Compare commits

...

22 Commits
3.1 ... dev-13

Author SHA1 Message Date
pschmidtke
7ec07dc24d dev-13 wrapping up final build with new qhull 2018-07-23 21:53:46 +00:00
Peter Schmidtke
ffe88f56df dev-13 build only what is needed in qhull 2018-07-23 23:35:41 +02:00
Peter Schmidtke
9d4e3dc010 dev-13 adding back makefile? 2018-07-23 23:30:38 +02:00
Peter Schmidtke
c16c54072d dropping gitignore? 2018-07-23 23:20:39 +02:00
Peter Schmidtke
c21bee5482 dev-13 now?2 2018-07-23 23:14:29 +02:00
Peter Schmidtke
9b3443c9dc dev-13 now? 2018-07-23 23:13:07 +02:00
Peter Schmidtke
229728bcd6 dev-13 dropping calls to prompts in qconex 2018-07-23 23:10:51 +02:00
Peter Schmidtke
a96e6e8f8b dev-13 dropping prompts from qconvex 2018-07-23 23:09:32 +02:00
Peter Schmidtke
232f546bfe dev-13 adding missing userprintf_rbox.o dependency 2018-07-23 23:04:24 +02:00
Peter Schmidtke
17d171401e devel-13 back to qobjs in makefile 2018-07-23 22:56:05 +02:00
Peter Schmidtke
9f737c4070 dev-13 make clean qhull in fpocket makefile 2018-07-23 22:52:29 +02:00
Peter Schmidtke
81a864715c dev-13 adding back run_qvoronoi and run_qconvex 2018-07-23 22:51:22 +02:00
Peter Schmidtke
633efaa841 dev-13 including full qhull with tests 2018-07-23 22:43:19 +02:00
Peter Schmidtke
bce0e0640a dev-13 dropped tests etc from qhull makefile 2018-07-23 22:41:16 +02:00
Peter Schmidtke
6d99b179bf dev-13 make qhull 2018-07-23 22:38:43 +02:00
Peter Schmidtke
e68ab59034 dev-13 make qhull introduced 2018-07-23 22:37:55 +02:00
Peter Schmidtke
402b611b71 dev-13 integrating new qhull source code 2018-07-23 22:34:52 +02:00
Peter
93f081ce13 dev-13 drop other remove 2018-07-23 14:26:42 +02:00
Peter
a58493977f dev-13 drop removal of voronoi tmp files for debugging purposes 2018-07-23 14:24:07 +02:00
Peter
c6f4a2620b dev-13 enable debugging mode 2018-07-23 14:10:42 +02:00
Peter Schmidtke
9b5d5b341d Merge pull request #12 from mshyu24/master
Update git clone in README
2018-07-23 14:03:03 +02:00
mshyu24
4a5d14afa6 Update git clone in README 2018-07-19 19:48:04 -05:00
316 changed files with 114512 additions and 1187 deletions

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@@ -43,7 +43,7 @@ Download the sources from github via the website or using git clone and then bui
```
git clone https://github.com/Discngine/fpocket.git .
git clone https://github.com/Discngine/fpocket.git
cd fpocket
make
sudo make install

3444
data/sample/5WA6.pdb Normal file

File diff suppressed because it is too large Load Diff

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@@ -28,8 +28,8 @@ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLI
#include "utils.h"
#include "../src/qhull/qvoronoi.h"
#include "../src/qhull/qconvex.h"
#include "../src/qhull/src//qvoronoi/qvoronoi.h"
#include "../src/qhull/src/qconvex/qconvex.h"
#include "memhandler.h"

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@@ -11,7 +11,7 @@ PATH_SRC = src/
PATH_HEADER = headers/
PATH_BIN = bin/
PATH_MAN = man/
PATH_QHULL = src/qhull/
PATH_QHULL = src/qhull/src
BINDIR = /usr/local/bin/
MANDIR = /usr/local/man/man8/
@@ -43,15 +43,16 @@ LFLAGS = -lm -L$(PLUGINDIR)/$(ARCH)/molfile $(PLUGINDIR)/$(ARCH)/molfile/lib
#------------------------------------------------------------
# BINARIES OBJECTS
#------------------------------------------------------------
#QOBJS = $(PATH_QHULL)/src/qvoronoi/qvoronoi.o $(PATH_QHULL)/src/qconvex/qconvex.o
QOBJS = $(PATH_QHULL)geom2.o $(PATH_QHULL)geom.o $(PATH_QHULL)global.o \
$(PATH_QHULL)io.o $(PATH_QHULL)io.h $(PATH_QHULL)libqhull.o \
$(PATH_QHULL)mem.o $(PATH_QHULL)merge.o $(PATH_QHULL)poly2.o \
$(PATH_QHULL)poly.o $(PATH_QHULL)qset.o \
$(PATH_QHULL)random.o $(PATH_QHULL)rboxlib.o \
$(PATH_QHULL)stat.o $(PATH_QHULL)user.o \
$(PATH_QHULL)usermem.o \
$(PATH_QHULL)userprintf.o $(PATH_QHULL)qvoronoi.o $(PATH_QHULL)qconvex.o
QOBJS = $(PATH_QHULL)/libqhull/geom2.o $(PATH_QHULL)/libqhull/geom.o $(PATH_QHULL)/libqhull/global.o \
$(PATH_QHULL)/libqhull/io.o $(PATH_QHULL)/libqhull/io.h $(PATH_QHULL)/libqhull/libqhull.o \
$(PATH_QHULL)/libqhull/mem.o $(PATH_QHULL)/libqhull/merge.o $(PATH_QHULL)/libqhull/poly2.o \
$(PATH_QHULL)/libqhull/poly.o $(PATH_QHULL)/libqhull/qset.o \
$(PATH_QHULL)/libqhull/random.o $(PATH_QHULL)/libqhull/rboxlib.o \
$(PATH_QHULL)/libqhull/stat.o $(PATH_QHULL)/libqhull/user.o \
$(PATH_QHULL)/libqhull/usermem.o \
$(PATH_QHULL)/libqhull/userprintf.o $(PATH_QHULL)/libqhull/userprintf_rbox.o $(PATH_QHULL)/qvoronoi/qvoronoi.o $(PATH_QHULL)/qconvex/qconvex.o
CHOBJ = $(PATH_OBJ)check.o $(PATH_OBJ)psorting.o $(PATH_OBJ)pscoring.o \
$(PATH_OBJ)utils.o $(PATH_OBJ)pertable.o $(PATH_OBJ)memhandler.o \
@@ -62,7 +63,7 @@ CHOBJ = $(PATH_OBJ)check.o $(PATH_OBJ)psorting.o $(PATH_OBJ)pscoring.o \
$(PATH_OBJ)fpocket.o $(PATH_OBJ)write_visu.o $(PATH_OBJ)fpout.o \
$(PATH_OBJ)atom.o $(PATH_OBJ)writepocket.o $(PATH_OBJ)voronoi_lst.o \
$(PATH_OBJ)neighbor.o $(PATH_OBJ)asa.o $(PATH_OBJ)clusterlib.o $(PATH_OBJ)energy.o \
$(QOBJS)
FPOBJ = $(PATH_OBJ)fpmain.o $(PATH_OBJ)psorting.o $(PATH_OBJ)pscoring.o \
$(PATH_OBJ)utils.o $(PATH_OBJ)pertable.o $(PATH_OBJ)memhandler.o \
@@ -85,7 +86,7 @@ TPOBJ = $(PATH_OBJ)tpmain.o $(PATH_OBJ)psorting.o $(PATH_OBJ)pscoring.o \
$(PATH_OBJ)fpout.o $(PATH_OBJ)atom.o $(PATH_OBJ)writepocket.o \
$(PATH_OBJ)voronoi_lst.o $(PATH_OBJ)neighbor.o $(PATH_OBJ)asa.o\
$(PATH_OBJ)clusterlib.o $(PATH_OBJ)energy.o $(PATH_OBJ)topology.o\
$(QOBJS)
$(PATH_QHULL)/qvoronoi/qvoronoi.o $(PATH_QHULL)/qconvex/qconvex.o
DPOBJ = $(PATH_OBJ)dpmain.o $(PATH_OBJ)psorting.o $(PATH_OBJ)pscoring.o \
$(PATH_OBJ)dpocket.o $(PATH_OBJ)dparams.o $(PATH_OBJ)voronoi.o \
@@ -127,8 +128,14 @@ $(PATH_OBJ)%.o: $(PATH_SRC)%.cpp
# RULES FOR EXECUTABLES
#-----------------------------------------------------------
all: $(MYPROGS) # $(PATH_BIN)$(CHECK)
all:
make qhull
make fpocket
fpocket: $(MYPROGS) # $(PATH_BIN)$(CHECK)
qhull:
cd src/qhull/ && make
$(PATH_BIN)$(CHECK): $(CHOBJ) $(QOBJS)
$(LINKER) $^ -o $@ $(LFLAGS)
@@ -166,6 +173,7 @@ clean:
rm -f $(PATH_BIN)$(TPOCKET)
rm -f $(PATH_BIN)$(DPOCKET)
rm -f $(PATH_BIN)$(MDPOCKET)
cd src/qhull && make clean
uninstall:
rm -f $(PATH_BIN)$(FPOCKET) $(BINDIR)$(FPOCKET)

47
src/qhull/Announce.txt Normal file
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@@ -0,0 +1,47 @@
Qhull 2015.2 2016/01/18
http://www.qhull.org
git@github.com:qhull/qhull.git
http://www.geomview.org
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
git@github.com:qhull/qhull.git
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, 22(4):469-483, Dec. 1996.
http://www.acm.org/pubs/citations/journals/toms/1996-22-4/p469-barber/
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405
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.

426
src/qhull/CMakeLists.txt Normal file
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@@ -0,0 +1,426 @@
# CMakeLists.txt -- CMake configuration file for qhull, qhull6, and related programs
#
# To install CMake
# Download from http://www.cmake.org/download/
#
# To find the available targets for CMake -G "..."
# cmake --help
#
# To build with MSYS/mingw
# cd build && cmake -G "MSYS Makefiles" .. && cmake ..
# make
# make install
#
# To uninstall on unix or MSYS/mingw
# xargs rm <build/install_manifest.txt
#
# To build Qhull with Visual Studio projects, run cmake twice
# To install bin/doc/include/lib in the current directory
# mkdir -p build-cmake && cd build-cmake && cmake -G "Visual Studio 11 2012" .. && cmake -DCMAKE_INSTALL_PREFIX=.. ..
# mkdir -p build-cmake && cd build-cmake && cmake -G "Visual Studio 11 2012 Win64" .. && cmake -DCMAKE_INSTALL_PREFIX=.. ..
# To install into Program Files/qhull
# mkdir -p build-cmake && cd build-cmake && cmake -G "Visual Studio 11 2012" .. && cmake ..
# mkdir -p build-cmake && cd build-cmake && cmake -G "Visual Studio 11 2012 Win64" .. && cmake ..
# To build for Visual Studio 2005 and install into Program Files/qhull
# mkdir -p build-cmake && cd build-cmake && cmake -G "Visual Studio 8 2005" .. && cmake ..
# mkdir -p build-cmake && cd build-cmake && cmake -G "Visual Studio 8 2005 Win64" .. && cmake ..
# Double click build-cmake/qhull-all.sln
# Build INSTALL to copy files into C:/Program Files/qhull
#
# Additional build targets
# qhullp -- Same as qhull using qh_QHpointer and deprecated libqhull_p
# user_egp -- Same as user_eg using qh_QHpointer and deprecated libqhull_p
#
# Notes on Visual Studio projects
# You may need to copy bin/msvcr80.dll into C:/Program Files/qhull/bin
# If using library debug targets, please rename with '_d' (e.g., qhullstatic_d.lib)
#
# Troubleshooting
# "No CMAKE_C_COMPILER could be found"
# cmake was not able to find the build environment specified (e.g., Visual Studio 11)
#
# To uninstall on Windows
# Delete C:/Program Files/qhull
#
# If creating a qhull package, please include a pkg-config file based on build/qhull*.pc.in
#
# For qhulltest, use the Qt build (src/qhull-all.pro)
#
# Qhull ships with cmake-derived sln and proj files for DevStudio 8 2005
# See eg/make-vcproj.sh
# Change to relative paths
# Remove ZERO_CHECK, ALL_BUILD, and INSTALL projects
# Change targets to bin/ and lib/ directories
# Disable incremental linking and ilk files (LinkIncremental="1")
# Disable Run-Time Type Info (rtti)
# Remove src/libqhullcpp from most of the AdditionalIncludeDirectories
# Remove CMAKE_INTDIR from PreprocessorDefinitions
# Adjust target names and destinations (e.g., lib/libqhullstatic_rd.a)
#
# $Id: //main/2015/qhull/CMakeLists.txt#8 $$Change: 2066 $
# $DateTime: 2016/01/18 19:29:17 $$Author: bbarber $
project(qhull)
cmake_minimum_required(VERSION 2.6)
# Define qhull_VERSION in CMakeLists.txt, Makefile, qhull-exports.def, qhull_p-exports.def, qhull_r-exports.def, qhull-warn.pri
set(qhull_VERSION2 "2015.2 2016/01/18") # not used, See global.c, global_r.c, rbox.c, rbox_r.c
set(qhull_VERSION "7.2.0") # Advance every release
# SOVERSION -- qhull 2003 = empty, 2009 = 5, 2010-2012 = 6, 2015 (reentrant) = 7
set(qhull_SOVERSION 7) # For SOVERSION
include(CMakeModules/CheckLFS.cmake)
option(WITH_LFS "Enable Large File Support" ON)
check_lfs(WITH_LFS)
if(INCLUDE_INSTALL_DIR)
else()
set(INCLUDE_INSTALL_DIR ${CMAKE_INSTALL_PREFIX}/include)
endif()
if(LIB_INSTALL_DIR)
else()
set(LIB_INSTALL_DIR ${CMAKE_INSTALL_PREFIX}/lib)
endif()
if(BIN_INSTALL_DIR)
else()
set(BIN_INSTALL_DIR ${CMAKE_INSTALL_PREFIX}/bin)
endif()
if(MAN_INSTALL_DIR)
else()
if(WIN32)
set(MAN_INSTALL_DIR ${CMAKE_INSTALL_PREFIX}/man/man1)
else()
set(MAN_INSTALL_DIR ${CMAKE_INSTALL_PREFIX}/share/man/man1)
endif()
endif()
if(DOC_INSTALL_DIR)
else()
if(WIN32)
set(DOC_INSTALL_DIR ${CMAKE_INSTALL_PREFIX}/doc)
else()
set(DOC_INSTALL_DIR ${CMAKE_INSTALL_PREFIX}/share/doc/qhull)
endif()
endif()
message(STATUS)
message(STATUS "========== qhull Build Information ==========")
message(STATUS "Build Version: ${qhull_VERSION}")
message(STATUS "Install Prefix (CMAKE_INSTALL_PREFIX): ${CMAKE_INSTALL_PREFIX}")
message(STATUS "Binary Directory (BIN_INSTALL_DIR): ${BIN_INSTALL_DIR}")
message(STATUS "Library Directory (LIB_INSTALL_DIR): ${LIB_INSTALL_DIR}")
message(STATUS "Include Directory (INCLUDE_INSTALL_DIR): ${INCLUDE_INSTALL_DIR}")
message(STATUS "Documentation Directory (DOC_INSTALL_DIR): ${DOC_INSTALL_DIR}")
message(STATUS "Man Pages Directory (MAN_INSTALL_DIR): ${MAN_INSTALL_DIR}")
message(STATUS "Build Type (CMAKE_BUILD_TYPE): ${CMAKE_BUILD_TYPE}")
message(STATUS "To override these options, add -D{OPTION_NAME}=... to the cmake command")
message(STATUS " Build the debug targets -DCMAKE_BUILD_TYPE=Debug")
message(STATUS)
message(STATUS "To build and install qhull, enter \"make\" and \"make install\"")
message(STATUS "To smoketest qhull, enter \"ctest\"")
message(STATUS)
# ---------------------------------------
# Define library source files and variables
#
# Files for individual targets are defined with the target
# ---------------------------------------
# Order libqhull object files by frequency of execution. Small files at end.
# Non-reentrant Qhull
set(
libqhull_HEADERS
src/libqhull/libqhull.h
src/libqhull/geom.h
src/libqhull/io.h
src/libqhull/mem.h
src/libqhull/merge.h
src/libqhull/poly.h
src/libqhull/qhull_a.h
src/libqhull/qset.h
src/libqhull/random.h
src/libqhull/stat.h
src/libqhull/user.h
)
set(
libqhull_SOURCES
src/libqhull/global.c
src/libqhull/stat.c
src/libqhull/geom2.c
src/libqhull/poly2.c
src/libqhull/merge.c
src/libqhull/libqhull.c
src/libqhull/geom.c
src/libqhull/poly.c
src/libqhull/qset.c
src/libqhull/mem.c
src/libqhull/random.c
src/libqhull/usermem.c
src/libqhull/userprintf.c
src/libqhull/io.c
src/libqhull/user.c
src/libqhull/rboxlib.c
src/libqhull/userprintf_rbox.c
${libqhull_HEADERS}
)
set(
libqhull_DOC
src/libqhull/index.htm
src/libqhull/qh-geom.htm
src/libqhull/qh-globa.htm
src/libqhull/qh-io.htm
src/libqhull/qh-mem.htm
src/libqhull/qh-merge.htm
src/libqhull/qh-poly.htm
src/libqhull/qh-qhull.htm
src/libqhull/qh-set.htm
src/libqhull/qh-stat.htm
src/libqhull/qh-user.htm
src/libqhull/DEPRECATED.txt
)
set(
testqset_HEADERS
src/libqhull/mem.h
src/libqhull/qset.h
)
set(
testqset_SOURCES
src/libqhull/qset.c
src/libqhull/mem.c
src/libqhull/usermem.c
src/testqset/testqset.c
${testqset_HEADERS}
)
# Reeentrant Qhull
set(
libqhullr_HEADERS
src/libqhull_r/libqhull_r.h
src/libqhull_r/geom_r.h
src/libqhull_r/io_r.h
src/libqhull_r/mem_r.h
src/libqhull_r/merge_r.h
src/libqhull_r/poly_r.h
src/libqhull_r/qhull_ra.h
src/libqhull_r/qset_r.h
src/libqhull_r/random_r.h
src/libqhull_r/stat_r.h
src/libqhull_r/user_r.h
)
set(
libqhullr_SOURCES
src/libqhull_r/global_r.c
src/libqhull_r/stat_r.c
src/libqhull_r/geom2_r.c
src/libqhull_r/poly2_r.c
src/libqhull_r/merge_r.c
src/libqhull_r/libqhull_r.c
src/libqhull_r/geom_r.c
src/libqhull_r/poly_r.c
src/libqhull_r/qset_r.c
src/libqhull_r/mem_r.c
src/libqhull_r/random_r.c
src/libqhull_r/usermem_r.c
src/libqhull_r/userprintf_r.c
src/libqhull_r/io_r.c
src/libqhull_r/user_r.c
src/libqhull_r/rboxlib_r.c
src/libqhull_r/userprintf_rbox_r.c
${libqhullr_HEADERS}
)
set(
libqhullr_DOC
src/libqhull_r/index.htm
src/libqhull_r/qh-geom_r.htm
src/libqhull_r/qh-globa_r.htm
src/libqhull_r/qh-io_r.htm
src/libqhull_r/qh-mem_r.htm
src/libqhull_r/qh-merge_r.htm
src/libqhull_r/qh-poly_r.htm
src/libqhull_r/qh-qhull_r.htm
src/libqhull_r/qh-set_r.htm
src/libqhull_r/qh-stat_r.htm
src/libqhull_r/qh-user_r.htm
)
set(
testqsetr_HEADERS
src/libqhull_r/mem_r.h
src/libqhull_r/qset_r.h
)
set(
testqsetr_SOURCES
src/libqhull_r/qset_r.c
src/libqhull_r/mem_r.c
src/libqhull_r/usermem_r.c
src/testqset_r/testqset_r.c
${testqsetr_HEADERS}
)
# C++ interface to reentrant Qhull
set(
libqhullcpp_HEADERS
src/libqhullcpp/Coordinates.h
src/libqhullcpp/functionObjects.h
src/libqhullcpp/PointCoordinates.h
src/libqhullcpp/Qhull.h
src/libqhullcpp/QhullError.h
src/libqhullcpp/QhullFacet.h
src/libqhullcpp/QhullFacetList.h
src/libqhullcpp/QhullFacetSet.h
src/libqhullcpp/QhullHyperplane.h
src/libqhullcpp/QhullIterator.h
src/libqhullcpp/QhullLinkedList.h
src/libqhullcpp/QhullPoint.h
src/libqhullcpp/QhullPoints.h
src/libqhullcpp/QhullPointSet.h
src/libqhullcpp/QhullQh.h
src/libqhullcpp/QhullRidge.h
src/libqhullcpp/QhullSet.h
src/libqhullcpp/QhullSets.h
src/libqhullcpp/QhullStat.h
src/libqhullcpp/QhullVertex.h
src/libqhullcpp/QhullVertexSet.h
src/libqhullcpp/RboxPoints.h
src/libqhullcpp/RoadError.h
src/libqhullcpp/RoadLogEvent.h
src/qhulltest/RoadTest.h
)
set(
libqhullcpp_SOURCES
src/libqhullcpp/Coordinates.cpp
src/libqhullcpp/PointCoordinates.cpp
src/libqhullcpp/Qhull.cpp
src/libqhullcpp/QhullFacet.cpp
src/libqhullcpp/QhullFacetList.cpp
src/libqhullcpp/QhullFacetSet.cpp
src/libqhullcpp/QhullHyperplane.cpp
src/libqhullcpp/QhullPoint.cpp
src/libqhullcpp/QhullPointSet.cpp
src/libqhullcpp/QhullPoints.cpp
src/libqhullcpp/QhullQh.cpp
src/libqhullcpp/QhullRidge.cpp
src/libqhullcpp/QhullSet.cpp
src/libqhullcpp/QhullStat.cpp
src/libqhullcpp/QhullVertex.cpp
src/libqhullcpp/QhullVertexSet.cpp
src/libqhullcpp/RboxPoints.cpp
src/libqhullcpp/RoadError.cpp
src/libqhullcpp/RoadLogEvent.cpp
${libqhullcpp_HEADERS}
)
# Documentation files (index.htm refers to html/...)
set(
doc_FILES
README.txt
REGISTER.txt
Announce.txt
COPYING.txt
index.htm
)
include_directories(${CMAKE_SOURCE_DIR}/src)
if(CMAKE_BUILD_TYPE MATCHES "[dD]ebug")
set(qhull_CPP qhullcpp_d)
set(qhull_SHARED qhull_d)
set(qhull_SHAREDP qhull_pd)
set(qhull_SHAREDR qhull_rd)
set(qhull_STATIC qhullstatic_d)
set(qhull_STATICR qhullstatic_rd)
else()
set(qhull_CPP qhullcpp)
set(qhull_SHARED libqhull) # Temporarily avoid name conflict with qhull executable
set(qhull_SHAREDP qhull_p)
set(qhull_SHAREDR qhull_r)
set(qhull_STATIC qhullstatic)
set(qhull_STATICR qhullstatic_r)
endif()
# ---------------------------------------
# Define static libraries qhullstatic (non-reentrant) and qhullstatic_r (reentrant)
# ---------------------------------------
add_library(${qhull_STATIC} STATIC ${libqhull_SOURCES})
set_target_properties(${qhull_STATIC} PROPERTIES
VERSION ${qhull_VERSION})
add_library(${qhull_STATICR} STATIC ${libqhullr_SOURCES})
set_target_properties(${qhull_STATICR} PROPERTIES
VERSION ${qhull_VERSION})
if(UNIX)
target_link_libraries(${qhull_STATIC} m)
target_link_libraries(${qhull_STATICR} m)
endif(UNIX)
# ---------------------------------------
# Define C++ static library qhullcpp
# Do not create libqhullcpp as a shared library. Qhull C++ classes may change layout and size.
# ---------------------------------------
add_library(${qhull_CPP} STATIC ${libqhullcpp_SOURCES})
set_target_properties(${qhull_CPP} PROPERTIES
VERSION ${qhull_VERSION})
# ---------------------------------------
# Define qhull executables linked to qhullstatic library
# qhull is linked to reentrant qhull (more flexible)
# the others are linked to non-reentrant qhull (somewhat faster)
# ---------------------------------------
set(qhull_SOURCES src/qhull/unix_r.c)
set(rbox_SOURCES src/rbox/rbox.c)
set(qconvex_SOURCES src/qconvex/qconvex.c)
set(qdelaunay_SOURCES src/qdelaunay/qdelaun.c)
set(qvoronoi_SOURCES src/qvoronoi/qvoronoi.c)
set(qhalf_SOURCES src/qhalf/qhalf.c)
add_executable(qhull ${qhull_SOURCES})
target_link_libraries(qhull ${qhull_STATICR})
add_executable(rbox ${rbox_SOURCES})
target_link_libraries(rbox ${qhull_STATIC})
add_executable(qconvex ${qconvex_SOURCES})
target_link_libraries(qconvex ${qhull_STATIC})
add_executable(qdelaunay ${qdelaunay_SOURCES})
target_link_libraries(qdelaunay ${qhull_STATIC})
add_executable(qvoronoi ${qvoronoi_SOURCES})
target_link_libraries(qvoronoi ${qhull_STATIC})
add_executable(qhalf ${qhalf_SOURCES})
target_link_libraries(qhalf ${qhull_STATIC})
# ---------------------------------------
# Define install
# ---------------------------------------
install(TARGETS ${qhull_TARGETS_INSTALL}
RUNTIME DESTINATION ${BIN_INSTALL_DIR}
LIBRARY DESTINATION ${LIB_INSTALL_DIR}
ARCHIVE DESTINATION ${LIB_INSTALL_DIR})
install(FILES ${libqhull_HEADERS} DESTINATION ${INCLUDE_INSTALL_DIR}/libqhull)
install(FILES ${libqhull_DOC} DESTINATION ${INCLUDE_INSTALL_DIR}/libqhull)
install(FILES ${libqhullr_HEADERS} DESTINATION ${INCLUDE_INSTALL_DIR}/libqhull_r)
install(FILES ${libqhullr_DOC} DESTINATION ${INCLUDE_INSTALL_DIR}/libqhull_r)
install(FILES ${libqhullcpp_HEADERS} DESTINATION ${INCLUDE_INSTALL_DIR}/libqhullcpp)
install(FILES html/qhull.man DESTINATION ${MAN_INSTALL_DIR} RENAME qhull.1)
install(FILES html/rbox.man DESTINATION ${MAN_INSTALL_DIR} RENAME rbox.1)
install(FILES ${doc_FILES} DESTINATION ${DOC_INSTALL_DIR})
install(DIRECTORY html/ DESTINATION ${DOC_INSTALL_DIR})

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@@ -0,0 +1,109 @@
## Checks for large file support ##
include(CheckIncludeFile)
include(CheckSymbolExists)
include(CheckTypeSize)
macro(check_lfs _isenable)
set(LFS_OFF_T "")
set(LFS_FOPEN "")
set(LFS_FSEEK "")
set(LFS_FTELL "")
set(LFS_PRID "")
if(${_isenable})
set(SAFE_CMAKE_REQUIRED_DEFINITIONS "${CMAKE_REQUIRED_DEFINITIONS}")
set(CMAKE_REQUIRED_DEFINITIONS ${CMAKE_REQUIRED_DEFINITIONS}
-D_LARGEFILE_SOURCE -D_LARGE_FILES -D_FILE_OFFSET_BITS=64
-D__STDC_LIMIT_MACROS -D__STDC_CONSTANT_MACROS -D__STDC_FORMAT_MACROS)
check_include_file("sys/types.h" HAVE_SYS_TYPES_H)
check_include_file("inttypes.h" HAVE_INTTYPES_H)
check_include_file("stddef.h" HAVE_STDDEF_H)
check_include_file("stdint.h" HAVE_STDINT_H)
# LFS type1: 8 <= sizeof(off_t), fseeko, ftello
check_type_size("off_t" SIZEOF_OFF_T)
if(SIZEOF_OFF_T GREATER 7)
check_symbol_exists("fseeko" "stdio.h" HAVE_FSEEKO)
check_symbol_exists("ftello" "stdio.h" HAVE_FTELLO)
if(HAVE_FSEEKO AND HAVE_FTELLO)
set(LFS_OFF_T "off_t")
set(LFS_FOPEN "fopen")
set(LFS_FSEEK "fseeko")
set(LFS_FTELL "ftello")
check_symbol_exists("PRIdMAX" "inttypes.h" HAVE_PRIDMAX)
if(HAVE_PRIDMAX)
set(LFS_PRID "PRIdMAX")
else(HAVE_PRIDMAX)
check_type_size("long" SIZEOF_LONG)
check_type_size("int" SIZEOF_INT)
if(SIZEOF_OFF_T GREATER SIZEOF_LONG)
set(LFS_PRID "\"lld\"")
elseif(SIZEOF_LONG GREATER SIZEOF_INT)
set(LFS_PRID "\"ld\"")
else(SIZEOF_OFF_T GREATER SIZEOF_LONG)
set(LFS_PRID "\"d\"")
endif(SIZEOF_OFF_T GREATER SIZEOF_LONG)
endif(HAVE_PRIDMAX)
endif(HAVE_FSEEKO AND HAVE_FTELLO)
endif(SIZEOF_OFF_T GREATER 7)
# LFS type2: 8 <= sizeof(off64_t), fopen64, fseeko64, ftello64
if(NOT LFS_OFF_T)
check_type_size("off64_t" SIZEOF_OFF64_T)
if(SIZEOF_OFF64_T GREATER 7)
check_symbol_exists("fopen64" "stdio.h" HAVE_FOPEN64)
check_symbol_exists("fseeko64" "stdio.h" HAVE_FSEEKO64)
check_symbol_exists("ftello64" "stdio.h" HAVE_FTELLO64)
if(HAVE_FOPEN64 AND HAVE_FSEEKO64 AND HAVE_FTELLO64)
set(LFS_OFF_T "off64_t")
set(LFS_FOPEN "fopen64")
set(LFS_FSEEK "fseeko64")
set(LFS_FTELL "ftello64")
check_symbol_exists("PRIdMAX" "inttypes.h" HAVE_PRIDMAX)
if(HAVE_PRIDMAX)
set(LFS_PRID "PRIdMAX")
else(HAVE_PRIDMAX)
check_type_size("long" SIZEOF_LONG)
check_type_size("int" SIZEOF_INT)
if(SIZEOF_OFF64_T GREATER SIZEOF_LONG)
set(LFS_PRID "\"lld\"")
elseif(SIZEOF_LONG GREATER SIZEOF_INT)
set(LFS_PRID "\"ld\"")
else(SIZEOF_OFF64_T GREATER SIZEOF_LONG)
set(LFS_PRID "\"d\"")
endif(SIZEOF_OFF64_T GREATER SIZEOF_LONG)
endif(HAVE_PRIDMAX)
endif(HAVE_FOPEN64 AND HAVE_FSEEKO64 AND HAVE_FTELLO64)
endif(SIZEOF_OFF64_T GREATER 7)
endif(NOT LFS_OFF_T)
# LFS type3: 8 <= sizeof(__int64), _fseeki64, _ftelli64
if(NOT LFS_OFF_T)
check_type_size("__int64" SIZEOF___INT64)
if(SIZEOF___INT64 GREATER 7)
check_symbol_exists("_fseeki64" "stdio.h" HAVE__FSEEKI64)
check_symbol_exists("_ftelli64" "stdio.h" HAVE__FTELLI64)
if(HAVE__FSEEKI64 AND HAVE__FTELLI64)
set(LFS_OFF_T "__int64")
set(LFS_FOPEN "fopen")
set(LFS_FSEEK "_fseeki64")
set(LFS_FTELL "_ftelli64")
set(LFS_PRID "\"I64d\"")
endif(HAVE__FSEEKI64 AND HAVE__FTELLI64)
endif(SIZEOF___INT64 GREATER 7)
endif(NOT LFS_OFF_T)
set(CMAKE_REQUIRED_DEFINITIONS "${SAFE_CMAKE_REQUIRED_DEFINITIONS}")
endif(${_isenable})
if(NOT LFS_OFF_T)
## not found
set(LFS_OFF_T "long")
set(LFS_FOPEN "fopen")
set(LFS_FSEEK "fseek")
set(LFS_FTELL "ftell")
set(LFS_PRID "\"ld\"")
endif(NOT LFS_OFF_T)
endmacro(check_lfs)

38
src/qhull/COPYING.txt Normal file
View File

@@ -0,0 +1,38 @@
Qhull, Copyright (c) 1993-2015
C.B. Barber
Arlington, MA
and
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 C.B. Barber and 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.

12
src/qhull/File_id.diz Normal file
View File

@@ -0,0 +1,12 @@
Qhull 2015.2 - 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
command window under Windows 95/NT/XP/7.
www.qhull.org, freeware.

682
src/qhull/Makefile Normal file
View File

@@ -0,0 +1,682 @@
# Unix Makefile for reentrant libqhull, qhull, and rbox (default gcc/g++)
#
# make help
# See README.txt
# For qhulltest of the C++ interface, use Qt project file at src/qhull-all.pro
# For static builds, a simple alternative is src/libqhull_r/Makefile
#
# Variables
# DESTDIR destination directory for 'make install'.
# BINDIR directory where to copy executables
# DOCDIR directory where to copy html documentation
# INCDIR directory where to copy headers
# LIBDIR directory where to copy libraries
# MANDIR directory where to copy manual pages
# PRINTMAN command for printing manual pages
# PRINTC command for printing C files
# CC ANSI C or C++ compiler
# CC_OPTS1 options used to compile .c files
# CC_OPTS2 options used to link .o files
# CC_OPTS3 options to build shared libraries
# CXX ANSI C++ compiler
# CXX_OPTS1 options used to compile .cpp files
# CXX_OPTS2 options used to link .o files
# CC_WARNINGS warnings for .c programs
# CXX_WARNINGS warnings for .cpp programs
#
# LIBQHULLS_RBOX_OBJS .o files for linking
# LIBQHULLR_HDRS non-reentrant .h files
# LIBQHULLR_HDRS reentrant .h files
# CFILES .c files for printing
# CXXFILES .cpp files for printing
# TESTFILES .cpp test files for printing
# DOCFILES documentation files
# FILES miscellaneous files for printing
# HTMFILES documentation source files
# TFILES .txt versions of html files
# FILES all other files
# LIBQHULLS_RBOX_OBJS specifies the object files of libqhullstatic.a
#
# Results
# rbox Generates points sets for qhull, qconvex, etc.
# qhull Computes convex hull and related structures with reentrant libqhullstatic_r
# qconvex, qdelaunay, qhalf, qvoronoi
# Specializations of qhull for each geometric structure
# Built with non-reentrant libqhullstatic (somewhat faster)
# libqhull_r.so Shared library with reentrant code
# libqhullstatic.a Non-reentrant static library with static qh_qh struct
# Called 'static' to avoid naming conflicts
# libqhullstatic_r.a Reentrant, static library
# libqhullcpp.a C++ static library with libqhullstatic_r.a
# testqset Standalone test program for non-reentrant qset.c with mem.c
# testqset_r Standalone test program for reentrant qset_r.c with mem_r.c
# user_eg An example of the reentrant, shared library qhull_r
# user_eg2 An example of the reentrant, static library libqhullstatic_r
# user_eg3 An example of the C++ interface with libqhullcpp and libqhullstatic_r
#
# Targets
# make Build results using gcc or another compiler
# make SO=dll For mingw on Windows, use SO=dll. It builds dlls
# make bin/qvoronoi Produce bin/qvoronoi (etc.)
# make qhullx Produce qhull, qconvex etc. without using library
#
# make clean Remove object files
# make cleanall Remove generated files, build/*.dlr/, buildqt/, and buildvc/
# make doc Print documentation
# make help
# make install Copy qhull, rbox, qhull.1, rbox.1 to BINDIR, MANDIR
# make new Rebuild qhull and rbox from source
# make printall Print all files
# make qtest Quick test of rbox and qhull
# make test Quick test of qhull programs
# make testall Test programs for manual review with eg/q_test-ok.txt
# make testall >eg/q_test.x 2>&1
# Build the C++ qhulltest with Qt
#
# Do not replace tabs with spaces. Needed for build rules
# Unix line endings (\n)
# $Id: //main/2015/qhull/Makefile#10 $
DESTDIR = /usr/local
BINDIR = $(DESTDIR)/bin
INCDIR = $(DESTDIR)/include
LIBDIR = $(DESTDIR)/lib
DOCDIR = $(DESTDIR)/share/doc/qhull
MANDIR = $(DESTDIR)/share/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, -O3 for optimization, -g for debugging, -pg for profiling
# -fpic needed for gcc x86_64-linux-gnu. Not needed for mingw
CC = gcc
CC_OPTS1 = -O3 -ansi -Isrc -fpic $(CC_WARNINGS)
CXX = g++
# libqhullcpp must be before libqhull_r
CXX_OPTS1 = -O3 -Isrc/ $(CXX_WARNINGS)
# for shared library link
CC_OPTS3 =
# Define qhull_VERSION in CMakeLists.txt, Makefile, and qhull-warn.pri
# Truncated version in qhull-exports.def, qhull_p-exports.def,
# qhull.so -- static qh_qhT global data structure (qh_QHpointer=0)
# qhull_p.so -- allocated qh_qhT global data structure (qh_QHpointer=1). Required for libqhullcpp
# qhull_m.so -- future version of Qhull with qh_qhT passed as an argument.
qhull_SOVERSION=7
SO = so.7.2.0
# On MinGW,
# make SO=dll
# Copy lib/libqhull6_p.dll and lib/libqhull.dll to bin/
# for Sun's cc compiler, -fast or O2 for optimization, -g for debugging, -Xc for ANSI
#CC = cc
#CC_OPTS1 = -Xc -v -fast
# for Silicon Graphics cc compiler, -O2 for optimization, -g for debugging
#CC = cc
#CC_OPTS1 = -ansi -O2
# for Next cc compiler with fat executable
#CC = cc
#CC_OPTS1 = -ansi -O2 -arch m68k -arch i386 -arch hppa
# For loader, ld,
CC_OPTS2 = $(CC_OPTS1)
CXX_OPTS2 = $(CXX_OPTS1)
# [gcc 4.4] Compiles without error (-Werror)
CC_WARNINGS = -Wall -Wcast-qual -Wextra -Wwrite-strings -Wshadow
CXX_WARNINGS = -Wall -Wcast-qual -Wextra -Wwrite-strings -Wno-sign-conversion -Wshadow -Wconversion
# [mar'11] Compiles OK with all gcc warnings except for -Wno-sign-conversion and -Wconversion
# Qhull reports -Wunused-but-set-variable warnings but these are OK (see annotations)
# --help=warnings
# Compiles OK with all g++ warnings except Qt source errors on -Wshadow and -Wconversion
# -Waddress -Warray-bounds -Wchar-subscripts -Wclobbered -Wcomment -Wunused-variable
# -Wempty-body -Wformat -Wignored-qualifiers -Wimplicit-function-declaration -Wimplicit-int
# -Wmain -Wmissing-braces -Wmissing-field-initializers -Wmissing-parameter-type -Wnonnull
# -Wold-style-declaration -Woverride-init -Wparentheses -Wpointer-sign -Wreturn-type
# -Wsequence-point -Wsign-compare -Wsign-compare -Wstrict-aliasing -Wstrict-overflow=1
# -Wswitch -Wtrigraphs -Wtype-limits -Wuninitialized -Wuninitialized -Wvolatile-register-var
# -Wunknown-pragmas -Wunused-function -Wunused-label -Wunused-parameter -Wunused-value
# Default targets for make
all: bin-lib bin/rbox bin/qdelaunay bin/qhalf bin/qhull src/qconvex/qconvex.o src/qvoronoi/qvoronoi.o
#all: bin-lib bin/rbox bin/qconvex bin/qdelaunay bin/qhalf bin/qvoronoi bin/qhull bin/testqset \
bin/testqset_r qtest bin/user_eg2 bin/user_eg3 bin/user_eg qconvex-prompt
help:
head -n 75 Makefile
bin-lib:
mkdir -p bin lib
# Remove intermediate files for all builds
clean:
rm -f src/*/*.o src/qhulltest/RoadTest.h.cpp build/*/*/*.o build/*/*.o
rm -f src/*/*.obj build/*/*/*.obj build/*/*/*/*/*.obj build/*/*.obj
rm -f bin/*.idb lib/*.idb build-cmake/*/*.idb eg/*.x *.x *.tmp
rm -f build/*/*/*.a build/*/*/*.rsp build/moc/*.moc
rm -f build-cmake/*/*.obj build-cmake/*/*/*.obj build-cmake/*/*.ilk
# Remove intermediate files and targets for all builds
# DevStudio prevents build/qhull.ncb deletes
cleanall: clean
rm -rf build/*.dir/
-rm -rf build/qhull.ncb
rm -rf buildvc/
rm -rf buildqt/
rm -rf build-qhull-all*/
rm -f eg/eg.* eg/t*.tmp
rm -f bin/qconvex bin/qdelaunay bin/qhalf bin/qvoronoi bin/qhull
rm -f bin/rbox core bin/core bin/user_eg bin/user_eg2 bin/user_eg3
rm -f bin/testqset bin/testqset_r bin/qhulltest
rm -f lib/libqhull* lib/qhull*.lib lib/qhull*.exp lib/qhull*.dll
rm -f bin/libqhull* bin/qhull*.dll bin/*.exe bin/*.pdb lib/*.pdb
rm -f build/*.dll build/*.exe build/*.a build/*.exp
rm -f build/*.lib build/*.pdb build/*.idb build/qhull-no-qt.sln
rm -f build-cmake/*/*.dll build-cmake/*/*.exe build-cmake/*/*.exp
rm -f build-cmake/*/*.lib build-cmake/*/*.pdb
rm -f src/libqhull/qconvex.c src/libqhull/qdelaun.c src/libqhull/qhalf.c
rm -f src/libqhull/qvoronoi.c src/libqhull/rbox.c src/libqhull/testqset.c
rm -f src/libqhull/unix.c src/libqhull/user_eg.c src/libqhull/user_eg2.c
rm -f src/libqhull/*.exe src/libqhull/libqhullstatic* src/libqhull/core
rm -f src/libqhull/qconvex src/libqhull/qdelaunay src/libqhull/qhalf src/libqhull/qvoronoi src/libqhull/qhull
rm -f src/libqhull/rbox src/libqhull/core src/libqhull/user_eg src/libqhull/user_eg2 src/libqhull/user_eg3
rm -f src/libqhull_r/unix_r.c src/libqhull_r/user_eg_r.c src/libqhull_r/user_eg2_r.c
rm -f src/libqhull_r/qconvex_r.c src/libqhull_r/qdelaun_r.c src/libqhull_r/qhalf_r.c
rm -f src/libqhull_r/qvoronoi_r.c src/libqhull_r/rbox_r.c src/libqhull_r/testqset_r.c
rm -f src/libqhull_r/unix_r.c src/libqhull_r/user_eg_r.c src/libqhull_r/user_eg2_r.c
rm -f src/libqhull_r/*.exe src/libqhull_r/libqhullstatic*
rm -f src/libqhull_r/qconvex src/libqhull_r/qdelaunay src/libqhull_r/qhalf src/libqhull_r/qvoronoi src/libqhull_r/qhull
rm -f src/libqhull_r/rbox src/libqhull_r/core src/libqhull_r/user_eg src/libqhull_r/user_eg2 src/libqhull_r/user_eg3
doc:
$(PRINTMAN) $(TXTFILES) $(DOCFILES)
install:
mkdir -p $(BINDIR)
mkdir -p $(DOCDIR)
mkdir -p $(INCDIR)/libqhull
mkdir -p $(INCDIR)/libqhull_r
mkdir -p $(INCDIR)/libqhullcpp
mkdir -p $(LIBDIR)
mkdir -p $(MANDIR)
cp bin/qconvex $(BINDIR)
cp bin/qdelaunay $(BINDIR)
cp bin/qhalf $(BINDIR)
cp bin/qhull $(BINDIR)
cp bin/qvoronoi $(BINDIR)
cp bin/rbox $(BINDIR)
cp html/qhull.man $(MANDIR)/qhull.1
cp html/rbox.man $(MANDIR)/rbox.1
cp html/* $(DOCDIR)
cp -P lib/* $(LIBDIR)
cp src/libqhull/DEPRECATED.txt src/libqhull/*.h src/libqhull/*.htm $(INCDIR)/libqhull
cp src/libqhull_r/*.h src/libqhull_r/*.htm $(INCDIR)/libqhull_r
cp src/libqhullcpp/*.h $(INCDIR)/libqhullcpp
cp src/qhulltest/*.h $(INCDIR)/libqhullcpp
new: cleanall all
printall: doc printh printc printf
printh:
$(PRINTC) $(LIBQHULL_HDRS)
$(PRINTC) $(LIBQHULLR_HDRS)
$(PRINTC) $(LIBQHULLCPP_HDRS)
printc:
$(PRINTC) $(CFILES)
$(PRINTC) $(CXXFILES)
$(PRINTC) $(TESTFILES)
printf:
$(PRINTC) $(FILES)
qtest:
@echo ============================================
@echo == make qtest ==============================
@echo ============================================
@echo -n "== "
@date
@echo
@echo ============================================
@echo == Test non-reentrant qset.c with mem.c ====
@echo ============================================
-bin/testqset 10000
@echo
@echo ============================================
@echo == Test reentrant qset_r.c with mem_r.c ====
@echo ============================================
-bin/testqset_r 10000
@echo
@echo ============================================
@echo == Run the qhull smoketest ====
@echo ============================================
-bin/rbox D4 | bin/qhull Tv
test: qtest
@echo ============================================
@echo == make test ===============================
@echo ============================================
@echo
@echo ==============================
@echo ========= rbox/qhull =======
@echo ==============================
-bin/rbox D4 | bin/qhull Tv
@echo
@echo ==============================
@echo ========= qconvex ============
@echo ==============================
-bin/rbox 10 | bin/qconvex Tv
@echo
@echo ==============================
@echo ========= qdelaunay ==========
@echo ==============================
-bin/rbox 10 | bin/qdelaunay Tv
@echo
@echo ==============================
@echo ========= qhalf ==============
@echo ==============================
-bin/rbox 10 | bin/qconvex FQ FV n Tv | bin/qhalf Tv
@echo
@echo ==============================
@echo ========= qvoronoi ===========
@echo ==============================
-bin/rbox 10 | bin/qvoronoi Tv
@echo
@echo ==============================
@echo ========= user_eg ============
@echo ==============================
-bin/user_eg
@echo
@echo ==============================
@echo ========= user_eg2 ===========
@echo ==============================
-bin/user_eg2
@echo
@echo ==============================
@echo ========= user_eg3 ===========
@echo ==============================
-bin/user_eg3 rbox "10 D2" "2 D2" qhull "s p" facets
# make testall >q_test.txt 2>&1
testall: test
@echo ============================================
@echo == make testall ============================
@echo ============================================
@echo -n "== "
@date
@echo
-eg/q_eg
-eg/q_egtest
-eg/q_test
qconvex-prompt:
bin/qconvex
@echo
@echo ============================================
@echo == Run the qconvex smoketest
@echo ============================================
bin/rbox D4 | bin/qconvex Tv
@echo
@echo ============================================
@echo == To enable user_eg and user_eg2
@echo ==
@echo == Windows -- make SO=dll
@echo '== cp -p lib/libqhull*.dll bin'
@echo ==
@echo == Unix/Macintosh -- make
@echo '== export LD_LIBRARY_PATH=$$PWD/lib:$$LD_LIBRARY_PATH'
@echo ============================================
@echo
@echo ============================================
@echo == To smoketest qhull programs
@echo '== make test'
@echo ============================================
@echo
@echo ============================================
@echo == To run qhull tests for manual review with eg/q_test-ok.txt
@echo '== make testall >q_test.txt 2>&1'
@echo ============================================
@echo
@echo ============================================
@echo == For all make targets
@echo '== make help'
@echo ============================================
@echo
# libqhull is source files for non-reentrant Qhull
# libqhull_r is source files and a shared library for reentrant Qhull
L= src/libqhull
LR= src/libqhull_r
# libqhullstatic is a static library for non-reentrant Qhull
# libqhullstatic_r is a static library for reentrant Qhull
LS= src/libqhullstatic
LSR= src/libqhullstatic_r
# libqhullcpp is a static library for C++ files and libqhull_r
# qhulltest is a Qt test of libqhullcpp
LCPP= src/libqhullcpp
TCPP= src/qhulltest
LIBQHULL_HDRS = $(L)/user.h $(L)/libqhull.h $(L)/qhull_a.h $(L)/geom.h \
$(L)/io.h $(L)/mem.h $(L)/merge.h $(L)/poly.h $(L)/random.h \
$(L)/qset.h $(L)/stat.h
LIBQHULLR_HDRS = $(LR)/user_r.h $(LR)/libqhull_r.h $(LR)/qhull_ra.h $(LR)/geom_r.h \
$(LR)/io_r.h $(LR)/mem_r.h $(LR)/merge_r.h $(LR)/poly_r.h $(LR)/random_r.h \
$(LR)/qset_r.h $(LR)/stat_r.h
# LIBQHULLS_OBJS and LIBQHULLSR_OBJS ordered by frequency of execution with
# small files at end. Better locality.
LIBQHULLS_OBJS= $(LS)/global.o $(LS)/stat.o $(LS)/geom2.o $(LS)/poly2.o \
$(LS)/merge.o $(LS)/libqhull.o $(LS)/geom.o $(LS)/poly.o \
$(LS)/qset.o $(LS)/mem.o $(LS)/random.o
LIBQHULLS_USER_OBJS = $(LIBQHULLS_OBJS) $(LS)/usermem.o $(LS)/userprintf.o \
$(LS)/io.o $(LS)/user.o
LIBQHULLS_RBOX_OBJS = $(LIBQHULLS_USER_OBJS) $(LS)/rboxlib.o $(LS)/userprintf_rbox.o
LIBQHULLSR_OBJS = $(LSR)/global_r.o $(LSR)/stat_r.o $(LSR)/geom2_r.o $(LSR)/poly2_r.o \
$(LSR)/merge_r.o $(LSR)/libqhull_r.o $(LSR)/geom_r.o $(LSR)/poly_r.o \
$(LSR)/qset_r.o $(LSR)/mem_r.o $(LSR)/random_r.o
LIBQHULLSR_USER_OBJS = $(LIBQHULLSR_OBJS) $(LSR)/usermem_r.o $(LSR)/userprintf_r.o \
$(LSR)/io_r.o $(LSR)/user_r.o
LIBQHULLSR_RBOX_OBJS = $(LIBQHULLSR_USER_OBJS) $(LSR)/rboxlib_r.o $(LSR)/userprintf_rbox_r.o
LIBQHULLCPP_HDRS = $(LCPP)/RoadError.h $(LCPP)/RoadLogEvent.h $(LCPP)/Coordinates.h \
$(LCPP)/QhullHyperplane.h $(LCPP)/functionObjects.h $(LCPP)/PointCoordinates.h \
$(LCPP)/Qhull.h $(LCPP)/QhullError.h $(LCPP)/QhullFacet.h \
$(LCPP)/QhullFacetList.h $(LCPP)/QhullFacetSet.h $(LCPP)/QhullIterator.h \
$(LCPP)/QhullLinkedList.h $(LCPP)/QhullPoint.h $(LCPP)/QhullPoints.h \
$(LCPP)/QhullPointSet.h $(LCPP)/QhullQh.h $(LCPP)/QhullRidge.h \
$(LCPP)/QhullSet.h $(LCPP)/QhullSets.h $(LCPP)/QhullStat.h \
$(LCPP)/QhullVertex.h $(LCPP)/RboxPoints.h
LIBQHULLCPP_OBJS = $(LCPP)/RoadError.o $(LCPP)/RoadLogEvent.o $(LCPP)/Coordinates.o \
$(LCPP)/PointCoordinates.o $(LCPP)/Qhull.o $(LCPP)/QhullFacet.o \
$(LCPP)/QhullFacetList.o $(LCPP)/QhullFacetSet.o \
$(LCPP)/QhullHyperplane.o $(LCPP)/QhullPoint.o \
$(LCPP)/QhullPoints.o $(LCPP)/QhullPointSet.o $(LCPP)/QhullQh.o \
$(LCPP)/QhullRidge.o $(LCPP)/QhullSet.o $(LCPP)/QhullStat.o \
$(LCPP)/QhullVertex.o $(LCPP)/QhullVertexSet.o $(LCPP)/RboxPoints.o
# CFILES for non-reentrant Qhull, ordered alphabetically after libqhull.c
CFILES= src/qhull/unix.c $(L)/libqhull.c $(L)/geom.c $(L)/geom2.c $(L)/global.c $(L)/io.c \
$(L)/mem.c $(L)/merge.c $(L)/poly.c $(L)/poly2.c $(L)/random.c $(L)/rboxlib.c \
$(L)/qset.c $(L)/stat.c $(L)/user.c $(L)/usermem.c $(L)/userprintf.c $(L)/userprintf_rbox.c \
src/qconvex/qconvex.c src/qdelaunay/qdelaun.c src/qhalf/qhalf.c src/qvoronoi/qvoronoi.c
# CFILESR for reentrant Qhull, ordered alphabetically after libqhull.c
CFILESR= src/qhull/unix_r.c $(LSR)/libqhull_r.c $(LSR)/geom_r.c $(LSR)/geom2_r.c $(LSR)/global_r.c $(LSR)/io_r.c \
$(LSR)/mem_r.c $(LSR)/merge_r.c $(LSR)/poly_r.c $(LSR)/poly2_r.c $(LSR)/random_r.c $(LSR)/rboxlib_r.c \
$(LSR)/qset_r.c $(LSR)/stat_r.c $(LSR)/user_r.c $(LSR)/usermem_r.c $(LSR)/userprintf_r.c $(LSR)/userprintf_rbox_r.c \
src/qconvex/qconvex_r.c src/qdelaunay/qdelaun_r.c src/qhalf/qhalf_r.c src/qvoronoi/qvoronoi_r.c
# CXXFILES for C++ sources using libqhull_r (reentrant qhull), alphabetical
CXXFILES= $(LCPP)/Coordinates.cpp $(LCPP)/PointCoordinates.cpp \
$(LCPP)/Qhull.cpp $(LCPP)/QhullFacet.cpp \
$(LCPP)/QhullFacetList.cpp $(LCPP)/QhullFacetSet.cpp \
$(LCPP)/QhullHyperplane.cpp $(LCPP)/QhullPoint.cpp \
$(LCPP)/QhullPoints.cpp $(LCPP)/QhullPointSet.cpp $(LCPP)/QhullQh.cpp \
$(LCPP)/QhullRidge.cpp $(LCPP)/QhullSet.cpp $(LCPP)/QhullStat.cpp \
$(LCPP)/QhullVertex.cpp $(LCPP)/QhullVertexSet.cpp $(LCPP)/RboxPoints.cpp \
$(LCPP)/RoadError.cpp $(LCPP)/RoadLogEvent.cpp src/user_eg3/user_eg3_r.cpp
# TESTFILES for Qt test of C++ sources using libqhull_r (reentrant qhull), alphabetical after qhulltest.cpp
TESTFILES= $(TCPP)/qhulltest.cpp $(TCPP)/Coordinates_test.cpp $(TCPP)/PointCoordinates_test.cpp \
$(TCPP)/Qhull_test.cpp $(TCPP)/QhullFacet_test.cpp $(TCPP)/QhullFacetList_test.cpp \
$(TCPP)/QhullFacetSet_test.cpp $(TCPP)/QhullHyperplane_test.cpp $(TCPP)/QhullLinkedList_test.cpp \
$(TCPP)/QhullPoint_test.cpp $(TCPP)/QhullPoints_test.cpp \
$(TCPP)/QhullPointSet_test.cpp $(TCPP)/QhullRidge_test.cpp \
$(TCPP)/QhullSet_test.cpp $(TCPP)/QhullVertex_test.cpp $(TCPP)/QhullVertexSet_test.cpp \
$(TCPP)/RboxPoints_test.cpp
TXTFILES= Announce.txt REGISTER.txt COPYING.txt README.txt src/Changes.txt
DOCFILES= html/rbox.txt html/qhull.txt
FILES= Makefile src/rbox/rbox.c src/user_eg/user_eg.c src/user_eg2/user_eg2.c \
src/testqset/testqset.c eg/q_test eg/q_egtest eg/q_eg
MANFILES= html/qhull.man html/rbox.man
# Source code is documented by src/libqhull/*.htm
HTMFILES= html/index.htm html/qh-quick.htm html/qh-impre.htm html/qh-eg.htm \
html/qh-optc.htm html/qh-opto.htm html/qh-optf.htm html/qh-optp.htm html/qh-optq.htm \
html/qh-c.htm html/qh-faq.htm html/qhull.htm html/qconvex.htm html/qdelaun.htm \
html/qh-geom.htm html/qh-globa.htm html/qh-io.htm html/qh-mem.htm html/qh-merge.htm \
html/qh-poly.htm html/qh-qhull.htm html/qh-set.htm html/qh-stat.htm html/qh-user.htm \
html/qconvex.htm html/qdelau_f.htm html/qdelaun.htm html/qhalf.htm html/qvoronoi.htm \
html/qvoron_f.htm html/rbox.htm
qhull/unix.o: $(L)/libqhull.h $(L)/user.h $(L)/mem.h
qconvex/qconvex.o: $(L)/libqhull.h $(L)/user.h $(L)/mem.h
qdelanay/qdelaun.o: $(L)/libqhull.h $(L)/user.h $(L)/mem.h
qhalf/qhalf.o: $(L)/libqhull.h $(L)/user.h $(L)/mem.h
qvoronoi/qvoronoi.o: $(L)/libqhull.h $(L)/user.h $(L)/mem.h
qhull/unix_r.o: $(LR)/libqhull_r.h $(LR)/user_r.h $(LR)/mem_r.h
qconvex/qconvex_r.o: $(LR)/libqhull_r.h $(LR)/user_r.h $(LR)/mem_r.h
qdelanay/qdelaun_r.o: $(LR)/libqhull_r.h $(LR)/user_r.h $(LR)/mem_r.h
qhalf/qhalf_r.o: $(LR)/libqhull_r.h $(LR)/user_r.h $(LR)/mem_r.h
qvoronoi/qvoronoi_r.o: $(LR)/libqhull_r.h $(LR)/user_r.h $(LR)/mem_r.h
$(LS)/libqhull.o: $(LIBQHULL_HDRS)
$(LS)/geom.o: $(LIBQHULL_HDRS)
$(LS)/geom2.o: $(LIBQHULL_HDRS)
$(LS)/global.o: $(LIBQHULL_HDRS)
$(LS)/io.o: $(LIBQHULL_HDRS)
$(LS)/mem.o: $(L)/mem.h
$(LS)/merge.o: $(LIBQHULL_HDRS)
$(LS)/poly.o: $(LIBQHULL_HDRS)
$(LS)/poly2.o: $(LIBQHULL_HDRS)
$(LS)/random.o: $(L)/libqhull.h $(L)/random.h $(L)/user.h
$(LS)/rboxlib.o: $(L)/libqhull.h $(L)/random.h $(L)/user.h
$(LS)/qset.o: $(L)/qset.h $(L)/mem.h
$(LS)/stat.o: $(LIBQHULL_HDRS)
$(LS)/user.o: $(LIBQHULL_HDRS)
$(LSR)/libqhull_r.o: $(LIBQHULLR_HDRS)
$(LSR)/geom_r.o: $(LIBQHULLR_HDRS)
$(LSR)/geom2_r.o: $(LIBQHULLR_HDRS)
$(LSR)/global_r.o: $(LIBQHULLR_HDRS)
$(LSR)/io_r.o: $(LIBQHULLR_HDRS)
$(LSR)/mem_r.o: $(LR)/mem_r.h
$(LSR)/merge_r.o: $(LIBQHULLR_HDRS)
$(LSR)/poly_r.o: $(LIBQHULLR_HDRS)
$(LSR)/poly2_r.o: $(LIBQHULLR_HDRS)
$(LSR)/random_r.o: $(LR)/libqhull_r.h $(LR)/random_r.h $(LR)/user_r.h $(LR)/mem_r.h
$(LSR)/rboxlib_r.o: $(LR)/libqhull_r.h $(LR)/random_r.h $(LR)/user_r.h $(LR)/mem_r.h
$(LSR)/qset_r.o: $(LR)/qset_r.h $(LR)/mem_r.h
$(LSR)/stat_r.o: $(LIBQHULLR_HDRS)
$(LSR)/user_r.o: $(LIBQHULLR_HDRS)
$(LCPP)/RoadError.o: $(LCPP)/RoadError.h $(LCPP)/RoadLogEvent.h
$(LCPP)/RoadLogEvent.o: $(LCPP)/RoadError.h
$(LCPP)/Coordinates.o: $(LIBQHULLCPP_HDRS) $(LIBQHULLR_HDRS)
$(LCPP)/PointCoordinates.o: $(LIBQHULLCPP_HDRS) $(LIBQHULLR_HDRS)
$(LCPP)/Qhull.o: $(LIBQHULLCPP_HDRS) $(LIBQHULLR_HDRS)
$(LCPP)/QhullFacet.o: $(LIBQHULLCPP_HDRS) $(LIBQHULLR_HDRS)
$(LCPP)/QhullFacetList.o: $(LIBQHULLCPP_HDRS) $(LIBQHULLR_HDRS)
$(LCPP)/QhullFacetSet.o: $(LIBQHULLCPP_HDRS) $(LIBQHULLR_HDRS)
$(LCPP)/QhullHyperplane.o: $(LIBQHULLCPP_HDRS) $(LIBQHULLR_HDRS)
$(LCPP)/QhullPoint.o: $(LIBQHULLCPP_HDRS) $(LIBQHULLR_HDRS)
$(LCPP)/QhullPoints.o: $(LIBQHULLCPP_HDRS) $(LIBQHULLR_HDRS)
$(LCPP)/QhullPointSet.o: $(LIBQHULLCPP_HDRS) $(LIBQHULLR_HDRS)
$(LCPP)/QhullQh.o: $(LIBQHULLR_HDRS)
$(LCPP)/QhullRidge.o: $(LIBQHULLCPP_HDRS) $(LIBQHULLR_HDRS)
$(LCPP)/QhullSet.o: $(LIBQHULLCPP_HDRS) $(LIBQHULLR_HDRS)
$(LCPP)/QhullStat.o: $(LIBQHULLCPP_HDRS) $(LIBQHULLR_HDRS)
$(LCPP)/QhullVertex.o: $(LIBQHULLCPP_HDRS) $(LIBQHULLR_HDRS)
$(LCPP)/QhullVertexSet.o: $(LIBQHULLCPP_HDRS) $(LIBQHULLR_HDRS)
$(LCPP)/RboxPoints.o: $(LIBQHULLCPP_HDRS) $(LIBQHULLR_HDRS)
.c.o:
$(CC) -c $(CC_OPTS1) -o $@ $<
.cpp.o:
$(CXX) -c $(CXX_OPTS1) -o $@ $<
# qhullx -- Compile qhull without using a qhull library. Must be after LIBQHULLS_RBOX_OBJS
# For qconvex, rbox, and other programs, qhullx produces the same results as libqhull/Makefile
# For qhull, 'make qhullx' produces the same results as libqhull_r/Makefile
qhullx: src/qconvex/qconvex.o src/qdelaunay/qdelaun.o src/qhalf/qhalf.o \
src/qvoronoi/qvoronoi.o src/rbox/rbox.o \
src/qhull/unix_r.o $(LIBQHULLS_RBOX_OBJS) $(LIBQHULLSR_USER_OBJS)
$(CC) -o bin/qconvex $(CC_OPTS2) -lm $(LIBQHULLS_USER_OBJS) src/qconvex/qconvex.o
$(CC) -o bin/qdelaunay $(CC_OPTS2) -lm $(LIBQHULLS_USER_OBJS) src/qdelaunay/qdelaun.o
$(CC) -o bin/qhalf $(CC_OPTS2) -lm $(LIBQHULLS_USER_OBJS) src/qhalf/qhalf.o
$(CC) -o bin/qvoronoi $(CC_OPTS2) -lm $(LIBQHULLS_USER_OBJS) src/qvoronoi/qvoronoi.o
$(CC) -o bin/qhull $(CC_OPTS2) -lm $(LIBQHULLSR_USER_OBJS) src/qhull/unix_r.o
$(CC) -o bin/rbox $(CC_OPTS2) -lm $(LIBQHULLS_RBOX_OBJS) src/rbox/rbox.o
$(CC) -o bin/testqset $(CC_OPTS2) -lm mem.o qset.o usermem.o testqset.o
$(CC) -o bin/testqset_r $(CC_OPTS2) -lm mem_r.o qset_r.o usermem_r.o testqset_r.o
-bin/rbox D4 | bin/qhull
# The static library, libqhullstatic, contains non-reentrant code for Qhull. It is somewhat faster than reentrant libqhullstatic_r
$(LS)/libqhull.o: $(L)/libqhull.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LS)/geom.o: $(L)/geom.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LS)/geom2.o: $(L)/geom2.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LS)/global.o: $(L)/global.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LS)/io.o: $(L)/io.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LS)/mem.o: $(L)/mem.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LS)/merge.o: $(L)/merge.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LS)/poly.o: $(L)/poly.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LS)/poly2.o: $(L)/poly2.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LS)/random.o: $(L)/random.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LS)/rboxlib.o: $(L)/rboxlib.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LS)/qset.o: $(L)/qset.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LS)/stat.o: $(L)/stat.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LS)/user.o: $(L)/user.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LS)/usermem.o: $(L)/usermem.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LS)/userprintf.o: $(L)/userprintf.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LS)/userprintf_rbox.o: $(L)/userprintf_rbox.c
$(CC) -c $(CC_OPTS1) -o $@ $<
# The static library, libqhullstatic_r, contains reentrant code with the same behavior as libqhullstatic
$(LSR)/libqhull_r.o: $(LR)/libqhull_r.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LSR)/geom_r.o: $(LR)/geom_r.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LSR)/geom2_r.o: $(LR)/geom2_r.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LSR)/global_r.o: $(LR)/global_r.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LSR)/io_r.o: $(LR)/io_r.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LSR)/mem_r.o: $(LR)/mem_r.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LSR)/merge_r.o: $(LR)/merge_r.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LSR)/poly_r.o: $(LR)/poly_r.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LSR)/poly2_r.o: $(LR)/poly2_r.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LSR)/random_r.o: $(LR)/random_r.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LSR)/rboxlib_r.o: $(LR)/rboxlib_r.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LSR)/qset_r.o: $(LR)/qset_r.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LSR)/stat_r.o: $(LR)/stat_r.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LSR)/user_r.o: $(LR)/user_r.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LSR)/usermem_r.o: $(LR)/usermem_r.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LSR)/userprintf_r.o: $(LR)/userprintf_r.c
$(CC) -c $(CC_OPTS1) -o $@ $<
$(LSR)/userprintf_rbox_r.o: $(LR)/userprintf_rbox_r.c
$(CC) -c $(CC_OPTS1) -o $@ $<
lib/libqhullstatic.a: $(LIBQHULLS_RBOX_OBJS)
@echo ==========================================
@echo ==== If 'ar' fails, try 'make qhullx' ====
@echo ==========================================
ar -rs $@ $^
#If 'ar -rs' fails try using 'ar -s' with 'ranlib'
#ranlib $@
lib/libqhullstatic_r.a: $(LIBQHULLSR_RBOX_OBJS)
ar -rs $@ $^
#ranlib $@
# Do not create libqhullcpp as a shared library. Qhull C++ classes may change layout and size.
lib/libqhullcpp.a: $(LIBQHULLCPP_OBJS)
ar -rs $@ $^
#ranlib $@
lib/libqhull_r.$(SO): $(LIBQHULLSR_RBOX_OBJS)
$(CC) -shared -o $@ $(CC_OPTS3) $^
cd lib && ln -f -s libqhull_r.$(SO) libqhull_r.so
# don't use ../qconvex. Does not work on Red Hat Linux
#bin/qconvex: src/qconvex/qconvex.o lib/libqhullstatic.a
# $(CC) -o $@ $< $(CC_OPTS2) -Llib -lqhullstatic -lm
bin/qdelaunay: src/qdelaunay/qdelaun.o lib/libqhullstatic.a
$(CC) -o $@ $< $(CC_OPTS2) -Llib -lqhullstatic -lm
bin/qhalf: src/qhalf/qhalf.o lib/libqhullstatic.a
$(CC) -o $@ $< $(CC_OPTS2) -Llib -lqhullstatic -lm
#bin/qvoronoi: src/qvoronoi/qvoronoi.o lib/libqhullstatic.a
# $(CC) -o $@ $< $(CC_OPTS2) -Llib -lqhullstatic -lm
bin/qhull: src/qhull/unix_r.o lib/libqhullstatic_r.a
$(CC) -o $@ $< $(CC_OPTS2) -Llib -lqhullstatic_r -lm
-chmod +x eg/q_test eg/q_eg eg/q_egtest
bin/rbox: src/rbox/rbox.o lib/libqhullstatic.a
$(CC) -o $@ $< $(CC_OPTS2) -Llib -lqhullstatic -lm
#bin/testqset: src/testqset/testqset.o src/libqhull/qset.o src/libqhull/mem.o src/libqhull/usermem.o
# $(CC) -o $@ $^ $(CC_OPTS2) -lm
#bin/testqset_r: src/testqset_r/testqset_r.o src/libqhull_r/qset_r.o src/libqhull_r/mem_r.o src/libqhull_r/usermem_r.o
# $(CC) -o $@ $^ $(CC_OPTS2) -lm
# You may use -lqhullstatic_r instead of -lqhull_r
#bin/user_eg: src/user_eg/user_eg_r.o lib/libqhull_r.$(SO)
# @echo -e '\n\n==================================================='
# @echo -e '== If user_eg fails to link on MinGW or Cygwin, use'
# @echo -e '== "make SO=dll" and copy lib/libqhull_r.dll to bin/'
# @echo -e '== Otherwise if user_eg fails to link, switch to -lqhullstatic_r'
# @echo -e '===================================================\n'
# $(CC) -o $@ $< $(CC_OPTS1) $(CC_OPTS3) -Llib -lqhull_r -lm
#bin/user_eg2: src/user_eg2/user_eg2_r.o lib/libqhullstatic_r.a
# @echo -e '\n\n==================================================='
# @echo -e '== user_eg2 links to qhullstatic_r. It may use libqhull_r instead.'
# @echo -e '===================================================\n'
# $(CC) -o $@ $< $(CC_OPTS2) -Llib -lqhullstatic_r -lm
#bin/user_eg3: src/user_eg3/user_eg3_r.o lib/libqhullstatic_r.a lib/libqhullcpp.a
# $(CXX) -o $@ $< $(CXX_OPTS2) -Llib -lqhullcpp -lqhullstatic_r -lm
# end of Makefile

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Name
qhull, rbox 2015.2 2016/01/18
Convex hull, Delaunay triangulation, Voronoi diagrams, Halfspace intersection
Documentation:
html/index.htm
<http://www.qhull.org/html>
Available from:
<http://www.qhull.org>
<http://www.qhull.org/download>
<http://github.com/qhull/qhull> (git@github.com:qhull/qhull.git)
News and a paper:
<http://www.qhull.org/news>
<http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405>
Version 1 (simplicial only):
<http://www.qhull.org/download/qhull-1.0.tar.gz>
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. It comes with examples and test scripts.
Qhull's C++ interface uses the STL. The C++ test program uses QTestLib
from the Qt Framework. Qhull's C++ interface may change without
notice. Eventually, it will move into the qhull shared library.
Qhull is copyrighted software. Please read COPYING.txt and REGISTER.txt
before using or distributing Qhull.
To cite Qhull, please use
Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., "The Quickhull
algorithm for convex hulls," ACM Trans. on Mathematical Software,
22(4):469-483, Dec 1996, http://www.qhull.org.
To modify Qhull, particularly the C++ interface
Qhull is on GitHub
(http://github.com/qhull/qhull, git@github.com:qhull/qhull.git)
For internal documentation, see html/qh-code.htm
To install Qhull
Qhull is precompiled for Windows 32-bit, otherwise it needs compilation.
Qhull includes Makefiles for gcc and other targets, CMakeLists.txt for CMake,
.sln/.vcproj/.vcxproj files for Microsoft Visual Studio, and .pro files
for Qt Creator. It compiles under Windows with mingw.
Install and build instructions follow.
See the end of this document for a list of distributed files.
-----------------
Installing Qhull on Windows 10, 8, 7 (32- or 64-bit), Windows XP, and Windows NT
The zip file contains rbox.exe, qhull.exe, qconvex.exe, qdelaunay.exe,
qhalf.exe, qvoronoi.exe, testqset.exe, user_eg*.exe, documentation files,
and source files. Qhull.exe and user-eg3.exe are compiled with the reentrant
library while the other executables use the non-reentrant library.
To install Qhull:
- Unzip the files into a directory (e.g., named 'qhull')
- Click on QHULL-GO or open a command window into Qhull's bin directory.
- Test with 'rbox D4 | qhull'
To uninstall Qhull
- Delete the qhull directory
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'.
- Browse the documentation: qhull\html\index.htm
- If an error occurs, Windows sends the error to stdout instead of stderr.
Use 'TO xxx' to send normal output to xxx
To improve the command window
- Double-click the window bar to increase the size of the window
- Right-click the window bar
- Select Properties
- Check QuickEdit Mode
Select text with right-click or Enter
Paste text with right-click
- Change Font to Lucinda Console
- Change Layout to Screen Buffer Height 999, Window Size Height 55
- Change Colors to Screen Background White, Screen Text Black
- Click OK
- Select 'Modify shortcut that started this window', then OK
If you use qhull a lot, install a bash shell such as
MSYS (www.mingw.org/wiki/msys), Road Bash (www.qhull.org/bash),
or Cygwin (www.cygwin.com).
-----------------
Installing Qhull on Unix with gcc
To build Qhull, static libraries, shared library, and C++ interface
- Download and extract Qhull (either GitHub, .tgz file, or .zip file)
- make
- export LD_LIBRARY_PATH=$PWD/lib:$LD_LIBRARY_PATH
The Makefiles may be edited for other compilers.
If 'testqset' exits with an error, qhull is broken
A simple Makefile for Qhull is in src/libqhull and src/libqhull_r.
To build the Qhull executables and libqhullstatic
- Extract Qhull from qhull...tgz or qhull...zip
- cd src/libqhull_r # cd src/libqhull
- make
-----------------
Installing Qhull with CMake 2.6 or later
See CMakeLists.txt for examples and further build instructions
To build Qhull, static libraries, shared library, and C++ interface
- Download and extract Qhull (either GitHub, .tgz file, or .zip file)
- cd build
- cmake --help # List build generators
- make -G "<generator>" .. && cmake ..
- cmake ..
- make
- make install
The ".." is important. It refers to the parent directory (i.e., qhull/)
On Windows, CMake installs to C:/Program Files/qhull. 64-bit generators
have a "Win64" tag.
If creating a qhull package, please include a pkg-config file based on build/qhull*.pc.in
If cmake fails with "No CMAKE_C_COMPILER could be found"
- cmake was not able to find the build environment specified by -G "..."
-----------------
Installing Qhull with Qt
To build Qhull, including its C++ test (qhulltest)
- Download and extract Qhull (either GitHub, .tgz file, or .zip file)
- Load src/qhull-all.pro into QtCreator
- Build
-------------------
Working with Qhull's C++ interface
See html/qh-code.htm#cpp for calling Qhull from C++ programs
See html/qh-code.htm#reentrant for converting from Qhull-2012
Examples of using the C++ interface
user_eg3_r.cpp
qhulltest/*_test.cpp
Qhull's C++ interface is likely to change. Stay current with GitHub.
To clone Qhull's next branch from http://github.com/qhull/qhull
git init
git clone git@github.com:qhull/qhull.git
cd qhull
git checkout next
...
git pull origin next
Compile qhullcpp and libqhullstatic_r with the same compiler. Both libraries
use the C routines setjmp() and longjmp() for error handling. They must
be compiled with the same compiler.
-------------------
Calling Qhull from C programs
See html/qh-code.htm#library for calling Qhull from C programs
See html/qh-code.htm#reentrant for converting from Qhull-2012
Warning: You will need to understand Qhull's data structures and read the
code. Most users will find it easier to call Qhull as an external command.
The new, reentrant 'C' code (src/libqhull_r), passes a pointer to qhT
to most Qhull routines. This allows multiple instances of Qhull to run
at the same time. It simplifies the C++ interface.
The non-reentrant 'C' code (src/libqhull) looks unusual. It refers to
Qhull's global data structure, qhT, through a 'qh' macro (e.g., 'qh ferr').
This allows the same code to use static memory or heap memory.
If qh_QHpointer is defined, qh_qh is a pointer to an allocated qhT;
otherwise qh_qh is a global static data structure of type qhT.
------------------
Compiling Qhull with Microsoft Visual C++
To compile 32-bit Qhull with Microsoft Visual C++ 2010 and later
- Download and extract Qhull (either GitHub, .tgz file, or .zip file)
- Load solution build/qhull-32.sln
- Build target 'Win32'
- Project qhulltest requires Qt for DevStudio (http://www.qt.io)
Set the QTDIR environment variable to your Qt directory (e.g., c:/qt/5.2.0/5.2.0/msvc2012)
If QTDIR is incorrect, precompile will fail with 'Can not locate the file specified'
To compile 64-bit Qhull with Microsoft Visual C++ 2010 and later
- 64-bit Qhull has larger data structures due to 64-bit pointers
- Download and extract Qhull (either GitHub, .tgz file, or .zip file)
- Load solution build/qhull-64.sln
- Build target 'Win32'
- Project qhulltest requires Qt for DevStudio (http://www.qt.io)
Set the QTDIR environment variable to your Qt directory (e.g., c:/qt/5.2.0/5.2.0/msvc2012_64)
If QTDIR is incorrect, precompile will fail with 'Can not locate the file specified'
To compile Qhull with Microsoft Visual C++ 2005 (vcproj files)
- Download and extract Qhull (either GitHub, .tgz file, or .zip file)
- Load solution build/qhull.sln
- Build target 'win32' (not 'x64')
- Project qhulltest requires Qt for DevStudio (http://www.qt.io)
Set the QTDIR environment variable to your Qt directory (e.g., c:/qt/4.7.4)
If QTDIR is incorrect, precompile will fail with 'Can not locate the file specified'
-----------------
Compiling Qhull with Qt Creator
Qt (http://www.qt.io) is a C++ framework for Windows, Linux, and Macintosh
Qhull uses QTestLib to test qhull's C++ interface (see src/qhulltest/)
To compile Qhull with Qt Creator
- Download and extract Qhull (either GitHub, .tgz file, or .zip file)
- Download the Qt SDK
- Start Qt Creator
- Load src/qhull-all.pro
- Build
-----------------
Compiling Qhull with mingw on Windows
To compile Qhull with MINGW
- Download and extract Qhull (either GitHub, .tgz file, or .zip file)
- Install Road Bash (http://www.qhull.org/bash)
or install MSYS (http://www.mingw.org/wiki/msys)
- Install MINGW-w64 (http://sourceforge.net/projects/mingw-w64).
Mingw is included with Qt SDK.
- make
-----------------
Compiling Qhull with cygwin on Windows
To compile Qhull with cygwin
- Download and extract Qhull (either GitHub, .tgz file, or .zip file)
- Install cygwin (http://www.cygwin.com)
- Include packages for gcc, make, ar, and ln
- make
-----------------
Compiling from Makfile without gcc
The file, qhull-src.tgz, contains documentation and source files for
qhull and rbox.
To unpack the tgz file
- tar zxf qhull-src.tgz
- cd qhull
- Use qhull/Makefile
Simpler Makefiles are qhull/src/libqhull/Makefile and qhull/src/libqhull_r/Makefile
Compiling qhull and rbox with Makefile
- 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 libqhull_r.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 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
- 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
- to install the programs and their man pages:
- define MANDIR and BINDIR
- type 'make install'
- 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)
------------------
Compiling on other machines and compilers
Qhull may compile with Borland C++ 5.0 bcc32. A Makefile is included.
Execute 'cd src/libqhull; make -f Mborland'. If you use the Borland IDE, set
the ANSI option in Options:Project:Compiler:Source:Language-compliance.
Qhull may compile with Borland C++ 4.02 for Win32 and DOS Power Pack.
Use 'cd src/libqhull; 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]
If you have troubles with the memory manager, you can turn it off by
defining qh_NOmem in mem.h.
-----------------
Distributed files
README.txt // Instructions for installing Qhull
REGISTER.txt // Qhull registration
COPYING.txt // Copyright notice
QHULL-GO.lnk // Windows icon for eg/qhull-go.bat
Announce.txt // Announcement
CMakeLists.txt // CMake build file (2.6 or later)
CMakeModules/CheckLFS.cmake // enables Large File Support in cmake
File_id.diz // Package descriptor
index.htm // Home page
Makefile // Makefile for gcc and other compilers
qhull*.md5sum // md5sum for all files
bin/* // Qhull executables and dll (.zip only)
build/qhull*.pc.in // pkg-config templates for qhull_r, qhull, and qhull_p
build/qhull-32.sln // 32-bit DevStudio solution and project files (2010 and later)
build/*-32.vcxproj
build/qhull-64.sln // 64-bit DevStudio solution and project files (2010 and later)
build/*-64.vcxproj
build/qhull.sln // DevStudio solution and project files (2005 and 2009)
build/*.vcproj
eg/* // Test scripts and geomview files from q_eg
html/index.htm // Manual
html/qh-faq.htm // Frequently asked questions
html/qh-get.htm // Download page
html/qhull-cpp.xml // C++ style notes as a Road FAQ (www.qhull.org/road)
src/Changes.txt // Change history for Qhull and rbox
src/qhull-all.pro // Qt project
eg/
q_eg // shell script for Geomview examples (eg.01.cube)
q_egtest // shell script for Geomview test examples
q_test // shell script to test qhull
q_test-ok.txt // output from q_test
qhulltest-ok.txt // output from qhulltest (Qt only)
make-vcproj.sh // bash shell script to create vcproj and vcxprog files
qhull-zip.sh // bash shell script for distribution files
rbox consists of (bin, html):
rbox.exe // Win32 executable (.zip only)
rbox.htm // html manual
rbox.man // Unix man page
rbox.txt
qhull consists of (bin, html):
qconvex.exe // Win32 executables and dlls (.zip download only)
qhull.exe // Built with the reentrant library (about 2% slower)
qdelaunay.exe
qhalf.exe
qvoronoi.exe
qhull_r.dll
qhull-go.bat // command window
qconvex.htm // html manual
qdelaun.htm
qdelau_f.htm
qhalf.htm
qvoronoi.htm
qvoron_f.htm
qh-eg.htm
qh-code.htm
qh-impre.htm
index.htm
qh-opt*.htm
qh-quick.htm
qh--*.gif // images for manual
normal_voronoi_knauss_oesterle.jpg
qhull.man // Unix man page
qhull.txt
bin/
msvcr80.dll // Visual C++ redistributable file (.zip download only)
src/
qhull/unix.c // Qhull and rbox applications using non-reentrant libqhullstatic.a
rbox/rbox.c
qconvex/qconvex.c
qhalf/qhalf.c
qdelaunay/qdelaunay.c
qvoronoi/qvoronoi.c
qhull/unix_r.c // Qhull and rbox applications using reentrant libqhullstatic_r.a
rbox/rbox_r.c
qconvex/qconvex_r.c // Qhull applications built with reentrant libqhull_r/Makefile
qhalf/qhalf_r.c
qdelaunay/qdelaun_r.c
qvoronoi/qvoronoi_r.c
user_eg/user_eg_r.c // example of using qhull_r.dll from a user program
user_eg2/user_eg2_r.c // example of using libqhullstatic_r.a from a user program
user_eg3/user_eg3_r.cpp // example of Qhull's C++ interface libqhullcpp with libqhullstatic_r.a
qhulltest/qhulltest.cpp // Test of Qhull's C++ interface using Qt's QTestLib
qhull-*.pri // Include files for Qt projects
testqset_r/testqset_r.c // Test of reentrant qset_r.c and mem_r.c
testqset/testqset.c // Test of non-rentrant qset.c and mem.c
src/libqhull
libqhull.pro // Qt project for non-rentrant, shared library (qhull.dll)
index.htm // design documentation for libqhull
qh-*.htm
qhull-exports.def // Export Definition file for Visual C++
Makefile // Simple gcc Makefile for qhull and libqhullstatic.a
Mborland // Makefile for Borland C++ 5.0
libqhull.h // header file for qhull
user.h // header file of user definable constants
libqhull.c // Quickhull algorithm with partitioning
user.c // user re-definable functions
usermem.c
userprintf.c
userprintf_rbox.c
qhull_a.h // include files for libqhull/*.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
random.c // utilities w/ Park & Miller's random number generator
random.h
rboxlib.c // point set generator for rbox
stat.c // statistics
stat.h
src/libqhull_r
libqhull_r.pro // Qt project for rentrant, shared library (qhull_r.dll)
index.htm // design documentation for libqhull_r
qh-*_r.htm
qhull-exports_r.def // Export Definition file for Visual C++
Makefile // Simple gcc Makefile for qhull and libqhullstatic.a
libqhull_r.h // header file for qhull
user_r.h // header file of user definable constants
libqhull_r.c // Quickhull algorithm wi_r.hpartitioning
user_r.c // user re-definable functions
usermem.c
userprintf.c
userprintf_rbox.c
qhull_ra.h // include files for libqhull/*_r.c
geom_r.c // geometric routines
geom2.c
geom_r.h
global_r.c // global variables
io_r.c // input-output routines
io_r.h
mem_r.c // memory routines, this is stand-alone code
mem.h
merge_r.c // merging of non-convex facets
merge.h
poly_r.c // polyhedron routines
poly2.c
poly_r.h
qset_r.c // set routines, this only depends on mem_r.c
qset.h
random_r.c // utilities w/ Park & Miller's random number generator
random.h
rboxlib_r.c // point set generator for rbox
stat_r.c // statistics
stat.h
src/libqhullcpp/
libqhullcpp.pro // Qt project for renentrant, static C++ library
Qhull.cpp // Calls libqhull_r.c from C++
Qhull.h
qt-qhull.cpp // Supporting methods for Qt
Coordinates.cpp // input classes
Coordinates.h
PointCoordinates.cpp
PointCoordinates.h
RboxPoints.cpp // call rboxlib.c from C++
RboxPoints.h
QhullFacet.cpp // data structure classes
QhullFacet.h
QhullHyperplane.cpp
QhullHyperplane.h
QhullPoint.cpp
QhullPoint.h
QhullQh.cpp
QhullRidge.cpp
QhullRidge.h
QhullVertex.cpp
QhullVertex.h
QhullFacetList.cpp // collection classes
QhullFacetList.h
QhullFacetSet.cpp
QhullFacetSet.h
QhullIterator.h
QhullLinkedList.h
QhullPoints.cpp
QhullPoints.h
QhullPointSet.cpp
QhullPointSet.h
QhullSet.cpp
QhullSet.h
QhullSets.h
QhullVertexSet.cpp
QhullVertexSet.h
functionObjects.h // supporting classes
QhullError.cpp
QhullError.h
QhullQh.cpp
QhullQh.h
QhullStat.cpp
QhullStat.h
RoadError.cpp // Supporting base classes
RoadError.h
RoadLogEvent.cpp
RoadLogEvent.h
usermem_r-cpp.cpp // Optional override for qh_exit() to throw an error
src/libqhullstatic/
libqhullstatic.pro // Qt project for non-reentrant, static library
src/libqhullstatic_r/
libqhullstatic_r.pro // Qt project for reentrant, static library
src/qhulltest/
qhulltest.pro // Qt project for test of C++ interface
Coordinates_test.cpp // Test of each class
PointCoordinates_test.cpp
Qhull_test.cpp
QhullFacet_test.cpp
QhullFacetList_test.cpp
QhullFacetSet_test.cpp
QhullHyperplane_test.cpp
QhullLinkedList_test.cpp
QhullPoint_test.cpp
QhullPoints_test.cpp
QhullPointSet_test.cpp
QhullRidge_test.cpp
QhullSet_test.cpp
QhullVertex_test.cpp
QhullVertexSet_test.cpp
RboxPoints_test.cpp
RoadTest.cpp // Run multiple test files with QTestLib
RoadTest.h
-----------------
Authors:
C. Bradford Barber Hannu Huhdanpaa (Version 1.0)
bradb@shore.net hannu@qhull.org
Qhull 1.0 and 2.0 were 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.

32
src/qhull/REGISTER.txt Normal file
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@@ -0,0 +1,32 @@
Dear Qhull User
We would like to find out how you are using our software. Think of
Qhull 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 Qhull, 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) How Qhull has helped you, for example, by increasing your
productivity or allowing you to do things you could not do
before. If Qhull had a direct bearing on your work, please
tell us about this.
We encourage you to cite Qhull in your publications.
To cite Qhull, please use
Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., "The Quickhull
algorithm for convex hulls," ACM Trans. on Mathematical Software,
22(4):469-483, Dec 1996, http://www.qhull.org.
Please send e-mail to
bradb@shore.net
Thank you!

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@@ -0,0 +1,7 @@
qhull/build
This directory contains Microsoft .proj and .sln files for building Qhull with DevStudio.
See ../README.txt for building with make, cmake, qt, and conftool
Qhull builds write intermediate files into this directory.

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@@ -0,0 +1,300 @@
<?xml version="1.0" encoding="UTF-8"?>
<Project DefaultTargets="Build" ToolsVersion="4.0" xmlns="http://schemas.microsoft.com/developer/msbuild/2003">
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<ProjectConfiguration Include="Release|Win32">
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<ProjectConfiguration Include="MinSizeRel|Win32">
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<ProjectConfiguration Include="RelWithDebInfo|Win32">
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<PropertyGroup Label="Globals">
<ProjectGUID>{AE297F0D-5402-41C0-83B1-0194B583B67E}</ProjectGUID>
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<Platform>Win32</Platform>
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<Import Project="$(VCTargetsPath)\Microsoft.Cpp.Default.props" />
<PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Debug|Win32'" Label="Configuration">
<ConfigurationType>DynamicLibrary</ConfigurationType>
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<PropertyGroup Condition="'$(Configuration)|$(Platform)'=='Release|Win32'" Label="Configuration">
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<PropertyGroup Condition="'$(Configuration)|$(Platform)'=='MinSizeRel|Win32'" Label="Configuration">
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<PropertyGroup Condition="'$(Configuration)|$(Platform)'=='RelWithDebInfo|Win32'" Label="Configuration">
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<Import Project="$(VCTargetsPath)\Microsoft.Cpp.props" />
<ImportGroup Label="ExtensionSettings">
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<ImportGroup Label="PropertySheets">
<Import Project="$(UserRootDir)\Microsoft.Cpp.$(Platform).user.props" Condition="exists('$(UserRootDir)\Microsoft.Cpp.$(Platform).user.props')" Label="LocalAppDataPlatform" />
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<PropertyGroup Label="UserMacros" />
<PropertyGroup>
<_ProjectFileVersion>10.0.20506.1</_ProjectFileVersion>
<OutDir Condition="'$(Configuration)|$(Platform)'=='Debug|Win32'">..\bin\</OutDir>
<IntDir Condition="'$(Configuration)|$(Platform)'=='Debug|Win32'">libqhull.dir\Debug\</IntDir>
<TargetName Condition="'$(Configuration)|$(Platform)'=='Debug|Win32'">qhull_d</TargetName>
<TargetExt Condition="'$(Configuration)|$(Platform)'=='Debug|Win32'">.dll</TargetExt>
<LinkIncremental Condition="'$(Configuration)|$(Platform)'=='Debug|Win32'">false</LinkIncremental>
<GenerateManifest Condition="'$(Configuration)|$(Platform)'=='Debug|Win32'">true</GenerateManifest>
<OutDir Condition="'$(Configuration)|$(Platform)'=='Release|Win32'">..\bin\</OutDir>
<IntDir Condition="'$(Configuration)|$(Platform)'=='Release|Win32'">libqhull.dir\Release\</IntDir>
<TargetName Condition="'$(Configuration)|$(Platform)'=='Release|Win32'">qhull</TargetName>
<TargetExt Condition="'$(Configuration)|$(Platform)'=='Release|Win32'">.dll</TargetExt>
<LinkIncremental Condition="'$(Configuration)|$(Platform)'=='Release|Win32'">false</LinkIncremental>
<GenerateManifest Condition="'$(Configuration)|$(Platform)'=='Release|Win32'">true</GenerateManifest>
<OutDir Condition="'$(Configuration)|$(Platform)'=='MinSizeRel|Win32'">..\bin\</OutDir>
<IntDir Condition="'$(Configuration)|$(Platform)'=='MinSizeRel|Win32'">libqhull.dir\MinSizeRel\</IntDir>
<TargetName Condition="'$(Configuration)|$(Platform)'=='MinSizeRel|Win32'">qhull</TargetName>
<TargetExt Condition="'$(Configuration)|$(Platform)'=='MinSizeRel|Win32'">.dll</TargetExt>
<LinkIncremental Condition="'$(Configuration)|$(Platform)'=='MinSizeRel|Win32'">false</LinkIncremental>
<GenerateManifest Condition="'$(Configuration)|$(Platform)'=='MinSizeRel|Win32'">true</GenerateManifest>
<OutDir Condition="'$(Configuration)|$(Platform)'=='RelWithDebInfo|Win32'">..\bin\</OutDir>
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View File

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View File

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Microsoft Visual Studio Solution File, Format Version 12.00
# Visual Studio 2012
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "libqhull", "libqhull-32.vcxproj", "{AE297F0D-5402-41C0-83B1-0194B583B67E}"
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "qconvex", "qconvex-32.vcxproj", "{14FC642B-13AD-43EE-98A1-A15D9373B9BA}"
ProjectSection(ProjectDependencies) = postProject
{F9AF9BC6-2CA5-4E0C-982B-CF7974723A0B} = {F9AF9BC6-2CA5-4E0C-982B-CF7974723A0B}
EndProjectSection
EndProject
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "qdelaunay", "qdelaunay-32.vcxproj", "{6120B9C5-847B-44DF-BD51-E3DCFC5BD7D8}"
ProjectSection(ProjectDependencies) = postProject
{F9AF9BC6-2CA5-4E0C-982B-CF7974723A0B} = {F9AF9BC6-2CA5-4E0C-982B-CF7974723A0B}
EndProjectSection
EndProject
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "qhalf", "qhalf-32.vcxproj", "{A5FC7430-68C4-4F67-BC69-C231FAC40A9A}"
ProjectSection(ProjectDependencies) = postProject
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "qhull", "qhull-32.vcxproj", "{E8BF0EA0-A09D-4155-BCEC-CC1B0DF8A67E}"
ProjectSection(ProjectDependencies) = postProject
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EndProjectSection
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "qhull_p", "qhull_p-32.vcxproj", "{9969E173-B078-4FC0-A35E-9F3B0FDA1CE9}"
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "qhull_r", "qhull_r-32.vcxproj", "{D1E7C352-C0F9-4E64-B0CB-6C4371280C86}"
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "qhullcpp", "qhullcpp-32.vcxproj", "{939F1F43-F252-486C-BB92-3166E44713A5}"
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "qhullstatic", "qhullstatic-32.vcxproj", "{F9AF9BC6-2CA5-4E0C-982B-CF7974723A0B}"
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "qhullstatic_r", "qhullstatic_r-32.vcxproj", "{526F05C7-E54E-4673-91DC-A3AF75041688}"
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "qvoronoi", "qvoronoi-32.vcxproj", "{7A587B07-AE31-4071-9D8B-105BFA3815C9}"
ProjectSection(ProjectDependencies) = postProject
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EndProjectSection
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "rbox", "rbox-32.vcxproj", "{F3F597F4-08BF-4567-8866-D8A66BB1B9BE}"
ProjectSection(ProjectDependencies) = postProject
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EndProjectSection
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "testqset", "testqset-32.vcxproj", "{9ECBCBA4-269F-4ED1-B359-7522F9D19DDA}"
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "testqset_r", "testqset_r-32.vcxproj", "{ACECEFF4-E332-4AD0-A89B-0D07A78FEA6A}"
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "user_eg", "user_eg-32.vcxproj", "{D1F6E2EB-53DB-44FB-AC8C-EC2A339683A7}"
ProjectSection(ProjectDependencies) = postProject
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EndProjectSection
EndProject
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "user_eg2", "user_eg2-32.vcxproj", "{5564AE35-E8FE-4039-BD33-76B920D02BC9}"
ProjectSection(ProjectDependencies) = postProject
{526F05C7-E54E-4673-91DC-A3AF75041688} = {526F05C7-E54E-4673-91DC-A3AF75041688}
EndProjectSection
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "user_eg3", "user_eg3-32.vcxproj", "{E615D779-7F0A-4521-B7AD-B3C0D328652E}"
ProjectSection(ProjectDependencies) = postProject
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EndProjectSection
EndProject
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "qhulltest-32", "qhulltest\qhulltest-32.vcxproj", "{59F000B6-1AEC-3107-979D-510DA098577A}"
ProjectSection(ProjectDependencies) = postProject
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EndProjectSection
EndProject
Global
GlobalSection(SolutionConfigurationPlatforms) = preSolution
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GlobalSection(ProjectConfigurationPlatforms) = postSolution
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EndGlobalSection
EndGlobal

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@@ -0,0 +1,272 @@
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Microsoft Visual Studio Solution File, Format Version 12.00
# Visual Studio 2012
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "libqhull", "libqhull-64.vcxproj", "{AE297F0D-5402-41C0-83B1-0194B583B67E}"
EndProject
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "qconvex", "qconvex-64.vcxproj", "{14FC642B-13AD-43EE-98A1-A15D9373B9BA}"
ProjectSection(ProjectDependencies) = postProject
{F9AF9BC6-2CA5-4E0C-982B-CF7974723A0B} = {F9AF9BC6-2CA5-4E0C-982B-CF7974723A0B}
EndProjectSection
EndProject
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "qdelaunay", "qdelaunay-64.vcxproj", "{6120B9C5-847B-44DF-BD51-E3DCFC5BD7D8}"
ProjectSection(ProjectDependencies) = postProject
{F9AF9BC6-2CA5-4E0C-982B-CF7974723A0B} = {F9AF9BC6-2CA5-4E0C-982B-CF7974723A0B}
EndProjectSection
EndProject
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "qhalf", "qhalf-64.vcxproj", "{A5FC7430-68C4-4F67-BC69-C231FAC40A9A}"
ProjectSection(ProjectDependencies) = postProject
{F9AF9BC6-2CA5-4E0C-982B-CF7974723A0B} = {F9AF9BC6-2CA5-4E0C-982B-CF7974723A0B}
EndProjectSection
EndProject
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "qhull", "qhull-64.vcxproj", "{E8BF0EA0-A09D-4155-BCEC-CC1B0DF8A67E}"
ProjectSection(ProjectDependencies) = postProject
{526F05C7-E54E-4673-91DC-A3AF75041688} = {526F05C7-E54E-4673-91DC-A3AF75041688}
EndProjectSection
EndProject
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "qhull_p", "qhull_p-64.vcxproj", "{9969E173-B078-4FC0-A35E-9F3B0FDA1CE9}"
EndProject
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "qhull_r", "qhull_r-64.vcxproj", "{D1E7C352-C0F9-4E64-B0CB-6C4371280C86}"
EndProject
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "qhullcpp", "qhullcpp-64.vcxproj", "{939F1F43-F252-486C-BB92-3166E44713A5}"
EndProject
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "qhullstatic", "qhullstatic-64.vcxproj", "{F9AF9BC6-2CA5-4E0C-982B-CF7974723A0B}"
EndProject
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "qhullstatic_r", "qhullstatic_r-64.vcxproj", "{526F05C7-E54E-4673-91DC-A3AF75041688}"
EndProject
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "qvoronoi", "qvoronoi-64.vcxproj", "{7A587B07-AE31-4071-9D8B-105BFA3815C9}"
ProjectSection(ProjectDependencies) = postProject
{F9AF9BC6-2CA5-4E0C-982B-CF7974723A0B} = {F9AF9BC6-2CA5-4E0C-982B-CF7974723A0B}
EndProjectSection
EndProject
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "rbox", "rbox-64.vcxproj", "{F3F597F4-08BF-4567-8866-D8A66BB1B9BE}"
ProjectSection(ProjectDependencies) = postProject
{F9AF9BC6-2CA5-4E0C-982B-CF7974723A0B} = {F9AF9BC6-2CA5-4E0C-982B-CF7974723A0B}
EndProjectSection
EndProject
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "testqset", "testqset-64.vcxproj", "{9ECBCBA4-269F-4ED1-B359-7522F9D19DDA}"
EndProject
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "testqset_r", "testqset_r-64.vcxproj", "{ACECEFF4-E332-4AD0-A89B-0D07A78FEA6A}"
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Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "user_eg", "user_eg-64.vcxproj", "{D1F6E2EB-53DB-44FB-AC8C-EC2A339683A7}"
ProjectSection(ProjectDependencies) = postProject
{D1E7C352-C0F9-4E64-B0CB-6C4371280C86} = {D1E7C352-C0F9-4E64-B0CB-6C4371280C86}
EndProjectSection
EndProject
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "user_eg2", "user_eg2-64.vcxproj", "{5564AE35-E8FE-4039-BD33-76B920D02BC9}"
ProjectSection(ProjectDependencies) = postProject
{526F05C7-E54E-4673-91DC-A3AF75041688} = {526F05C7-E54E-4673-91DC-A3AF75041688}
EndProjectSection
EndProject
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "user_eg3", "user_eg3-64.vcxproj", "{E615D779-7F0A-4521-B7AD-B3C0D328652E}"
ProjectSection(ProjectDependencies) = postProject
{939F1F43-F252-486C-BB92-3166E44713A5} = {939F1F43-F252-486C-BB92-3166E44713A5}
{526F05C7-E54E-4673-91DC-A3AF75041688} = {526F05C7-E54E-4673-91DC-A3AF75041688}
EndProjectSection
EndProject
Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "qhulltest-64", "qhulltest\qhulltest-64.vcxproj", "{59F000B6-1AEC-3107-979D-510DA098577A}"
ProjectSection(ProjectDependencies) = postProject
{939F1F43-F252-486C-BB92-3166E44713A5} = {939F1F43-F252-486C-BB92-3166E44713A5}
{526F05C7-E54E-4673-91DC-A3AF75041688} = {526F05C7-E54E-4673-91DC-A3AF75041688}
EndProjectSection
EndProject
Global
GlobalSection(SolutionConfigurationPlatforms) = preSolution
Debug|x64 = Debug|x64
MinSizeRel|x64 = MinSizeRel|x64
Release|x64 = Release|x64
RelWithDebInfo|x64 = RelWithDebInfo|x64
EndGlobalSection
GlobalSection(ProjectConfigurationPlatforms) = postSolution
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{AE297F0D-5402-41C0-83B1-0194B583B67E}.Debug|x64.Build.0 = Debug|x64
{AE297F0D-5402-41C0-83B1-0194B583B67E}.MinSizeRel|x64.ActiveCfg = MinSizeRel|x64
{AE297F0D-5402-41C0-83B1-0194B583B67E}.MinSizeRel|x64.Build.0 = MinSizeRel|x64
{AE297F0D-5402-41C0-83B1-0194B583B67E}.Release|x64.ActiveCfg = Release|x64
{AE297F0D-5402-41C0-83B1-0194B583B67E}.Release|x64.Build.0 = Release|x64
{AE297F0D-5402-41C0-83B1-0194B583B67E}.RelWithDebInfo|x64.ActiveCfg = RelWithDebInfo|x64
{AE297F0D-5402-41C0-83B1-0194B583B67E}.RelWithDebInfo|x64.Build.0 = RelWithDebInfo|x64
{14FC642B-13AD-43EE-98A1-A15D9373B9BA}.Debug|x64.ActiveCfg = Debug|x64
{14FC642B-13AD-43EE-98A1-A15D9373B9BA}.Debug|x64.Build.0 = Debug|x64
{14FC642B-13AD-43EE-98A1-A15D9373B9BA}.MinSizeRel|x64.ActiveCfg = MinSizeRel|x64
{14FC642B-13AD-43EE-98A1-A15D9373B9BA}.MinSizeRel|x64.Build.0 = MinSizeRel|x64
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{14FC642B-13AD-43EE-98A1-A15D9373B9BA}.Release|x64.Build.0 = Release|x64
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{6120B9C5-847B-44DF-BD51-E3DCFC5BD7D8}.Debug|x64.Build.0 = Debug|x64
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{6120B9C5-847B-44DF-BD51-E3DCFC5BD7D8}.RelWithDebInfo|x64.ActiveCfg = RelWithDebInfo|x64
{6120B9C5-847B-44DF-BD51-E3DCFC5BD7D8}.RelWithDebInfo|x64.Build.0 = RelWithDebInfo|x64
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{A5FC7430-68C4-4F67-BC69-C231FAC40A9A}.Debug|x64.Build.0 = Debug|x64
{A5FC7430-68C4-4F67-BC69-C231FAC40A9A}.MinSizeRel|x64.ActiveCfg = MinSizeRel|x64
{A5FC7430-68C4-4F67-BC69-C231FAC40A9A}.MinSizeRel|x64.Build.0 = MinSizeRel|x64
{A5FC7430-68C4-4F67-BC69-C231FAC40A9A}.Release|x64.ActiveCfg = Release|x64
{A5FC7430-68C4-4F67-BC69-C231FAC40A9A}.Release|x64.Build.0 = Release|x64
{A5FC7430-68C4-4F67-BC69-C231FAC40A9A}.RelWithDebInfo|x64.ActiveCfg = RelWithDebInfo|x64
{A5FC7430-68C4-4F67-BC69-C231FAC40A9A}.RelWithDebInfo|x64.Build.0 = RelWithDebInfo|x64
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View File

@@ -0,0 +1,14 @@
prefix=@prefix@
exec_prefix=@exec_prefix@
includedir=@includedir@
libdir=@libdir@
Name: qhull
Description: Non-reentrant library (global struct) for convex hull, Delaunay triangulation, Voronoi diagram, and halfspace intersection about a point
# qh_QHpointer==0
Version: @VERSION@
URL: http://www.qhull.org
Requires:
Conflicts:
Libs: -L${libdir} -lqhull -lm
Cflags: -I${includedir}

233
src/qhull/build/qhull.sln Normal file
View File

@@ -0,0 +1,233 @@
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View File

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<Command Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Release|Win32&apos;">$(QTDIR)\bin\moc.exe -DUNICODE -DWIN32 -DQT_NO_DEBUG -DQT_TESTLIB_LIB -DQT_GUI_LIB -DQT_CORE_LIB -DQT_OPENGL_ES_2 -DQT_OPENGL_ES_2_ANGLE -DQT_TESTCASE_BUILDDIR=\&quot;../../build/qhulltest\&quot; -DQT_NO_DYNAMIC_CAST -D_MSC_VER=1700 -D_WIN32 -I&quot;..\..\src&quot; -I&quot;..\..\src&quot; -I&quot;$(QTDIR)\include&quot; -I&quot;$(QTDIR)\include\QtTest&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include\QtGui&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include\QtANGLE&quot; -I&quot;C:\include&quot; -I&quot;C:\include\QtGui&quot; -I&quot;$(QTDIR)\include\QtCore&quot; -I&quot;moc&quot; -I&quot;.&quot; -I$(QTDIR)\mkspecs\win32-msvc2012 ..\..\src\qhulltest\RoadTest.h -o moc\moc_RoadTest.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo /*-------------------------------------------------------------------- >..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo * Precompiled header source file used by Visual Studio.NET to generate>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo * the .pch file.>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo *>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo * Due to issues with the dependencies checker within the IDE, it>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo * sometimes fails to recompile the PCH file, if we force the IDE to>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo * create the PCH file directly from the header file.>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo *>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo * This file is auto-generated by qmake since no PRECOMPILED_SOURCE was>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo * specified, and is used as the common stdafx.cpp. The file is only>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo * generated when creating -64.vcxproj project files, and is not used for>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo * command line compilations by nmake.>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo *>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo * WARNING: All changes made in this file will be lost.>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo --------------------------------------------------------------------*/>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo #include &quot;RoadTest.h&quot;>>..\..\src\qhulltest\RoadTest.h.cpp</Command>
<Message Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Release|Win32&apos;">Generating precompiled header source file &apos;..\..\src\qhulltest\RoadTest.h.cpp&apos; ...</Message>
<Outputs Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Release|Win32&apos;">moc\moc_RoadTest.cpp;..\..\src\qhulltest\RoadTest.h.cpp;%(Outputs)</Outputs>
<AdditionalInputs Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Debug|Win32&apos;">..\..\src\qhulltest\RoadTest.h;%(AdditionalInputs)</AdditionalInputs>
<Command Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Debug|Win32&apos;">$(QTDIR)\bin\moc.exe -DUNICODE -DWIN32 -DQT_TESTLIB_LIB -DQT_GUI_LIB -DQT_CORE_LIB -DQT_OPENGL_ES_2 -DQT_OPENGL_ES_2_ANGLE -DQT_TESTCASE_BUILDDIR=\&quot;../../build/qhulltest\&quot; -DQT_NO_DYNAMIC_CAST -D_MSC_VER=1700 -D_WIN32 -I&quot;..\..\src&quot; -I&quot;..\..\src&quot; -I&quot;$(QTDIR)\include&quot; -I&quot;$(QTDIR)\include\QtTest&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include\QtGui&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include\QtANGLE&quot; -I&quot;C:\include&quot; -I&quot;C:\include\QtGui&quot; -I&quot;$(QTDIR)\include\QtCore&quot; -I&quot;moc&quot; -I&quot;.&quot; -I$(QTDIR)\mkspecs\win32-msvc2012 ..\..\src\qhulltest\RoadTest.h -o moc\moc_RoadTest.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo /*-------------------------------------------------------------------- >..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo * Precompiled header source file used by Visual Studio.NET to generate>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo * the .pch file.>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo *>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo * Due to issues with the dependencies checker within the IDE, it>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo * sometimes fails to recompile the PCH file, if we force the IDE to>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo * create the PCH file directly from the header file.>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo *>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo * This file is auto-generated by qmake since no PRECOMPILED_SOURCE was>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo * specified, and is used as the common stdafx.cpp. The file is only>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo * generated when creating -64.vcxproj project files, and is not used for>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo * command line compilations by nmake.>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo *>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo * WARNING: All changes made in this file will be lost.>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo --------------------------------------------------------------------*/>>..\..\src\qhulltest\RoadTest.h.cpp&#x000D;&#x000A;if errorlevel 1 goto VCEnd&#x000D;&#x000A;echo #include &quot;RoadTest.h&quot;>>..\..\src\qhulltest\RoadTest.h.cpp</Command>
<Message Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Debug|Win32&apos;">Generating precompiled header source file &apos;..\..\src\qhulltest\RoadTest.h.cpp&apos; ...</Message>
<Outputs Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Debug|Win32&apos;">moc\moc_RoadTest.cpp;..\..\src\qhulltest\RoadTest.h.cpp;%(Outputs)</Outputs>
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<AdditionalInputs Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Release|Win32&apos;">..\..\src\qhulltest\Coordinates_test.cpp;%(AdditionalInputs)</AdditionalInputs>
<Command Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Release|Win32&apos;">$(QTDIR)\bin\moc.exe -DUNICODE -DWIN32 -DQT_NO_DEBUG -DQT_TESTLIB_LIB -DQT_GUI_LIB -DQT_CORE_LIB -DQT_OPENGL_ES_2 -DQT_OPENGL_ES_2_ANGLE -DQT_TESTCASE_BUILDDIR=\&quot;../../build/qhulltest\&quot; -DQT_NO_DYNAMIC_CAST -D_MSC_VER=1700 -D_WIN32 -I&quot;..\..\src&quot; -I&quot;..\..\src&quot; -I&quot;$(QTDIR)\include&quot; -I&quot;$(QTDIR)\include\QtTest&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include\QtGui&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include\QtANGLE&quot; -I&quot;C:\include&quot; -I&quot;C:\include\QtGui&quot; -I&quot;$(QTDIR)\include\QtCore&quot; -I&quot;moc&quot; -I&quot;.&quot; -I$(QTDIR)\mkspecs\win32-msvc2012 ..\..\src\qhulltest\Coordinates_test.cpp -o moc\Coordinates_test.moc</Command>
<Message Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Release|Win32&apos;">MOC ..\..\src\qhulltest\Coordinates_test.cpp</Message>
<Outputs Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Release|Win32&apos;">moc\Coordinates_test.moc;%(Outputs)</Outputs>
<AdditionalInputs Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Debug|Win32&apos;">..\..\src\qhulltest\Coordinates_test.cpp;%(AdditionalInputs)</AdditionalInputs>
<Command Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Debug|Win32&apos;">$(QTDIR)\bin\moc.exe -DUNICODE -DWIN32 -DQT_TESTLIB_LIB -DQT_GUI_LIB -DQT_CORE_LIB -DQT_OPENGL_ES_2 -DQT_OPENGL_ES_2_ANGLE -DQT_TESTCASE_BUILDDIR=\&quot;../../build/qhulltest\&quot; -DQT_NO_DYNAMIC_CAST -D_MSC_VER=1700 -D_WIN32 -I&quot;..\..\src&quot; -I&quot;..\..\src&quot; -I&quot;$(QTDIR)\include&quot; -I&quot;$(QTDIR)\include\QtTest&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include\QtGui&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include\QtANGLE&quot; -I&quot;C:\include&quot; -I&quot;C:\include\QtGui&quot; -I&quot;$(QTDIR)\include\QtCore&quot; -I&quot;moc&quot; -I&quot;.&quot; -I$(QTDIR)\mkspecs\win32-msvc2012 ..\..\src\qhulltest\Coordinates_test.cpp -o moc\Coordinates_test.moc</Command>
<Message Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Debug|Win32&apos;">MOC ..\..\src\qhulltest\Coordinates_test.cpp</Message>
<Outputs Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Debug|Win32&apos;">moc\Coordinates_test.moc;%(Outputs)</Outputs>
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<CustomBuild Include="moc\PointCoordinates_test.moc">
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<AdditionalInputs Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Release|Win32&apos;">..\..\src\qhulltest\PointCoordinates_test.cpp;%(AdditionalInputs)</AdditionalInputs>
<Command Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Release|Win32&apos;">$(QTDIR)\bin\moc.exe -DUNICODE -DWIN32 -DQT_NO_DEBUG -DQT_TESTLIB_LIB -DQT_GUI_LIB -DQT_CORE_LIB -DQT_OPENGL_ES_2 -DQT_OPENGL_ES_2_ANGLE -DQT_TESTCASE_BUILDDIR=\&quot;../../build/qhulltest\&quot; -DQT_NO_DYNAMIC_CAST -D_MSC_VER=1700 -D_WIN32 -I&quot;..\..\src&quot; -I&quot;..\..\src&quot; -I&quot;$(QTDIR)\include&quot; -I&quot;$(QTDIR)\include\QtTest&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include\QtGui&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include\QtANGLE&quot; -I&quot;C:\include&quot; -I&quot;C:\include\QtGui&quot; -I&quot;$(QTDIR)\include\QtCore&quot; -I&quot;moc&quot; -I&quot;.&quot; -I$(QTDIR)\mkspecs\win32-msvc2012 ..\..\src\qhulltest\PointCoordinates_test.cpp -o moc\PointCoordinates_test.moc</Command>
<Message Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Release|Win32&apos;">MOC ..\..\src\qhulltest\PointCoordinates_test.cpp</Message>
<Outputs Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Release|Win32&apos;">moc\PointCoordinates_test.moc;%(Outputs)</Outputs>
<AdditionalInputs Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Debug|Win32&apos;">..\..\src\qhulltest\PointCoordinates_test.cpp;%(AdditionalInputs)</AdditionalInputs>
<Command Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Debug|Win32&apos;">$(QTDIR)\bin\moc.exe -DUNICODE -DWIN32 -DQT_TESTLIB_LIB -DQT_GUI_LIB -DQT_CORE_LIB -DQT_OPENGL_ES_2 -DQT_OPENGL_ES_2_ANGLE -DQT_TESTCASE_BUILDDIR=\&quot;../../build/qhulltest\&quot; -DQT_NO_DYNAMIC_CAST -D_MSC_VER=1700 -D_WIN32 -I&quot;..\..\src&quot; -I&quot;..\..\src&quot; -I&quot;$(QTDIR)\include&quot; -I&quot;$(QTDIR)\include\QtTest&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include\QtGui&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include\QtANGLE&quot; -I&quot;C:\include&quot; -I&quot;C:\include\QtGui&quot; -I&quot;$(QTDIR)\include\QtCore&quot; -I&quot;moc&quot; -I&quot;.&quot; -I$(QTDIR)\mkspecs\win32-msvc2012 ..\..\src\qhulltest\PointCoordinates_test.cpp -o moc\PointCoordinates_test.moc</Command>
<Message Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Debug|Win32&apos;">MOC ..\..\src\qhulltest\PointCoordinates_test.cpp</Message>
<Outputs Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Debug|Win32&apos;">moc\PointCoordinates_test.moc;%(Outputs)</Outputs>
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<CustomBuild Include="moc\QhullFacetList_test.moc">
<FileType>Document</FileType>
<AdditionalInputs Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Release|Win32&apos;">..\..\src\qhulltest\QhullFacetList_test.cpp;%(AdditionalInputs)</AdditionalInputs>
<Command Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Release|Win32&apos;">$(QTDIR)\bin\moc.exe -DUNICODE -DWIN32 -DQT_NO_DEBUG -DQT_TESTLIB_LIB -DQT_GUI_LIB -DQT_CORE_LIB -DQT_OPENGL_ES_2 -DQT_OPENGL_ES_2_ANGLE -DQT_TESTCASE_BUILDDIR=\&quot;../../build/qhulltest\&quot; -DQT_NO_DYNAMIC_CAST -D_MSC_VER=1700 -D_WIN32 -I&quot;..\..\src&quot; -I&quot;..\..\src&quot; -I&quot;$(QTDIR)\include&quot; -I&quot;$(QTDIR)\include\QtTest&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include\QtGui&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include\QtANGLE&quot; -I&quot;C:\include&quot; -I&quot;C:\include\QtGui&quot; -I&quot;$(QTDIR)\include\QtCore&quot; -I&quot;moc&quot; -I&quot;.&quot; -I$(QTDIR)\mkspecs\win32-msvc2012 ..\..\src\qhulltest\QhullFacetList_test.cpp -o moc\QhullFacetList_test.moc</Command>
<Message Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Release|Win32&apos;">MOC ..\..\src\qhulltest\QhullFacetList_test.cpp</Message>
<Outputs Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Release|Win32&apos;">moc\QhullFacetList_test.moc;%(Outputs)</Outputs>
<AdditionalInputs Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Debug|Win32&apos;">..\..\src\qhulltest\QhullFacetList_test.cpp;%(AdditionalInputs)</AdditionalInputs>
<Command Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Debug|Win32&apos;">$(QTDIR)\bin\moc.exe -DUNICODE -DWIN32 -DQT_TESTLIB_LIB -DQT_GUI_LIB -DQT_CORE_LIB -DQT_OPENGL_ES_2 -DQT_OPENGL_ES_2_ANGLE -DQT_TESTCASE_BUILDDIR=\&quot;../../build/qhulltest\&quot; -DQT_NO_DYNAMIC_CAST -D_MSC_VER=1700 -D_WIN32 -I&quot;..\..\src&quot; -I&quot;..\..\src&quot; -I&quot;$(QTDIR)\include&quot; -I&quot;$(QTDIR)\include\QtTest&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include\QtGui&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include\QtANGLE&quot; -I&quot;C:\include&quot; -I&quot;C:\include\QtGui&quot; -I&quot;$(QTDIR)\include\QtCore&quot; -I&quot;moc&quot; -I&quot;.&quot; -I$(QTDIR)\mkspecs\win32-msvc2012 ..\..\src\qhulltest\QhullFacetList_test.cpp -o moc\QhullFacetList_test.moc</Command>
<Message Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Debug|Win32&apos;">MOC ..\..\src\qhulltest\QhullFacetList_test.cpp</Message>
<Outputs Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Debug|Win32&apos;">moc\QhullFacetList_test.moc;%(Outputs)</Outputs>
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<CustomBuild Include="moc\QhullFacetSet_test.moc">
<FileType>Document</FileType>
<AdditionalInputs Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Release|Win32&apos;">..\..\src\qhulltest\QhullFacetSet_test.cpp;%(AdditionalInputs)</AdditionalInputs>
<Command Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Release|Win32&apos;">$(QTDIR)\bin\moc.exe -DUNICODE -DWIN32 -DQT_NO_DEBUG -DQT_TESTLIB_LIB -DQT_GUI_LIB -DQT_CORE_LIB -DQT_OPENGL_ES_2 -DQT_OPENGL_ES_2_ANGLE -DQT_TESTCASE_BUILDDIR=\&quot;../../build/qhulltest\&quot; -DQT_NO_DYNAMIC_CAST -D_MSC_VER=1700 -D_WIN32 -I&quot;..\..\src&quot; -I&quot;..\..\src&quot; -I&quot;$(QTDIR)\include&quot; -I&quot;$(QTDIR)\include\QtTest&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include\QtGui&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include\QtANGLE&quot; -I&quot;C:\include&quot; -I&quot;C:\include\QtGui&quot; -I&quot;$(QTDIR)\include\QtCore&quot; -I&quot;moc&quot; -I&quot;.&quot; -I$(QTDIR)\mkspecs\win32-msvc2012 ..\..\src\qhulltest\QhullFacetSet_test.cpp -o moc\QhullFacetSet_test.moc</Command>
<Message Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Release|Win32&apos;">MOC ..\..\src\qhulltest\QhullFacetSet_test.cpp</Message>
<Outputs Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Release|Win32&apos;">moc\QhullFacetSet_test.moc;%(Outputs)</Outputs>
<AdditionalInputs Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Debug|Win32&apos;">..\..\src\qhulltest\QhullFacetSet_test.cpp;%(AdditionalInputs)</AdditionalInputs>
<Command Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Debug|Win32&apos;">$(QTDIR)\bin\moc.exe -DUNICODE -DWIN32 -DQT_TESTLIB_LIB -DQT_GUI_LIB -DQT_CORE_LIB -DQT_OPENGL_ES_2 -DQT_OPENGL_ES_2_ANGLE -DQT_TESTCASE_BUILDDIR=\&quot;../../build/qhulltest\&quot; -DQT_NO_DYNAMIC_CAST -D_MSC_VER=1700 -D_WIN32 -I&quot;..\..\src&quot; -I&quot;..\..\src&quot; -I&quot;$(QTDIR)\include&quot; -I&quot;$(QTDIR)\include\QtTest&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include\QtGui&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include\QtANGLE&quot; -I&quot;C:\include&quot; -I&quot;C:\include\QtGui&quot; -I&quot;$(QTDIR)\include\QtCore&quot; -I&quot;moc&quot; -I&quot;.&quot; -I$(QTDIR)\mkspecs\win32-msvc2012 ..\..\src\qhulltest\QhullFacetSet_test.cpp -o moc\QhullFacetSet_test.moc</Command>
<Message Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Debug|Win32&apos;">MOC ..\..\src\qhulltest\QhullFacetSet_test.cpp</Message>
<Outputs Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Debug|Win32&apos;">moc\QhullFacetSet_test.moc;%(Outputs)</Outputs>
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<CustomBuild Include="moc\QhullFacet_test.moc">
<FileType>Document</FileType>
<AdditionalInputs Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Release|Win32&apos;">..\..\src\qhulltest\QhullFacet_test.cpp;%(AdditionalInputs)</AdditionalInputs>
<Command Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Release|Win32&apos;">$(QTDIR)\bin\moc.exe -DUNICODE -DWIN32 -DQT_NO_DEBUG -DQT_TESTLIB_LIB -DQT_GUI_LIB -DQT_CORE_LIB -DQT_OPENGL_ES_2 -DQT_OPENGL_ES_2_ANGLE -DQT_TESTCASE_BUILDDIR=\&quot;../../build/qhulltest\&quot; -DQT_NO_DYNAMIC_CAST -D_MSC_VER=1700 -D_WIN32 -I&quot;..\..\src&quot; -I&quot;..\..\src&quot; -I&quot;$(QTDIR)\include&quot; -I&quot;$(QTDIR)\include\QtTest&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include\QtGui&quot; -I&quot;$(QTDIR)\..\Src\qtbase\include\QtANGLE&quot; -I&quot;C:\include&quot; -I&quot;C:\include\QtGui&quot; -I&quot;$(QTDIR)\include\QtCore&quot; -I&quot;moc&quot; -I&quot;.&quot; -I$(QTDIR)\mkspecs\win32-msvc2012 ..\..\src\qhulltest\QhullFacet_test.cpp -o moc\QhullFacet_test.moc</Command>
<Message Condition="&apos;$(Configuration)|$(Platform)&apos;==&apos;Release|Win32&apos;">MOC ..\..\src\qhulltest\QhullFacet_test.cpp</Message>
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View File

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View File

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View File

@@ -0,0 +1,274 @@
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<ClCompile Include="..\src\user_eg3\user_eg3_r.cpp" />
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<ProjectReference Include="../build/qhullcpp-64.vcxproj">
<Project>939F1F43-F252-486C-BB92-3166E44713A5</Project>
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<ImportGroup Label="ExtensionTargets">
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View File

@@ -0,0 +1,429 @@
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ProjectType="Visual C++"
Version="8.00"
Name="user_eg3"
ProjectGUID="{83203305-79D5-412C-9819-0F9AD5C34EC1}"
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OutputDirectory="Debug"
IntermediateDirectory="user_eg3.dir\Debug"
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UseOfMFC="0"
ATLMinimizesCRunTimeLibraryUsage="false"
CharacterSet="2"
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GenerateStublessProxies="true"
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OutputDirectory="$(IntDir)"
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DLLDataFileName=""
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ProxyFileName="$(InputName)_p.c"
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AdditionalOptions=" /Zm1000"
Optimization="0"
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WarningLevel="3"
DebugInformationFormat="3"
CompileAs="2"
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Name="VCResourceCompilerTool"
PreprocessorDefinitions="WIN32;_WINDOWS;_DEBUG"
AdditionalIncludeDirectories="..\src;"
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<Tool
Name="VCPreLinkEventTool"
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Name="VCLinkerTool"
LinkLibraryDependencies="false"
AdditionalOptions=" /STACK:10000000 /machine:X86 /debug"
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ImportLibrary="..\lib\user_eg3_d.lib"
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OutputDirectory="Release"
IntermediateDirectory="user_eg3.dir\Release"
ConfigurationType="1"
UseOfMFC="0"
ATLMinimizesCRunTimeLibraryUsage="false"
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Optimization="2"
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WarningLevel="3"
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<Tool
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Name="VCResourceCompilerTool"
PreprocessorDefinitions="WIN32;_WINDOWS;NDEBUG"
AdditionalIncludeDirectories="..\src;"
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Name="VCLinkerTool"
LinkLibraryDependencies="false"
AdditionalOptions=" /STACK:10000000 /machine:X86"
AdditionalDependencies="$(NOINHERIT) kernel32.lib user32.lib gdi32.lib winspool.lib shell32.lib ole32.lib oleaut32.lib uuid.lib comdlg32.lib advapi32.lib ..\lib\qhullcpp.lib ..\lib\qhullstatic_r.lib "
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ProgramDatabaseFile="..\bin\user_eg3.pdb"
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ImportLibrary="..\lib\user_eg3.lib"
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Name="VCXDCMakeTool"
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Name="VCBscMakeTool"
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Name="VCFxCopTool"
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Name="VCAppVerifierTool"
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Name="VCWebDeploymentTool"
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Name="VCPostBuildEventTool"
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Name="MinSizeRel|Win32"
OutputDirectory="MinSizeRel"
IntermediateDirectory="user_eg3.dir\MinSizeRel"
ConfigurationType="1"
UseOfMFC="0"
ATLMinimizesCRunTimeLibraryUsage="false"
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MkTypLibCompatible="false"
TargetEnvironment="1"
GenerateStublessProxies="true"
TypeLibraryName="$(InputName).tlb"
OutputDirectory="$(IntDir)"
HeaderFileName="$(InputName).h"
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InterfaceIdentifierFileName="$(InputName)_i.c"
ProxyFileName="$(InputName)_p.c"
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<Tool
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AdditionalOptions=" /Zm1000"
Optimization="1"
InlineFunctionExpansion="1"
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RuntimeLibrary="2"
RuntimeTypeInfo="false"
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ProgramDataBaseFileName="..\bin\user_eg3.pdb"
WarningLevel="3"
CompileAs="2"
/>
<Tool
Name="VCManagedResourceCompilerTool"
/>
<Tool
Name="VCResourceCompilerTool"
PreprocessorDefinitions="WIN32;_WINDOWS;NDEBUG"
AdditionalIncludeDirectories="..\src;"
/>
<Tool
Name="VCPreLinkEventTool"
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Name="VCLinkerTool"
LinkLibraryDependencies="false"
AdditionalOptions=" /STACK:10000000 /machine:X86"
AdditionalDependencies="$(NOINHERIT) kernel32.lib user32.lib gdi32.lib winspool.lib shell32.lib ole32.lib oleaut32.lib uuid.lib comdlg32.lib advapi32.lib ..\lib\qhullcpp.lib ..\lib\qhullstatic_r.lib "
OutputFile="..\bin\user_eg3.exe"
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OutputDirectory="RelWithDebInfo"
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ProxyFileName="$(InputName)_p.c"
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AdditionalIncludeDirectories="..\src;"
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AdditionalOptions=" /STACK:10000000 /machine:X86 /debug"
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18
src/qhull/eg/Qhull-go.bat Normal file
View File

@@ -0,0 +1,18 @@
: Qhull-go.bat invoked as cmd.com from QHULL-GO
@echo off
echo.
echo ========= Qhull with rbox, qconvex, qdelaunay, qvoronoi, qhalf ============
echo.
echo Use arrow keys to repeat and edit commands.
echo.
echo Double-click window bar for full height, or
echo "right-click > Properties > Layout > Window Size > Height > 50 "
echo.
echo Type 'qconvex' for synopsis and examples.
echo.
echo =========
echo.
title Qhull
cd bin
%comspec%

229
src/qhull/eg/make-vcproj.sh Normal file
View File

@@ -0,0 +1,229 @@
#!/bin/bash
#
# make-vcproj.sh -- Make sln and vcproj files from CMakeLists.txt and qhull-all.pro
#
# CMake vcproj files includes absolute paths and does not handle 'd' annotatios for debug versions
# Remove CMake targets
# Change absolute paths to '../...'
# Append '_d' to debug products
# Write targets to '../lib/' and ../bin/'
#
# $Id: //main/2015/qhull/eg/make-vcproj.sh#4 $$Change: 2070 $
# $DateTime: 2016/01/18 22:45:12 $$Author: bbarber $
if [[ "$1" != "" && "$1" != "Win64" && "$1" != "sed-only" ]]; then
echo "eg/make-vcproj.sh [Win64] [sed-only]"
echo "Written for 'sed 4.0.7', 'Visual Studio 11 2012 Win64', and 'Visual Studio 8 2005'"
echo "Other variations are likely to fail"
exit
fi
if [[ "$1" == "Win64" ]]; then
if [[ "$2" != "" && "$2" != "sed-only" ]]; then
echo "working/make-vcproj.sh [Win64] [sed-only]"
exit
fi
win64=1
else
win64=0
fi
if [[ "$1" == "sed-only" || "$2" == "sed-only" ]]; then
echo Skip creating buildvc/ and buildqt/
else # Matches 'sed-only'
if [[ ! -f CMakeLists.txt || ! -f src/qhull-all.pro ]]; then
echo "Excute eg/make-vcproj.sh from qhull directory with CMakeLists.txt and src/qhull-all.pro"
exit
fi
echo "Set up build directories..."
if [[ ! -d build-prev ]]; then
echo "Backup previous build"
cp -r build build-prev && rm -rf build
fi
rm -rf buildvc buildqt
mkdir -p build
mkdir -p build/qhulltest
mkdir -p buildvc
mkdir -p buildqt
echo "Create vcproj files with cmake and qmake..."
if [[ $win64 -eq 1 ]]; then
echo Running -- cmake -G "Visual Studio 11 2012 Win64"
cd buildvc && cmake -G "Visual Studio 11 2012 Win64" .. && cmake ..
else
echo Running -- cmake -G "Visual Studio 8 2005"
cd buildvc && cmake -G "Visual Studio 8 2005" .. && cmake ..
fi
cd ..
cd buildqt && qmake -tp vc -r ../src/qhull-all.pro
cd ..
if [[ ! -f CMakeLists.txt ]]; then
echo "Missing CMakeLists.txt. Cannot run cmake"
exit
elif [[ (! -f buildvc/qhull.vcproj && ! -f buildvc/qhull.vcxproj) || (! -f buildqt/qhulltest/qhulltest.vcproj && ! -f buildqt/qhulltest/qhulltest.vcxproj) ]]; then
echo "qmake and cmake did not build vcproj or vcxproj files in buildvc/ and buildqt/"
exit
fi
echo
echo 'Create build/*.vcproj by converting absolute paths to relative paths'
echo Removes INSTALL/ALL_BUILD/ZERO_CHECK/RUN_TESTS projects
echo Turn off LinkIncremental and RuntimeTypeInfo
echo Add 'd' flags to debug lib/dll files...
echo 'Delete <file> CMake...</file> and other instances of CMake'
echo 'WARN: These sed replacements depend on how CMake creates vcproj or vcxproj files. It is likely to change.'
fi # Skipped if 'sed-only'
for f in buildvc/*.vc*proj buildqt/qhulltest/*.vc*proj; do
echo -n $f
if [[ ! ${f##*INSTALL*} || ! ${f##*ALL_BUILD*} || ! ${f##*ZERO_CHECK*} || ! ${f##*RUN_TESTS*} ]]; then
echo " removed"
continue
fi
if [[ $win64 -eq 1 ]]; then
ext=${f##*.}
base=${f#*\/}
base=${base%.*}
dest=build/$base-64.$ext
echo " => $dest"
# sed requires a blank or \ before address ranges
# sed requires a \/ for s|...|...| !
# the ConfigurationType clauses depend on Debug being first
sed -r \
-e ' /CustomBuild.*CMake/,/CustomBuild/ d' \
-e ' /ZERO_CHECK/,/ProjectReference/ d' \
-e ' />qhulltest<S/,/Project>/ s|[cC]:\\bash\\local\\qhull|..\\..|g' \
-e ' />qhulltest</,/Project>/ s|[cC]:\/bash\/local\/qhull|..\/..|g' \
-e 's|[cC]:\\bash\\local\\qhull|..|g' \
-e 's|[cC]:\/bash\/local\/qhull|..|g' \
-e '\|CMake| d' \
-e '\|VCWebServiceProxyGeneratorTool| d' \
-e 's/;CMAKE_INTDIR=[^;]*;/;/' \
-e 's/;[a-zA-Z]*\\([_a-z0-9]*\.lib[;<])/;..\\lib\\\1/g' \
-e ' /LinkIncremental/ s/true/false/' \
-e 's/buildvc/build/g' \
-e 's/buildqt/build/g' \
-e 's/c:\\qt\\[0-9]\.[0-9]\.[0-9]/\$(QTDIR)/g' \
-e 's|..\/build\/[a-zA-Z]*[\\/]([_a-z0-9]*.pdb)|..\/bin\/\1|g' \
-e 's|..\/build\/[a-zA-Z]*[\\/]([_a-z0-9]*.exe)|..\/bin\/\1|g' \
-e 's|..\/build\/[a-zA-Z]*[\\/]([_a-z0-9]*.lib)|..\/lib\/\1|g' \
-e 's|..\/build\/[a-zA-Z]*[\\/]([_a-z0-9]*.dll)|..\/bin\/\1|g' \
-e 's| [a-zA-Z]*[\\/]([_a-z0-9]*\.lib)| ..\\lib\\\1|g' \
-e 's/"([_a-z0-9]*.exe)/"..\\bin\\\1/g' \
-e ' /ConfigurationType>Application/,/ClInclude/ s/(OutDir.*\.\.)[\\a-zA-Z]*</\1\\bin\\</' \
-e ' /ConfigurationType>DynamicLibrary/,/ClInclude/ s/(OutDir.*\.\.)[\\a-zA-Z]*</\1\\bin\\</' \
-e ' /ConfigurationType>DynamicLibrary/,/ImportLibrary/ s/(ImportLibrary.*_[rp])\.lib</\1d.lib</' \
-e ' /ConfigurationType>DynamicLibrary/,/ImportLibrary/ s/(ImportLibrary.*[^d])\.lib</\1_d.lib</' \
-e ' /ConfigurationType>DynamicLibrary/,/TargetName.*Debug/ s/(TargetName.*_[pr])</\1d</' \
-e ' /ConfigurationType>DynamicLibrary/,/TargetName.*Debug/ s/(TargetName.*Debug.*[^d])</\1_d</' \
-e ' /ConfigurationType>DynamicLibrary/,/ProgramDataBaseFile/ s/(ProgramDataBaseFile.*_[pr])\.pdb/\1d.pdb/' \
-e ' /ConfigurationType>DynamicLibrary/,/ProgramDataBaseFile/ s/(ProgramDataBaseFile.*[^d])\.pdb/\1_d.pdb/' \
-e ' /ConfigurationType>StaticLibrary/,/ClInclude/ s/(OutDir.*\.\.)[\\a-zA-Z]*</\1\\lib\\</' \
-e ' /ConfigurationType>StaticLibrary/,/ImportLibrary/ s/(ImportLibrary.*_[rp])\.lib</\1d.lib</' \
-e ' /ConfigurationType>StaticLibrary/,/ImportLibrary/ s/(ImportLibrary.*[^d])\.lib</\1_d.lib</' \
-e ' /ConfigurationType>StaticLibrary/,/TargetName.*Debug/ s/(TargetName.*_[pr])</\1d</' \
-e ' /ConfigurationType>StaticLibrary/,/TargetName.*Debug/ s/(TargetName.*Debug.*[^d])</\1_d</' \
-e ' /ConfigurationType>StaticLibrary/,/ProgramDataBaseFile/ s/(ProgramDataBaseFile.*_[pr])\.pdb/\1d.pdb/' \
-e ' /ConfigurationType>StaticLibrary/,/ProgramDataBaseFile/ s/(ProgramDataBaseFile.*[^d])\.pdb/\1_d.pdb/' \
-e ' /ItemDefinitionGroup.*Debug/,/AdditionalDependencies/ s/(AdditionalDependencies.*_r)\.lib/\1d.lib/g' \
-e ' /ItemDefinitionGroup.*Debug/,/AdditionalDependencies/ s/(AdditionalDependencies.*qhull[a-z]*[^d])\.lib/\1_d.lib/g' \
-e ' /AdditionalDependencies/ s/;[a-zA-Z]*\\/;..\\lib\\/g' \
-e 's/[cC]:\\[qQ]t\\[qQt0-9.\\]*msvc[_0-9]*/\$(QTDIR)/g' \
-e 's/[cC]:\\[qQ]t\\[qQt0-9.\\]*/\$(QTDIR)\\..\\/g' \
-e 's/([|>])Win32/\1x64/' \
-e 's/machine:X86/machine:x64/' \
-e 's/\.vcxproj/-64.vcxproj/' \
$f | awk '/<File$/ && !SkipFirstFile,/<\/File>/{ next } /<Filter$/{SkipFirstFile=1} {print $0}' > $dest
else
dest=build/${f##*\/}
# sed requires a blank or \ before address ranges
sed -r -e 's|[cC]:\\bash\\local\\qhull|..|g' \
-e 's|[cC]:/bash/local/qhull|..|g' \
-e '\|CMake| d' \
-e '\|VCWebServiceProxyGeneratorTool| d' \
-e 's/;CMAKE_INTDIR=..quot;[A-Za-z]*..quot;//' \
-e 's/LinkIncremental="2"/LinkIncremental="1"/' \
-e 's/RuntimeLibrary[=]/RuntimeTypeInfo="false" RuntimeLibrary=/' \
-e 's/.*RuntimeTypeInfo."TRUE".*//' \
-e 's/buildvc/build/g' \
-e 's/buildqt/build/g' \
-e 's/\.\.\\\.\./../g' \
-e 's|\.\./\.\.|..|g' \
-e 's/c:\\qt\\[0-9]\.[0-9]\.[0-9]/\$(QTDIR)/g' \
-e 's|..\\build\\[a-zA-Z]*[\\/]([_a-z0-9]*.pdb)|..\\bin\\\1|g' \
-e 's|..\\build\\[a-zA-Z]*[\\/]([_a-z0-9]*.exe)|..\\bin\\\1|g' \
-e 's|..\\build\\[a-zA-Z]*[\\/]([_a-z0-9]*.lib)|..\\lib\\\1|g' \
-e 's|..\\build\\[a-zA-Z]*[\\/]([_a-z0-9]*.dll)|..\\bin\\\1|g' \
-e 's| [a-zA-Z]*[\\/]([_a-z0-9]*\.lib)| ..\\lib\\\1|g' \
-e 's/"([_a-z0-9]*.exe)/"..\\bin\\\1/g' \
-e ' /Name="Debug/,/OutputFile/ s/(OutputFile.*_[rp])\.(dll|lib)"/\1d.\2"/' \
-e ' /Name="Debug/,/OutputFile/ s/(OutputFile.*[^d])\.(dll|lib)"/\1_d.\2"/' \
-e ' /Name="Debug/,/ImportLibrary/ s/(ImportLibrary.*_[rp])\.lib"/\1d.lib"/' \
-e ' /Name="Debug/,/ImportLibrary/ s/(ImportLibrary.*[^d])\.lib"/\1_d.lib"/' \
-e ' /Name="Debug/,/AdditionalDependencies/ s/(AdditionalDependencies.*_[rp])\.lib/\1d.lib/' \
-e ' /Name="Debug/,/AdditionalDependencies/ s/(AdditionalDependencies.*qhull[a-z]*[^d])\.lib/\1_d.lib/' \
-e ' /Name="Debug/,/ProgramDatabaseFile/ s/(ProgramDatabaseFile.*_r)\.pdb/\1d.pdb/' \
-e ' /Name="Debug/,/ProgramDatabaseFile/ s/(ProgramDatabaseFile.*qhull[a-z]*[^d])\.pdb/\1_d.pdb/' \
-e 's/[cC]:\\Qt\\[0-9.]*/\$(QTDIR)/g' \
-e 's/\.vcxproj/-32.vcxproj/' \
$f | awk '/<File$/ && !SkipFirstFile,/<\/File>/{ next } /<Filter$/{SkipFirstFile=1} {print $0}' > $dest
fi
# grep -E '\.\.[\\/]|_[a-z]?d[^a-z]' $dest
done
echo
echo Create build/qhull.sln or build/qhull-64.sln from buildvc/qhull.sln
if [[ $win64 -eq 1 ]]; then
echo Create qhull-64.sln
sed -r \
-e '\|Project.*ALL_BUILD|,\|EndProject$| d' \
-e '\|Project.*INSTALL|,\|EndProject$| d' \
-e '\|Project.*ZERO_CHECK|,\|EndProject$| d' \
-e '\|Project.*RUN_TESTS|,\|EndProject$| d' \
-e '\|ProjectDependencies|,\| = | s/^.* = \{.*$//' \
-e 's/\.vcxproj/-64.vcxproj/' \
buildvc/qhull.sln >build/qhull-64.sln
echo Create qhull-32.sln from qhull-64 with 32 GUIDs
# Need to keep the original GUIDs. Otherwise get -- can't locate project ''
sed -r \
-e 's/-64\.vcxproj/-32.vcxproj/' \
-e 's/([|>])x64/\1Win32/g' \
build/qhull-64.sln >build/qhull-32.sln
echo Create *-32.vcxproj with 32 GUIDs
for f in build/*-64.vcxproj build/qhulltest/*-64.vcxproj; do
dest=${f%64.vcxproj}32.vcxproj
sed -r \
-e 's/([|>])x64/\1Win32/' \
-e 's/machine:x64/machine:X86/' \
$f >$dest
done
echo Convert vcxproj/sln files to DOS format
for f in build/*.vcxproj build/*-32.sln build/*-64.sln; do
u2d $f
done
else
sed -e '\|Project.*ALL_BUILD|,\|EndProject$| d' \
-e '\|Project.*INSTALL|,\|EndProject$| d' \
-e '\|Project.*ZERO_CHECK|,\|EndProject$| d' \
-e '\|Project.*RUN_TESTS|,\|EndProject$| d' \
buildvc/qhull.sln >build/qhull.sln
echo Convert vcproj/sln files to DOS format
for f in build/*.vcproj build/*.sln; do
u2d $f
done
fi
echo
echo 'Add qhulltest.vcproj to qhull.sln'
echo ' Open qhull.sln with DevStudio'
echo ' Add build/qhulltest/qhulltest.vcproj or qhulltest-64.vcxproj'
echo ' Add dependencies on qhullcpp and qhullstatic_r'
echo ' Remove qhulltest via Configuration Manager from Release,Debug,etc. Qt is optional'
echo
echo 'Update Perforce for build/...vcproj, otherwise qhull-zip.sh will revert the files'

77
src/qhull/eg/q_eg Executable file
View File

@@ -0,0 +1,77 @@
#!/bin/sh
# writes examples to eg/
# see html/qh_eg.htm
if ! qconvex >/dev/null 2>&1; then
if [ ! -d bin ]; then
echo Run eg/q_eg from the Qhull directory
exit
fi
if [ ! -e bin/qconvex -a ! -e bin/qconvex.exe ]; then
echo 'Build qhull first. qconvex is missing from bin/ directory and $PATH'
exit
fi
if ! qconvex >/dev/null 2>&1; then
PATH=$PWD/bin:$PATH
fi
fi
mkdir -p eg
echo ==============================
echo ========= eg/q_eg ============
echo == Create geomview examples ==
echo ==============================
echo
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 -n +3 >>eg/eg.data.17
rbox 6 r s D2 B0.2 | tail -n +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 preceding should report flipped and concave facets== >/dev/null

52
src/qhull/eg/q_egtest Executable file
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@@ -0,0 +1,52 @@
#!/bin/sh
# writes examples to eg/
if ! qconvex >/dev/null 2>&1; then
if [ ! -d bin ]; then
echo Run eg/q_eg from the Qhull directory
exit
fi
if [ ! -e bin/qconvex -a ! -e bin/qconvex.exe ]; then
echo 'Build qhull first. qconvex is missing from bin/ directory and $PATH'
exit
fi
if ! qconvex >/dev/null 2>&1; then
PATH=$PWD/bin:$PATH
fi
fi
mkdir -p eg
echo ==============================
echo ========= eg/q_egtest ========
echo == Create geomview tests =====
echo ==============================
echo
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

425
src/qhull/eg/q_test Executable file
View File

@@ -0,0 +1,425 @@
#!/bin/sh
#
# NOTE: all tests duplicated in q_test.bat
if ! qconvex >/dev/null 2>&1; then
if [ ! -d bin ]; then
echo Run eg/q_test from the Qhull directory
exit
fi
if [ ! -e bin/qconvex -a ! -e bin/qconvex.exe ]; then
echo 'Build qhull first. qconvex is missing from bin/ directory and $PATH'
exit
fi
if ! qconvex >/dev/null 2>&1; then
PATH=$PWD/bin:$PATH
fi
fi
if ! user_eg >/dev/null; then
echo user_eg failed to run. It uses the shared qhull library
echo 'On Linux, export LD_LIBRARY_PATH=$PWD/lib:$LD_LIBRARY_PATH'
fi
echo ==============================
echo ========= eg/q_test ==========
echo == Check qhull programs ======
echo ==============================
echo
echo "qhull => $(qhull -V)"
echo "qconvex => $(qconvex -V)"
echo "qvoronoi => $(qconvex -V)"
echo "qdelaunay => $(qdelaunay -V)"
echo "qhalf => $(qhalf -V)"
echo
echo ==============================
echo == check user_eg, user_eg2, and user_eg3
echo == errors if 'user_eg' and 'user_eg2' not found
echo ==============================
set -v
user_eg "QR1 p n Qt" "v p" Fp
user_eg2 "QR1 p" "v p" Fp
user_eg3 rbox "10 D2" "2 D2" qhull "p"
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 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 B10 D2 C2,1E-13,1
rbox 3 z B10 D2
rbox 4 L2 r D2
rbox 4 L2 r D2
rbox 8 L2 D2 C1,1E-13,2
rbox 4 L4 r D3
rbox 4 L4 s D5 W1e-3
rbox 4 L4 s D5 W1e-3 C1,1E-12
rbox y
rbox 10 M3,4
rbox 10 M3,4 C1,1E-14
rbox 27 M1,0,1
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 -n -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
echo === this may generate an error e.g., t1263080158 ${d:-`date`}
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
rbox L100 10000 D4 s C1,1e-13 t2 | qhull
rbox L100 10000 D4 s C1,1e-13 t2 | qhull Q12
rbox 50 C1,1E-13 t1447644703 | qhull d
rbox 50 C1,1E-13 t1447644703 | qhull d Q12
qhull
qhull .
qhull -
rbox
cat html/qhull.txt html/rbox.txt
# end of q_test

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echo Run q_test for Windows from the bin/ directory. >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 'user_eg3 rbox "10 D2" "2 D2" qhull "p"' >>q_test.x
user_eg3 rbox "10 D2" "2 D2" qhull "p" >>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 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

317
src/qhull/eg/qhull-zip.sh Normal file
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@@ -0,0 +1,317 @@
#!/bin/sh
#
# qhull-zip.sh version -- Make zip and tgz files for Qhull release
#
# wzzip from http://www.winzip.com/wzcline.htm
# can not use path with $zip_file
# odd error messages if can't locate directory
#
# $Id: //main/2015/qhull/eg/qhull-zip.sh#16 $$Change: 2071 $
# $DateTime: 2016/01/18 23:12:45 $$Author: bbarber $
if [[ $# -ne 3 ]]; then
echo 'Missing date stamp, e.g., qhull-zip.sh 2015 2015.2 7.2.0'
exit
fi
versionyear=$1
version=$2
versionunix=$3
err_program=qhull-zip
err_log=/var/tmp/qhull-zip.log
[[ -e $HOME/bash/etc/road-script.sh ]] && source $HOME/bash/etc/road-script.sh \
|| source /etc/road-script.sh
check_err_log $LINENO "$err_log"
check_err_log $LINENO "$err_step_log"
log_step $LINENO "Logging to $err_log\n... and $err_step_log"
log_note $LINENO "Find Qhull directory"
if [[ ! -d qhull/eg && ! -d ../qhull/eg && -d ../../qhull/eg ]]; then
exit_err $LINENO "qhull/eg directory not found at or above $PWD"
fi
if [[ ! -d qhull/eg ]]; then
if [[ -d ../qhull/eg ]]; then
cd ..
else
cd ../.. # Tested above
fi
fi
root_dir=$(pwd)
TEMP_DIR="$TMP/qhull-zip-$(ro_today2)"
TEMP_FILE="$TMP/qhull-zip-$(ro_today2).txt"
qhull_zip_file=qhull-$version.zip # no path or spaces
qhull_tgz_file=qhull-$versionyear-src-$versionunix.tgz
qhullmd5_file=qhull-$version.md5sum
exit_if_fail $LINENO "rm -f $qhull_zip_file $qhull_tgz_file $qhullmd5_file"
#############################
log_step $LINENO "Check files"
#############################
exit_if_fail $LINENO "cd qhull"
if ! grep "if 0 .* QHULL_CRTDBG" src/libqhull/user.h >/dev/null; then
exit_err $LINENO "QHULL_CRTDBG is defined in src/libqhull/user.h"
elif ! grep "if 0 .* QHULL_CRTDBG" src/libqhull_r/user_r.h >/dev/null; then
exit_err $LINENO "QHULL_CRTDBG is defined in src/libqhull_r/user_r.h"
elif ! grep "^#define qh_QHpointer 0" src/libqhull/user.h >/dev/null; then
exit_err $LINENO "qh_QHpointer is defined in src/libqhull/user.h"
fi
if (od -a Makefile src/libqhull/Makefile src/libqhull_r/Makefile build/*.in html/*.man eg/*.sh eg/q_eg eg/q_egtest eg/q_test | grep cr >/dev/null); then
exit_err $LINENO "A Makefile contains DOS line endings (od -a Makefile | grep cr)"
fi
NOT_OK=$(grep -h "^ " Makefile src/libqhull/Makefile src/libqhull_r/Makefile | grep -vE '^[ \t]+[$()a-zA-Z_/]+\.[oh]|bin/testqset_r qtest')
if [[ -n "$NOT_OK" ]]; then
exit_err $LINENO "A Makefile contains a leading space instead of tabs:\n$NOT_OK"
fi
TXTFILES=$(find *.diz *.htm *.txt html/ src/ working/qhull-news.html -type f -name '*.c' -o -name '*.cpp' -o -name '*.def' -o -name '*.diz' -o -name '*.h' -o -name '*.htm*' -o -name '*.txt' -o -name '*.pri' -o -name '*.pro' -o -name '*.txt' -o -name '*.txt' -o -name '*.xml')
NOT_OK=$(for f in $TXTFILES; do if (od -a $f | grep '[^r0-9 ] *nl' >/dev/null); then echo $f; fi; done)
if [[ -n "$NOT_OK" ]]; then
exit_err $LINENO "Text files with Unix line endings:\n$NOT_OK\nu2d *.diz *.htm *.txt html/*.txt html/*.htm html/*.xml src/*.pr* src/*.txt src/*/*.c;\nu2d src/*/*.cpp src/*/*.def src/*/*.h src/*/*.htm src/*/*.pro src/*/*.txt working/qhull-news.html"
fi
exit_if_fail $LINENO "cd .."
#############################
log_step $LINENO "Check environment"
#############################
[[ $(type -p md5sum) ]] || exit_err $LINENO "md5sum is missing"
[[ $(cp --help || grep '[-]-parents') ]] || exit_err $LINENO "cp does not have --parents option"
#############################
log_step $LINENO "Define functions"
#############################
function check_zip_file #zip_file
{
local zip_file=$1
local HERE=$(ro_here)
log_note $HERE "Check $zip_file"
ls -l $zip_file >>$err_log
exit_if_err $HERE "Did not create $zip_file"
wzunzip -ybc -t $zip_file | grep -E -v -e '( OK|Zip)' >>$err_log
exit_if_err $HERE "Error while checking $zip_file"
}
function check_tgz_file #tgz_file
{
local tgz_file=$1
local HERE=$(ro_here)
log_note $HERE "Check $tgz_file"
ls -l $tgz_file >>$err_log
exit_if_err $HERE "Did not create $tgz_file"
tar -tzf $tgz_file >/dev/null 2>>$err_log
exit_if_err $HERE "Can not extract -- tar -tzf $tgz_file"
}
function convert_to_unix #dir $qhull_2ufiles -- convert files to Unix, preserving modtime from $root_dir
{
local temp_dir=$1
local HERE=$(ro_here)
log_note $HERE "Convert files to unix format in $1"
for f in $(find $temp_dir -type f | grep -E '^([^.]*|.*\.(ac|am|bashrc|c|cfg|cpp|css|d|dpatch|h|htm|html|man|pl|pri|pro|profile|sh|sql|termcap|txt|xml|xsd|xsl))$'); do
exit_if_fail $HERE "d2u '$f' && touch -r '$root_dir/${f#$temp_dir/}' '$f'"
done
for f in $qhull_2ufiles; do
exit_if_fail $HERE "d2u '$temp_dir/$f' && touch -r '$root_dir/$f' '$temp_dir/$f'"
done
}
function create_md5sum #md5_file -- create md5sum of current directory
{
local md5_file=$1
local HERE=$(ro_here)
log_step $HERE "Compute $md5_file"
exit_if_fail $HERE "rm -f $md5_file"
find . -type f | sed 's|^\./||' | sort | xargs md5sum >>$md5_file
exit_if_err $HERE "md5sum failed"
log_note $HERE "$(md5sum $md5_file)"
}
#############################
log_step $LINENO "Configure $0 for $(pwd)/qhull"
#############################
md5_zip_file=qhull-$version.zip.md5sum
md5_tgz_file=qhull-$versionyear-src-$versionunix.tgz.md5sum
# recursive
qhull_dirs="qhull/CMakeModules qhull/eg qhull/html qhull/src"
qhull_files="qhull/build/*.sln qhull/build/*.vcproj qhull/build/qhulltest/*.vcproj \
qhull/build/*.vcxproj qhull/build/qhulltest/*.vcxproj \
qhull/Announce.txt qhull/CMakeLists.txt qhull/COPYING.txt \
qhull/File_id.diz qhull/QHULL-GO.lnk qhull/README.txt \
qhull/REGISTER.txt qhull/index.htm qhull/Makefile \
qhull/bin/qconvex.exe qhull/bin/qdelaunay.exe qhull/bin/qhalf.exe \
qhull/bin/qhull.exe qhull/bin/qhull_r.dll qhull/bin/qvoronoi.exe \
qhull/bin/rbox.exe qhull/bin/user_eg.exe qhull/bin/user_eg2.exe \
qhull/bin/testqset_r.exe \
qhull/bin/user_eg3.exe qhull/bin/testqset.exe qhull/bin/msvcr80.dll"
qhull_ufiles="$qhull_dirs qhull/build/*.sln qhull/build/*.vcproj \
qhull/Announce.txt qhull/CMakeLists.txt qhull/COPYING.txt \
qhull/File_id.diz qhull/QHULL-GO.lnk qhull/README.txt \
qhull/REGISTER.txt qhull/index.htm qhull/Makefile"
qhull_d2ufiles="Makefile src/libqhull/Makefile src/libqhull_r/Makefile \
src/*/DEPRECATED.txt src/*/*.pro src/*/*.htm html/*.htm html/*.txt \
src/libqhull/MBorland eg/q_eg eg/q_egtest eg/q_test "
#############################
log_step $LINENO "Clean distribution directories"
#############################
rm -r qhull/build/*
p4 sync -f qhull/build/...
exit_if_err $LINENO "Can not 'p4 sync -f qhull.sln *.vcproj'"
rm qhull/build/user_egp.vcproj qhull/build/qhullp.vcproj
cd qhull && make clean
exit_if_err $LINENO "Can not 'make clean'"
cd ..
# Includes many files from 'cleanall' (Makefile)
rm -f qhull/src/qhull-all.pro.user* qhull/src/libqhull/BCC32tmp.cfg
rm -f qhull/eg/eg.*
rm -f qhull/bin/qhulltest.exe qhull/bin/qhulltest qhull/bin/qhullp.exe qhull/bin/user_egp.exe
rm -f qhull/src/libqhull/*.exe qhull/src/libqhull/*.a
rm -f qhull/src/libqhull_r/*.exe qhull/src/libqhull_r/*.a
rm -f qhull/src/libqhull/qconvex.c qhull/src/libqhull/unix.c
rm -f qhull/src/libqhull/qdelaun.c qhull/src/libqhull/qhalf.c
rm -f qhull/src/libqhull/qvoronoi.c qhull/src/libqhull/rbox.c
rm -f qhull/src/libqhull/user_eg.c qhull/src/libqhull/user_eg2.c
rm -f qhull/src/libqhull/testqset.c
rm -f qhull/src/libqhull_r/qconvex_r.c qhull/src/libqhull_r/unix_r.c
rm -f qhull/src/libqhull_r/qdelaun_r.c qhull/src/libqhull_r/qhalf_r.c
rm -f qhull/src/libqhull_r/qvoronoi_r.c qhull/src/libqhull_r/rbox_r.c
rm -f qhull/src/libqhull_r/user_eg_r.c qhull/src/libqhull_r/user_eg2_r.c
rm -f qhull/src/libqhull_r/testqset_r.c
find qhull/ -type f -name x -o -name 'x.*' -o -name '*.x' | xargs -r rm
set noglob
if [[ -e /bin/msysinfo && $(type -p wzzip) && $(type -p wzunzip) ]]; then
#############################
log_step $LINENO "Build zip directory, $TEMP_DIR/qhull"
#############################
ls -l $qhull_files $qhull_dirs >>$err_log
exit_if_err $LINENO "Missing files for zip directory. Release build only"
log_note $LINENO "Copy \$qhull_files \$qhull_dirs to $TEMP_DIR/qhull"
exit_if_fail $LINENO "rm -rf $TEMP_DIR && mkdir $TEMP_DIR"
exit_if_fail $LINENO "cp -r -p --parents $qhull_files $qhull_dirs $TEMP_DIR"
#############################
log_step $LINENO "Write md5sum to $md5_tgz_file"
#############################
exit_if_fail $LINENO "pushd $TEMP_DIR/qhull"
create_md5sum $md5_zip_file
exit_if_fail $LINENO "cp -p $md5_zip_file $root_dir"
#############################
log_step $LINENO "Write $qhull_zip_file"
#############################
log_note $LINENO "Write \$qhull_files to $qhull_zip_file"
exit_if_fail $LINENO "cd .. && mv qhull qhull-$version && md5sum qhull-$version/$md5_zip_file >>$root_dir/$qhullmd5_file"
wzzip -P -r -u $qhull_zip_file qhull-$version >>$err_log
exit_if_err $LINENO "wzzip does not exist or error while zipping files"
check_zip_file $qhull_zip_file
exit_if_fail $LINENO "popd"
exit_if_fail $LINENO "mv $TEMP_DIR/$qhull_zip_file ."
fi
#############################
log_step $LINENO "Build tgz directory, $TEMP_DIR/qhull"
#############################
log_note $LINENO "Archive these files as $qhull_tgz_file"
ls -l $qhull_ufiles >>$err_log
exit_if_err $LINENO "Missing files for tgz"
exit_if_fail $LINENO "rm -rf $TEMP_DIR && mkdir -p $TEMP_DIR"
exit_if_fail $LINENO "cp -r -p --parents $qhull_ufiles $TEMP_DIR"
if [[ $IS_WINDOWS && $(type -p d2u) ]]; then
log_step $LINENO "Convert to Unix line endings"
convert_to_unix "$TEMP_DIR"
fi
#############################
log_step $LINENO "Write md5sum to $md5_tgz_file"
#############################
exit_if_fail $LINENO "pushd $TEMP_DIR && cd qhull"
create_md5sum $md5_tgz_file
exit_if_fail $LINENO "cp -p $md5_tgz_file $root_dir"
exit_if_fail $LINENO "cd .. && mv qhull qhull-$version && md5sum qhull-$version/$md5_tgz_file >>$root_dir/$qhullmd5_file"
#############################
log_step $LINENO "Write $qhull_tgz_file"
#############################
exit_if_fail $LINENO "tar -zcf $root_dir/$qhull_tgz_file * && popd"
check_tgz_file $qhull_tgz_file
log_note $LINENO "md5sum of zip and tgz files"
for f in $qhull_zip_file $qhull_tgz_file; do
if [[ -r $f ]]; then
exit_if_fail $LINENO "md5sum $f >>$qhullmd5_file"
fi
done
#############################
log_step $LINENO "Extract zip and tgz files to ($TEMP_DIR)"
#############################
exit_if_fail $LINENO "rm -rf $TEMP_DIR"
if [[ -r $root_dir/$qhull_zip_file ]]; then
exit_if_fail $LINENO "mkdir -p $TEMP_DIR/zip && cd $TEMP_DIR/zip"
exit_if_fail $LINENO "wzunzip -yb -d $root_dir/$qhull_zip_file"
log_step $LINENO "Search for date stamps to zip/Dates.txt"
find . -type f | grep -v '/bin/' | xargs grep '\-20' | grep -v -E '(page=|ISBN|sql-2005|utility-2000|written 2002-2003|tail -n -20|Spinellis|WEBSIDESTORY|D:06-5-2007|server-2005)' >Dates.txt
find . -type f | grep -v '/bin/' | xargs grep -i 'qhull *20' >>Dates.txt
find . -type f | grep -v '/bin/' | xargs grep -E 'SO=|SO |VERSION' >>Dates.txt
fi
if [[ -r $root_dir/$qhull_tgz_file ]]; then
exit_if_fail $LINENO "mkdir -p $TEMP_DIR/tgz && cd $TEMP_DIR/tgz"
exit_if_fail $LINENO "tar -zxf $root_dir/$qhull_tgz_file"
fi
#############################
log_step $LINENO "====================================================================="
log_step $LINENO "Check for 18 projects in Release mode, including qhulltest"
log_step $LINENO "Check build dependencies for programs."
log_step $LINENO "Test unix compile"
log_step $LINENO " cd .. && scp $qhull_tgz_file qhull@qhull.org:"
log_step $LINENO " tar zxf $qhull_tgz_file && cd qhull-$version && make >../make.x 2>&1"
log_step $LINENO " make test"
log_step $LINENO "Test qhull and compare to q_test-ok.txt"
log_step $LINENO " cd $TEMP_DIR/zip/qhull* && make testall >/c/bash/local/qhull/eg/q_test.x 2>&1"
log_step $LINENO "Build and test testqhull. Compare to qhulltest-ok.txt"
log_step $LINENO " cd /c/bash/local/qhull && bin/qhulltest --all >eg/qhulltest.x 2>&1"
log_step $LINENO "Build qhull with gcc"
log_step $LINENO " cd $TEMP_DIR/zip/qhull* && make SO=dll"
log_step $LINENO "Test qhull and compare to q_test-ok.txt"
log_step $LINENO " cp -p lib/libqhull*.dll bin && make testall >/c/bash/local/qhull/eg/q_test-make.x 2>&1"
log_step $LINENO "Build and test libqhull"
log_step $LINENO " cd src/libqhull && make && cp *.exe ../../bin && cd ../.. && make test && ls -l bin/qhull.exe"
log_step $LINENO " make testall >/c/bash/local/qhull/eg/q_test-libqhull.x 2>&1"
log_step $LINENO "Build and test libqhull_r"
log_step $LINENO " cd src/libqhull_r && make && cp *.exe ../../bin && cd ../.. && make test && ls -l bin/qhull.exe"
log_step $LINENO " make testall >/c/bash/local/qhull/eg/q_test-libqhull_r.x 2>&1"
log_step $LINENO "Compare previous zip release, Dates.txt, and md5sum. Check for virus."
log_step $LINENO "Compare zip and tgz for CRLF vs LF"
log_step $LINENO "Search xml files for UNDEFINED. Check page links"
log_step $LINENO "Extract zip to Qhull/ and compare directories"
log_step $LINENO "Copy tarballs to qhull.org"
log_step $LINENO " scp qhull-2015*x qhull@qhull.org:web/download/"
log_step $LINENO "Finished successfully"
#############################

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<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>
&#149; <a href="qh-quick.htm#options">Options</a>
&#149; <a href="qh-opto.htm#output">Output</a>
&#149; <a href="qh-optf.htm#format">Formats</a>
&#149; <a href="qh-optg.htm#geomview">Geomview</a>
&#149; <a href="qh-optp.htm#print">Print</a>
&#149; <a href="qh-optq.htm#qhull">Qhull</a>
&#149; <a href="qh-optc.htm#prec">Precision</a>
&#149; <a href="qh-optt.htm#trace">Trace</a>
&#149; <a href="../src/libqhull_r/index.htm">Functions</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.cs.mcgill.ca/~fukuda/soft/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. Each program includes instructions and examples.
<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, Arlington, MA</i></p>
<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
<hr>
<h2><a href="#TOP">&#187;</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 &#149; <a
href="#input">in</a>put &#149; <a href="#output">ou</a>tput
&#149; <a href="#algorithm">al</a>gorithm &#149; <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="qh-eg.htm">Examples</a> of Qhull</li>
</ul>
<p>
<li><a href=qh-quick.htm#programs>Qhull programs</a>, with instructions and examples
<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><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="#geomview">Geomview</a>, Qhull's graphical viewer</li>
<ul>
<li><a href="#geomview-install">Installing Geomview</a></li>
<li><a href="#geomview-use">Using Geomview</a></li>
<li><a href="#geomview-win">Building Geomview for Windows</a></li>
</ul>
<p>
<li><a href="qh-code.htm">Qhull internals</a><ul>
<li><a href="qh-code.htm#reentrant">Reentrant</a> Qhull</li>
<li><a href="qh-code.htm#convert">How to convert</a> code to reentrant Qhull</li>
<li><a href="qh-code.htm#64bit">Qhull</a> on 64-bit computers</li>
<li><a href="qh-code.htm#cpp">Calling</a> Qhull
from C++ programs</li>
<li><a href="qh-code.htm#library">Calling</a> Qhull
from C programs</li>
<li><a href="qh-code.htm#performance">Performance</a>
of Qhull</li>
<li><a href="qh-code.htm#enhance">Enhancements</a> to
Qhull</li>
<li><a href="../src/libqhull_r/index.htm">Reentrant</a> Qhull functions, macros, and
data structures </li>
<li><a href="../src/libqhull/index.htm">Qhull</a> functions, macros, and
data structures </li>
</ul>
</li>
<p>
<li>Related URLs
<ul>
<li><a href="news:comp.graphics.algorithms">Newsgroup</a>:
comp.graphics.algorithms
<li><a
href="http://www.faqs.org/faqs/graphics/algorithms-faq/">FAQ</a> for computer graphics algorithms and
Exaflop's <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.cs.mcgill.ca/~fukuda/soft/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="#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">&#187;</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-code.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>[2016] A newly discovered, bad case for Qhull is multiple, nearly incident points within a 10^-13 ball of 3-d and higher
Delaunay triangulations (input sites in the unit cube). Nearly incident points within substantially
smaller or larger balls are OK. Error QH6271 is reported if a problem occurs. A future release of Qhull
will handle this case. For more information, see "Nearly coincident points on an edge" in <a href="../html/qh-impre.htm#limit">Limitations of merged facets</a>
<p>If you need a short code for convex hull, Delaunay
triangulation, or Voronoi volumes consider Clarkson's <a
href="http://www.netlib.org/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="http://www.netlib.org/voronoi/">http://www.netlib.org/voronoi/</a>.
<p>If your input is in general position (i.e., no coplanar or colinear points),
<li><a href="https://github.com/tomilov/quickhull/blob/master/include/quickhull.hpp">Tomilov's quickhull.hpp</a> (<a href"http://habrahabr.ru/post/245221/"documentation-ru</a/>)
or Qhull <a
href="http://www.qhull.org/download">version
1.0</a> may meet your needs. Both programs detect precision problems,
but do not handle them.</p>
<p><a href=http://www.cgal.org>CGAL</a> is a library of efficient and reliable
geometric algorithms. It uses C++ templates and the Boost library to produce dimension-specific
code. This allows more efficient use of memory than Qhull's general-dimension
code. CGAL simulates arbitrary precision while Qhull handles round-off error
with thick facets. Compare the two approaches with <a href="http://doc.cgal.org/latest/Manual/devman_robustness.html">Robustness Issues in CGAL</a>,
and <a href+"qh-impre.htm">Imprecision in Qhull</a>.
<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.robertschneiders.de/meshgeneration/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">&#187;</a><a name="description">Description of
Qhull </a></h2>
<blockquote>
<h3><a href="#TOC">&#187;</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 &lt;= [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
&quot;thick&quot; 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">&#187;</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">&#187;</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 command window with <tt>doskey</tt>
and a window scroller (e.g., <tt>peruse</tt>). </p>
</blockquote>
<h3><a href="#TOC">&#187;</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-code.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">&#187;</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 &amp; Shamos <a
href="#pre-sha85">'85</a>]. It is similar to the randomized
algorithms of Clarkson and others [Clarkson &amp; 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">&#187;</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 &lt;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/libqhull/qh-poly.htm">polyhedron operations</a> for further
design documentation. </p>
</blockquote>
<h3><a href="#TOC">&#187;</a>Imprecision in Qhull</h3>
<blockquote>
<p>See <a href="qh-impre.htm">Imprecision in Qhull</a> and <a href="qh-impre.htm#joggle">Merged facets or joggled input</a></p>
</blockquote>
<h3><a href="#TOC">&#187;</a>Examples of Qhull</h3>
<blockquote>
<p>See <a href="qh-eg.htm">Examples of Qhull</a>. Most of these examples require <a href="#geomview">Geomview</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">&#187;</a>Options for using Qhull </h2>
<blockquote>
<p>See <a href="qh-quick.htm#options">Options</a>.</p>
</blockquote>
<h2><a href="#TOC">&#187;</a>Qhull internals </h2>
<blockquote>
<p>See <a href="qh-code.htm">Internals</a>.</p>
</blockquote>
<h2><a href="#TOC">&#187;</a><a name="geomview">Geomview, Qhull's
graphical viewer</a></h2>
<blockquote>
<p><a href="http://www.geomview.org">Geomview</a>
is an interactive geometry viewing program.
Geomview provides a good visualization of Qhull's 2-d and 3-d results.
<p>Qhull includes <a href="qh-eg.htm">Examples of Qhull</a> that may be viewed with Geomview.
<p>Geomview can help visulalize a 3-d Delaunay triangulation or the surface of a 4-d convex hull,
Use option '<a href="qh-optq.htm#QVn">QVn</a>' to select the 3-D facets adjacent to a vertex.
<p>You may use Geomview to create movies that animate your objects (c.f., <a href="http://www.geomview.org/FAQ/answers.shtml#mpeg">How can I create a video animation?</a>).
Geomview helped create the <a href="http://www.geom.uiuc.edu/video/">mathematical videos</a> "Not Knot", "Outside In", and "The Shape of Space" from the Geometry Center.
<h3><a href="#TOC">&#187;</a><a name="geomview-install">Installing Geomview</a></h3>
<blockquote>
<p>Geomview is an <a href=http://sourceforge.net/projects/geomview>open source project</a>
under SourceForge.
<p>
For build instructions see
<a href="http://www.geomview.org/download/">Downloading Geomview</a>.
Geomview builds under Linux, Unix, Macintosh OS X, and Windows.
<p>Geomview has <a href="https://packages.debian.org/search?keywords=geomview">installable packages</a> for Debian and Ubuntu.
The OS X build needs Xcode, an X11 SDK, and Lesstif or Motif.
The Windows build uses Cygwin (see <a href="#geomview-win">Building Geomview</a> below for instructions).
<p>If using Xforms (e.g., for Geomview's <a href="http://www.geomview.org/docs/html/Modules.html">External Modules</a>), install the 'libXpm-devel' package from cygwin and move the xforms directory into your geomview directory, e.g.,<br><tt>mv xforms-1.2.4 geomview-1.9.5/xforms</tt>
<p>Geomview's <a href="http://www.geom.uiuc.edu/software/geomview/docs/NDview/manpagehelp.html">ndview<a/> provides multiple views into 4-d and higher objects.
This module is out-of-date (<a href="http://sourceforge.net/p/geomview/mailman/message/2004152/">geomview-users: 4dview</a>).
Download NDview-sgi.tar.Z at <a href="ftp://www.geom.uiuc.edu/pub/software/geomview/newpieces/sgi">newpieces</a> and 4dview at <a href="https://stuff.mit.edu/afs/sipb/project/3d/arch/sgi_62/lib/Geomview/modules/">Geomview/modules</a>.
</blockquote>
<h3><a href="#TOC">&#187;</a><a name="geomview-use">Using Geomview</a></h3>
<blockquote>
<p>Use Geomview to view <a href="qh-eg.htm">Examples of Qhull</a>. You can spin the convex hull, fly a camera through its facets,
and see how Qhull produces thick facets in response to round-off error.
<p>Follow these instructions to view 'eg,01.cube' from Examples of Qhull
<ol>
<li>Launch an XTerm command shell
<ul>
<li>If needed, start the X terminal server, Use 'xinit' or 'startx' in /usr/X11R6/bin<br><tt>xinit -- -multiwindow -clipboard</tt><br><tt>startx</tt>
<li>Start an XTerm command shell. In Windows, click the Cygwin/bash icon on your desktop.
<li>Set the DISPLAY variable, e.g.,<br><tt>export DISPLAY=:0</tt><br><tt>export DISPLAY=:0 >>~/.bashenv</tt>
</ul>
<li>Use Qhull's <a href="qh-optg.htm">Geomview options</a> to create a geomview object
<ul>
<li><tt>rbox c D3 | qconvex G >eg.01.cube</tt>
<li>On windows, convert the output to Unix text format with 'd2u'<br><tt>rbox c D3 | qconvex G | d2u >eg.01.cube</tt><br><tt>d2u eg.*</tt>
</ul>
<li>Run Geomview
<ul>
<li>Start Geomview with your example<br><tt>./geomview eg.01.cube</tt>
<li>Follow the instructions in <a href="http://www.geomview.org/docs/html/Tutorial.html">Gemoview Tutorial</a>
<li>Geomview creates the <i>Geomview control panel</i> with Targets and External Module, the <i>Geomview toolbar</i> with buttons for controlling Geomview, and the <i>Geomview camera window</i> showing a cube.
<li>Clear the camera window by selecting your object in the Targets list and 'Edit > Delete' or 'dd'
<li>Load the <i>Geomview files panel</i>. Select 'Open' in the 'File' menu.
<li>Set 'Filter' in the files panel to your example directory followed by '/*' (e.g., '/usr/local/qhull-2015.2/eg/*')
<li>Click 'Filter' in the files panel to view your examples in the 'Files' list.
<li>Load another example into the camera window by selecting it and clicking 'OK'.
<li>Review the instructions for <a href="http://www.geomview.org/docs/html/Interaction.html">Interacting with Geomview</a>
<li>When viewing multiple objects at once, you may want to turn off normalization. In the 'Inspect > Apperance' control panel, set 'Normalize' to 'None'.
</ul>
</ol>
<p>Geomview defines GCL (a textual API for controlling Geomview) and OOGL (a textual file format for defining objects).
<ul>
<li>To control Geomview, you may use any program that reads and writes from stdin and stdout. For example, it could report Qhull's information about a vertex identified by a double-click 'pick' event.
<li><a href="http://www.geomview.org/docs/html/GCL.html">GCL</a> command language for controlling Geomview
<li><a href="http://www.geomview.org/docs/html/OOGL-File-Formats.html">OOGL</a> file format for defining objects (<a href="http://www.geomview.org/docs/oogltour.html">tutorial</a>).
<li><a href="http://www.geomview.org/docs/html/Modules.html">External Modules</a> for interacting with Geomview via GCL
<li>Interact with your objects via <a href="http://www.geomview.org/docs/html/pick.html">pick</a> commands in response to right-mouse double clicks. Enable pick events with the <a href="http://www.geomview.org/docs/html/interest.html">interest</a> command.
</ul>
</blockquote>
<h3><a href="#TOC">&#187;</a><a name="geomview-win">Building Geomview for Windows</a></h3>
<blockquote>
<p>Compile Geomview under Cygwin. For detailed instructions, see
<a href="http://www.ee.surrey.ac.uk/Personal/L.Wood/software/SaVi/building-under-Windows/"
>Building Savi and Geomview under Windows</a>. These instructions are somewhat out-of-date. Updated
instructions follow.
<p>How to compile Geomview under 32-bit Cygwin (October 2015)</p>
<ol>
<li><b>Note:</b> L. Wood has run into multiple issues with Geomview on Cygwin. He recommends Virtualbox/Ubuntu
and a one-click install of geomview via the Ubuntu package. See his Savi/Geomview link above.
<li>Install 32-bit <a href="http://cygwin.com/">Cygwin</a> as follows.
For additional guidance, see Cygwin's <a href="https://cygwin.com/install.html">Installing and Updating Cygwin Packages</a>
and <a href="http://www.qhull.org/road/road-faq/xml/cmdline.xml#setup-cygwin">Setup cygwin</a>.
<ul>
<li>Launch the cygwin installer.
<li>Select a mirror from <a href="http://cygwin.com/mirrors.html">Cygwin mirrors</a> (e.g., http://mirrors.kernel.org/sourceware/cygwin/ in California).
<li>Select the packages to install. Besides the cygwin packages listed in the Savi/Windows instructions consider adding
<ul>
<li><b>Default</b> -- libXm-devel (required for /usr/include/Xm/Xm.h)
<li><b>Devel</b> -- bashdb, gcc-core (in place of gcc), gdb
<li><b>Lib</b> -- libGL-devel, libGLU1 (required, obsolete), libGLU-devel (required, obsolete), libjpeg-devel(XForms), libXext-devel (required), libXpm-devel (Xforms)
libGL and lib
<li><b>Math</b> -- bc
<li><b>Net</b> -- autossh, inetutils, openssh
<li><b>System</b> -- chere
<li><b>Utils</b> -- dos2unix (required for qhull), keychain
<li>If installing perl, ActiveState Perl may be a better choice than cygwin's perl. Perl is not used by Geomview or Qhull.
<li><a href="https://cygwin.com/cgi-bin2/package-grep.cgi">Cygwin Package Search</a> -- Search for cygwin programs and packages
</ul>
<li>Click 'Next' to download and install the packages.
<li>If the download is incomplete, try again.
<li>If you try again after a successful install, cygwin will uninstall and reinstall all modules..
<li>Click on the 'Cywin Terminal' icon on the Desktop. It sets up a user directory in /home from /etc/skel/...
<li>Mount your disk drives<br>mount c: /c # Ignore the warning /c does not exist
</ul>
<li>Consider installing the <a href="http://www.qhull.org/bash/doc/road-bash.html">Road Bash</a> scripts (/etc/road-*) from <a href="http://www.qhull.org/road/">Road</a>.
They define aliases and functions for Unix command shells (Unix, Linux, Mac OS X, Windows),
<ul>
<li>Download Road Bash and unzip the downloaded file
<li>Copy .../bash/etc/road-* to the Cywin /etc directory (by default, C:\cygwin\etc).
<li>Using the cygwin terminal, convert the road scripts to Unix format<br>d2u /etc/road-*
<li>Try it<br>source /etc/road-home.bashrc
<li>Install it<br>cp /etc/road-home.bashrc ~/.bashrc
</ul>
<li>Launch the X terminal server from '<tt>Start > All programs > Cygwin-X > Xwin Server</tt>'. Alternatively, run 'startx'
<li>Launch an XTerm shell
<ul>
<li>Right click the Cywin icon on the system tray in the Windows taskbar.
<li>Select '<tt>System Tools > XTerm</tt>'
</ul>
<li>Download and extract Geomview -- <a href="http://www.geomview.org/download/">Downloading Geomview</a>
<li>Compile Geomview
<ul>
<li>./configure
<li>make
</ul>
<li>If './configure' fails, check 'config.log' at the failing step. Look carefully for missing libraries, etc. The <a href="http://www.geomview.org/FAQ/answers.shtml">Geomview FAQ</a> contains suggestions (e.g., "configure claims it can't find OpenGl").
<li>If 'make' fails, read the output carefully for error messages. Usually it is a missing include file or package. Locate and install the missing cygwin packages
(<a href="https://cygwin.com/cgi-bin2/package-grep.cgi">Cygwin Package Search</a>).
</ol>
</blockquote>
</blockquote>
<h2><a href="#TOC">&#187;</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 &quot;internal error&quot;. 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">&#187;</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. 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">&#187;</a><a name="authors">Authors</a></h2>
<blockquote>
<pre>
C. Bradford Barber Hannu Huhdanpaa
bradb@shore.net hannu@qhull.org
</pre>
</blockquote>
<h2><a href="#TOC">&#187;</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/libqhull/index.htm>src/libqhull/index.htm</a>). They use Qhull to build 3-d models of
heart chambers.</p>
<p>Qhull 1.0 and 2.0 were 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">&#187;</a><a name="ref">References</a></h2>
<blockquote>
<p><a name="aure91">Aurenhammer</a>, F., &quot;Voronoi diagrams
-- A survey of a fundamental geometric data structure,&quot; <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, &quot;The Quickhull Algorithm for Convex Hulls,&quot; <i>ACM
Transactions on Mathematical Software</i>, 22(4):469-483, Dec 1996, www.qhull.org
[<a
href="http://portal.acm.org/citation.cfm?doid=235815.235821">http://portal.acm.org</a>;
<a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405">http://citeseerx.ist.psu.edu</a>].
</p>
<p><a name="cla-sho89">Clarkson</a>, K.L. and P.W. Shor,
&quot;Applications of random sampling in computational geometry,
II&quot;, <i>Discrete Computational Geometry</i>, 4:387-421, 1989</p>
<p><a name="cla-meh93">Clarkson</a>, K.L., K. Mehlhorn, and R.
Seidel, &quot;Four results on randomized incremental
construction,&quot; <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,
&quot;Determining the separation of preprocessed polyhedra--a
unified approach,&quot; 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=golub83>Golub, G.H. and van Loan, C.F.</a>, <i>Matric Computations</i>, Baltimore, Maryland, USA: John Hopkins Press, 1983
<p><a name="fort93">Fortune, S.</a>, &quot;Computational
geometry,&quot; 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>, &quot;Robust polygon
modeling,&quot; 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>
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<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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</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>&nbsp;</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 &copy; 1995-2015 C.B. Barber</b></p>
<hr>
<h3><a href="#TOP">&#187;</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">&#187;</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 &lt; 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 &gt; 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 &lt; 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">&#187;</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>&nbsp;</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 4-d and
higher, triangulate non-simplicial facets by adding an extra point.</dd>
<dt>&nbsp;</dt>
<dt>&nbsp;</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>&nbsp;</dt>
<dt>&nbsp;</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>&nbsp;</dt>
<dt>&nbsp;</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>&nbsp;</dt>
<dt>&nbsp;</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>&nbsp;</dt>
<dt>&nbsp;</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>&nbsp;</dt>
<dt>&nbsp;</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">&#187;</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">&#187;</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">&#187;</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">&#187;</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">&#187;</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] &lt;= 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>
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<title>qdelaunay Qu -- furthest-site Delaunay triangulation</title>
</head>
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<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>&nbsp;</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>&nbsp;</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
&quot;vertical&quot; 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 &copy; 1995-2015 C.B. Barber</b></p>
<hr>
<h3><a href="#TOP">&#187;</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">&#187;</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 &lt; 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 &gt; 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 &lt; 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">&#187;</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>&nbsp;</dt>
<dt>&nbsp;</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>&nbsp;</dt>
<dt>&nbsp;</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">&#187;</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">&#187;</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">&#187;</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/libqhull/user.h#ZEROdelaunay">qh_ZEROdelaunay</a>).
</blockquote>
<h3><a href="#TOP">&#187;</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">&#187;</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>
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<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>&nbsp;</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>&nbsp;</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.
<p>Use option '<a href="qh-optq.htm#Qz">Qz</a>' if the input is circular, cospherical, or
nearly so. It improves precision by adding a point "at infinity," above the corresponding paraboloid.
<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 &copy; 1995-2015 C.B. Barber</b></p>
<hr>
<h3><a href="#TOP">&#187;</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">&#187;</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 &lt; 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 &gt; 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 &lt; 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">&#187;</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>&nbsp;</dt>
<dt>&nbsp;</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>&nbsp;</dt>
<dt>&nbsp;</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">&#187;</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">&#187;</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">&#187;</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/libqhull/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-code.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 &lt;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">&#187;</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">&#187;</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] &lt;= 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>
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<title>Examples of Qhull</title>
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<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 &copy; 1995-2015 C.B. Barber</b></p>
<hr>
<h2><a href="#TOP">&#187;</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">&#187;</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">&#187;</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">&#187;</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">&#187;</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">&#187;</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">&#187;</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">&#187;</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">&#187;</a>2-d and 3-d examples</h2>
<h3><a href="#2d">&#187;</a><a name="01">rbox c D3 | qconvex G
&gt;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">&#187;</a><a name="02">rbox c d G3.0 | qconvex G
&gt;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">&#187;</a><a name="03">rbox s 100 D3 | qconvex G
&gt;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 &gt;eg.99</i>.</p>
<h3><a href="#2d">&#187;</a><a name="04">rbox s 100 D2 | qconvex G
&gt;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 &amp; Shamos <a
href="index.htm#pre-sha85">'85</a>]. It was the model for
Qhull.</p>
<h3><a href="#2d">&#187;</a><a name="05">rbox 10 l | qconvex G
&gt;eg.05.spiral </a></h3>
<p>One rotation of a spiral.</p>
<h3><a href="#2d">&#187;</a><a name="06">rbox 1000 D2 | qconvex C-0.03
Qc Gapcv &gt;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">&#187;</a><a name="07">rbox 1000 D3 | qconvex G
&gt;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">&#187;</a><a name="08a">rbox c G0.4 s 500 | qconvex G
&gt;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">&#187;</a><a name="08b">rbox d G0.6 s 500 | qconvex G
&gt;eg.08b.diamond.sphere </a></h3>
<p>This is a combination of the diamond distribution and the
sphere.</p>
<h3><a href="#2d">&#187;</a><a name="09">rbox 100 L3 G0.5 s | qconvex
G &gt;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">&#187;</a>How Qhull adds a point</h2>
<h3><a href="#how">&#187;</a><a name="10a">rbox 100 s P0.5,0.5,0.5 |
qconvex Ga QG0 &gt;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">&#187;</a><a name="10b">rbox 100 s
P0.5,0.5,0.5|qconvex Ga QG-0 &gt;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">&#187;</a><a name="10c">rbox 100 s P0.5,0.5,0.5 |
qconvex PG Ga QG0 &gt;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">&#187;</a><a name="10d">rbox 100 s P0.5,0.5,0.5 |
qconvex Ga QV0 PgG &gt;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">&#187;</a><a name="10e">rbox 100 s P0.5,0.5,0.5 |
qconvex Ga &gt;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">&#187;</a><a name="14">rbox 100 s P0.5,0.5,0.5 |
qhull Ga QV0g Q0 &gt;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">&#187;</a>Triangulated output or joggled input</h2>
<h3><a href="#joggle">&#187;</a><a name="15a">rbox 500 W0 | qconvex QR0 Qc Gvp &gt;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">&#187;</a><a name="15b">rbox 500 W0 | qconvex QR0 Qt Qc Gvp &gt;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">&#187;</a><a name="15c">rbox 500 W0 | qconvex QR0 QJ5e-2 Qc Gvp &gt;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">&#187;</a>Delaunay and Voronoi diagrams</h2>
<h3><a href="#delaunay">&#187;</a><a name="17a">qdelaunay Qt
&lt;eg.data.17 GnraD2 &gt;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">&#187;</a><a name="17b">qdelaunay &lt;eg.data.17
GnraD2 &gt;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">&#187;</a><a name="17c">qdelaunay &lt;eg.data.17
Ga &gt;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">&#187;</a><a name="17d">qvoronoi QJ
&lt;eg.data.17 Gna &gt;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">&#187;</a><a name="17e">qvoronoi &lt;eg.data.17
Gna &gt;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 &lt;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">&#187;</a><a name="17f"> rbox c G0.1 d |
qdelaunay Gt Qz &lt;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 &quot;at infinity&quot;. This avoids a degenerate
input due to cospherical points.</p>
<h3><a href="#delaunay">&#187;</a><a name="18a">rbox 10 D2 d | qdelaunay
Qu G &gt;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">&#187;</a><a name="18b">rbox 10 D2 d | qdelaunay
Qu Pd2 G &gt;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">&#187;</a><a name="18c">rbox 10 D2 d | qvoronoi
Qu Gv &gt;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">&#187;</a><a name="19">rbox 10 D3 | qvoronoi QV5
p | qconvex G &gt;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">&#187;</a>Facet merging for imprecision</h2>
<h3><a href="#merge">&#187;</a><a name="20">rbox r s 20 Z1 G0.2 |
qconvex G &gt;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">&#187;</a><a name="21a">rbox 200 s | qhull Q0
R0.01 Gav Po &gt;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">&#187;</a><a name="21b">rbox 200 s | qconvex Qc
R0.01 Gpav &gt;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">&#187;</a><a name="22a">rbox 1000 s| qconvex C0.01
Qc Gcrp &gt;eg.22a.merge.sphere.01</a></h3>
<h3><a href="#merge">&#187;</a><a name="22b">rbox 1000 s| qconvex
C-0.01 Qc Gcrp &gt;eg.22b.merge.sphere.-01</a></h3>
<h3><a href="#merge">&#187;</a><a name="22c">rbox 1000 s| qconvex C0.05
Qc Gcrpv &gt;eg.22c.merge.sphere.05</a></h3>
<h3><a href="#merge">&#187;</a><a name="22d">rbox 1000 s| qconvex
C-0.05 Qc Gcrpv &gt;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">&#187;</a><a name="23">rbox 1000 | qconvex s
Gcprvah C0.1 Qc &gt;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">&#187;</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">&#187;</a><a name="24">rbox 5000 D4 | qconvex s GD0v
Pd0:0.5 C-0.02 C0.1 &gt;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">&#187;</a><a name="30">rbox 5000 D4 | qconvex s
C-0.02 C0.1 Gh &gt;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">&#187;</a><a name="31">rbox 20 D3 | qdelaunay G
&gt;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">&#187;</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">&#187;</a>Halfspace intersections</h2>
<h3><a href="#half">&#187;</a><a name="33a">rbox 10 r s Z1 G0.3 |
qconvex G &gt;eg.33a.cone </a></h3>
<h3><a href="#half">&#187;</a><a name="33b">rbox 10 r s Z1 G0.3 |
qconvex FV n | qhalf G &gt;eg.33b.cone.dual</a></h3>
<h3><a href="#half">&#187;</a><a name="33c">rbox 10 r s Z1 G0.3 |
qconvex FV n | qhalf Fp | qconvex G &gt;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>
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<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 the convex hull, Delaunay triangulation, Voronoi diagram, halfspace
intersection about a point, furthest-site Delaunay
triangulation, and furthest-site Voronoi diagram. 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.
If you use Qhull 2003.1 or 2009.1, please upgrade to 2015.2 or apply
<a href="http://www.qhull.org/download/poly.c-qh_gethash.patch">poly.c-qh_gethash.patch</a>.</p>
</li>
<li><a
href="http://www.qhull.org/download/qhull-2015.2.zip">Download:
Qhull 2015.2 for Windows 10, 8, 7, XP, and NT</a> (2.6 MB,
<a href="http://www.qhull.org/README.txt">readme</a>,
<a href="http://www.qhull.org/download/qhull-2015.2.md5sum">md5sum</a>,
<a href="http://www.qhull.org/download/qhull-2015.2.zip.md5sum">contents</a>)
<p>Type: console programs for Windows (32- or 64-bit)</p>
<p>Includes 32-bit executables, documentation, and sources files. It runs in a
command window. Qhull may be compiled for 64-bits.</p>
</li>
<li><a href="http://github.com/qhull/qhull/wiki">GitHub Qhull</a> (git@github.com:qhull/qhull.git)
<p>Type: git repository for Qhull. See recent <a href="https://github.com/qhull/qhull/blob/master/src/Changes.txt">Changes.txt</a></p>
<p>Includes documentation, source files, C++ interface, and test programs. It builds with gcc, mingw,
CMake, DevStudio, and Qt Creator.
</p>
</li>
<li><a href="http://www.qhull.org/download/qhull-2015-src-7.2.0.tgz">Download: Qhull 2015.2 for Unix</a> (1.0 MB,
<a href="http://www.qhull.org/README.txt">readme</a>,
<a href="http://www.qhull.org/download/qhull-2015.2.md5sum">md5sum</a>,
<a href="http://www.qhull.org/download/qhull-2015-src-7.2.0.tgz.md5sum">contents</a>)
<p>Type: C/C++ source code for 32-bit and 64-bit architectures. See <a href="http://www.qhull.org/src/Changes.txt">Changes.txt</a></p>
<p>Includes documentation, source files, Makefiles, CMakeLists.txt, DevStudio projects, and Qt projects.
Includes preliminary C++ support.</p>
<p>Download and search sites for pre-built packages include
<ul>
<li><a href="https://launchpad.net/ubuntu/+source/qhull">https://launchpad.net/ubuntu/+source/qhull</a>
<li><a href="http://software.opensuse.org/download.html?project=openSUSE%3AFactory&package=qhull">http://software.opensuse.org/download.html?project=openSUSE%3AFactory&package=qhull</a>
<li><a href="https://www.archlinux.org/packages/extra/i686/qhull/">https://www.archlinux.org/packages/extra/i686/qhull/</a>
<li><a href="http://rpmfind.net/linux/rpm2html/search.php?query=qhull">http://rpmfind.net/linux/rpm2html/search.php?query=qhull</a>
<li><a href="http://rpm.pbone.net/index.php3/stat/3/srodzaj/1/search/qhull">http://rpm.pbone.net/index.php3/stat/3/srodzaj/1/search/qhull</a>
</ul></p>
</li>
<li><a
href="http://dl.acm.org/author_page.cfm?id=81100129162">Download:
Article about Qhull</a> (307K)
<p>Type: PDF on ACM Digital Library (from this page only)</p>
<p>Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T.,
&quot;The Quickhull algorithm for convex hulls,&quot; <i>ACM
Transactions on Mathematical Software</i>, 22(4):469-483, Dec 1996 [<a
href="http://portal.acm.org/citation.cfm?doid=235815.235821">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
&quot;bcc32 -WX -w- -O2-e -erbox -lc rbox.c&quot;. The
options for qhull are the same. [D. Zwick] </p>
</li>
</ul>
<!-- Navigation links -->
<hr>
<p><b>Up:</b> <a href="http://www.qhull.org"><i>Qhull Home Page</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>
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<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 &copy; 1995-2015 C.B. Barber</b></p>
<hr>
<h2><a href="#TOP">&#187;</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="#halfspace">Halfspace intersection/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">&#187;</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 (&quot;flipped&quot; 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">&#187;</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/libqhull/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">&#187;</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">&#187;</a><a name="halfspace">Halfspace intersection</a></h2>
<p>
The identity pipe for Qhull reveals some precision questions for
halfspace intersections. The identity pipe creates the convex hull of
a set of points and intersects the facets' hyperplanes. It should return the input
points, but narrow distributions may drop points while offset distributions may add
points. It may be better to normalize the input set about the origin.
For example, compare the first results with the later two results: [T. Abraham]
<blockquote>
rbox 100 s t | tee r | qconvex FV n | qhalf Fp | cat - r | /bin/sort -n | tail
<br>
rbox 100 L1e5 t | tee r | qconvex FV n | qhalf Fp | cat - r | /bin/sort -n | tail
<br>
rbox 100 s O10 t | tee r | qconvex FV n | qhalf Fp | cat - r | /bin/sort -n | tail
</blockquote>
<h2><a href="#TOC">&#187;</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">&#187;</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">&#187;</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 &quot;dents&quot; 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., &quot;(3.4x)&quot;. 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>Nearly coincident points within 1e-13</b> --
Multiple, nearly coincident points within a 1e-13 ball of points in the unit cube
may lead to wide facets or quadratic running time.
For example, the convex hull a 1000 coincident, cospherical points in 4-D,
or the 3-D Delaunay triangulation of nearly coincident points, may lead to very
wide facets (e.g., 2267021951.3x).
<p>For Delaunay triangulations, the problem typically occurs for extreme points of the input
set (i.e., on the edge between the upper and lower convex hull). After multiple facet merges, four
facets may share the same, duplicate ridge and must be merged.
Some of these facets may be long and narrow, leading to a very wide merged facet.
If so, error QH6271 is reported. It may be overriden with option '<a href="qh-optq.htm#Q12">Q12</a>'.
<p>Duplicate ridges occur when the horizon facets for a new point is "pinched".
In a duplicate ridge, a subridge (e.g., a line segment in 3-d) is shared by two horizon facets.
At least two of its vertices are nearly coincident. It is easy to generate coincident points with
option 'Cn,r,m' of rbox. It generates n points within an r ball for each of m input sites. For example,
every point of the following distributions has a nearly coincident point within a 1e-13 ball.
Substantially smaller or larger balls do not lead to pinched horizons.
<pre>
rbox 1000 C1,1e-13 D4 s t | qhull
rbox 75 C1,1e-13 t | qhull d
</pre>
For Delaunay triangulations, a bounding box may alleviate this error (e.g., <tt>rbox 500 C1,1E-13 t c G1 | qhull d</tt>).
A later release of qhull will avoid pinched horizons by merging duplicate subridges. A subridge is
merged by merging adjacent vertices.
<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">&#187;</a><a name="injoggle">Joggled input</a></h2>
<p>Joggled input is a simple work-around for precision problems
in computational geometry [&quot;joggle: to shake or jar
slightly,&quot; 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">&#187;</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://www.netlib.org/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">&#187;</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>
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<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 &copy; 1995-2015 C.B. Barber</b></p>
<hr>
<p><a href="index.htm#TOC">&#187;</a> <a href="qh-quick.htm#programs">Programs</a>
<a name="prec">&#149;</a> <a href="qh-quick.htm#options">Options</a>
&#149; <a href="qh-opto.htm#output">Output</a>
&#149; <a href="qh-optf.htm#format">Formats</a>
&#149; <a href="qh-optg.htm#geomview">Geomview</a>
&#149; <a href="qh-optp.htm#print">Print</a>
&#149; <a href="qh-optq.htm#qhull">Qhull</a>
&#149; <a href="qh-optc.htm#prec">Precision</a>
&#149; <a href="qh-optt.htm#trace">Trace</a>
&#149; <a href="../src/libqhull_r/index.htm">Functions</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>&nbsp;</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>&nbsp;</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">&#187;</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">&#187;</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">&#187;</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' (&quot;_zero-centrum&quot;) 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">&#187;</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">&#187;</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">&#187;</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 &quot;max. distance of a new vertex to a
facet&quot; (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">&#187;</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">&#187;</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">&#187;</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">&#187;</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>
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<p><a href="http://www.geom.uiuc.edu/"><img src="qh--geom.gif"
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