qh_printallstatistics (FILE *fp, char *string) {};
-void qh_printstatistics (FILE *fp, char *string) {}
-#endif
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/stat.h b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/stat.h
deleted file mode 100644
index 6e7b0fc60e59b0b60d74d338425efe5812a1b554..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/stat.h
+++ /dev/null
@@ -1,528 +0,0 @@
-/*<html><pre> -<a href="qh-stat.htm"
->-------------------------------</a><a name="TOP">-</a>
-
- stat.h
- contains all statistics that are collected for qhull
-
- see qh-stat.htm and stat.c
-
- copyright (c) 1993-2003, The Geometry Center
-
- recompile qhull if you change this file
-
- Integer statistics are Z* while real statistics are W*.
-
- define maydebugx to call a routine at every statistic event
-
-*/
-
-#ifndef qhDEFstat
-#define qhDEFstat 1
-
-
-/*-<a href="qh-stat.htm#TOC"
- >-------------------------------</a><a name="KEEPstatistics">-</a>
-
- qh_KEEPstatistics
- 0 turns off statistic gathering (except zzdef/zzinc/zzadd/zzval/wwval)
-*/
-#ifndef qh_KEEPstatistics
-#define qh_KEEPstatistics 1
-#endif
-
-/*-<a href="qh-stat.htm#TOC"
- >-------------------------------</a><a name="statistics">-</a>
-
- Zxxx for integers, Wxxx for reals
-
- notes:
- be sure that all statistics are defined in stat.c
- otherwise initialization may core dump
- can pick up all statistics by:
- grep '[zw].*_[(][ZW]' *.c >z.x
- remove trailers with query">-</a>
- remove leaders with query-replace-regexp [ ^I]+ (
-*/
-#if qh_KEEPstatistics
-enum statistics /* alphabetical after Z/W */
-{
- Zacoplanar,
- Wacoplanarmax,
- Wacoplanartot,
- Zangle,
- Wangle,
- Wanglemax,
- Wanglemin,
- Zangletests,
- Wareatot,
- Wareamax,
- Wareamin,
- Zavoidold,
- Wavoidoldmax,
- Wavoidoldtot,
- Zback0,
- Zbestcentrum,
- Zbestdist,
- Zbestlower,
- Zbestlowerv,
- Zcentrumtests,
- Zcheckpart,
- Zcomputefurthest,
- Zconcave,
- Wconcavemax,
- Wconcavetot,
- Zconcaveridges,
- Zconcaveridge,
- Zcoplanar,
- Wcoplanarmax,
- Wcoplanartot,
- Zcoplanarangle,
- Zcoplanarcentrum,
- Zcoplanarhorizon,
- Zcoplanarinside,
- Zcoplanarpart,
- Zcoplanarridges,
- Wcpu,
- Zcyclefacetmax,
- Zcyclefacettot,
- Zcyclehorizon,
- Zcyclevertex,
- Zdegen,
- Wdegenmax,
- Wdegentot,
- Zdegenvertex,
- Zdelfacetdup,
- Zdelridge,
- Zdelvertextot,
- Zdelvertexmax,
- Zdetsimplex,
- Zdistcheck,
- Zdistconvex,
- Zdistgood,
- Zdistio,
- Zdistplane,
- Zdiststat,
- Zdistvertex,
- Zdistzero,
- Zdoc1,
- Zdoc2,
- Zdoc3,
- Zdoc4,
- Zdoc5,
- Zdoc6,
- Zdoc7,
- Zdoc8,
- Zdoc9,
- Zdoc10,
- Zdoc11,
- Zdoc12,
- Zdropdegen,
- Zdropneighbor,
- Zdupflip,
- Zduplicate,
- Wduplicatemax,
- Wduplicatetot,
- Zdupridge,
- Zdupsame,
- Zflipped,
- Wflippedmax,
- Wflippedtot,
- Zflippedfacets,
- Zfindbest,
- Zfindbestmax,
- Zfindbesttot,
- Zfindcoplanar,
- Zfindfail,
- Zfindhorizon,
- Zfindhorizonmax,
- Zfindhorizontot,
- Zfindjump,
- Zfindnew,
- Zfindnewmax,
- Zfindnewtot,
- Zfindnewjump,
- Zfindnewsharp,
- Zgauss0,
- Zgoodfacet,
- Zhashlookup,
- Zhashridge,
- Zhashridgetest,
- Zhashtests,
- Zinsidevisible,
- Zintersect,
- Zintersectfail,
- Zintersectmax,
- Zintersectnum,
- Zintersecttot,
- Zmaxneighbors,
- Wmaxout,
- Wmaxoutside,
- Zmaxridges,
- Zmaxvertex,
- Zmaxvertices,
- Zmaxvneighbors,
- Zmemfacets,
- Zmempoints,
- Zmemridges,
- Zmemvertices,
- Zmergeflipdup,
- Zmergehorizon,
- Zmergeinittot,
- Zmergeinitmax,
- Zmergeinittot2,
- Zmergeintohorizon,
- Zmergenew,
- Zmergesettot,
- Zmergesetmax,
- Zmergesettot2,
- Zmergesimplex,
- Zmergevertex,
- Wmindenom,
- Wminvertex,
- Zminnorm,
- Zmultiridge,
- Znearlysingular,
- Zneighbor,
- Wnewbalance,
- Wnewbalance2,
- Znewfacettot,
- Znewfacetmax,
- Znewvertex,
- Wnewvertex,
- Wnewvertexmax,
- Znoarea,
- Znonsimplicial,
- Znowsimplicial,
- Znotgood,
- Znotgoodnew,
- Znotmax,
- Znumfacets,
- Znummergemax,
- Znummergetot,
- Znumneighbors,
- Znumridges,
- Znumvertices,
- Znumvisibility,
- Znumvneighbors,
- Zonehorizon,
- Zpartangle,
- Zpartcoplanar,
- Zpartflip,
- Zparthorizon,
- Zpartinside,
- Zpartition,
- Zpartitionall,
- Zpartnear,
- Zpbalance,
- Wpbalance,
- Wpbalance2,
- Zpostfacets,
- Zpremergetot,
- Zprocessed,
- Zremvertex,
- Zremvertexdel,
- Zrenameall,
- Zrenamepinch,
- Zrenameshare,
- Zretry,
- Wretrymax,
- Zridge,
- Wridge,
- Wridgemax,
- Zridge0,
- Wridge0,
- Wridge0max,
- Zridgemid,
- Wridgemid,
- Wridgemidmax,
- Zridgeok,
- Wridgeok,
- Wridgeokmax,
- Zsearchpoints,
- Zsetplane,
- Ztestvneighbor,
- Ztotcheck,
- Ztothorizon,
- Ztotmerge,
- Ztotpartcoplanar,
- Ztotpartition,
- Ztotridges,
- Ztotvertices,
- Ztotvisible,
- Ztricoplanar,
- Ztricoplanarmax,
- Ztricoplanartot,
- Ztridegen,
- Ztrimirror,
- Ztrinull,
- Wvertexmax,
- Wvertexmin,
- Zvertexridge,
- Zvertexridgetot,
- Zvertexridgemax,
- Zvertices,
- Zvisfacettot,
- Zvisfacetmax,
- Zvisvertextot,
- Zvisvertexmax,
- Zwidefacet,
- Zwidevertices,
- ZEND
-};
-
-/*-<a href="qh-stat.htm#TOC"
- >-------------------------------</a><a name="ZZstat">-</a>
-
- Zxxx/Wxxx statistics that remain defined if qh_KEEPstatistics=0
-
- notes:
- be sure to use zzdef, zzinc, etc. with these statistics (no double checking!)
-*/
-#else
-enum statistics /* for zzdef etc. macros */
-{
- Zback0,
- Zbestdist,
- Zcentrumtests,
- Zcheckpart,
- Zconcaveridges,
- Zcoplanarhorizon,
- Zcoplanarpart,
- Zcoplanarridges,
- Zcyclefacettot,
- Zcyclehorizon,
- Zdelvertextot,
- Zdistcheck,
- Zdistconvex,
- Zdistzero,
- Zdoc1,
- Zdoc2,
- Zdoc3,
- Zdoc11,
- Zflippedfacets,
- Zgauss0,
- Zminnorm,
- Zmultiridge,
- Znearlysingular,
- Wnewvertexmax,
- Znumvisibility,
- Zpartcoplanar,
- Zpartition,
- Zpartitionall,
- Zprocessed,
- Zretry,
- Zridge,
- Wridge,
- Wridgemax,
- Zridge0,
- Wridge0,
- Wridge0max,
- Zridgemid,
- Wridgemid,
- Wridgemidmax,
- Zridgeok,
- Wridgeok,
- Wridgeokmax,
- Zsetplane,
- Ztotmerge,
- ZEND
-};
-#endif
-
-/*-<a href="qh-stat.htm#TOC"
- >-------------------------------</a><a name="ztype">-</a>
-
- ztype
- the type of a statistic sets its initial value.
-
- notes:
- The type should be the same as the macro for collecting the statistic
-*/
-enum ztypes {zdoc, zinc, zadd, zmax, zmin, ZTYPEreal, wadd, wmax, wmin, ZTYPEend};
-
-/*========== macros and constants =============*/
-
-/*-<a href="qh-stat.htm#TOC"
- >--------------------------------</a><a name="MAYdebugx">-</a>
-
- MAYdebugx
- define as maydebug() to be called frequently for error trapping
-*/
-#define MAYdebugx
-
-/*-<a href="qh-stat.htm#TOC"
- >--------------------------------</a><a name="zdef_">-</a>
-
- zzdef_, zdef_( type, name, doc, -1)
- define a statistic (assumes 'qhstat.next= 0;')
-
- zdef_( type, name, doc, count)
- define an averaged statistic
- printed as name/count
-*/
-#define zzdef_(stype,name,string,cnt) qhstat id[qhstat next++]=name; \
- qhstat doc[name]= string; qhstat count[name]= cnt; qhstat type[name]= stype
-#if qh_KEEPstatistics
-#define zdef_(stype,name,string,cnt) qhstat id[qhstat next++]=name; \
- qhstat doc[name]= string; qhstat count[name]= cnt; qhstat type[name]= stype
-#else
-#define zdef_(type,name,doc,count)
-#endif
-
-/*-<a href="qh-stat.htm#TOC"
- >--------------------------------</a><a name="zinc_">-</a>
-
- zzinc_( name ), zinc_( name)
- increment an integer statistic
-*/
-#define zzinc_(id) {MAYdebugx; qhstat stats[id].i++;}
-#if qh_KEEPstatistics
-#define zinc_(id) {MAYdebugx; qhstat stats[id].i++;}
-#else
-#define zinc_(id) {}
-#endif
-
-/*-<a href="qh-stat.htm#TOC"
- >--------------------------------</a><a name="zadd_">-</a>
-
- zzadd_( name, value ), zadd_( name, value ), wadd_( name, value )
- add value to an integer or real statistic
-*/
-#define zzadd_(id, val) {MAYdebugx; qhstat stats[id].i += (val);}
-#define wwadd_(id, val) {MAYdebugx; qhstat stats[id].r += (val);}
-#if qh_KEEPstatistics
-#define zadd_(id, val) {MAYdebugx; qhstat stats[id].i += (val);}
-#define wadd_(id, val) {MAYdebugx; qhstat stats[id].r += (val);}
-#else
-#define zadd_(id, val) {}
-#define wadd_(id, val) {}
-#endif
-
-/*-<a href="qh-stat.htm#TOC"
- >--------------------------------</a><a name="zval_">-</a>
-
- zzval_( name ), zval_( name ), wwval_( name )
- set or return value of a statistic
-*/
-#define zzval_(id) ((qhstat stats[id]).i)
-#define wwval_(id) ((qhstat stats[id]).r)
-#if qh_KEEPstatistics
-#define zval_(id) ((qhstat stats[id]).i)
-#define wval_(id) ((qhstat stats[id]).r)
-#else
-#define zval_(id) qhstat tempi
-#define wval_(id) qhstat tempr
-#endif
-
-/*-<a href="qh-stat.htm#TOC"
- >--------------------------------</a><a name="zmax_">-</a>
-
- zmax_( id, val ), wmax_( id, value )
- maximize id with val
-*/
-#define wwmax_(id, val) {MAYdebugx; maximize_(qhstat stats[id].r,(val));}
-#if qh_KEEPstatistics
-#define zmax_(id, val) {MAYdebugx; maximize_(qhstat stats[id].i,(val));}
-#define wmax_(id, val) {MAYdebugx; maximize_(qhstat stats[id].r,(val));}
-#else
-#define zmax_(id, val) {}
-#define wmax_(id, val) {}
-#endif
-
-/*-<a href="qh-stat.htm#TOC"
- >--------------------------------</a><a name="zmin_">-</a>
-
- zmin_( id, val ), wmin_( id, value )
- minimize id with val
-*/
-#if qh_KEEPstatistics
-#define zmin_(id, val) {MAYdebugx; minimize_(qhstat stats[id].i,(val));}
-#define wmin_(id, val) {MAYdebugx; minimize_(qhstat stats[id].r,(val));}
-#else
-#define zmin_(id, val) {}
-#define wmin_(id, val) {}
-#endif
-
-/*================== stat.h types ==============*/
-
-
-/*-<a href="qh-stat.htm#TOC"
- >--------------------------------</a><a name="intrealT">-</a>
-
- intrealT
- union of integer and real, used for statistics
-*/
-typedef union intrealT intrealT; /* union of int and realT */
-union intrealT
-{
- int i;
- realT r;
-};
-
-/*-<a href="qh-stat.htm#TOC"
- >--------------------------------</a><a name="qhstat">-</a>
-
- qhstat
- global data structure for statistics
-
- notes:
- access to qh_qhstat is via the "qhstat" macro. There are two choices
- qh_QHpointer = 1 access globals via a pointer
- enables qh_saveqhull() and qh_restoreqhull()
- = 0 qh_qhstat is a static data structure
- only one instance of qhull() can be active at a time
- default value
- qh_QHpointer is defined in qhull.h
-
- allocated in stat.c
-*/
-typedef struct qhstatT qhstatT;
-#if qh_QHpointer
-#define qhstat qh_qhstat->
-extern qhstatT* qh_qhstat;
-#else
-#define qhstat qh_qhstat.
-extern qhstatT qh_qhstat;
-#endif
-struct qhstatT
-{
- intrealT stats[ZEND]; /* integer and real statistics */
- unsigned char id[ZEND + 10]; /* id's in print order */
- char* doc[ZEND]; /* array of documentation strings */
- short int count[ZEND]; /* -1 if none, else index of count to use */
- char type[ZEND]; /* type, see ztypes above */
- char printed[ZEND]; /* true, if statistic has been printed */
- intrealT init[ZTYPEend]; /* initial values by types, set initstatistics */
-
- int next; /* next index for zdef_ */
- int precision; /* index for precision problems */
- int vridges; /* index for Voronoi ridges */
- int tempi;
- realT tempr;
-};
-
-/*========== function prototypes ===========*/
-
-void qh_allstatA(void);
-void qh_allstatB(void);
-void qh_allstatC(void);
-void qh_allstatD(void);
-void qh_allstatE(void);
-void qh_allstatE2(void);
-void qh_allstatF(void);
-void qh_allstatG(void);
-void qh_allstatH(void);
-void qh_allstatI(void);
-void qh_allstatistics(void);
-void qh_collectstatistics(void);
-void qh_freestatistics(void);
-void qh_initstatistics(void);
-boolT qh_newstats(int index, int* nextindex);
-boolT qh_nostatistic(int i);
-void qh_printallstatistics(FILE* fp, char* string);
-void qh_printstatistics(FILE* fp, char* string);
-void qh_printstatlevel(FILE* fp, int id, int start);
-void qh_printstats(FILE* fp, int index, int* nextindex);
-realT qh_stddev(int num, realT tot, realT tot2, realT* ave);
-
-#endif /* qhDEFstat */
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/user.c b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/user.c
deleted file mode 100644
index b9a75a0b15c3d3786dff33afefe3b3d81301a6c7..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/user.c
+++ /dev/null
@@ -1,324 +0,0 @@
-/*<html><pre> -<a href="qh-user.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- user.c
- user redefinable functions
-
- see README.txt see COPYING.txt for copyright information.
-
- see qhull.h for data structures, macros, and user-callable functions.
-
- see user_eg.c, unix.c, and qhull_interface.cpp for examples.
-
- see user.h for user-definable constants
-
- use qh_NOmem in mem.h to turn off memory management
- use qh_NOmerge in user.h to turn off facet merging
- set qh_KEEPstatistics in user.h to 0 to turn off statistics
-
- This is unsupported software. You're welcome to make changes,
- but you're on your own if something goes wrong. Use 'Tc' to
- check frequently. Usually qhull will report an error if
- a data structure becomes inconsistent. If so, it also reports
- the last point added to the hull, e.g., 102. You can then trace
- the execution of qhull with "T4P102".
-
- Please report any errors that you fix to qhull@qhull.org
-
- call_qhull is a template for calling qhull from within your application
-
- if you recompile and load this module, then user.o will not be loaded
- from qhull.a
-
- you can add additional quick allocation sizes in qh_user_memsizes
-
- if the other functions here are redefined to not use qh_print...,
- then io.o will not be loaded from qhull.a. See user_eg.c for an
- example. We recommend keeping io.o for the extra debugging
- information it supplies.
-*/
-
-#include "qhull_a.h"
-
-/*-<a href="qh-user.htm#TOC"
- >-------------------------------</a><a name="call_qhull">-</a>
-
- qh_call_qhull( void )
- template for calling qhull from inside your program
- remove #if 0, #endif to compile
-
- returns:
- exit code (see qh_ERR... in qhull.h)
- all memory freed
-
- notes:
- This can be called any number of times.
-
- see:
- qh_call_qhull_once()
-
-*/
-#if 0
-{
- int dim; /* dimension of points */
- int numpoints; /* number of points */
- coordT *points; /* array of coordinates for each point */
- boolT ismalloc; /* True if qhull should free points in qh_freeqhull() or reallocation */
- char flags[]= "qhull Tv"; /* option flags for qhull, see qh_opt.htm */
- FILE *outfile= stdout; /* output from qh_produce_output()
- use NULL to skip qh_produce_output() */
- FILE *errfile= stderr; /* error messages from qhull code */
- int exitcode; /* 0 if no error from qhull */
- facetT *facet; /* set by FORALLfacets */
- int curlong, totlong; /* memory remaining after qh_memfreeshort */
-
- /* initialize dim, numpoints, points[], ismalloc here */
- exitcode= qh_new_qhull (dim, numpoints, points, ismalloc,
- flags, outfile, errfile);
- if (!exitcode) { /* if no error */
- /* 'qh facet_list' contains the convex hull */
- FORALLfacets {
- /* ... your code ... */
- }
- }
- qh_freeqhull(!qh_ALL);
- qh_memfreeshort (&curlong, &totlong);
- if (curlong || totlong)
- fprintf (errfile, "qhull internal warning (main): did not free %d bytes of long memory (%d pieces)\n", totlong, curlong);
-}
-#endif
-
-/*-<a href="qh-user.htm#TOC"
- >-------------------------------</a><a name="new_qhull">-</a>
-
- qh_new_qhull( dim, numpoints, points, ismalloc, qhull_cmd, outfile, errfile )
- build new qhull data structure and return exitcode (0 if no errors)
-
- notes:
- do not modify points until finished with results.
- The qhull data structure contains pointers into the points array.
- do not call qhull functions before qh_new_qhull().
- The qhull data structure is not initialized until qh_new_qhull().
-
- outfile may be null
- qhull_cmd must start with "qhull "
- projects points to a new point array for Delaunay triangulations ('d' and 'v')
- transforms points into a new point array for halfspace intersection ('H')
-
-
- To allow multiple, concurrent calls to qhull()
- - set qh_QHpointer in user.h
- - use qh_save_qhull and qh_restore_qhull to swap the global data structure between calls.
- - use qh_freeqhull(qh_ALL) to free intermediate convex hulls
-
- see:
- user_eg.c for an example
-*/
-int qh_new_qhull (int dim, int numpoints, coordT *points, boolT ismalloc,
- char *qhull_cmd, FILE *outfile, FILE *errfile) {
- int exitcode, hulldim;
- boolT new_ismalloc;
- static boolT firstcall = True;
- coordT *new_points;
-
- if (firstcall) {
- qh_meminit (errfile);
- firstcall= False;
- }
- if (strncmp (qhull_cmd,"qhull ", 6)) {
- fprintf (errfile, "qh_new_qhull: start qhull_cmd argument with \"qhull \"\n");
- exit(1);
- }
- qh_initqhull_start (NULL, outfile, errfile);
- trace1(( qh ferr, "qh_new_qhull: build new Qhull for %d %d-d points with %s\n", numpoints, dim, qhull_cmd));
- exitcode = setjmp (qh errexit);
- if (!exitcode)
- {
- qh NOerrexit = False;
- qh_initflags (qhull_cmd);
- if (qh DELAUNAY)
- qh PROJECTdelaunay= True;
- if (qh HALFspace) {
- /* points is an array of halfspaces,
- the last coordinate of each halfspace is its offset */
- hulldim= dim-1;
- qh_setfeasible (hulldim);
- new_points= qh_sethalfspace_all (dim, numpoints, points, qh feasible_point);
- new_ismalloc= True;
- if (ismalloc)
- free (points);
- }else {
- hulldim= dim;
- new_points= points;
- new_ismalloc= ismalloc;
- }
- qh_init_B (new_points, numpoints, hulldim, new_ismalloc);
- qh_qhull();
- qh_check_output();
- if (outfile)
- qh_produce_output();
- if (qh VERIFYoutput && !qh STOPpoint && !qh STOPcone)
- qh_check_points();
- }
- qh NOerrexit = True;
- return exitcode;
-} /* new_qhull */
-
-/*-<a href="qh-user.htm#TOC"
- >-------------------------------</a><a name="errexit">-</a>
-
- qh_errexit( exitcode, facet, ridge )
- report and exit from an error
- report facet and ridge if non-NULL
- reports useful information such as last point processed
- set qh.FORCEoutput to print neighborhood of facet
-
- see:
- qh_errexit2() in qhull.c for printing 2 facets
-
- design:
- check for error within error processing
- compute qh.hulltime
- print facet and ridge (if any)
- report commandString, options, qh.furthest_id
- print summary and statistics (including precision statistics)
- if qh_ERRsingular
- print help text for singular data set
- exit program via long jump (if defined) or exit()
-*/
-void qh_errexit(int exitcode, facetT *facet, ridgeT *ridge) {
-
- if (qh ERREXITcalled) {
- fprintf (qh ferr, "\nqhull error while processing previous error. Exit program\n");
- exit(1);
- }
- qh ERREXITcalled= True;
- if (!qh QHULLfinished)
- qh hulltime= qh_CPUclock - qh hulltime;
- qh_errprint("ERRONEOUS", facet, NULL, ridge, NULL);
- fprintf (qh ferr, "\nWhile executing: %s | %s\n", qh rbox_command, qh qhull_command);
- fprintf(qh ferr, "Options selected for Qhull %s:\n%s\n", qh_version, qh qhull_options);
- if (qh furthest_id >= 0) {
- fprintf(qh ferr, "Last point added to hull was p%d.", qh furthest_id);
- if (zzval_(Ztotmerge))
- fprintf(qh ferr, " Last merge was #%d.", zzval_(Ztotmerge));
- if (qh QHULLfinished)
- fprintf(qh ferr, "\nQhull has finished constructing the hull.");
- else if (qh POSTmerging)
- fprintf(qh ferr, "\nQhull has started post-merging.");
- fprintf (qh ferr, "\n");
- }
- if (qh FORCEoutput && (qh QHULLfinished || (!facet && !ridge)))
- qh_produce_output();
- else {
- if (exitcode != qh_ERRsingular && zzval_(Zsetplane) > qh hull_dim+1) {
- fprintf (qh ferr, "\nAt error exit:\n");
- qh_printsummary (qh ferr);
- if (qh PRINTstatistics) {
- qh_collectstatistics();
- qh_printstatistics(qh ferr, "at error exit");
- qh_memstatistics (qh ferr);
- }
- }
- if (qh PRINTprecision)
- qh_printstats (qh ferr, qhstat precision, NULL);
- }
- if (!exitcode)
- exitcode= qh_ERRqhull;
- else if (exitcode == qh_ERRsingular)
- qh_printhelp_singular(qh ferr);
- else if (exitcode == qh_ERRprec && !qh PREmerge)
- qh_printhelp_degenerate (qh ferr);
- if (qh NOerrexit) {
- fprintf (qh ferr, "qhull error while ending program. Exit program\n");
- exit(1);
- }
- qh NOerrexit= True;
- longjmp(qh errexit, exitcode);
-} /* errexit */
-
-
-/*-<a href="qh-user.htm#TOC"
- >-------------------------------</a><a name="errprint">-</a>
-
- qh_errprint( fp, string, atfacet, otherfacet, atridge, atvertex )
- prints out the information of facets and ridges to fp
- also prints neighbors and geomview output
-
- notes:
- except for string, any parameter may be NULL
-*/
-void qh_errprint(char *string, facetT *atfacet, facetT *otherfacet, ridgeT *atridge, vertexT *atvertex) {
- int i;
-
- if (atfacet) {
- fprintf(qh ferr, "%s FACET:\n", string);
- qh_printfacet(qh ferr, atfacet);
- }
- if (otherfacet) {
- fprintf(qh ferr, "%s OTHER FACET:\n", string);
- qh_printfacet(qh ferr, otherfacet);
- }
- if (atridge) {
- fprintf(qh ferr, "%s RIDGE:\n", string);
- qh_printridge(qh ferr, atridge);
- if (atridge->top && atridge->top != atfacet && atridge->top != otherfacet)
- qh_printfacet(qh ferr, atridge->top);
- if (atridge->bottom
- && atridge->bottom != atfacet && atridge->bottom != otherfacet)
- qh_printfacet(qh ferr, atridge->bottom);
- if (!atfacet)
- atfacet= atridge->top;
- if (!otherfacet)
- otherfacet= otherfacet_(atridge, atfacet);
- }
- if (atvertex) {
- fprintf(qh ferr, "%s VERTEX:\n", string);
- qh_printvertex (qh ferr, atvertex);
- }
- if (qh fout && qh FORCEoutput && atfacet && !qh QHULLfinished && !qh IStracing) {
- fprintf(qh ferr, "ERRONEOUS and NEIGHBORING FACETS to output\n");
- for (i= 0; i < qh_PRINTEND; i++) /* use fout for geomview output */
- qh_printneighborhood (qh fout, qh PRINTout[i], atfacet, otherfacet,
- !qh_ALL);
- }
-} /* errprint */
-
-
-/*-<a href="qh-user.htm#TOC"
- >-------------------------------</a><a name="printfacetlist">-</a>
-
- qh_printfacetlist( fp, facetlist, facets, printall )
- print all fields for a facet list and/or set of facets to fp
- if !printall,
- only prints good facets
-
- notes:
- also prints all vertices
-*/
-void qh_printfacetlist(facetT *facetlist, setT *facets, boolT printall) {
- facetT *facet, **facetp;
-
- qh_printbegin (qh ferr, qh_PRINTfacets, facetlist, facets, printall);
- FORALLfacet_(facetlist)
- qh_printafacet(qh ferr, qh_PRINTfacets, facet, printall);
- FOREACHfacet_(facets)
- qh_printafacet(qh ferr, qh_PRINTfacets, facet, printall);
- qh_printend (qh ferr, qh_PRINTfacets, facetlist, facets, printall);
-} /* printfacetlist */
-
-
-/*-<a href="qh-globa.htm#TOC"
- >-------------------------------</a><a name="user_memsizes">-</a>
-
- qh_user_memsizes()
- allocate up to 10 additional, quick allocation sizes
-
- notes:
- increase maximum number of allocations in qh_initqhull_mem()
-*/
-void qh_user_memsizes (void) {
-
- /* qh_memsize (size); */
-} /* user_memsizes */
-
diff --git a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/user.h b/GraspPlanning/ExternalDependencies/qhull-2003.1/src/user.h
deleted file mode 100644
index 63ee9e5b77500cba8fbbc5ed2f4769d24b38d663..0000000000000000000000000000000000000000
--- a/GraspPlanning/ExternalDependencies/qhull-2003.1/src/user.h
+++ /dev/null
@@ -1,762 +0,0 @@
-/*<html><pre> -<a href="qh-user.htm"
- >-------------------------------</a><a name="TOP">-</a>
-
- user.h
- user redefinable constants
-
- see qh-user.htm. see COPYING for copyright information.
-
- before reading any code, review qhull.h for data structure definitions and
- the "qh" macro.
-*/
-
-#ifndef qhDEFuser
-#define qhDEFuser 1
-
-/*============= data types and configuration macros ==========*/
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="realT">-</a>
-
- realT
- set the size of floating point numbers
-
- qh_REALdigits
- maximimum number of significant digits
-
- qh_REAL_1, qh_REAL_2n, qh_REAL_3n
- format strings for printf
-
- qh_REALmax, qh_REALmin
- maximum and minimum (near zero) values
-
- qh_REALepsilon
- machine roundoff. Maximum roundoff error for addition and multiplication.
-
- notes:
- Select whether to store floating point numbers in single precision (float)
- or double precision (double).
-
- Use 'float' to save about 8% in time and 25% in space. This is particularly
- help if high-d where convex hulls are space limited. Using 'float' also
- reduces the printed size of Qhull's output since numbers have 8 digits of
- precision.
-
- Use 'double' when greater arithmetic precision is needed. This is needed
- for Delaunay triangulations and Voronoi diagrams when you are not merging
- facets.
-
- If 'double' gives insufficient precision, your data probably includes
- degeneracies. If so you should use facet merging (done by default)
- or exact arithmetic (see imprecision section of manual, qh-impre.htm).
- You may also use option 'Po' to force output despite precision errors.
-
- You may use 'long double', but many format statements need to be changed
- and you may need a 'long double' square root routine. S. Grundmann
- (sg@eeiwzb.et.tu-dresden.de) has done this. He reports that the code runs
- much slower with little gain in precision.
-
- WARNING: on some machines, int f(){realT a= REALmax;return (a == REALmax);}
- returns False. Use (a > REALmax/2) instead of (a == REALmax).
-
- REALfloat = 1 all numbers are 'float' type
- = 0 all numbers are 'double' type
-*/
-#define REALfloat 0
-
-#if (REALfloat == 1)
-#define realT float
-#define REALmax FLT_MAX
-#define REALmin FLT_MIN
-#define REALepsilon FLT_EPSILON
-#define qh_REALdigits 8 /* maximum number of significant digits */
-#define qh_REAL_1 "%6.8g "
-#define qh_REAL_2n "%6.8g %6.8g\n"
-#define qh_REAL_3n "%6.8g %6.8g %6.8g\n"
-
-#elif (REALfloat == 0)
-#define realT double
-#define REALmax DBL_MAX
-#define REALmin DBL_MIN
-#define REALepsilon DBL_EPSILON
-#define qh_REALdigits 16 /* maximum number of significant digits */
-#define qh_REAL_1 "%6.16g "
-#define qh_REAL_2n "%6.16g %6.16g\n"
-#define qh_REAL_3n "%6.16g %6.16g %6.16g\n"
-
-#else
-#error unknown float option
-#endif
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="CPUclock">-</a>
-
- qh_CPUclock
- define the clock() function for reporting the total time spent by Qhull
- returns CPU ticks as a 'long int'
- qh_CPUclock is only used for reporting the total time spent by Qhull
-
- qh_SECticks
- the number of clock ticks per second
-
- notes:
- looks for CLOCKS_PER_SEC, CLOCKS_PER_SECOND, or assumes microseconds
- to define a custom clock, set qh_CLOCKtype to 0
-
- if your system does not use clock() to return CPU ticks, replace
- qh_CPUclock with the corresponding function. It is converted
- to unsigned long to prevent wrap-around during long runs.
-
-
- Set qh_CLOCKtype to
-
- 1 for CLOCKS_PER_SEC, CLOCKS_PER_SECOND, or microsecond
- Note: may fail if more than 1 hour elapsed time
-
- 2 use qh_clock() with POSIX times() (see global.c)
-*/
-#define qh_CLOCKtype 1 /* change to the desired number */
-
-#if (qh_CLOCKtype == 1)
-
-#if defined (CLOCKS_PER_SECOND)
-#define qh_CPUclock ((unsigned long)clock()) /* return CPU clock */
-#define qh_SECticks CLOCKS_PER_SECOND
-
-#elif defined (CLOCKS_PER_SEC)
-#define qh_CPUclock ((unsigned long)clock()) /* return CPU clock */
-#define qh_SECticks CLOCKS_PER_SEC
-
-#elif defined (CLK_TCK)
-#define qh_CPUclock ((unsigned long)clock()) /* return CPU clock */
-#define qh_SECticks CLK_TCK
-
-#else
-#define qh_CPUclock ((unsigned long)clock()) /* return CPU clock */
-#define qh_SECticks 1E6
-#endif
-
-#elif (qh_CLOCKtype == 2)
-#define qh_CPUclock qh_clock() /* return CPU clock */
-#define qh_SECticks 100
-
-#else /* qh_CLOCKtype == ? */
-#error unknown clock option
-#endif
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="RANDOM">-</a>
-
- qh_RANDOMtype, qh_RANDOMmax, qh_RANDOMseed
- define random number generator
-
- qh_RANDOMint generates a random integer between 0 and qh_RANDOMmax.
- qh_RANDOMseed sets the random number seed for qh_RANDOMint
-
- Set qh_RANDOMtype (default 5) to:
- 1 for random() with 31 bits (UCB)
- 2 for rand() with RAND_MAX or 15 bits (system 5)
- 3 for rand() with 31 bits (Sun)
- 4 for lrand48() with 31 bits (Solaris)
- 5 for qh_rand() with 31 bits (included with Qhull)
-
- notes:
- Random numbers are used by rbox to generate point sets. Random
- numbers are used by Qhull to rotate the input ('QRn' option),
- simulate a randomized algorithm ('Qr' option), and to simulate
- roundoff errors ('Rn' option).
-
- Random number generators differ between systems. Most systems provide
- rand() but the period varies. The period of rand() is not critical
- since qhull does not normally use random numbers.
-
- The default generator is Park & Miller's minimal standard random
- number generator [CACM 31:1195 '88]. It is included with Qhull.
-
- If qh_RANDOMmax is wrong, qhull will report a warning and Geomview
- output will likely be invisible.
-*/
-#define qh_RANDOMtype 5 /* *** change to the desired number *** */
-
-#if (qh_RANDOMtype == 1)
-#define qh_RANDOMmax ((realT)0x7fffffffUL) /* 31 bits, random()/MAX */
-#define qh_RANDOMint random()
-#define qh_RANDOMseed_(seed) srandom(seed);
-
-#elif (qh_RANDOMtype == 2)
-#ifdef RAND_MAX
-#define qh_RANDOMmax ((realT)RAND_MAX)
-#else
-#define qh_RANDOMmax ((realT)32767) /* 15 bits (System 5) */
-#endif
-#define qh_RANDOMint rand()
-#define qh_RANDOMseed_(seed) srand((unsigned)seed);
-
-#elif (qh_RANDOMtype == 3)
-#define qh_RANDOMmax ((realT)0x7fffffffUL) /* 31 bits, Sun */
-#define qh_RANDOMint rand()
-#define qh_RANDOMseed_(seed) srand((unsigned)seed);
-
-#elif (qh_RANDOMtype == 4)
-#define qh_RANDOMmax ((realT)0x7fffffffUL) /* 31 bits, lrand38()/MAX */
-#define qh_RANDOMint lrand48()
-#define qh_RANDOMseed_(seed) srand48(seed);
-
-#elif (qh_RANDOMtype == 5)
-#define qh_RANDOMmax ((realT)2147483646UL) /* 31 bits, qh_rand/MAX */
-#define qh_RANDOMint qh_rand()
-#define qh_RANDOMseed_(seed) qh_srand(seed);
-/* unlike rand(), never returns 0 */
-
-#else
-#error: unknown random option
-#endif
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="ORIENTclock">-</a>
-
- qh_ORIENTclock
- 0 for inward pointing normals by Geomview convention
-*/
-#define qh_ORIENTclock 0
-
-
-/*========= performance related constants =========*/
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="HASHfactor">-</a>
-
- qh_HASHfactor
- total hash slots / used hash slots. Must be at least 1.1.
-
- notes:
- =2 for at worst 50% occupancy for qh hash_table and normally 25% occupancy
-*/
-#define qh_HASHfactor 2
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="VERIFYdirect">-</a>
-
- qh_VERIFYdirect
- with 'Tv' verify all points against all facets if op count is smaller
-
- notes:
- if greater, calls qh_check_bestdist() instead
-*/
-#define qh_VERIFYdirect 1000000
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="INITIALsearch">-</a>
-
- qh_INITIALsearch
- if qh_INITIALmax, search points up to this dimension
-*/
-#define qh_INITIALsearch 6
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="INITIALmax">-</a>
-
- qh_INITIALmax
- if dim >= qh_INITIALmax, use min/max coordinate points for initial simplex
-
- notes:
- from points with non-zero determinants
- use option 'Qs' to override (much slower)
-*/
-#define qh_INITIALmax 8
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="JOGGLEdefault">-</a>
-
- qh_JOGGLEdefault
- default qh.JOGGLEmax is qh.DISTround * qh_JOGGLEdefault
-
- notes:
- rbox s r 100 | qhull QJ1e-15 QR0 generates 90% faults at distround 7e-16
- rbox s r 100 | qhull QJ1e-14 QR0 generates 70% faults
- rbox s r 100 | qhull QJ1e-13 QR0 generates 35% faults
- rbox s r 100 | qhull QJ1e-12 QR0 generates 8% faults
- rbox s r 100 | qhull QJ1e-11 QR0 generates 1% faults
- rbox s r 100 | qhull QJ1e-10 QR0 generates 0% faults
- rbox 1000 W0 | qhull QJ1e-12 QR0 generates 86% faults
- rbox 1000 W0 | qhull QJ1e-11 QR0 generates 20% faults
- rbox 1000 W0 | qhull QJ1e-10 QR0 generates 2% faults
- the later have about 20 points per facet, each of which may interfere
-
- pick a value large enough to avoid retries on most inputs
-*/
-#define qh_JOGGLEdefault 30000.0
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="JOGGLEincrease">-</a>
-
- qh_JOGGLEincrease
- factor to increase qh.JOGGLEmax on qh_JOGGLEretry or qh_JOGGLEagain
-*/
-#define qh_JOGGLEincrease 10.0
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="JOGGLEretry">-</a>
-
- qh_JOGGLEretry
- if ZZretry = qh_JOGGLEretry, increase qh.JOGGLEmax
-
- notes:
- try twice at the original value in case of bad luck the first time
-*/
-#define qh_JOGGLEretry 2
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="JOGGLEagain">-</a>
-
- qh_JOGGLEagain
- every following qh_JOGGLEagain, increase qh.JOGGLEmax
-
- notes:
- 1 is OK since it's already failed qh_JOGGLEretry times
-*/
-#define qh_JOGGLEagain 1
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="JOGGLEmaxincrease">-</a>
-
- qh_JOGGLEmaxincrease
- maximum qh.JOGGLEmax due to qh_JOGGLEincrease
- relative to qh.MAXwidth
-
- notes:
- qh.joggleinput will retry at this value until qh_JOGGLEmaxretry
-*/
-#define qh_JOGGLEmaxincrease 1e-2
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="JOGGLEmaxretry">-</a>
-
- qh_JOGGLEmaxretry
- stop after qh_JOGGLEmaxretry attempts
-*/
-#define qh_JOGGLEmaxretry 100
-
-/*========= memory constants =========*/
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="MEMalign">-</a>
-
- qh_MEMalign
- memory alignment for qh_meminitbuffers() in global.c
-
- notes:
- to avoid bus errors, memory allocation must consider alignment requirements.
- malloc() automatically takes care of alignment. Since mem.c manages
- its own memory, we need to explicitly specify alignment in
- qh_meminitbuffers().
-
- A safe choice is sizeof(double). sizeof(float) may be used if doubles
- do not occur in data structures and pointers are the same size. Be careful
- of machines (e.g., DEC Alpha) with large pointers.
-
- If using gcc, best alignment is
- #define qh_MEMalign fmax_(__alignof__(realT),__alignof__(void *))
-*/
-#define qh_MEMalign fmax_(sizeof(realT), sizeof(void *))
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="MEMbufsize">-</a>
-
- qh_MEMbufsize
- size of additional memory buffers
-
- notes:
- used for qh_meminitbuffers() in global.c
-*/
-#define qh_MEMbufsize 0x10000 /* allocate 64K memory buffers */
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="MEMinitbuf">-</a>
-
- qh_MEMinitbuf
- size of initial memory buffer
-
- notes:
- use for qh_meminitbuffers() in global.c
-*/
-#define qh_MEMinitbuf 0x20000 /* initially allocate 128K buffer */
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="INFINITE">-</a>
-
- qh_INFINITE
- on output, indicates Voronoi center at infinity
-*/
-#define qh_INFINITE -10.101
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="DEFAULTbox">-</a>
-
- qh_DEFAULTbox
- default box size (Geomview expects 0.5)
-*/
-#define qh_DEFAULTbox 0.5
-
-/*======= conditional compilation ============================*/
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="compiler">-</a>
-
- __cplusplus
- defined by C++ compilers
-
- __MSC_VER
- defined by Microsoft Visual C++
-
- __MWERKS__ && __POWERPC__
- defined by Metrowerks when compiling for the Power Macintosh
-
- __STDC__
- defined for strict ANSI C
-*/
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="COMPUTEfurthest">-</a>
-
- qh_COMPUTEfurthest
- compute furthest distance to an outside point instead of storing it with the facet
- =1 to compute furthest
-
- notes:
- computing furthest saves memory but costs time
- about 40% more distance tests for partitioning
- removes facet->furthestdist
-*/
-#define qh_COMPUTEfurthest 0
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="KEEPstatistics">-</a>
-
- qh_KEEPstatistics
- =0 removes most of statistic gathering and reporting
-
- notes:
- if 0, code size is reduced by about 4%.
-*/
-#define qh_KEEPstatistics 1
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="MAXoutside">-</a>
-
- qh_MAXoutside
- record outer plane for each facet
- =1 to record facet->maxoutside
-
- notes:
- this takes a realT per facet and slightly slows down qhull
- it produces better outer planes for geomview output
-*/
-#define qh_MAXoutside 1
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="NOmerge">-</a>
-
- qh_NOmerge
- disables facet merging if defined
-
- notes:
- This saves about 10% space.
-
- Unless 'Q0'
- qh_NOmerge sets 'QJ' to avoid precision errors
-
- #define qh_NOmerge
-
- see:
- <a href="mem.h#NOmem">qh_NOmem</a> in mem.c
-
- see user.c/user_eg.c for removing io.o
-*/
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="NOtrace">-</a>
-
- qh_NOtrace
- no tracing if defined
-
- notes:
- This saves about 5% space.
-
- #define qh_NOtrace
-*/
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="QHpointer">-</a>
-
- qh_QHpointer
- access global data with pointer or static structure
-
- qh_QHpointer = 1 access globals via a pointer to allocated memory
- enables qh_saveqhull() and qh_restoreqhull()
- costs about 8% in time and 2% in space
-
- = 0 qh_qh and qh_qhstat are static data structures
- only one instance of qhull() can be active at a time
- default value
-
- notes:
- all global variables for qhull are in qh, qhmem, and qhstat
- qh is defined in qhull.h
- qhmem is defined in mem.h
- qhstat is defined in stat.h
-
- see:
- user_eg.c for an example
-*/
-#define qh_QHpointer 0
-#if 0 /* sample code */
-qhT* oldqhA, *oldqhB;
-
-exitcode = qh_new_qhull(dim, numpoints, points, ismalloc,
- flags, outfile, errfile);
-/* use results from first call to qh_new_qhull */
-oldqhA = qh_save_qhull();
-exitcode = qh_new_qhull(dimB, numpointsB, pointsB, ismalloc,
- flags, outfile, errfile);
-/* use results from second call to qh_new_qhull */
-oldqhB = qh_save_qhull();
-qh_restore_qhull(&oldqhA);
-/* use results from first call to qh_new_qhull */
-qh_freeqhull(qh_ALL); /* frees all memory used by first call */
-qh_restore_qhull(&oldqhB);
-/* use results from second call to qh_new_qhull */
-qh_freeqhull(!qh_ALL); /* frees long memory used by second call */
-qh_memfreeshort(&curlong, &totlong); /* frees short memory and memory allocator */
-#endif
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="QUICKhelp">-</a>
-
- qh_QUICKhelp
- =1 to use abbreviated help messages, e.g., for degenerate inputs
-*/
-#define qh_QUICKhelp 0
-
-/* ============ -merge constants- ====================
-
- These constants effect facet merging. You probably will not need
- to modify these. They effect the performance of facet merging.
-*/
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="DIMmergeVertex">-</a>
-
- qh_DIMmergeVertex
- max dimension for vertex merging (it is not effective in high-d)
-*/
-#define qh_DIMmergeVertex 6
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="DIMreduceBuild">-</a>
-
- qh_DIMreduceBuild
- max dimension for vertex reduction during build (slow in high-d)
-*/
-#define qh_DIMreduceBuild 5
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="BESTcentrum">-</a>
-
- qh_BESTcentrum
- if > 2*dim+n vertices, qh_findbestneighbor() tests centrums (faster)
- else, qh_findbestneighbor() tests all vertices (much better merges)
-
- qh_BESTcentrum2
- if qh_BESTcentrum2 * DIM3 + BESTcentrum < #vertices tests centrums
-*/
-#define qh_BESTcentrum 20
-#define qh_BESTcentrum2 2
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="BESTnonconvex">-</a>
-
- qh_BESTnonconvex
- if > dim+n neighbors, qh_findbestneighbor() tests nonconvex ridges.
-
- notes:
- It is needed because qh_findbestneighbor is slow for large facets
-*/
-#define qh_BESTnonconvex 15
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="MAXnewmerges">-</a>
-
- qh_MAXnewmerges
- if >n newmerges, qh_merge_nonconvex() calls qh_reducevertices_centrums.
-
- notes:
- It is needed because postmerge can merge many facets at once
-*/
-#define qh_MAXnewmerges 2
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="MAXnewcentrum">-</a>
-
- qh_MAXnewcentrum
- if <= dim+n vertices (n approximates the number of merges),
- reset the centrum in qh_updatetested() and qh_mergecycle_facets()
-
- notes:
- needed to reduce cost and because centrums may move too much if
- many vertices in high-d
-*/
-#define qh_MAXnewcentrum 5
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="COPLANARratio">-</a>
-
- qh_COPLANARratio
- for 3-d+ merging, qh.MINvisible is n*premerge_centrum
-
- notes:
- for non-merging, it's DISTround
-*/
-#define qh_COPLANARratio 3
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="DISToutside">-</a>
-
- qh_DISToutside
- When is a point clearly outside of a facet?
- Stops search in qh_findbestnew or qh_partitionall
- qh_findbest uses qh.MINoutside since since it is only called if no merges.
-
- notes:
- 'Qf' always searches for best facet
- if !qh.MERGING, same as qh.MINoutside.
- if qh_USEfindbestnew, increase value since neighboring facets may be ill-behaved
- [Note: Zdelvertextot occurs normally with interior points]
- RBOX 1000 s Z1 G1e-13 t1001188774 | QHULL Tv
- When there is a sharp edge, need to move points to a
- clearly good facet; otherwise may be lost in another partitioning.
- if too big then O(n^2) behavior for partitioning in cone
- if very small then important points not processed
- Needed in qh_partitionall for
- RBOX 1000 s Z1 G1e-13 t1001032651 | QHULL Tv
- Needed in qh_findbestnew for many instances of
- RBOX 1000 s Z1 G1e-13 t | QHULL Tv
-
- See:
- qh_DISToutside -- when is a point clearly outside of a facet
- qh_SEARCHdist -- when is facet coplanar with the best facet?
- qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
-*/
-#define qh_DISToutside ((qh_USEfindbestnew ? 2 : 1) * \
- fmax_((qh MERGING ? 2 : 1)*qh MINoutside, qh max_outside))
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="RATIOnearinside">-</a>
-
- qh_RATIOnearinside
- ratio of qh.NEARinside to qh.ONEmerge for retaining inside points for
- qh_check_maxout().
-
- notes:
- This is overkill since do not know the correct value.
- It effects whether 'Qc' reports all coplanar points
- Not used for 'd' since non-extreme points are coplanar
-*/
-#define qh_RATIOnearinside 5
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="SEARCHdist">-</a>
-
- qh_SEARCHdist
- When is a facet coplanar with the best facet?
- qh_findbesthorizon: all coplanar facets of the best facet need to be searched.
-
- See:
- qh_DISToutside -- when is a point clearly outside of a facet
- qh_SEARCHdist -- when is facet coplanar with the best facet?
- qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
-*/
-#define qh_SEARCHdist ((qh_USEfindbestnew ? 2 : 1) * \
- (qh max_outside + 2 * qh DISTround + fmax_( qh MINvisible, qh MAXcoplanar)));
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="USEfindbestnew">-</a>
-
- qh_USEfindbestnew
- Always use qh_findbestnew for qh_partitionpoint, otherwise use
- qh_findbestnew if merged new facet or sharpnewfacets.
-
- See:
- qh_DISToutside -- when is a point clearly outside of a facet
- qh_SEARCHdist -- when is facet coplanar with the best facet?
- qh_USEfindbestnew -- when to use qh_findbestnew for qh_partitionpoint()
-*/
-#define qh_USEfindbestnew (zzval_(Ztotmerge) > 50)
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="WIDEcoplanar">-</a>
-
- qh_WIDEcoplanar
- n*MAXcoplanar or n*MINvisible for a WIDEfacet
-
- if vertex is further than qh.WIDEfacet from the hyperplane
- then its ridges are not counted in computing the area, and
- the facet's centrum is frozen.
-
- notes:
- qh.WIDEfacet= max(qh.MAXoutside,qh_WIDEcoplanar*qh.MAXcoplanar,
- qh_WIDEcoplanar * qh.MINvisible);
-*/
-#define qh_WIDEcoplanar 6
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="MAXnarrow">-</a>
-
- qh_MAXnarrow
- max. cosine in initial hull that sets qh.NARROWhull
-
- notes:
- If qh.NARROWhull, the initial partition does not make
- coplanar points. If narrow, a coplanar point can be
- coplanar to two facets of opposite orientations and
- distant from the exact convex hull.
-
- Conservative estimate. Don't actually see problems until it is -1.0
-*/
-#define qh_MAXnarrow -0.99999999
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="WARNnarrow">-</a>
-
- qh_WARNnarrow
- max. cosine in initial hull to warn about qh.NARROWhull
-
- notes:
- this is a conservative estimate.
- Don't actually see problems until it is -1.0. See qh-impre.htm
-*/
-#define qh_WARNnarrow -0.999999999999999
-
-/*-<a href="qh-user.htm#TOC"
- >--------------------------------</a><a name="ZEROdelaunay">-</a>
-
- qh_ZEROdelaunay
- a zero Delaunay facet occurs for input sites coplanar with their convex hull
- the last normal coefficient of a zero Delaunay facet is within
- qh_ZEROdelaunay * qh.ANGLEround of 0
-
- notes:
- qh_ZEROdelaunay does not allow for joggled input ('QJ').
-
- You can avoid zero Delaunay facets by surrounding the input with a box.
-
- Use option 'PDk:-n' to explicitly define zero Delaunay facets
- k= dimension of input sites (e.g., 3 for 3-d Delaunay triangulation)
- n= the cutoff for zero Delaunay facets (e.g., 'PD3:-1e-12')
-*/
-#define qh_ZEROdelaunay 2
-
-#endif /* qh_DEFuser */
-
-
-