Input buildinfo: https://buildinfos.debian.net/buildinfo-pool/q/qhull/qhull_2020.2-3_all.buildinfo Use metasnap for getting required timestamps New buildinfo file: /tmp/qhull-2020.2-3lpc432br/qhull_2020.2-3_all.buildinfo Get source package info: qhull=2020.2-3 Source URL: http://snapshot.notset.fr/mr/package/qhull/2020.2-3/srcfiles?fileinfo=1 env -i PATH=/usr/sbin:/usr/bin:/sbin:/bin TMPDIR=/tmp mmdebstrap --arch=amd64 --include=autoconf=2.69-11.1 automake=1:1.16.3-1 autopoint=0.19.8.1-10 autotools-dev=20180224.1 base-files=11 base-passwd=3.5.48 bash=5.1~rc3-1 binutils=2.35.1-3 binutils-common=2.35.1-3 binutils-x86-64-linux-gnu=2.35.1-3 bsdextrautils=2.36.1-2 bsdutils=1:2.36.1-2 build-essential=12.8 bzip2=1.0.8-4 cmake=3.18.4-1 cmake-data=3.18.4-1 coreutils=8.32-4+b1 cpp=4:10.2.0-1 cpp-10=10.2.0-19 dash=0.5.11+git20200708+dd9ef66-2 debconf=1.5.74 debhelper=13.2.1 debianutils=4.11.2 dh-autoreconf=19 dh-strip-nondeterminism=1.9.0-1 diffutils=1:3.7-3 dpkg=1.20.5 dpkg-dev=1.20.5 dwz=0.13-5 file=1:5.39-3 findutils=4.7.0+git20201010-2 g++=4:10.2.0-1 g++-10=10.2.0-19 gcc=4:10.2.0-1 gcc-10=10.2.0-19 gcc-10-base=10.2.0-19 gettext=0.19.8.1-10 gettext-base=0.19.8.1-10 grep=3.6-1 groff-base=1.22.4-5 gzip=1.10-2 hostname=3.23 init-system-helpers=1.59 intltool-debian=0.35.0+20060710.5 libacl1=2.2.53-8 libarchive-zip-perl=1.68-1 libarchive13=3.4.3-2 libasan6=10.2.0-19 libatomic1=10.2.0-19 libattr1=1:2.4.48-5 libaudit-common=1:2.8.5-3.1 libaudit1=1:2.8.5-3.1 libbinutils=2.35.1-3 libblkid1=2.36.1-2 libbrotli1=1.0.9-2+b1 libbz2-1.0=1.0.8-4 libc-bin=2.31-4 libc-dev-bin=2.31-4 libc6=2.31-4 libc6-dev=2.31-4 libcap-ng0=0.7.9-2.2+b1 libcc1-0=10.2.0-19 libcom-err2=1.45.6-1 libcroco3=0.6.13-1 libcrypt-dev=1:4.4.17-1 libcrypt1=1:4.4.17-1 libctf-nobfd0=2.35.1-3 libctf0=2.35.1-3 libcurl4=7.72.0-1 libdb5.3=5.3.28+dfsg1-0.6 libdebconfclient0=0.255 libdebhelper-perl=13.2.1 libdpkg-perl=1.20.5 libelf1=0.182-1 libexpat1=2.2.10-1 libffi7=3.3-5 libfile-stripnondeterminism-perl=1.9.0-1 libgcc-10-dev=10.2.0-19 libgcc-s1=10.2.0-19 libgcrypt20=1.8.7-2 libgdbm-compat4=1.18.1-5.1 libgdbm6=1.18.1-5.1 libglib2.0-0=2.66.3-1 libgmp10=2:6.2.1+dfsg-1 libgnutls30=3.6.15-4 libgomp1=10.2.0-19 libgpg-error0=1.38-2 libgssapi-krb5-2=1.18.3-4 libhogweed6=3.6-2 libicu67=67.1-4 libidn2-0=2.3.0-4 libisl23=0.23-1 libitm1=10.2.0-19 libjsoncpp1=1.7.4-3.1 libk5crypto3=1.18.3-4 libkeyutils1=1.6.1-2 libkrb5-3=1.18.3-4 libkrb5support0=1.18.3-4 libldap-2.4-2=2.4.56+dfsg-1 liblsan0=10.2.0-19 liblz4-1=1.9.2-2 liblzma5=5.2.4-1+b1 libmagic-mgc=1:5.39-3 libmagic1=1:5.39-3 libmount1=2.36.1-2 libmpc3=1.2.0-1 libmpfr6=4.1.0-3 libncurses6=6.2+20201114-1 libncursesw6=6.2+20201114-1 libnettle8=3.6-2 libnghttp2-14=1.42.0-1 libnsl-dev=1.3.0-2 libnsl2=1.3.0-2 libnss-nis=3.1-4 libnss-nisplus=1.3-4 libp11-kit0=0.23.21-2 libpam-modules=1.3.1-5 libpam-modules-bin=1.3.1-5 libpam-runtime=1.3.1-5 libpam0g=1.3.1-5 libpcre2-8-0=10.34-7 libpcre3=2:8.39-13 libperl5.32=5.32.0-5 libpipeline1=1.5.3-1 libprocps8=2:3.3.16-5 libpsl5=0.21.0-1.1 libpython3-stdlib=3.9.0-3 libpython3.9-minimal=3.9.1~rc1-2 libpython3.9-stdlib=3.9.1~rc1-2 libquadmath0=10.2.0-19 libreadline8=8.1~rc3-1 librhash0=1.4.0-1 librtmp1=2.4+20151223.gitfa8646d.1-2+b2 libsasl2-2=2.1.27+dfsg-2 libsasl2-modules-db=2.1.27+dfsg-2 libseccomp2=2.5.0-3 libselinux1=3.1-2+b1 libsigsegv2=2.12-2 libsmartcols1=2.36.1-2 libsqlite3-0=3.33.0-1 libssh2-1=1.8.0-2.1 libssl1.1=1.1.1h-1 libstdc++-10-dev=10.2.0-19 libstdc++6=10.2.0-19 libsub-override-perl=0.09-2 libsystemd0=246.6-5 libtasn1-6=4.16.0-2 libtinfo6=6.2+20201114-1 libtirpc-common=1.2.6-3 libtirpc-dev=1.2.6-3 libtirpc3=1.2.6-3 libtool=2.4.6-14 libtsan0=10.2.0-19 libubsan1=10.2.0-19 libuchardet0=0.0.7-1 libudev1=246.6-5 libunistring2=0.9.10-4 libuuid1=2.36.1-2 libuv1=1.40.0-1 libxml2=2.9.10+dfsg-6.3 libzstd1=1.4.5+dfsg-4 linux-libc-dev=5.9.11-1 login=1:4.8.1-1 lsb-base=11.1.0 m4=1.4.18-4 mailcap=3.67 make=4.3-4 man-db=2.9.3-2 mawk=1.3.4.20200120-2 media-types=1.0.1 mime-support=3.66 ncurses-base=6.2+20201114-1 ncurses-bin=6.2+20201114-1 patch=2.7.6-6 perl=5.32.0-5 perl-base=5.32.0-5 perl-modules-5.32=5.32.0-5 pkg-kde-tools=0.15.32 po-debconf=1.0.21 procps=2:3.3.16-5 python3=3.9.0-3 python3-minimal=3.9.0-3 python3.9=3.9.1~rc1-2 python3.9-minimal=3.9.1~rc1-2 readline-common=8.1~rc3-1 sed=4.7-1 sensible-utils=0.0.12+nmu1 sysvinit-utils=2.96-5 tar=1.32+dfsg-1 tzdata=2020d-1 util-linux=2.36.1-2 xz-utils=5.2.4-1+b1 zlib1g=1:1.2.11.dfsg-2 --variant=apt --aptopt=Acquire::Check-Valid-Until "false" --aptopt=Acquire::http::Dl-Limit "1000"; --aptopt=Acquire::https::Dl-Limit "1000"; --aptopt=Acquire::Retries "5"; --aptopt=APT::Get::allow-downgrades "true"; --keyring=/usr/share/keyrings/ --essential-hook=chroot "$1" sh -c "apt-get --yes install fakeroot util-linux" --essential-hook=copy-in /usr/share/keyrings/debian-archive-bullseye-automatic.gpg /usr/share/keyrings/debian-archive-bullseye-security-automatic.gpg /usr/share/keyrings/debian-archive-bullseye-stable.gpg /usr/share/keyrings/debian-archive-buster-automatic.gpg /usr/share/keyrings/debian-archive-buster-security-automatic.gpg /usr/share/keyrings/debian-archive-buster-stable.gpg /usr/share/keyrings/debian-archive-keyring.gpg /usr/share/keyrings/debian-archive-removed-keys.gpg /usr/share/keyrings/debian-archive-stretch-automatic.gpg /usr/share/keyrings/debian-archive-stretch-security-automatic.gpg /usr/share/keyrings/debian-archive-stretch-stable.gpg /usr/share/keyrings/debian-ports-archive-keyring-removed.gpg /usr/share/keyrings/debian-ports-archive-keyring.gpg /usr/share/keyrings/debian-keyring.gpg /etc/apt/trusted.gpg.d/ --essential-hook=chroot "$1" sh -c "rm /etc/apt/sources.list && echo 'deb http://snapshot.notset.fr/archive/debian/20210814T212851Z/ bookworm main deb-src http://snapshot.notset.fr/archive/debian/20210814T212851Z/ bookworm main deb http://snapshot.notset.fr/archive/debian/20201201T091156Z/ unstable main' >> /etc/apt/sources.list && apt-get update" --customize-hook=chroot "$1" useradd --no-create-home -d /nonexistent -p "" builduser -s /bin/bash --customize-hook=chroot "$1" env sh -c "apt-get source --only-source -d qhull=2020.2-3 && mkdir -p /build/qhull-vzozxV && dpkg-source --no-check -x /*.dsc /build/qhull-vzozxV/qhull-2020.2 && chown -R builduser:builduser /build/qhull-vzozxV" --customize-hook=chroot "$1" env --unset=TMPDIR runuser builduser -c "cd /build/qhull-vzozxV/qhull-2020.2 && env DEB_BUILD_OPTIONS="parallel=4" LANG="C.UTF-8" LC_ALL="C.UTF-8" SOURCE_DATE_EPOCH="1606431566" dpkg-buildpackage -uc -a amd64 --build=all" --customize-hook=sync-out /build/qhull-vzozxV /tmp/qhull-2020.2-3lpc432br bullseye /dev/null deb http://snapshot.notset.fr/archive/debian/20201201T091156Z unstable main I: automatically chosen mode: root I: chroot architecture amd64 is equal to the host's architecture I: automatically chosen format: tar I: using /tmp/mmdebstrap.tZ1KXmBowC as tempdir I: running apt-get update... I: downloading packages with apt... I: extracting archives... I: installing essential packages... I: running --essential-hook in shell: sh -c 'chroot "$1" sh -c "apt-get --yes install fakeroot util-linux"' exec /tmp/mmdebstrap.tZ1KXmBowC Reading package lists... Building dependency tree... util-linux is already the newest version (2.36.1-2). The following NEW packages will be installed: fakeroot libfakeroot 0 upgraded, 2 newly installed, 0 to remove and 0 not upgraded. Need to get 134 kB of archives. After this operation, 397 kB of additional disk space will be used. Get:1 http://snapshot.notset.fr/archive/debian/20201201T091156Z unstable/main amd64 libfakeroot amd64 1.25.3-1.1 [47.0 kB] Get:2 http://snapshot.notset.fr/archive/debian/20201201T091156Z unstable/main amd64 fakeroot amd64 1.25.3-1.1 [87.0 kB] debconf: delaying package configuration, since apt-utils is not installed Fetched 134 kB in 0s (984 kB/s) Selecting previously unselected package libfakeroot:amd64. (Reading database ... (Reading database ... 5% (Reading database ... 10% (Reading database ... 15% (Reading database ... 20% (Reading database ... 25% (Reading database ... 30% (Reading database ... 35% (Reading database ... 40% (Reading database ... 45% (Reading database ... 50% (Reading database ... 55% (Reading database ... 60% (Reading database ... 65% (Reading database ... 70% (Reading database ... 75% (Reading database ... 80% (Reading database ... 85% (Reading database ... 90% (Reading database ... 95% (Reading database ... 100% (Reading database ... 4697 files and directories currently installed.) Preparing to unpack .../libfakeroot_1.25.3-1.1_amd64.deb ... Unpacking libfakeroot:amd64 (1.25.3-1.1) ... Selecting previously unselected package fakeroot. Preparing to unpack .../fakeroot_1.25.3-1.1_amd64.deb ... Unpacking fakeroot (1.25.3-1.1) ... Setting up libfakeroot:amd64 (1.25.3-1.1) ... Setting up fakeroot (1.25.3-1.1) ... update-alternatives: using /usr/bin/fakeroot-sysv to provide /usr/bin/fakeroot (fakeroot) in auto mode Processing triggers for libc-bin (2.31-4) ... I: running special hook: copy-in /usr/share/keyrings/debian-archive-bullseye-automatic.gpg /usr/share/keyrings/debian-archive-bullseye-security-automatic.gpg /usr/share/keyrings/debian-archive-bullseye-stable.gpg /usr/share/keyrings/debian-archive-buster-automatic.gpg /usr/share/keyrings/debian-archive-buster-security-automatic.gpg /usr/share/keyrings/debian-archive-buster-stable.gpg /usr/share/keyrings/debian-archive-keyring.gpg /usr/share/keyrings/debian-archive-removed-keys.gpg /usr/share/keyrings/debian-archive-stretch-automatic.gpg /usr/share/keyrings/debian-archive-stretch-security-automatic.gpg /usr/share/keyrings/debian-archive-stretch-stable.gpg /usr/share/keyrings/debian-ports-archive-keyring-removed.gpg /usr/share/keyrings/debian-ports-archive-keyring.gpg /usr/share/keyrings/debian-keyring.gpg /etc/apt/trusted.gpg.d/ I: running --essential-hook in shell: sh -c 'chroot "$1" sh -c "rm /etc/apt/sources.list && echo 'deb http://snapshot.notset.fr/archive/debian/20210814T212851Z/ bookworm main deb-src http://snapshot.notset.fr/archive/debian/20210814T212851Z/ bookworm main deb http://snapshot.notset.fr/archive/debian/20201201T091156Z/ unstable main' >> /etc/apt/sources.list && apt-get update"' exec /tmp/mmdebstrap.tZ1KXmBowC Get:1 http://snapshot.notset.fr/archive/debian/20210814T212851Z bookworm InRelease [81.6 kB] Hit:2 http://snapshot.notset.fr/archive/debian/20201201T091156Z unstable InRelease Ign:3 http://snapshot.notset.fr/archive/debian/20210814T212851Z bookworm/main Sources Ign:4 http://snapshot.notset.fr/archive/debian/20210814T212851Z bookworm/main amd64 Packages Ign:3 http://snapshot.notset.fr/archive/debian/20210814T212851Z bookworm/main Sources Ign:4 http://snapshot.notset.fr/archive/debian/20210814T212851Z bookworm/main amd64 Packages Ign:3 http://snapshot.notset.fr/archive/debian/20210814T212851Z bookworm/main Sources Ign:4 http://snapshot.notset.fr/archive/debian/20210814T212851Z bookworm/main amd64 Packages Get:3 http://snapshot.notset.fr/archive/debian/20210814T212851Z bookworm/main Sources [11.4 MB] Get:4 http://snapshot.notset.fr/archive/debian/20210814T212851Z bookworm/main amd64 Packages [11.1 MB] Fetched 22.6 MB in 19s (1199 kB/s) Reading package lists... I: installing remaining packages inside the chroot... I: running --customize-hook in shell: sh -c 'chroot "$1" useradd --no-create-home -d /nonexistent -p "" builduser -s /bin/bash' exec /tmp/mmdebstrap.tZ1KXmBowC I: running --customize-hook in shell: sh -c 'chroot "$1" env sh -c "apt-get source --only-source -d qhull=2020.2-3 && mkdir -p /build/qhull-vzozxV && dpkg-source --no-check -x /*.dsc /build/qhull-vzozxV/qhull-2020.2 && chown -R builduser:builduser /build/qhull-vzozxV"' exec /tmp/mmdebstrap.tZ1KXmBowC Reading package lists... NOTICE: 'qhull' packaging is maintained in the 'Git' version control system at: https://salsa.debian.org/science-team/qhull.git Please use: git clone https://salsa.debian.org/science-team/qhull.git to retrieve the latest (possibly unreleased) updates to the package. Need to get 1320 kB of source archives. Get:1 http://snapshot.notset.fr/archive/debian/20210814T212851Z bookworm/main qhull 2020.2-3 (dsc) [2171 B] Get:2 http://snapshot.notset.fr/archive/debian/20210814T212851Z bookworm/main qhull 2020.2-3 (tar) [1299 kB] Get:3 http://snapshot.notset.fr/archive/debian/20210814T212851Z bookworm/main qhull 2020.2-3 (diff) [18.5 kB] Fetched 1320 kB in 1s (1226 kB/s) Download complete and in download only mode W: Download is performed unsandboxed as root as file 'qhull_2020.2-3.dsc' couldn't be accessed by user '_apt'. - pkgAcquire::Run (13: Permission denied) dpkg-source: info: extracting qhull in /build/qhull-vzozxV/qhull-2020.2 dpkg-source: info: unpacking qhull_2020.2.orig.tar.gz dpkg-source: info: unpacking qhull_2020.2-3.debian.tar.xz dpkg-source: info: using patch list from debian/patches/series dpkg-source: info: applying 0001-debianize-test-failure-msg.patch dpkg-source: info: applying 0002-Fix-privacy-breach.patch dpkg-source: info: applying 0003-Use-local-version-of-function-index.patch dpkg-source: info: applying 0004-Build-qhullcpp-as-shared-library.patch dpkg-source: info: applying 0005-Fix-CMake-target-export.patch dpkg-source: info: applying 0006-Build-deprecated-libqhull-for-now.patch I: running --customize-hook in shell: sh -c 'chroot "$1" env --unset=TMPDIR runuser builduser -c "cd /build/qhull-vzozxV/qhull-2020.2 && env DEB_BUILD_OPTIONS="parallel=4" LANG="C.UTF-8" LC_ALL="C.UTF-8" SOURCE_DATE_EPOCH="1606431566" dpkg-buildpackage -uc -a amd64 --build=all"' exec /tmp/mmdebstrap.tZ1KXmBowC dpkg-buildpackage: info: source package qhull dpkg-buildpackage: info: source version 2020.2-3 dpkg-buildpackage: info: source distribution unstable dpkg-buildpackage: info: source changed by Timo Röhling dpkg-source --before-build . debian/rules clean dh clean --buildsystem=cmake --with pkgkde_symbolshelper dh_auto_clean -O--buildsystem=cmake dh_autoreconf_clean -O--buildsystem=cmake dh_clean -O--buildsystem=cmake debian/rules binary-indep dh binary-indep --buildsystem=cmake --with pkgkde_symbolshelper dh_update_autotools_config -i -O--buildsystem=cmake dh_autoreconf -i -O--buildsystem=cmake debian/rules override_dh_auto_configure make[1]: Entering directory '/build/qhull-vzozxV/qhull-2020.2' dh_auto_configure \ --buildsystem=cmake \ --builddir=/build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu \ -- \ -DCMAKE_SKIP_RPATH=ON \ -DINCLUDE_INSTALL_DIR=include \ -DLINK_APPS_SHARED=ON \ -DLIB_INSTALL_DIR=lib/x86_64-linux-gnu \ -DBIN_INSTALL_DIR=bin \ -DMAN_INSTALL_DIR=share/man/man1 \ -DDOC_INSTALL_DIR=share/doc/libqhull-dev/qhull cd obj-x86_64-linux-gnu && cmake -DCMAKE_INSTALL_PREFIX=/usr -DCMAKE_BUILD_TYPE=None -DCMAKE_INSTALL_SYSCONFDIR=/etc -DCMAKE_INSTALL_LOCALSTATEDIR=/var -DCMAKE_EXPORT_NO_PACKAGE_REGISTRY=ON -DCMAKE_FIND_PACKAGE_NO_PACKAGE_REGISTRY=ON -DCMAKE_INSTALL_RUNSTATEDIR=/run -DCMAKE_SKIP_INSTALL_ALL_DEPENDENCY=ON "-GUnix Makefiles" -DCMAKE_VERBOSE_MAKEFILE=ON -DCMAKE_INSTALL_LIBDIR=lib/x86_64-linux-gnu -DCMAKE_SKIP_RPATH=ON -DINCLUDE_INSTALL_DIR=include -DLINK_APPS_SHARED=ON -DLIB_INSTALL_DIR=lib/x86_64-linux-gnu -DBIN_INSTALL_DIR=bin -DMAN_INSTALL_DIR=share/man/man1 -DDOC_INSTALL_DIR=share/doc/libqhull-dev/qhull .. -- The C compiler identification is GNU 10.2.0 -- The CXX compiler identification is GNU 10.2.0 -- Detecting C compiler ABI info -- Detecting C compiler ABI info - done -- Check for working C compiler: /usr/bin/cc - skipped -- Detecting C compile features -- Detecting C compile features - done -- Detecting CXX compiler ABI info -- Detecting CXX compiler ABI info - done -- Check for working CXX compiler: /usr/bin/c++ - skipped -- Detecting CXX compile features -- Detecting CXX compile features - done -- Looking for sys/types.h -- Looking for sys/types.h - found -- Looking for inttypes.h -- Looking for inttypes.h - found -- Looking for stddef.h -- Looking for stddef.h - found -- Looking for stdint.h -- Looking for stdint.h - found -- Check size of off_t -- Check size of off_t - done -- Looking for fseeko -- Looking for fseeko - found -- Looking for ftello -- Looking for ftello - found -- Looking for PRIdMAX -- Looking for PRIdMAX - found -- -- ========== qhull Build Information ========== -- Build Version: 8.0.2 -- Install Prefix (CMAKE_INSTALL_PREFIX): /usr -- Binary Directory (BIN_INSTALL_DIR): bin -- Library Directory (LIB_INSTALL_DIR): lib/x86_64-linux-gnu -- Include Directory (INCLUDE_INSTALL_DIR): include -- Documentation Directory (DOC_INSTALL_DIR): share/doc/libqhull-dev/qhull -- Man Pages Directory (MAN_INSTALL_DIR): share/man/man1 -- Build Type (CMAKE_BUILD_TYPE): None -- Build static libraries: ON -- Build shared library: ON -- Use shared library for linking apps: ON -- To override these options, add -D{OPTION_NAME}=... to the cmake command -- Build the debug targets -DCMAKE_BUILD_TYPE=Debug -- -- To build and install qhull, enter "make" and "make install" -- To smoketest qhull, enter "ctest" -- -- Configuring done -- Generating done CMake Warning: Manually-specified variables were not used by the project: CMAKE_EXPORT_NO_PACKAGE_REGISTRY CMAKE_FIND_PACKAGE_NO_PACKAGE_REGISTRY CMAKE_INSTALL_LIBDIR CMAKE_INSTALL_LOCALSTATEDIR CMAKE_INSTALL_RUNSTATEDIR CMAKE_INSTALL_SYSCONFDIR -- Build files have been written to: /build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu make[1]: Leaving directory '/build/qhull-vzozxV/qhull-2020.2' dh_auto_build -i -O--buildsystem=cmake cd obj-x86_64-linux-gnu && make -j4 "INSTALL=install --strip-program=true" make[1]: Entering directory '/build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu' /usr/bin/cmake -S/build/qhull-vzozxV/qhull-2020.2 -B/build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu --check-build-system CMakeFiles/Makefile.cmake 0 /usr/bin/cmake -E cmake_progress_start /build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu/CMakeFiles /build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu//CMakeFiles/progress.marks make -f CMakeFiles/Makefile2 all make[2]: Entering directory '/build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu' make -f CMakeFiles/qhullstatic_r.dir/build.make CMakeFiles/qhullstatic_r.dir/depend make -f CMakeFiles/qhull_r.dir/build.make CMakeFiles/qhull_r.dir/depend make -f CMakeFiles/testqset_r.dir/build.make CMakeFiles/testqset_r.dir/depend make -f CMakeFiles/testqset.dir/build.make CMakeFiles/testqset.dir/depend make[3]: Entering directory '/build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu' cd /build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu && /usr/bin/cmake -E cmake_depends "Unix Makefiles" /build/qhull-vzozxV/qhull-2020.2 /build/qhull-vzozxV/qhull-2020.2 /build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu /build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu /build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu/CMakeFiles/qhullstatic_r.dir/DependInfo.cmake --color= make[3]: Entering directory '/build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu' cd 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'/build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu' cd /build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu && /usr/bin/cmake -E cmake_depends "Unix Makefiles" /build/qhull-vzozxV/qhull-2020.2 /build/qhull-vzozxV/qhull-2020.2 /build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu /build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu /build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu/CMakeFiles/user_eg3.dir/DependInfo.cmake --color= Scanning dependencies of target user_eg3 make[3]: Leaving directory '/build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu' make -f CMakeFiles/user_eg3.dir/build.make CMakeFiles/user_eg3.dir/build make[3]: Entering directory '/build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu' [ 91%] Building CXX object CMakeFiles/user_eg3.dir/src/user_eg3/user_eg3_r.cpp.o /usr/bin/c++ -I/build/qhull-vzozxV/qhull-2020.2/src -g -O2 -ffile-prefix-map=/build/qhull-vzozxV/qhull-2020.2=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time 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-I/build/qhull-vzozxV/qhull-2020.2/src -g -O2 -ffile-prefix-map=/build/qhull-vzozxV/qhull-2020.2=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -fPIC -o CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullVertexSet.cpp.o -c /build/qhull-vzozxV/qhull-2020.2/src/libqhullcpp/QhullVertexSet.cpp [ 97%] Building CXX object CMakeFiles/qhullcpp.dir/src/libqhullcpp/RboxPoints.cpp.o /usr/bin/c++ -Dqhullcpp_EXPORTS -I/build/qhull-vzozxV/qhull-2020.2/src -g -O2 -ffile-prefix-map=/build/qhull-vzozxV/qhull-2020.2=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -fPIC -o CMakeFiles/qhullcpp.dir/src/libqhullcpp/RboxPoints.cpp.o -c /build/qhull-vzozxV/qhull-2020.2/src/libqhullcpp/RboxPoints.cpp [ 98%] Building CXX object CMakeFiles/qhullcpp.dir/src/libqhullcpp/RoadError.cpp.o /usr/bin/c++ -Dqhullcpp_EXPORTS -I/build/qhull-vzozxV/qhull-2020.2/src -g -O2 -ffile-prefix-map=/build/qhull-vzozxV/qhull-2020.2=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -fPIC -o CMakeFiles/qhullcpp.dir/src/libqhullcpp/RoadError.cpp.o -c /build/qhull-vzozxV/qhull-2020.2/src/libqhullcpp/RoadError.cpp [ 98%] Building CXX object CMakeFiles/qhullcpp.dir/src/libqhullcpp/RoadLogEvent.cpp.o /usr/bin/c++ -Dqhullcpp_EXPORTS -I/build/qhull-vzozxV/qhull-2020.2/src -g -O2 -ffile-prefix-map=/build/qhull-vzozxV/qhull-2020.2=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -fPIC -o CMakeFiles/qhullcpp.dir/src/libqhullcpp/RoadLogEvent.cpp.o -c /build/qhull-vzozxV/qhull-2020.2/src/libqhullcpp/RoadLogEvent.cpp [ 98%] Linking CXX executable user_eg3 /usr/bin/cmake -E cmake_link_script CMakeFiles/user_eg3.dir/link.txt --verbose=1 /usr/bin/c++ -g -O2 -ffile-prefix-map=/build/qhull-vzozxV/qhull-2020.2=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -Wl,-z,relro -Wl,-z,now -rdynamic CMakeFiles/user_eg3.dir/src/user_eg3/user_eg3_r.cpp.o -o user_eg3 libqhullcpp.a libqhullstatic_r.a -lm make[3]: Leaving directory '/build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu' [ 98%] Built target user_eg3 [100%] Linking CXX shared library libqhullcpp.so /usr/bin/cmake -E cmake_link_script CMakeFiles/qhullcpp.dir/link.txt --verbose=1 /usr/bin/c++ -fPIC -g -O2 -ffile-prefix-map=/build/qhull-vzozxV/qhull-2020.2=. -fstack-protector-strong -Wformat -Werror=format-security -Wdate-time -D_FORTIFY_SOURCE=2 -Wl,-z,relro -Wl,-z,now -shared -Wl,-soname,libqhullcpp.so.8.0 -o libqhullcpp.so.8.0.2 CMakeFiles/qhullcpp.dir/src/libqhullcpp/Coordinates.cpp.o CMakeFiles/qhullcpp.dir/src/libqhullcpp/PointCoordinates.cpp.o CMakeFiles/qhullcpp.dir/src/libqhullcpp/Qhull.cpp.o CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullFacet.cpp.o CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullFacetList.cpp.o CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullFacetSet.cpp.o CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullHyperplane.cpp.o CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullPoint.cpp.o CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullPointSet.cpp.o CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullPoints.cpp.o CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullQh.cpp.o CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullRidge.cpp.o CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullSet.cpp.o CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullStat.cpp.o CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullUser.cpp.o CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullVertex.cpp.o CMakeFiles/qhullcpp.dir/src/libqhullcpp/QhullVertexSet.cpp.o CMakeFiles/qhullcpp.dir/src/libqhullcpp/RboxPoints.cpp.o CMakeFiles/qhullcpp.dir/src/libqhullcpp/RoadError.cpp.o CMakeFiles/qhullcpp.dir/src/libqhullcpp/RoadLogEvent.cpp.o libqhull_r.so.8.0.2 -lm /usr/bin/cmake -E cmake_symlink_library libqhullcpp.so.8.0.2 libqhullcpp.so.8.0 libqhullcpp.so make[3]: Leaving directory '/build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu' [100%] Built target qhullcpp make[2]: Leaving directory '/build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu' /usr/bin/cmake -E cmake_progress_start /build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu/CMakeFiles 0 make[1]: Leaving directory '/build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu' debian/rules execute_after_dh_auto_build make[1]: Entering directory '/build/qhull-vzozxV/qhull-2020.2' Building man pages cd debian && \ for info in \ "qconvex:compute the convex hull:qconvex" \ "qdelaunay:compute the Delaunay triangulation:qdelaun" \ "qhalf:halfspace intersection about a point:qhalf" \ "qvoronoi:compute the Voronoi diagram:qvoronoi"; \ do \ comm=$(echo $info | cut -d: -f1) && \ purp=$(echo $info | cut -d: -f2) && \ doc=$(echo $info | cut -d: -f3) && \ COMM=$(echo $comm | tr [:lower:] [:upper:]) && \ echo -n Building man page for $comm... && \ sed -e "s/#command#/$comm/g" -e "s/#purpose#/$purp/g" \ -e "s/#COMMAND#/$COMM/g" -e "s/#doc#/$doc/g" \ manpage.in > $comm.1 && \ echo " done"; \ done Building man page for qconvex... done Building man page for qdelaunay... done Building man page for qhalf... done Building man page for qvoronoi... done make[1]: Leaving directory '/build/qhull-vzozxV/qhull-2020.2' debian/rules override_dh_auto_test make[1]: Entering directory '/build/qhull-vzozxV/qhull-2020.2' env LD_LIBRARY_PATH=/build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu \ PATH=/build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu:$PATH \ eg/q_test Convex hull of 8 points in 3-d: Number of vertices: 8 Number of facets: 6 Number of non-simplicial facets: 6 Statistics for: | qhull s Tcv Number of points processed: 8 Number of hyperplanes created: 11 Number of distance tests for qhull: 34 Number of distance tests for merging: 96 Number of distance tests for checking: 100 Number of merged facets: 6 CPU seconds to compute hull (after input): 0.000133 Output completed. Verifying that all points are below outer planes of all facets. Will make 48 distance computations. Delaunay triangulation by the convex hull of 8 points in 4-d: Number of input sites: 8 Number of Delaunay regions: 9 Statistics for: | qhull s d Tcv Number of points processed: 8 Number of hyperplanes created: 30 Number of facets in hull: 17 Number of distance tests for qhull: 29 CPU seconds to compute hull (after input): 5.9e-05 Output completed. Verifying that all points are below 1.2e-14 of all facets. Will make 72 distance computations. Delaunay triangulation by the convex hull of 8 points in 4-d: Number of input sites: 8 Number of Delaunay regions: 10 Statistics for: | qhull s d Tcv Number of points processed: 8 Number of hyperplanes created: 23 Number of facets in hull: 17 Number of distance tests for qhull: 26 CPU seconds to compute hull (after input): 5e-05 Output completed. Verifying that all points are below 1.3e-14 of all facets. Will make 80 distance computations. Halfspace intersection by the convex hull of 8 points in 3-d: Number of halfspaces: 8 Number of non-redundant halfspaces: 8 Number of intersection points: 6 Number of non-simplicial intersection points: 6 Statistics for: | qhull H0 s Tcv Fp Number of points processed: 8 Number of hyperplanes created: 11 Number of distance tests for qhull: 34 Number of distance tests for merging: 96 Number of distance tests for checking: 100 Number of merged facets: 6 CPU seconds to compute hull (after input): 7e-05 Output completed. Verifying that all points are below outer planes of all facets. Will make 48 distance computations. ============================== ========= eg/q_test ========== == Check qhull programs ====== ============================== qhull => qhull_r 8.0.2 (2020.2.r 2020/08/31) qconvex => qhull_r 8.0.2 (2020.2.r 2020/08/31) qvoronoi => qhull_r 8.0.2 (2020.2.r 2020/08/31) qdelaunay => qhull_r 8.0.2 (2020.2.r 2020/08/31) qhalf => qhull_r 8.0.2 (2020.2.r 2020/08/31) -rwxr-xr-x 1 builduser builduser 47888 Oct 5 22:50 /build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu/qconvex -rwxr-xr-x 1 builduser builduser 47576 Oct 5 22:50 /build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu/qdelaunay -rwxr-xr-x 1 builduser builduser 47912 Oct 5 22:50 /build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu/qhalf -rwxr-xr-x 1 builduser builduser 51392 Oct 5 22:50 /build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu/qhull -rwxr-xr-x 1 builduser builduser 47016 Oct 5 22:50 /build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu/qvoronoi -rwxr-xr-x 1 builduser builduser 46624 Oct 5 22:49 /build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu/user_eg -rwxr-xr-x 1 builduser builduser 1551560 Oct 5 22:50 /build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu/user_eg2 -rwxr-xr-x 1 builduser builduser 4998072 Oct 5 22:50 /build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu/user_eg3 ============================== == check user_eg, user_eg2, and user_eg3 == errors if user_eg and user_eg2 not found ============================== user_eg ======== user_eg 'cube qhull options' 'Delaunay options' 'halfspace options' This is the output from user_eg_r.c. It shows how qhull() may be called from an application, via Qhull's shared, reentrant library. user_eg is not part of Qhull itself. If user_eg fails immediately, user_eg_r.c was incorrectly linked to Qhull's non-reentrant library, libqhull. Try -- user_eg 'T1' 'T1' 'T1' ======== compute convex hull of cube after rotating input input -1 -1 -1 1 -1 -1 -1 1 -1 1 1 -1 -1 -1 1 1 -1 1 -1 1 1 1 1 1 Convex hull of 8 points in 3-d: Number of vertices: 8 Number of facets: 6 Number of non-simplicial facets: 6 Statistics for: | qhull s Tcv Number of points processed: 8 Number of hyperplanes created: 11 Number of distance tests for qhull: 34 Number of distance tests for merging: 96 Number of distance tests for checking: 100 Number of merged facets: 6 CPU seconds to compute hull (after input): 0.000131 Output completed. Verifying that all points are below outer planes of all facets. Will make 48 distance computations. 8 vertices and 6 facets with normals: -0 -0 -1 0 -1 0 1 -0 -0 -1 -0 -0 0 1 -0 -0 -0 1 ======== compute 3-d Delaunay triangulation seed: 1633474211 input -0.655 0.408 -0.000135 -0.263 0.557 -0.743 -0.294 0.524 0.118 0.448 -0.111 0.0884 -0.782 0.933 -0.754 -0.251 0.237 0.295 0.204 -0.616 0.462 -0.0812 0.976 -0.778 Delaunay triangulation by the convex hull of 8 points in 4-d: Number of input sites: 8 Number of Delaunay regions: 9 Statistics for: | qhull s d Tcv Number of points processed: 8 Number of hyperplanes created: 30 Number of facets in hull: 17 Number of distance tests for qhull: 29 CPU seconds to compute hull (after input): 7.6e-05 Output completed. Verifying that all points are below 1.2e-14 of all facets. Will make 72 distance computations. 8 vertices and 17 facets with normals: 0.24 -0.65 -0.64 0.32 0.46 -0.55 -0.67 0.2 -0.41 -0.58 -0.47 -0.53 -0.39 -0.59 -0.53 -0.47 -0.36 -0.43 -0.56 -0.61 -0.2 0.24 0.88 0.35 -0.57 -0.68 -0.46 -0.038 -0.062 0.15 -0.53 -0.83 0.42 0.64 -0.32 -0.56 0.45 0.45 0.76 0.14 0.49 0.48 0.69 0.25 -0.34 0.095 -0.51 -0.78 -0.068 0.32 0.88 0.36 0.26 0.43 0.78 0.37 -0.19 0.32 0.87 0.32 -0.36 0.79 -0.26 -0.43 -0.42 0.74 -0.28 -0.45 find 3-d Delaunay triangle or adjacent triangle closest to [0.5, 0.5, ...] -0.29 0.52 0.12 -0.26 0.56 -0.74 -0.08 0.98 -0.78 0.45 -0.11 0.09 ======== Compute a new triangulation as a separate instance of Qhull seed: 1633474212 input -0.655 0.671 -0.489 0.655 -0.377 -0.305 -0.2 -0.118 -0.523 0.318 0.656 -0.873 0.88 -0.998 -0.647 0.809 -0.42 0.31 0.971 -0.482 -0.703 -0.708 0.154 -0.917 Delaunay triangulation by the convex hull of 8 points in 4-d: Number of input sites: 8 Number of Delaunay regions: 10 Statistics for: | qhull s d Tcv Number of points processed: 8 Number of hyperplanes created: 23 Number of facets in hull: 17 Number of distance tests for qhull: 26 CPU seconds to compute hull (after input): 5.3e-05 Output completed. Verifying that all points are below 1.3e-14 of all facets. Will make 80 distance computations. 8 vertices and 17 facets with normals: 0.028 -0.35 -0.91 -0.24 -0.59 -0.68 0.43 0.052 0.087 -0.086 -0.99 0.037 0.48 0.52 0.45 0.55 0.1 -0.17 -0.94 -0.26 -0.54 -0.31 0.67 0.4 -0.15 0.43 0.0094 0.89 0.12 0.47 0.58 0.65 -0.66 -0.43 0.62 0.027 -0.2 0.41 -0.75 -0.49 0.25 0.7 0.36 -0.57 0.87 0.4 -0.078 -0.26 0.37 -0.059 -0.82 -0.44 0.39 0.63 0.22 -0.64 0.8 -0.49 -0.09 -0.34 0.19 -0.52 -0.73 -0.4 -0.18 -0.92 0.12 -0.32 ======== Free memory allocated by the new instance of Qhull, and redisplay the old results. 8 vertices and 17 facets with normals: 0.24 -0.65 -0.64 0.32 0.46 -0.55 -0.67 0.2 -0.41 -0.58 -0.47 -0.53 -0.39 -0.59 -0.53 -0.47 -0.36 -0.43 -0.56 -0.61 -0.2 0.24 0.88 0.35 -0.57 -0.68 -0.46 -0.038 -0.062 0.15 -0.53 -0.83 0.42 0.64 -0.32 -0.56 0.45 0.45 0.76 0.14 0.49 0.48 0.69 0.25 -0.34 0.095 -0.51 -0.78 -0.068 0.32 0.88 0.36 0.26 0.43 0.78 0.37 -0.19 0.32 0.87 0.32 -0.36 0.79 -0.26 -0.43 -0.42 0.74 -0.28 -0.45 ======== compute halfspace intersection about the origin for a diamond input as halfspace coefficients + offsets -1 -1 -1 -1 1 -1 -1 -1 -1 1 -1 -1 1 1 -1 -1 -1 -1 1 -1 1 -1 1 -1 -1 1 1 -1 1 1 1 -1 Halfspace intersection by the convex hull of 8 points in 3-d: Number of halfspaces: 8 Number of non-redundant halfspaces: 8 Number of intersection points: 6 Number of non-simplicial intersection points: 6 Statistics for: | qhull H0 s Tcv Fp Number of points processed: 8 Number of hyperplanes created: 11 Number of distance tests for qhull: 34 Number of distance tests for merging: 96 Number of distance tests for checking: 100 Number of merged facets: 6 CPU seconds to compute hull (after input): 7.2e-05 3 6 0 0 -1 0 -1 0 1 0 0 -1 0 0 0 1 0 0 0 1 Output completed. Verifying that all points are below outer planes of all facets. Will make 48 distance computations. 8 vertices and 6 facets with normals: -0 -0 -1 0 -1 0 1 -0 -0 -1 -0 -0 0 1 -0 -0 -0 1 user_eg 'QR1 p n Qt' 'v p' 'Fp' ======== user_eg 'cube qhull options' 'Delaunay options' 'halfspace options' This is the output from user_eg_r.c. It shows how qhull() may be called from an application, via Qhull's shared, reentrant library. user_eg is not part of Qhull itself. If user_eg fails immediately, user_eg_r.c was incorrectly linked to Qhull's non-reentrant library, libqhull. Try -- user_eg 'T1' 'T1' 'T1' ======== compute convex hull of cube after rotating input input -1 -1 -1 1 -1 -1 -1 1 -1 1 1 -1 -1 -1 1 1 -1 1 -1 1 1 1 1 1 Convex hull of 8 points in 3-d: Number of vertices: 8 Number of facets: 12 Number of triangulated facets: 6 Statistics for: | qhull s Tcv QR1 p n Qt QR1 Number of points processed: 8 Number of hyperplanes created: 12 Number of distance tests for qhull: 22 Number of distance tests for merging: 100 Number of distance tests for checking: 100 Number of merged facets: 6 CPU seconds to compute hull (after input): 0.000102 3 8 0.9124763375291641 1.390833937612012 -0.4826674750136243 -0.5764091147442416 0.565375258822974 -1.532352227508615 -0.1847368907548403 1.250953879569599 1.183632828365285 -1.673622343028246 0.4254952007805605 0.1339480758702939 1.673622343028246 -0.4254952007805605 -0.1339480758702939 0.1847368907548403 -1.250953879569599 -1.183632828365285 0.5764091147442416 -0.565375258822974 1.532352227508615 -0.9124763375291641 -1.390833937612012 0.4826674750136243 4 12 -0.744442726136703 -0.4127293393945193 -0.5248423762474955 -1 -0.744442726136703 -0.4127293393945193 -0.5248423762474955 -1 0.380573002749541 -0.9081645691962865 0.1743596995716653 -1 0.380573002749541 -0.9081645691962865 0.1743596995716653 -1 -0.5486066141420022 -0.06994002902120684 0.8331501516894545 -1 -0.5486066141420022 -0.06994002902120684 0.8331501516894545 -1 0.5486066141420022 0.06994002902120672 -0.8331501516894545 -1 0.5486066141420022 0.06994002902120672 -0.8331501516894545 -1 0.7444427261367031 0.4127293393945192 0.5248423762474955 -1 0.7444427261367031 0.4127293393945192 0.5248423762474955 -1 -0.380573002749541 0.9081645691962864 -0.1743596995716652 -1 -0.380573002749541 0.9081645691962864 -0.1743596995716652 -1 Output completed. Verifying that all points are below outer planes of all facets. Will make 96 distance computations. 8 vertices and 12 facets with normals: -0.74 -0.41 -0.52 -0.74 -0.41 -0.52 0.38 -0.91 0.17 0.38 -0.91 0.17 -0.55 -0.07 0.83 -0.55 -0.07 0.83 0.55 0.07 -0.83 0.55 0.07 -0.83 0.74 0.41 0.52 0.74 0.41 0.52 -0.38 0.91 -0.17 -0.38 0.91 -0.17 ======== compute 3-d Delaunay triangulation seed: 1633474211 input -0.655 0.408 -0.000135 -0.263 0.557 -0.743 -0.294 0.524 0.118 0.448 -0.111 0.0884 -0.782 0.933 -0.754 -0.251 0.237 0.295 0.204 -0.616 0.462 -0.0812 0.976 -0.778 Voronoi diagram by the convex hull of 8 points in 4-d: Number of Voronoi regions: 8 Number of Voronoi vertices: 9 Statistics for: | qhull s d Tcv v p Number of points processed: 8 Number of hyperplanes created: 30 Number of facets in hull: 17 Number of distance tests for qhull: 29 CPU seconds to compute hull (after input): 6.3e-05 3 9 -0.3903438877173294 -0.5449869659343975 -0.4394828814070229 -0.4197659285716724 -0.6306820451892561 -0.5745547775014087 -0.2981652654164769 -0.3512416306055145 -0.4541185663092805 -7.446889759715291 -8.962936147893853 -5.963603492796453 -0.03758999710045619 0.0926813999342086 -0.3204369778629371 0.371997867964177 0.5702019103909891 -0.2872189502085201 -0.2166416785466392 0.06047034404807766 -0.328285231034312 -0.4127189509802914 0.9085534639183548 -0.303489256991588 -0.4712670109806324 0.8275822706111227 -0.3087180990573104 Output completed. Verifying that all points are below 1.2e-14 of all facets. Will make 72 distance computations. 8 vertices and 17 facets with normals: 0.24 -0.65 -0.64 0.32 0.46 -0.55 -0.67 0.2 -0.41 -0.58 -0.47 -0.53 -0.39 -0.59 -0.53 -0.47 -0.36 -0.43 -0.56 -0.61 -0.2 0.24 0.88 0.35 -0.57 -0.68 -0.46 -0.038 -0.062 0.15 -0.53 -0.83 0.42 0.64 -0.32 -0.56 0.45 0.45 0.76 0.14 0.49 0.48 0.69 0.25 -0.34 0.095 -0.51 -0.78 -0.068 0.32 0.88 0.36 0.26 0.43 0.78 0.37 -0.19 0.32 0.87 0.32 -0.36 0.79 -0.26 -0.43 -0.42 0.74 -0.28 -0.45 find 3-d Delaunay triangle or adjacent triangle closest to [0.5, 0.5, ...] -0.29 0.52 0.12 -0.26 0.56 -0.74 -0.08 0.98 -0.78 0.45 -0.11 0.09 ======== Compute a new triangulation as a separate instance of Qhull seed: 1633474212 input -0.655 0.671 -0.489 0.655 -0.377 -0.305 -0.2 -0.118 -0.523 0.318 0.656 -0.873 0.88 -0.998 -0.647 0.809 -0.42 0.31 0.971 -0.482 -0.703 -0.708 0.154 -0.917 Voronoi diagram by the convex hull of 8 points in 4-d: Number of Voronoi regions: 8 Number of Voronoi vertices: 10 Statistics for: | qhull s d Tcv v p Number of points processed: 8 Number of hyperplanes created: 23 Number of facets in hull: 17 Number of distance tests for qhull: 26 CPU seconds to compute hull (after input): 5.1e-05 3 10 0.05825984202966955 -0.7205835786623698 -1.890160141546615 0.1981811233994007 -0.3187007564910971 -1.793014052793014 -0.2057347570902819 0.4158528021287921 -0.7653688671228064 0.222762903324297 0.6161131708623554 0.3133361180939666 1.655741040965108 0.7625317776123748 -0.1480976554549814 0.4109060979047706 -0.06627044373890806 -0.9186911900273333 0.3040192688979008 0.4978913184554199 0.172032745645352 1.18189586706251 -0.7258972948130707 -0.1329653652474928 0.2327353815694611 -0.6442379993810017 -0.9081880923813652 -0.2863912903381659 -1.43533280837678 0.1854167422924133 Output completed. Verifying that all points are below 1.3e-14 of all facets. Will make 80 distance computations. 8 vertices and 17 facets with normals: 0.028 -0.35 -0.91 -0.24 -0.59 -0.68 0.43 0.052 0.087 -0.086 -0.99 0.037 0.48 0.52 0.45 0.55 0.1 -0.17 -0.94 -0.26 -0.54 -0.31 0.67 0.4 -0.15 0.43 0.0094 0.89 0.12 0.47 0.58 0.65 -0.66 -0.43 0.62 0.027 -0.2 0.41 -0.75 -0.49 0.25 0.7 0.36 -0.57 0.87 0.4 -0.078 -0.26 0.37 -0.059 -0.82 -0.44 0.39 0.63 0.22 -0.64 0.8 -0.49 -0.09 -0.34 0.19 -0.52 -0.73 -0.4 -0.18 -0.92 0.12 -0.32 ======== Free memory allocated by the new instance of Qhull, and redisplay the old results. 8 vertices and 17 facets with normals: 0.24 -0.65 -0.64 0.32 0.46 -0.55 -0.67 0.2 -0.41 -0.58 -0.47 -0.53 -0.39 -0.59 -0.53 -0.47 -0.36 -0.43 -0.56 -0.61 -0.2 0.24 0.88 0.35 -0.57 -0.68 -0.46 -0.038 -0.062 0.15 -0.53 -0.83 0.42 0.64 -0.32 -0.56 0.45 0.45 0.76 0.14 0.49 0.48 0.69 0.25 -0.34 0.095 -0.51 -0.78 -0.068 0.32 0.88 0.36 0.26 0.43 0.78 0.37 -0.19 0.32 0.87 0.32 -0.36 0.79 -0.26 -0.43 -0.42 0.74 -0.28 -0.45 ======== compute halfspace intersection about the origin for a diamond input as halfspace coefficients + offsets -1 -1 -1 -1 1 -1 -1 -1 -1 1 -1 -1 1 1 -1 -1 -1 -1 1 -1 1 -1 1 -1 -1 1 1 -1 1 1 1 -1 Halfspace intersection by the convex hull of 8 points in 3-d: Number of halfspaces: 8 Number of non-redundant halfspaces: 8 Number of intersection points: 6 Number of non-simplicial intersection points: 6 Statistics for: | qhull H0 s Tcv Fp Number of points processed: 8 Number of hyperplanes created: 11 Number of distance tests for qhull: 34 Number of distance tests for merging: 96 Number of distance tests for checking: 100 Number of merged facets: 6 CPU seconds to compute hull (after input): 7.5e-05 3 6 0 0 -1 0 -1 0 1 0 0 -1 0 0 0 1 0 0 0 1 Output completed. Verifying that all points are below outer planes of all facets. Will make 48 distance computations. 8 vertices and 6 facets with normals: -0 -0 -1 0 -1 0 1 -0 -0 -1 -0 -0 0 1 -0 -0 -0 1 user_eg2 ======== user_eg2 'cube qhull options' 'Delaunay options' 'halfspace options' This is the output from user_eg2_r.c. It shows how qhull() may be called from an application, via Qhull's static, reentrant library. user_eg2 is not part of Qhull itself. If user_eg2 fails immediately, user_eg2_r.c was incorrectly linked to Qhull's non-reentrant library, libqhullstatic. Try -- user_eg2 'T1' 'T1' 'T1' ======== compute triangulated convex hull of cube after rotating input Output completed. Verifying that all points are below outer planes of all facets. Will make 96 distance computations. 8 vertices and 12 facets with normals: -0 -0 -1 -0 -0 -1 0 -1 0 0 -1 0 1 -0 -0 1 -0 -0 -1 -0 -0 -1 -0 -0 0 1 -0 0 1 -0 -0 -0 1 -0 -0 1 add points in a diamond 9 vertices and 14 facets 10 vertices and 16 facets 11 vertices and 16 facets 12 vertices and 16 facets 13 vertices and 14 facets 14 vertices and 12 facets 14 vertices and 12 facets with normals: 0.71 -0.71 -0 -0.71 -0.71 0 -0.71 0.71 -0 0.71 0.71 -0 -0.71 -0 -0.71 -0 0.71 -0.71 0 -0.71 -0.71 0.71 0 -0.71 -0 -0.71 0.71 -0.71 0 0.71 0.71 0 0.71 -0 0.71 0.71 Convex hull of 14 points in 3-d: Number of vertices: 14 Number of facets: 12 Number of non-simplicial facets: 12 Statistics for: user_eg2 cube example | qhull s Tcv Q11 Number of points processed: 14 Number of hyperplanes created: 23 Number of distance tests for qhull: 64 Number of distance tests for merging: 276 Number of distance tests for checking: 324 Number of merged facets: 18 CPU seconds to compute hull (after input): 0.000142 Output completed. Verifying that all points are below outer planes of all facets. Will make 168 distance computations. ======== compute 2-d Delaunay triangulation seed: 1633474211 8 vertices and 12 facets with normals: -0.34 -0.55 0.76 -0.97 0.13 -0.22 -0.71 0.068 -0.71 0.79 0.49 0.37 -0.27 -0.9 -0.35 -0.58 -0.29 -0.77 0.81 -0.016 -0.58 0.58 0.07 -0.81 -0.59 0.33 -0.74 -0.19 0.56 -0.81 -0.54 0.69 -0.49 0.061 0.95 -0.32 Delaunay triangulation by the convex hull of 8 points in 3-d: Number of input sites: 8 Number of Delaunay regions: 10 Statistics for: user_eg2 Delaunay example | qhull s d Tcv Number of points processed: 8 Number of hyperplanes created: 20 Number of facets in hull: 12 Number of distance tests for qhull: 31 CPU seconds to compute hull (after input): 4.5e-05 Output completed. Verifying that all points are below 6.2e-15 of all facets. Will make 80 distance computations. ======== add points to triangulation added point p8: -1 -0.7369 1.543 9 points, 0 extra points, 9 vertices, and 14 facets in total added point p9: 0.5112 -0.0827 0.2682 10 points, 0 extra points, 10 vertices, and 16 facets in total added point p10: 0.06553 -0.5621 0.3202 11 points, 0 extra points, 11 vertices, and 18 facets in total added point p11: -0.9059 0.3577 0.9486 12 points, 0 extra points, 12 vertices, and 20 facets in total added point p12: 0.3586 0.8694 0.8844 13 points, 0 extra points, 13 vertices, and 22 facets in total added point p13: -0.233 0.03883 0.0558 14 points, 0 extra points, 14 vertices, and 24 facets in total find Delaunay triangle or adjacent triangle closest to [0.5, 0.5, ...] 0.36 0.87 0.51 -0.08 0.12 0.45 Delaunay triangulation by the convex hull of 14 points in 3-d: Number of input sites: 14 Number of Delaunay regions: 20 Statistics for: user_eg2 Delaunay example | qhull s d Tcv Number of points processed: 14 Number of hyperplanes created: 48 Number of facets in hull: 24 Number of distance tests for qhull: 69 CPU seconds to compute hull (after input): 4.5e-05 Output completed. Verifying that all points are below 6.2e-15 of all facets. Will make 280 distance computations. ======== compute halfspace intersection about the origin for a diamond Halfspace intersection by the convex hull of 8 points in 3-d: Number of halfspaces: 8 Number of non-redundant halfspaces: 8 Number of intersection points: 6 Number of non-simplicial intersection points: 6 Statistics for: user_eg2 halfspace example | qhull H0 s Tcv Number of points processed: 8 Number of hyperplanes created: 11 Number of distance tests for qhull: 34 Number of distance tests for merging: 96 Number of distance tests for checking: 100 Number of merged facets: 6 CPU seconds to compute hull (after input): 7.2e-05 Output completed. Verifying that all points are below outer planes of all facets. Will make 48 distance computations. ======== add halfspaces for cube to intersection added offset -1 and normal 1.732 0 0 8 points, 1 extra points, 9 vertices, and 9 facets in total added offset -1 and normal -1.732 0 0 8 points, 2 extra points, 10 vertices, and 12 facets in total added offset -1 and normal 0 1.732 0 8 points, 3 extra points, 11 vertices, and 15 facets in total added offset -1 and normal 0 -1.732 0 8 points, 4 extra points, 12 vertices, and 18 facets in total added offset -1 and normal 0 0 1.732 8 points, 5 extra points, 13 vertices, and 21 facets in total added offset -1 and normal 0 0 -1.732 8 points, 6 extra points, 14 vertices, and 24 facets in total Halfspace intersection by the convex hull of 14 points in 3-d: Number of halfspaces: 14 Number of non-redundant halfspaces: 14 Number of intersection points: 24 Statistics for: user_eg2 halfspace example | qhull H0 s Tcv Number of points processed: 14 Number of hyperplanes created: 35 Number of distance tests for qhull: 58 Number of distance tests for merging: 248 Number of distance tests for checking: 256 Number of merged facets: 6 CPU seconds to compute hull (after input): 7.2e-05 Output completed. Verifying that all points are below outer planes of all facets. Will make 192 distance computations. user_eg2 'QR1 p' 'v p' 'Fp' ======== user_eg2 'cube qhull options' 'Delaunay options' 'halfspace options' This is the output from user_eg2_r.c. It shows how qhull() may be called from an application, via Qhull's static, reentrant library. user_eg2 is not part of Qhull itself. If user_eg2 fails immediately, user_eg2_r.c was incorrectly linked to Qhull's non-reentrant library, libqhullstatic. Try -- user_eg2 'T1' 'T1' 'T1' ======== compute triangulated convex hull of cube after rotating input Output completed. Verifying that all points are below outer planes of all facets. Will make 96 distance computations. 8 vertices and 12 facets with normals: -0.74 -0.41 -0.52 -0.74 -0.41 -0.52 0.38 -0.91 0.17 0.38 -0.91 0.17 -0.55 -0.07 0.83 -0.55 -0.07 0.83 0.55 0.07 -0.83 0.55 0.07 -0.83 0.74 0.41 0.52 0.74 0.41 0.52 -0.38 0.91 -0.17 -0.38 0.91 -0.17 add points in a diamond 9 vertices and 14 facets 10 vertices and 16 facets 11 vertices and 18 facets 12 vertices and 20 facets 13 vertices and 22 facets 14 vertices and 24 facets 14 vertices and 24 facets with normals: -0.67 0.63 -0.39 0.67 -0.63 0.39 -0.1 -0.71 0.7 -0.65 -0.65 -0.41 -0.62 -0.62 -0.49 0.63 -0.7 -0.34 0.65 -0.66 0.37 -0.65 0.66 -0.37 0.1 0.71 -0.7 -0.63 0.7 0.34 0.62 0.62 0.49 0.65 0.65 0.41 -0.7 -0.13 -0.7 -0.62 -0.49 -0.62 0.11 0.7 -0.71 0.68 0.29 -0.68 0.66 -0.34 -0.67 0.67 -0.3 -0.67 -0.66 0.34 0.67 -0.67 0.3 0.67 0.62 0.49 0.62 0.7 0.13 0.7 -0.11 -0.7 0.71 -0.68 -0.29 0.68 Convex hull of 14 points in 3-d: Number of vertices: 14 Number of facets: 24 Statistics for: user_eg2 cube example | qhull s Tcv Q11 QR1 p QR1 Number of points processed: 14 Number of hyperplanes created: 46 Number of distance tests for qhull: 68 Number of distance tests for merging: 284 Number of distance tests for checking: 244 Number of merged facets: 6 CPU seconds to compute hull (after input): 0.000101 3 14 0.9124763375291641 1.390833937612012 -0.4826674750136243 -0.5764091147442416 0.565375258822974 -1.532352227508615 -0.1847368907548403 1.250953879569599 1.183632828365285 -1.673622343028246 0.4254952007805605 0.1339480758702939 1.673622343028246 -0.4254952007805605 -0.1339480758702939 0.1847368907548403 -1.250953879569599 -1.183632828365285 0.5764091147442416 -0.565375258822974 1.532352227508615 -0.9124763375291641 -1.390833937612012 0.4826674750136243 -2 0 0 2 0 0 0 -2 0 0 2 0 0 0 -2 0 0 2 Output completed. Verifying that all points are below outer planes of all facets. Will make 192 distance computations. ======== compute 2-d Delaunay triangulation seed: 1633474211 8 vertices and 12 facets with normals: -0.34 -0.55 0.76 -0.97 0.13 -0.22 -0.71 0.068 -0.71 0.79 0.49 0.37 -0.27 -0.9 -0.35 -0.58 -0.29 -0.77 0.81 -0.016 -0.58 0.58 0.07 -0.81 -0.59 0.33 -0.74 -0.19 0.56 -0.81 -0.54 0.69 -0.49 0.061 0.95 -0.32 Voronoi diagram by the convex hull of 8 points in 3-d: Number of Voronoi regions: 8 Number of Voronoi vertices: 10 Statistics for: user_eg2 Delaunay example | qhull s d Tcv v p Number of points processed: 8 Number of hyperplanes created: 20 Number of facets in hull: 12 Number of distance tests for qhull: 31 CPU seconds to compute hull (after input): 4.4e-05 2 10 -2.230817053635195 0.3068130254597601 -0.5003366999174907 0.04800833179119612 -0.3932643313293493 -1.281703402842064 -0.3758512482368633 -0.1881223439826356 0.7001940148830702 -0.01373969616322185 0.3579282738896121 0.04321359259718011 -0.3967707745296005 0.2246136767768658 -0.1144444989265631 0.3435538261942026 -0.5537781235884731 0.7098600972332378 0.09537816102240348 1.483877441080219 Output completed. Verifying that all points are below 6.2e-15 of all facets. Will make 80 distance computations. ======== add points to triangulation added point p8: -1 -0.7369 1.543 9 points, 0 extra points, 9 vertices, and 14 facets in total added point p9: 0.5112 -0.0827 0.2682 10 points, 0 extra points, 10 vertices, and 16 facets in total added point p10: 0.06553 -0.5621 0.3202 11 points, 0 extra points, 11 vertices, and 18 facets in total added point p11: -0.9059 0.3577 0.9486 12 points, 0 extra points, 12 vertices, and 20 facets in total added point p12: 0.3586 0.8694 0.8844 13 points, 0 extra points, 13 vertices, and 22 facets in total added point p13: -0.233 0.03883 0.0558 14 points, 0 extra points, 14 vertices, and 24 facets in total find Delaunay triangle or adjacent triangle closest to [0.5, 0.5, ...] 0.36 0.87 0.51 -0.08 0.12 0.45 Voronoi diagram by the convex hull of 14 points in 3-d: Number of Voronoi regions: 14 Number of Voronoi vertices: 20 Statistics for: user_eg2 Delaunay example | qhull s d Tcv v p Number of points processed: 14 Number of hyperplanes created: 48 Number of facets in hull: 24 Number of distance tests for qhull: 69 CPU seconds to compute hull (after input): 4.4e-05 2 20 -0.1144444989265631 0.3435538261942026 -0.5537781235884731 0.7098600972332378 0.2331413585844803 0.1225545992118438 0.1974007824788372 -0.007395311647927866 -0.3808653950623399 -0.5030221216703439 -0.4579789649016728 -0.7058493930724274 -0.2268978160862076 -2.114093361964666 0.3959927190013294 -0.4224439822344098 0.3178651771818528 -0.3498096499503855 -0.8324680258979206 0.6428818374885281 -0.7204464887210509 0.08092719523993458 -1.584860650667058 -0.1352914453356738 -0.1985242380786841 1.133444795359411 -0.02837562403799204 0.8113125066245186 0.6445568522420289 0.4269504189366061 -0.586024973015584 0.06082357538670824 -0.2604321550154716 0.2820512487553397 -0.409257453873538 0.2632049687854979 -0.1045301012157069 -0.1025839366444835 -0.3778513255759362 -0.3137317310536677 Output completed. Verifying that all points are below 6.2e-15 of all facets. Will make 280 distance computations. ======== compute halfspace intersection about the origin for a diamond Halfspace intersection by the convex hull of 8 points in 3-d: Number of halfspaces: 8 Number of non-redundant halfspaces: 8 Number of intersection points: 6 Number of non-simplicial intersection points: 6 Statistics for: user_eg2 halfspace example | qhull H0 s Tcv Fp Number of points processed: 8 Number of hyperplanes created: 11 Number of distance tests for qhull: 34 Number of distance tests for merging: 96 Number of distance tests for checking: 100 Number of merged facets: 6 CPU seconds to compute hull (after input): 7.3e-05 3 6 0 0 -1 0 -1 0 1 0 0 -1 0 0 0 1 0 0 0 1 Output completed. Verifying that all points are below outer planes of all facets. Will make 48 distance computations. ======== add halfspaces for cube to intersection added offset -1 and normal 1.732 0 0 8 points, 1 extra points, 9 vertices, and 9 facets in total added offset -1 and normal -1.732 0 0 8 points, 2 extra points, 10 vertices, and 12 facets in total added offset -1 and normal 0 1.732 0 8 points, 3 extra points, 11 vertices, and 15 facets in total added offset -1 and normal 0 -1.732 0 8 points, 4 extra points, 12 vertices, and 18 facets in total added offset -1 and normal 0 0 1.732 8 points, 5 extra points, 13 vertices, and 21 facets in total added offset -1 and normal 0 0 -1.732 8 points, 6 extra points, 14 vertices, and 24 facets in total Halfspace intersection by the convex hull of 14 points in 3-d: Number of halfspaces: 14 Number of non-redundant halfspaces: 14 Number of intersection points: 24 Statistics for: user_eg2 halfspace example | qhull H0 s Tcv Fp Number of points processed: 14 Number of hyperplanes created: 35 Number of distance tests for qhull: 58 Number of distance tests for merging: 248 Number of distance tests for checking: 256 Number of merged facets: 6 CPU seconds to compute hull (after input): 7.3e-05 3 24 0.5773502691896257 0 -0.4226497308103742 0.5773502691896257 -0.4226497308103742 0 0.5773502691896257 0.4226497308103742 0 0.5773502691896257 0 0.4226497308103742 -0.5773502691896257 0 -0.4226497308103742 -0.5773502691896257 -0.4226497308103742 0 -0.5773502691896257 0 0.4226497308103742 -0.5773502691896257 0.4226497308103742 0 0 0.5773502691896257 -0.4226497308103742 0.4226497308103742 0.5773502691896257 0 -0.4226497308103742 0.5773502691896257 0 0 0.5773502691896257 0.4226497308103742 0 -0.5773502691896257 -0.4226497308103742 -0.4226497308103742 -0.5773502691896257 0 0 -0.5773502691896257 0.4226497308103742 0.4226497308103742 -0.5773502691896257 0 0 -0.4226497308103742 0.5773502691896257 0.4226497308103742 0 0.5773502691896257 0 0.4226497308103742 0.5773502691896257 -0.4226497308103742 0 0.5773502691896257 -0.4226497308103742 0 -0.5773502691896257 0 -0.4226497308103742 -0.5773502691896257 0 0.4226497308103742 -0.5773502691896257 0.4226497308103742 0 -0.5773502691896257 Output completed. Verifying that all points are below outer planes of all facets. Will make 192 distance computations. user_eg3 ======== user_eg3 commands... -- demonstrate calling rbox and qhull from C++. user_eg3 is statically linked to qhullcpp and reentrant qhull. If user_eg3 fails immediately, it is probably linked to the non-reentrant qhull library. Commands: eg-100 Run the example in qh-code.htm eg-convex 'rbox d | qconvex o' with std::vector and C++ classes eg-delaunay 'rbox y c | qdelaunay o' with std::vector and C++ classes eg-voronoi 'rbox y c | qvoronoi o' with std::vector and C++ classes eg-fifo 'rbox y c | qvoronoi FN Fi Fo' with QhullUser and qh_fprintf Rbox and Qhull commands: rbox "200 D4" ... Generate points from rbox qhull "d p" ... Run qhull with options and produce output qhull-cout "o" ... Run qhull with options and produce output to cout qhull "T1" ... Run qhull with level-1 trace to cerr qhull-cout "T1z" ... Run qhull with level-1 trace to cout facets Print qhull's facets when done For example user_eg3 rbox qhull user_eg3 rbox qhull T1 user_eg3 rbox qhull d user_eg3 rbox D2 10 2 "s r 5" qhull "s p" facets user_eg3 eg-convex user_eg3 rbox 10 eg-delaunay qhull "d o" user_eg3 rbox D5 c P2 qhull d eg-delaunay user_eg3 rbox "D5 c P2" qhull v eg-voronoi o user_eg3 rbox D2 10 qhull "v" eg-fifo p Fi Fo user_eg3 eg-100 - f24 - flags: bottom simplicial - normal: -0.721696 -0.658796 -0.212466 - offset: -0.549277 - vertices: p40(v10) p27(v7) p0(v1) - neighboring facets: f34 f47 f54 - f32 - flags: top simplicial - normal: 0.389612 -0.428663 0.815138 - offset: -0.449315 - vertices: p22(v12) p13(v6) p82(v2) - neighboring facets: f61 f72 f77 - f34 - flags: top simplicial - normal: -0.452613 -0.760661 0.465335 - offset: -0.62552 - vertices: p22(v12) p27(v7) p0(v1) - neighboring facets: f24 f80 f73 - f38 - flags: top simplicial - normal: 0.998285 0.058513 -0.00174787 - offset: -0.477764 - vertices: p90(v13) p48(v8) p82(v2) - neighboring facets: f100 f97 f57 - f46 - flags: bottom simplicial - normal: -0.406035 0.904011 0.133791 - offset: -0.547585 - vertices: p73(v15) p76(v9) p97(v5) - neighboring facets: f51 f87 f82 - f47 - flags: bottom simplicial - normal: -0.992416 -0.0122817 -0.122308 - offset: -0.469463 - vertices: p73(v15) p40(v10) p0(v1) - neighboring facets: f24 f81 f88 - f49 - flags: top simplicial - normal: -0.107843 0.991034 0.0788761 - offset: -0.50132 - vertices: p21(v16) p97(v5) p29(v3) - neighboring facets: f116 f66 f51 - f51 - flags: top simplicial - normal: -0.177935 0.975873 0.126537 - offset: -0.506339 - vertices: p21(v16) p76(v9) p97(v5) - neighboring facets: f46 f49 f67 - f52 - flags: top simplicial - normal: -0.378163 -0.891276 -0.250241 - offset: -0.526009 - vertices: p98(v17) p27(v7) p83(v4) - neighboring facets: f75 f53 f54 - f53 - flags: bottom simplicial - normal: -0.430163 -0.821913 -0.373389 - offset: -0.546784 - vertices: p98(v17) p40(v10) p83(v4) - neighboring facets: f108 f52 f54 - f54 - flags: top simplicial - normal: -0.548096 -0.791241 -0.271162 - offset: -0.537299 - vertices: p98(v17) p40(v10) p27(v7) - neighboring facets: f24 f52 f53 - f57 - flags: bottom simplicial - normal: 0.974428 0.137974 -0.177349 - offset: -0.521881 - vertices: p19(v18) p90(v13) p48(v8) - neighboring facets: f38 f60 f113 - f59 - flags: bottom simplicial - normal: 0.239508 -0.0103785 -0.970839 - offset: -0.517616 - vertices: p19(v18) p4(v14) p83(v4) - neighboring facets: f76 f110 f60 - f60 - flags: top simplicial - normal: 0.567061 -0.0365561 -0.822865 - offset: -0.572132 - vertices: p19(v18) p4(v14) p48(v8) - neighboring facets: f85 f57 f59 - f61 - flags: bottom simplicial - normal: 0.433241 -0.284128 0.855321 - offset: -0.426268 - vertices: p37(v19) p13(v6) p82(v2) - neighboring facets: f32 f69 f95 - f65 - flags: top simplicial - normal: -0.198254 0.211674 0.957021 - offset: -0.497913 - vertices: p67(v20) p12(v11) p76(v9) - neighboring facets: f79 f67 f68 - f66 - flags: top simplicial - normal: -0.155514 0.97946 0.128347 - offset: -0.504016 - vertices: p67(v20) p21(v16) p29(v3) - neighboring facets: f49 f71 f67 - f67 - flags: bottom simplicial - normal: -0.16055 0.978089 0.132539 - offset: -0.504235 - vertices: p67(v20) p21(v16) p76(v9) - neighboring facets: f51 f65 f66 - f68 - flags: top simplicial - normal: 0.598999 -0.0537935 0.798941 - offset: -0.457967 - vertices: p67(v20) p37(v19) p12(v11) - neighboring facets: f96 f65 f69 - f69 - flags: bottom simplicial - normal: 0.69477 -0.0317528 0.718531 - offset: -0.45153 - vertices: p67(v20) p37(v19) p82(v2) - neighboring facets: f61 f98 f68 - f71 - flags: bottom simplicial - normal: 0.877687 0.308225 0.366966 - offset: -0.494379 - vertices: p67(v20) p90(v13) p29(v3) - neighboring facets: f115 f66 f99 - f72 - flags: top simplicial - normal: 0.245263 -0.887198 0.390801 - offset: -0.480731 - vertices: p41(v21) p22(v12) p82(v2) - neighboring facets: f32 f74 f73 - f73 - flags: bottom simplicial - normal: 0.0168085 -0.963019 0.268908 - offset: -0.510609 - vertices: p41(v21) p22(v12) p27(v7) - neighboring facets: f34 f75 f72 - f74 - flags: bottom simplicial - normal: 0.227082 -0.964773 0.132845 - offset: -0.464868 - vertices: p41(v21) p4(v14) p82(v2) - neighboring facets: f84 f72 f76 - f75 - flags: bottom simplicial - normal: 0.0345717 -0.998303 0.0468616 - offset: -0.47919 - vertices: p41(v21) p27(v7) p83(v4) - neighboring facets: f52 f76 f73 - f76 - flags: top simplicial - normal: 0.137757 -0.987556 0.0758723 - offset: -0.471349 - vertices: p41(v21) p4(v14) p83(v4) - neighboring facets: f59 f75 f74 - f77 - flags: bottom simplicial - normal: -0.323398 -0.00535492 0.946248 - offset: -0.501516 - vertices: p15(v22) p22(v12) p13(v6) - neighboring facets: f32 f78 f80 - f78 - flags: top simplicial - normal: -0.20543 0.0915675 0.974379 - offset: -0.474687 - vertices: p15(v22) p12(v11) p13(v6) - neighboring facets: f94 f77 f79 - f79 - flags: bottom simplicial - normal: -0.218614 0.160888 0.962457 - offset: -0.484859 - vertices: p15(v22) p12(v11) p76(v9) - neighboring facets: f65 f82 f78 - f80 - flags: top simplicial - normal: -0.593167 -0.119334 0.796186 - offset: -0.544059 - vertices: p15(v22) p22(v12) p0(v1) - neighboring facets: f34 f81 f77 - f81 - flags: bottom simplicial - normal: -0.974282 0.088044 0.20742 - offset: -0.50771 - vertices: p15(v22) p73(v15) p0(v1) - neighboring facets: f47 f80 f82 - f82 - flags: top simplicial - normal: -0.826328 0.394399 0.402034 - offset: -0.559684 - vertices: p15(v22) p73(v15) p76(v9) - neighboring facets: f46 f79 f81 - f84 - flags: top simplicial - normal: 0.82988 -0.542609 -0.129903 - offset: -0.585213 - vertices: p57(v23) p4(v14) p82(v2) - neighboring facets: f74 f101 f85 - f85 - flags: bottom simplicial - normal: 0.906692 -0.29884 -0.297664 - offset: -0.57209 - vertices: p57(v23) p4(v14) p48(v8) - neighboring facets: f60 f102 f84 - f86 - flags: top simplicial - normal: -0.85363 0.243861 -0.460269 - offset: -0.522928 - vertices: p11(v24) p40(v10) p97(v5) - neighboring facets: f89 f87 f88 - f87 - flags: bottom simplicial - normal: -0.890339 0.291001 -0.350165 - offset: -0.531756 - vertices: p11(v24) p73(v15) p97(v5) - neighboring facets: f46 f86 f88 - f88 - flags: top simplicial - normal: -0.987894 0.0156004 -0.154345 - offset: -0.477251 - vertices: p11(v24) p73(v15) p40(v10) - neighboring facets: f47 f86 f87 - f89 - flags: bottom simplicial - normal: -0.492188 0.332666 -0.804416 - offset: -0.526118 - vertices: p25(v25) p40(v10) p97(v5) - neighboring facets: f86 f114 f109 - f94 - flags: bottom simplicial - normal: 0.368779 -0.208614 0.905805 - offset: -0.440207 - vertices: p7(v26) p12(v11) p13(v6) - neighboring facets: f78 f95 f96 - f95 - flags: top simplicial - normal: 0.417114 -0.259346 0.871066 - offset: -0.429768 - vertices: p7(v26) p37(v19) p13(v6) - neighboring facets: f61 f94 f96 - f96 - flags: bottom simplicial - normal: 0.469304 -0.162419 0.867971 - offset: -0.446808 - vertices: p7(v26) p37(v19) p12(v11) - neighboring facets: f68 f94 f95 - f97 - flags: top simplicial - normal: 0.911891 0.1675 0.374697 - offset: -0.446013 - vertices: p28(v27) p90(v13) p82(v2) - neighboring facets: f38 f98 f99 - f98 - flags: bottom simplicial - normal: 0.888791 0.148029 0.433749 - offset: -0.448933 - vertices: p28(v27) p67(v20) p82(v2) - neighboring facets: f69 f97 f99 - f99 - flags: top simplicial - normal: 0.903592 0.183305 0.387197 - offset: -0.447956 - vertices: p28(v27) p67(v20) p90(v13) - neighboring facets: f71 f97 f98 - f100 - flags: bottom simplicial - normal: 0.93763 -0.294784 -0.184262 - offset: -0.546054 - vertices: p42(v28) p48(v8) p82(v2) - neighboring facets: f38 f101 f102 - f101 - flags: top simplicial - normal: 0.933493 -0.306605 -0.185968 - offset: -0.547862 - vertices: p42(v28) p57(v23) p82(v2) - neighboring facets: f84 f100 f102 - f102 - flags: bottom simplicial - normal: 0.928146 -0.300441 -0.219729 - offset: -0.55469 - vertices: p42(v28) p57(v23) p48(v8) - neighboring facets: f85 f100 f101 - f108 - flags: top simplicial - normal: 0.00135876 0.0103445 -0.999946 - offset: -0.494086 - vertices: p5(v30) p40(v10) p83(v4) - neighboring facets: f53 f110 f109 - f109 - flags: top simplicial - normal: -0.106214 0.129184 -0.985916 - offset: -0.504323 - vertices: p5(v30) p25(v25) p40(v10) - neighboring facets: f89 f108 f111 - f110 - flags: bottom simplicial - normal: 0.125474 0.0262996 -0.991748 - offset: -0.496467 - vertices: p5(v30) p19(v18) p83(v4) - neighboring facets: f59 f108 f111 - f111 - flags: bottom simplicial - normal: 0.0358445 0.163534 -0.985886 - offset: -0.514407 - vertices: p5(v30) p25(v25) p19(v18) - neighboring facets: f112 f110 f109 - f112 - flags: top simplicial - normal: 0.0769357 0.958704 -0.273801 - offset: -0.543222 - vertices: p78(v31) p25(v25) p19(v18) - neighboring facets: f111 f113 f114 - f113 - flags: top simplicial - normal: 0.129005 0.982313 -0.135717 - offset: -0.512909 - vertices: p78(v31) p19(v18) p90(v13) - neighboring facets: f57 f115 f112 - f114 - flags: bottom simplicial - normal: -0.0450665 0.957786 -0.283929 - offset: -0.551711 - vertices: p78(v31) p25(v25) p97(v5) - neighboring facets: f89 f116 f112 - f115 - flags: top simplicial - normal: 0.102483 0.993113 -0.0567803 - offset: -0.497056 - vertices: p78(v31) p90(v13) p29(v3) - neighboring facets: f71 f116 f113 - f116 - flags: bottom simplicial - normal: -0.00662022 0.999903 -0.0122926 - offset: -0.49314 - vertices: p78(v31) p97(v5) p29(v3) - neighboring facets: f49 f115 f114 user_eg3 eg-convex A 3-d diamond (rbox d) 3 rbox "d" 6 0 0 -0.5 0 0 0.5 0 -0.5 0 0 0.5 0 -0.5 0 0 0.5 0 0 Input points and facetlist of its convex hull (qhull o) 3 6 8 12 0 0 -0.5 0 0 0.5 0 -0.5 0 0 0.5 0 -0.5 0 0 0.5 0 0 3 2 0 4 3 0 2 5 3 1 2 4 3 2 1 5 3 3 0 5 3 0 3 4 3 1 3 5 3 3 1 4 Input points and facetlist using std::vector and C++ classes 3 6 8 12 0 0 -0.5 0 0 0.5 0 -0.5 0 0 0.5 0 -0.5 0 0 0.5 0 0 3 2 0 4 3 0 2 5 3 1 2 4 3 2 1 5 3 3 0 5 3 0 3 4 3 1 3 5 3 3 1 4 Its outward pointing normals as vector plus offset (qhull n) 4 8 -0.5773502691896258 -0.5773502691896258 -0.5773502691896258 -0.2886751345948129 0.5773502691896258 -0.5773502691896258 -0.5773502691896258 -0.2886751345948129 -0.5773502691896258 -0.5773502691896258 0.5773502691896258 -0.2886751345948129 0.5773502691896258 -0.5773502691896258 0.5773502691896258 -0.2886751345948129 0.5773502691896258 0.5773502691896258 -0.5773502691896258 -0.2886751345948129 -0.5773502691896258 0.5773502691896258 -0.5773502691896258 -0.2886751345948129 0.5773502691896258 0.5773502691896258 0.5773502691896258 -0.2886751345948129 -0.5773502691896258 0.5773502691896258 0.5773502691896258 -0.2886751345948129 user_eg3 eg-delaunay A 2-d triangle in a square (rbox y c D2) 2 rbox "y c D2" 7 0.0795233 -0.451105 0.279706 0.0133225 -0.0888864 0.0861965 -0.5 -0.5 -0.5 0.5 0.5 -0.5 0.5 0.5 The 2-d input sites are lifted to a 3-d paraboloid. A Delaunay region is a facet of the paraboloid's convex hull. The Delaunay triangulation as input sites and Delaunay regions (qhull d o) 3 7 8 12 0.07952334739223432 -0.4511049142583319 0.209819606448483 0.2797056779076398 0.01332249167684696 0.07841275503825199 -0.08888640449278651 0.08619647248293871 0.01533062477215727 -0.5 -0.5 0.5 -0.5 0.5 0.5 0.5 -0.5 0.5 0.5 0.5 0.5 3 2 4 3 3 2 6 4 3 5 0 3 3 0 2 3 3 6 1 5 3 1 6 2 3 1 0 5 3 0 1 2 The same results using std::vector and C++ classes 3 7 8 12 0.0795233 -0.451105 0.20982 0.279706 0.0133225 0.0784128 -0.0888864 0.0861965 0.0153306 -0.5 -0.5 0.5 -0.5 0.5 0.5 0.5 -0.5 0.5 0.5 0.5 0.5 3 2 4 3 3 2 6 4 3 5 0 3 3 0 2 3 3 6 1 5 3 1 6 2 3 1 0 5 3 0 1 2 user_eg3 eg-voronoi A 2-d triangle in a square (rbox y c D2) 2 rbox "y c D2" 7 0.0795233 -0.451105 0.279706 0.0133225 -0.0888864 0.0861965 -0.5 -0.5 -0.5 0.5 0.5 -0.5 0.5 0.5 Its Voronoi diagram as vertices and regions (qhull v o) The Voronoi diagram is the dual of the Delaunay triangulation Voronoi vertices are Delaunay regions, and Voronoi regions are Delaunay input sites The Voronoi vertex at infinity is represented as '-10.101 -10.101' 2 9 7 1 -10.101 -10.101 -0.5894591914795221 -2.775557561562891e-17 0 0.5856274089010268 -1.387778780781446e-17 -2.967377898513707 -0.2290343684408742 -0.2527745420948135 0.9568726986640038 2.081668171172169e-17 0.1571419516493774 0.3619977084558904 0.3129256373384354 -0.2763523586794005 0.05307821633938364 -0.1643502208872393 4 8 4 3 7 4 8 6 5 7 5 8 4 1 2 6 4 4 1 0 3 3 2 0 1 4 7 3 0 5 4 6 2 0 5 The same results using std::vector and C++ classes Qhull::prepareVoronoi assigns facetT.visit_id and vertexT.neighbors The Voronoi regions are rotated by one Voronoi vertex (prepareVoronoi occurs twice) 2 9 7 1 -10.101 -10.101 -0.589459 -2.77556e-17 0 0.585627 -1.38778e-17 -2.96738 -0.229034 -0.252775 0.956873 2.08167e-17 0.157142 0.361998 0.312926 -0.276352 0.0530782 -0.16435 4 7 8 4 3 4 7 8 6 5 5 6 8 4 1 2 4 3 4 1 0 3 1 2 0 4 5 7 3 0 4 5 6 2 0 user_eg3 eg-fifo A 2-d triangle in a square (rbox y c D2) 2 rbox "y c D2" 7 0.0795233 -0.451105 0.279706 0.0133225 -0.0888864 0.0861965 -0.5 -0.5 -0.5 0.5 0.5 -0.5 0.5 0.5 Its Voronoi vertices (qhull v p) This is the first part of eg-voronoi, but without infinity 2 8 -0.5894591914795221 -2.775557561562891e-17 0 0.5856274089010268 -1.387778780781446e-17 -2.967377898513707 -0.2290343684408742 -0.2527745420948135 0.9568726986640038 2.081668171172169e-17 0.1571419516493774 0.3619977084558904 0.3129256373384354 -0.2763523586794005 0.05307821633938364 -0.1643502208872393 Its Voronoi regions (qhull v FN) This is the second part of eg-voronoi, with ids one less Regions are ordered by the corresponding input site. 7 4 7 3 2 6 4 7 5 4 6 5 7 3 0 1 5 4 3 0 -1 2 3 1 -1 0 4 6 2 -1 4 4 5 1 -1 4 The same results as 'qhull v p FN' using std::vector and C++ classes Qhull::prepareVoronoi assigns facet.visit_id and vertex.neighbors prepareVoronoi is also called by q.outputQhull("FN"), hence the rotated vertices 2 8 -0.589459 -2.77556e-17 0 0.585627 -1.38778e-17 -2.96738 -0.229034 -0.252775 0.956873 2.08167e-17 0.157142 0.361998 0.312926 -0.276352 0.0530782 -0.16435 7 4 6 7 3 2 4 6 7 5 4 5 5 7 3 0 1 4 2 3 0 -1 3 0 1 -1 4 4 6 2 -1 4 4 5 1 -1 Hyperplanes for bounded facets between Voronoi regions (qhull v Fi) Each hyperplane is the perpendicular bisector of 2 input sites. 10 5 0 1 0.3958261856523667 0.9183254492563615 0.1299172425168069 5 0 5 0.9933067158065388 -0.1155065726858348 -0.3427516509210134 5 0 2 -0.2990888272252211 0.954225273941663 0.1727022360246516 5 0 3 -0.9964596398753636 -0.08407250501478321 -0.2494748932535505 5 1 5 0.3943714145865591 -0.9189511343684148 -0.3773632397513814 5 1 2 -0.9810105005095815 0.1939546284313432 0.08394677360204827 5 1 6 0.4123709353479589 0.9110160326142727 -0.3945864897570009 5 2 6 0.8181972788475073 0.5749375730342683 -0.3366992011759034 5 2 3 -0.574189571650573 -0.8187223801800775 -0.3384613206611199 5 2 4 -0.7047972640762143 0.7094087795838752 -0.4154492254393445 Hyperplanes for unbounded rays of unbounded facets (qhull v Fo) Each ray goes through the midpoint of 2 input sites, oriented outwards 4 5 3 5 1 -5.624508437144599e-18 -2.812254218572297e-18 5 3 4 -3.10259629632159e-16 1 -1.551298148160795e-16 5 4 6 1 -0 -0 5 5 6 -4.55634179336919e-17 1 2.278170896684595e-17 The same result as 'qhull v Fi' using QhullUser and its custom qh_fprintf qh_fprintf captures the output from qh_eachvoronoi in io_r.c (qhull v Fi Fo Ta) 10 5 0 1 0.395826 0.918325 0.129917 5 0 5 0.993307 -0.115507 -0.342752 5 0 2 -0.299089 0.954225 0.172702 5 0 3 -0.99646 -0.0840725 -0.249475 5 1 5 0.394371 -0.918951 -0.377363 5 1 2 -0.981011 0.193955 0.0839468 5 1 6 0.412371 0.911016 -0.394586 5 2 6 0.818197 0.574938 -0.336699 5 2 3 -0.57419 -0.818722 -0.338461 5 2 4 -0.704797 0.709409 -0.415449 The same result as 'qhull v Fo' using QhullUser and its custom qh_fprintf 4 5 3 5 1 -5.62451e-18 -2.81225e-18 5 3 4 -3.1026e-16 1 -1.5513e-16 5 4 6 1 -0 -0 5 5 6 -4.55634e-17 1 2.27817e-17 Message codes captured by qh_fprintf in QhullUser.cpp (qhull v Fo Ta): 9231 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274 user_eg3 rbox qhull Results of qhull Convex hull of 10 points in 2-d: Number of vertices: 4 Number of facets: 4 Statistics for: rbox "10 D2" | qhull Number of points processed: 4 Number of hyperplanes created: 5 Number of distance tests for qhull: 51 CPU seconds to compute hull (after input): 3.4e-05 user_eg3 rbox qhull T1 Results of T1 [QH0013]qh_initqhull_globals: for rbox "10 D2" | qhull T1 qh_meminitbuffers: memory initialized with alignment 8 qh_maxmin: dim min max width nearzero min-point max-point 0 -4.28543191e-01 3.79031236e-01 8.07574428e-01 7.6125e-15 p1 p4 1 -4.97972782e-01 4.74582647e-01 9.72555429e-01 1.6458e-14 p0 p1 qh_maxmin: found the max and min points (by dim): p1 p4 p0 p1 [QH1002]qh_maxsimplex: selected point p0 for 3`th initial vertex, det=0.7462, targetdet=0.7854, mindet=0.007854 [QH1028]qh_createsimplex: created simplex qh_initialhull: qh.interior_point p-2: -0.02391 0.1182 [QH1027]qh_checkpolygon: check all facets from f1, qh.NEWtentative? 0 [QH1064]qh_checkconvex: check that facets are not-flipped and for qh.ZEROcentrum that simplicial vertices are below their neighbor (dist<0.0) qh_initialhull: simplex constructed [QH1042]qh_partitionall: partition all points into outside sets Trace level T0, IStracing 1, point TP-3, merge TM0, dist TW1.8e+308, qh.tracefacet_id -1, traceridge_id -1, tracevertex_id -1, last qh.RERUN 0, rbox "10 D2" | qhull T1 Options selected for Qhull 2020.2.r 2020/08/31: run-id 370121029 _pre-merge _zero-centrum _max-width 0.97 Error-roundoff 4.3e-16 _one-merge 2.1e-15 _near-inside 1.1e-14 Visible-distance 8.5e-16 U-max-coplanar 8.5e-16 Width-outside 1.7e-15 _wide-facet 5.1e-15 [QH1029]qh_furthestnext: made f3 next facet(dist 0.19) [QH1030]qh_initbuild: initial hull created and points partitioned [QH1037]qh_buildhull: start build hull [QH1049]qh_addpoint: add p8(v4) 0.19 above f3 to hull of 3 facets, 0 merges, 3 outside at 6e-05 CPU secs. Previous p-1(v3) delta 6e-05 CPU, 3 facets, 0 merges, 3 hyperplanes, 61 distplanes, 0 retries [QH1040]qh_findhorizon: find horizon for point p8 facet f3 [QH1041]qh_findhorizon: 2 horizon facets(good 2), 1 visible(good 1), 0 coplanar [QH1032]qh_makenewfacets: created 2 new facets f4..f5 from point p8 to horizon [QH1019]qh_matchnewfacets: match neighbors for new facets. [QH1043]qh_partitionvisible: partitioned 2 points from outsidesets, 0 points from coplanarsets, and 0 deleted vertices [QH1018]qh_deletevisible: delete 1 visible facets and 0 vertices [QH1039]qh_buildhull: completed the hull construction [QH1036]Qhull: algorithm completed [QH1027]qh_checkpolygon: check all facets from f1, qh.NEWtentative? 0 [QH1064]qh_checkconvex: check that facets are not-flipped and for qh.ZEROcentrum that simplicial vertices are below their neighbor (dist<0.0) Convex hull of 10 points in 2-d: Number of vertices: 4 Number of facets: 4 Statistics for: rbox "10 D2" | qhull T1 Number of points processed: 4 Number of hyperplanes created: 5 Number of distance tests for qhull: 51 CPU seconds to compute hull (after input): 7.7e-05 user_eg3 rbox qhull d Results of d Delaunay triangulation by the convex hull of 10 points in 3-d: Number of input sites: 10 Number of Delaunay regions: 14 Statistics for: rbox "10 D2" | qhull d Number of points processed: 10 Number of hyperplanes created: 28 Number of facets in hull: 16 Number of distance tests for qhull: 47 CPU seconds to compute hull (after input): 6.1e-05 user_eg3 rbox y c rbox y rbox c 3 rbox "y" "c" 12 -0.306292 0.149266 -0.289011 -0.409906 -0.282924 -0.0983473 0.0770774 0.440163 -0.185531 -0.212802 0.438723 -0.375664 -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 user_eg3 rbox D2 10 2 "s r 5" qhull 's p' facets rbox D2 rbox 10 rbox 2 rbox s r 5 Results of s p Convex hull of 17 points in 2-d: Number of vertices: 7 Number of facets: 7 Statistics for: rbox "10 D2" "2 D2" "s r 5 D2" | qhull s p Number of points processed: 7 Number of hyperplanes created: 11 Number of distance tests for qhull: 78 CPU seconds to compute hull (after input): 4.3e-05 2 7 -0.02222276248244826 -0.4979727817680433 -0.4285431913366012 0.4745826469497594 0.3790312361708201 0.3779794437605696 0.1545084971874737 0.4755282581475768 -0.4045084971874738 -0.2938926261462365 0.1545084971874736 -0.4755282581475768 0.5 -1.224646799147353e-16 Facets created by Qhull::runQhull() - f5 - flags: bottom simplicial - normal: 0.952413 0.304811 - offset: -0.476206 - vertices: p4(v4) p16(v2) - neighboring facets: f8 f11 - f6 - flags: bottom simplicial - normal: -0.999511 -0.0312605 - offset: -0.413498 - vertices: p14(v5) p1(v1) - neighboring facets: f10 f7 - f7 - flags: top simplicial - normal: -0.470938 -0.882167 - offset: -0.44976 - vertices: p14(v5) p0(v3) - neighboring facets: f9 f6 - f8 - flags: top simplicial - normal: 0.809017 -0.587785 - offset: -0.404508 - vertices: p15(v6) p16(v2) - neighboring facets: f5 f9 - f9 - flags: bottom simplicial - normal: 0.125986 -0.992032 - offset: -0.491205 - vertices: p15(v6) p0(v3) - neighboring facets: f7 f8 - f10 - flags: top simplicial - normal: -0.00162183 0.999999 - offset: -0.475277 - vertices: p12(v7) p1(v1) - neighboring facets: f6 f11 - f11 - flags: bottom simplicial - normal: 0.398486 0.917174 - offset: -0.497712 - vertices: p12(v7) p4(v4) - neighboring facets: f5 f10 user_eg3 rbox "10 D2" eg-convex rbox 10 D2 Input points and facetlist for convex hull of rbox "10 D2" via C++ classes 2 10 4 4 -0.0222228 -0.497973 -0.428543 0.474583 0.31054 0.240018 -0.0188396 0.363026 0.379031 0.377979 -0.299496 0.377661 0.347182 0.0836553 -0.0048582 0.348268 0.344312 -0.143731 0.309331 -0.077581 2 4 1 2 1 0 2 8 4 2 0 8 user_eg3 rbox '10 D2' qhull s eg-convex rbox 10 D2 Results of s Convex hull of 10 points in 2-d: Number of vertices: 4 Number of facets: 4 Statistics for: rbox "10 D2" | qhull s Number of points processed: 4 Number of hyperplanes created: 5 Number of distance tests for qhull: 51 CPU seconds to compute hull (after input): 3.3e-05 Input points and facetlist for 'qhull s' via C++ classes 2 10 4 4 -0.0222228 -0.497973 -0.428543 0.474583 0.31054 0.240018 -0.0188396 0.363026 0.379031 0.377979 -0.299496 0.377661 0.347182 0.0836553 -0.0048582 0.348268 0.344312 -0.143731 0.309331 -0.077581 2 4 1 2 1 0 2 8 4 2 0 8 user_eg3 rbox 10 eg-delaunay qhull 'd o' rbox 10 Delaunay triangulation of 10 points as 4-d paraboloid via C++ classes 4 10 15 30 -0.374949 0.224726 -0.0378235 0.192519 0.300492 0.369454 0.421096 0.404114 0.364148 0.233952 0.0348979 0.188555 -0.470713 -0.281065 0.135495 0.318928 0.264275 -0.326571 0.317506 0.2773 0.318323 0.0506033 0.489822 0.343815 0.433436 -0.248039 0.203767 0.290911 -0.285595 -0.00222701 -0.42931 0.265876 -0.40759 -0.362593 -0.0978938 0.307186 -0.301385 -0.378685 0.434172 0.422741 4 5 2 1 6 4 5 4 2 6 4 2 4 7 6 4 4 0 5 2 4 0 5 2 1 4 0 4 9 3 4 4 0 9 5 4 0 9 5 1 4 4 8 7 6 4 4 8 9 3 4 8 0 7 3 4 0 8 4 3 4 4 8 2 7 4 8 0 2 7 4 8 0 4 2 Results of d o 4 10 15 30 -0.374949442106252 0.2247255418679914 -0.03782349642163468 0.1925192701852094 0.3004920247946792 0.3694544596313075 0.4210962191420572 0.4041140804824029 0.3641479121187217 0.2339522165562512 0.03489791698278666 0.1885552061417448 -0.4707134565997063 -0.2810653003687648 0.1354949890035158 0.3189277533404903 0.2642752088273644 -0.3265712199048802 0.3175057017407433 0.2773000183087906 0.3183227589524563 0.05060330969337679 0.4898217078203537 0.3438153792710754 0.4334355904100794 -0.2480392830893763 0.2037671452423252 0.2909109464698327 -0.2855954200826543 -0.002227006947833121 -0.4293096679535784 0.2658764945305452 -0.4075898489985521 -0.3625928418362446 -0.09789381697577781 0.3071862533596335 -0.3013850588364387 -0.3786854184034145 0.4341719447953365 0.4227408774485775 4 5 2 1 6 4 5 4 2 6 4 2 4 7 6 4 4 0 5 2 4 0 5 2 1 4 0 4 9 3 4 4 0 9 5 4 0 9 5 1 4 4 8 7 6 4 4 8 9 3 4 8 0 7 3 4 0 8 4 3 4 4 8 2 7 4 8 0 2 7 4 8 0 4 2 user_eg3 rbox D5 c P2 qhull d eg-delaunay rbox D5 rbox c rbox P2 Results of d Delaunay triangulation by the convex hull of 33 points in 6-d: Number of input sites: 33 Number of Delaunay regions: 2 Number of non-simplicial Delaunay regions: 2 Statistics for: rbox "c D5" "P2 D5" | qhull d Number of points processed: 33 Number of hyperplanes created: 87 Number of facets in hull: 11 Number of distance tests for qhull: 826 Number of distance tests for merging: 3868 Number of distance tests for checking: 363 Number of merged facets: 296 CPU seconds to compute hull (after input): 0.001241 Vertices and Delaunay regions of paraboloid from 'qhull d' via C++ classes 6 33 2 6 -0.5 -0.5 -0.5 -0.5 -0.5 1.25 -0.5 -0.5 -0.5 -0.5 0.5 1.25 -0.5 -0.5 -0.5 0.5 -0.5 1.25 -0.5 -0.5 -0.5 0.5 0.5 1.25 -0.5 -0.5 0.5 -0.5 -0.5 1.25 -0.5 -0.5 0.5 -0.5 0.5 1.25 -0.5 -0.5 0.5 0.5 -0.5 1.25 -0.5 -0.5 0.5 0.5 0.5 1.25 -0.5 0.5 -0.5 -0.5 -0.5 1.25 -0.5 0.5 -0.5 -0.5 0.5 1.25 -0.5 0.5 -0.5 0.5 -0.5 1.25 -0.5 0.5 -0.5 0.5 0.5 1.25 -0.5 0.5 0.5 -0.5 -0.5 1.25 -0.5 0.5 0.5 -0.5 0.5 1.25 -0.5 0.5 0.5 0.5 -0.5 1.25 -0.5 0.5 0.5 0.5 0.5 1.25 0.5 -0.5 -0.5 -0.5 -0.5 1.25 0.5 -0.5 -0.5 -0.5 0.5 1.25 0.5 -0.5 -0.5 0.5 -0.5 1.25 0.5 -0.5 -0.5 0.5 0.5 1.25 0.5 -0.5 0.5 -0.5 -0.5 1.25 0.5 -0.5 0.5 -0.5 0.5 1.25 0.5 -0.5 0.5 0.5 -0.5 1.25 0.5 -0.5 0.5 0.5 0.5 1.25 0.5 0.5 -0.5 -0.5 -0.5 1.25 0.5 0.5 -0.5 -0.5 0.5 1.25 0.5 0.5 -0.5 0.5 -0.5 1.25 0.5 0.5 -0.5 0.5 0.5 1.25 0.5 0.5 0.5 -0.5 -0.5 1.25 0.5 0.5 0.5 -0.5 0.5 1.25 0.5 0.5 0.5 0.5 -0.5 1.25 0.5 0.5 0.5 0.5 0.5 1.25 2 0 0 0 0 4 32 17 18 3 20 5 6 24 9 10 12 19 21 22 7 25 26 11 28 13 14 23 27 29 30 15 31 16 1 2 4 8 0 17 17 18 20 24 19 21 22 25 26 28 23 27 29 30 31 16 32 user_eg3 rbox '10 D2' eg-voronoi rbox 10 D2 Voronoi vertices and regions for rbox "10 D2" via C++ classes 2 15 10 1 -10.101 -10.101 -0.129438 -0.0724741 0.0826769 -0.239764 0.129526 1.71603 0.174036 0.531752 0.185142 0.388255 -0.906594 -0.296296 -0.195481 -0.0711189 -0.140758 0.723386 -0.16763 0.208062 0.0586831 0.0663207 0.0880634 0.105408 0.476159 -0.0316837 3.09421 -0.0647219 0.541052 0.211562 5 7 1 2 0 6 4 8 3 0 6 3 14 5 11 4 9 4 3 8 6 14 5 4 3 0 13 4 9 7 6 8 5 14 11 10 12 13 7 11 5 4 9 7 1 10 4 13 0 2 12 4 12 2 1 10 user_eg3 rbox "D5 c P2" qhull v eg-voronoi o rbox D5 c P2 Results of v Voronoi diagram by the convex hull of 33 points in 6-d: Number of Voronoi regions: 33 Number of Voronoi vertices: 2 Number of non-simplicial Voronoi vertices: 2 Statistics for: rbox "D5 c P2" | qhull v Number of points processed: 33 Number of hyperplanes created: 87 Number of facets in hull: 11 Number of distance tests for qhull: 826 Number of distance tests for merging: 3868 Number of distance tests for checking: 363 Number of merged facets: 296 CPU seconds to compute hull (after input): 0.001214 Voronoi vertices and regions for 'qhull v' via C++ classes 5 3 33 1 -10.101 -10.101 -10.101 -10.101 -10.101 0 0 0 0 0 0.916667 0 0 0 0 2 0 2 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 Results of o 5 3 33 1 -10.101 -10.101 -10.101 -10.101 -10.101 0 0 0 0 0 0.9166666666666667 0 0 0 0 2 0 2 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 2 0 1 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 user_eg3 rbox '10 D2' eg-fifo rbox 10 D2 Voronoi vertices for rbox "10 D2" via QhullUser and qh_fprintf 2 14 -0.129438 -0.0724741 0.0826769 -0.239764 0.129526 1.71603 0.174036 0.531752 0.185142 0.388255 -0.906594 -0.296296 -0.195481 -0.0711189 -0.140758 0.723386 -0.16763 0.208062 0.0586831 0.0663207 0.0880634 0.105408 0.476159 -0.0316837 3.09421 -0.0647219 0.541052 0.211562 10 5 6 0 1 -1 5 4 7 2 -1 5 3 13 4 10 4 8 3 2 7 6 13 4 3 2 -1 12 4 8 6 5 7 5 13 10 9 11 12 7 10 4 3 8 6 0 9 4 12 -1 1 11 4 11 1 0 9 Hyperplanes for bounded facets between Voronoi regions via QhullUser and qh_fprintf 19 5 0 5 -0.301881 0.953346 0.00878913 5 0 7 0.0205153 0.99979 0.0751143 5 0 9 0.619259 0.785187 0.137061 5 1 5 0.799595 -0.600539 0.546971 5 1 3 0.964872 -0.262721 0.325862 5 2 6 0.22816 -0.973624 0.0825353 5 2 4 0.444671 0.895694 -0.430084 5 2 7 -0.945841 0.32463 0.0490754 5 3 5 -0.998643 0.0520745 -0.178237 5 3 7 0.687752 -0.725945 0.26633 5 3 4 0.999294 0.037557 -0.193884 5 4 6 -0.107584 -0.994196 0.268542 5 4 7 -0.997018 -0.0771644 0.214549 5 5 7 0.995061 -0.0992661 0.187455 5 6 7 -0.799364 0.600847 0.00706064 5 6 9 -0.228542 -0.973534 0.077977 5 6 8 -0.0126184 -0.99992 -0.0256728 5 7 9 0.593695 -0.80469 0.0185277 5 8 9 -0.467479 0.884004 0.250603 Hyperplanes for unbounded facets between Voronoi regions via QhullUser and qh_fprintf 4 5 0 8 0.719063 0.694945 0.107173 5 0 1 -0.385496 0.92271 -0.076093 5 1 4 0.992921 -0.118775 0.0752121 5 4 8 -0.0664014 -0.997793 0.140881 Message codes captured by qh_fprintf in QhullUser.cpp (qhull v Fo Ta): 9231 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274 user_eg3 rbox D2 10 qhull v eg-fifo p Fi Fo rbox D2 rbox 10 Results of v Voronoi diagram by the convex hull of 10 points in 3-d: Number of Voronoi regions: 10 Number of Voronoi vertices: 14 Statistics for: rbox "10 D2" | qhull v Number of points processed: 10 Number of hyperplanes created: 28 Number of facets in hull: 16 Number of distance tests for qhull: 47 CPU seconds to compute hull (after input): 6.1e-05 Voronoi vertices for 'qhull v' via C++ classes 2 14 -0.129438 -0.0724741 0.0826769 -0.239764 0.129526 1.71603 0.174036 0.531752 0.185142 0.388255 -0.906594 -0.296296 -0.195481 -0.0711189 -0.140758 0.723386 -0.16763 0.208062 0.0586831 0.0663207 0.0880634 0.105408 0.476159 -0.0316837 3.09421 -0.0647219 0.541052 0.211562 10 5 6 0 1 -1 5 4 7 2 -1 5 3 13 4 10 4 8 3 2 7 6 13 4 3 2 -1 12 4 8 6 5 7 5 13 10 9 11 12 7 10 4 3 8 6 0 9 4 12 -1 1 11 4 11 1 0 9 Hyperplanes for bounded facets between Voronoi regions via QhullUser and qh_fprintf 19 5 0 5 -0.301881 0.953346 0.00878913 5 0 7 0.0205153 0.99979 0.0751143 5 0 9 0.619259 0.785187 0.137061 5 1 5 0.799595 -0.600539 0.546971 5 1 3 0.964872 -0.262721 0.325862 5 2 6 0.22816 -0.973624 0.0825353 5 2 4 0.444671 0.895694 -0.430084 5 2 7 -0.945841 0.32463 0.0490754 5 3 5 -0.998643 0.0520745 -0.178237 5 3 7 0.687752 -0.725945 0.26633 5 3 4 0.999294 0.037557 -0.193884 5 4 6 -0.107584 -0.994196 0.268542 5 4 7 -0.997018 -0.0771644 0.214549 5 5 7 0.995061 -0.0992661 0.187455 5 6 7 -0.799364 0.600847 0.00706064 5 6 9 -0.228542 -0.973534 0.077977 5 6 8 -0.0126184 -0.99992 -0.0256728 5 7 9 0.593695 -0.80469 0.0185277 5 8 9 -0.467479 0.884004 0.250603 Hyperplanes for unbounded facets between Voronoi regions via QhullUser and qh_fprintf 4 5 0 8 0.719063 0.694945 0.107173 5 0 1 -0.385496 0.92271 -0.076093 5 1 4 0.992921 -0.118775 0.0752121 5 4 8 -0.0664014 -0.997793 0.140881 Message codes captured by qh_fprintf in QhullUser.cpp (qhull v Fo Ta): 9231 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274 9271 9272 9272 9273 9274 Results of p 2 14 -0.1294381801544404 -0.07247409101984709 0.08267689532419764 -0.2397644955865706 0.1295260566906467 1.716033573116839 0.1740355150742391 0.5317519038435656 0.1851415205797576 0.3882545794457364 -0.9065939866848106 -0.2962957610652136 -0.1954805620516264 -0.07111892482963184 -0.1407581310832469 0.7233857048236081 -0.1676297826663961 0.2080621273999384 0.05868313821742954 0.06632066014880161 0.08806341399736983 0.1054080604689984 0.4761588899009251 -0.03168366595227294 3.094213357897476 -0.064721945677682 0.5410515627308723 0.211561543495592 Results of Fi 19 5 0 5 -0.301880639203215 0.9533457293522944 0.008789126238507639 5 0 7 0.02051532578114256 0.9997895385570373 0.0751143044524602 5 0 9 0.619259133056969 0.7851866823409139 0.1370614663104577 5 1 5 0.7995952824356682 -0.6005392446015695 0.5469710423089691 5 1 3 0.9648718030091262 -0.2627211520946076 0.3258622775065155 5 2 6 0.2281595097543264 -0.9736237661995856 0.0825352874566877 5 2 4 0.4446710312325422 0.895693962234081 -0.4300843534994401 5 2 7 -0.9458410914974846 0.324629988810102 0.04907537812572163 5 3 5 -0.9986432053419565 0.05207445078292225 -0.1782370644858235 5 3 7 0.6877523324625964 -0.7259454037269318 0.2663295190946446 5 3 4 0.99929448732669 0.03755699133966526 -0.1938837324602515 5 4 6 -0.1075842248297359 -0.9941959739245502 0.2685422477498993 5 4 7 -0.9970183790688238 -0.07716444646969949 0.2145489484590234 5 5 7 0.995060920624513 -0.09926612839179721 0.1874553677160639 5 6 7 -0.7993641842155071 0.6008468199079334 0.007060641163779156 5 6 9 -0.2285415587894344 -0.9735341575446109 0.07797696388863322 5 6 8 -0.01261839651625044 -0.9999203848653946 -0.02567278177543585 5 7 9 0.5936952885926361 -0.8046899429612046 0.01852766555277021 5 8 9 -0.4674785097727935 0.8840044360186254 0.2506025495170938 Results of Fo 4 5 0 8 0.7190625207842074 0.6949453872092838 0.1071733734620183 5 0 1 -0.3854955578888163 0.922709691532494 -0.07609298438083834 5 1 4 0.9929212365203528 -0.1187746524595787 0.0752121188850394 5 4 8 -0.06640144810487485 -0.9977929883946747 0.1408811441173877 set +v === check front ends and examples Tue Oct 5 22:50:11 UTC 2021 ================== qconvex - qconvex -- compute the convex hull http://www.qhull.org 2020.2.r 2020/08/31 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: Qc - keep coplanar points with nearest facet Qi - keep interior points with nearest facet QJ - joggled input instead of merged facets Qt - triangulated output Qhull control options: Qa - allow input with fewer or more points than coordinates 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 Qhull extra options: QGn - good facet if visible from point n, -n for not visible QVn - good facet if it includes point n, -n if not Qw - allow option warnings Q12 - allow wide facets and wide dupridge Q14 - merge pinched vertices that create a dupridge T options: TFn - report summary when n or more facets created TI file - input file, may be enclosed in single quotes TO file - output file, may be enclosed in single quotes Ts - statistics Tv - verify result: structure, convexity, and in-circle test Tz - send all output to stdout Trace options: T4 - trace at level n, 4=all, 5=mem/gauss, -1= events Ta - annotate output with message codes TAn - stop qhull after adding n vertices TCn - stop qhull after building cone for point n TVn - stop qhull after adding point n, -n for before Tc - check frequently during execution Tf - flush each qh_fprintf for debugging segfaults TPn - turn on tracing when point n added to hull TMn - turn on tracing at merge n TWn - trace merge facets when width > n 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) 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, output: #vertices, #facets, #coplanars, #nonsimplicial #real (2), max outer plane, min vertex FS - sizes: #int (0) #real (2) tot area, tot volume Ft - triangulation with centrums for non-simplicial facets (OFF format) Fv - count plus vertices for each facet 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 Gc - centrums GDn - drop dimension n in 3-d and 4-d output Gh - hyperplane intersections Gi - inner planes only Gn - no planes Go - outer planes only Gr - ridges Print options: PAn - keep n largest facets by area Pdk:n - drop facet if normal[k] <= n (default 0.0) PDk:n - drop facet if normal[k] >= n PFn - keep facets whose area is at least n Pg - print good facets (needs 'QGn' or 'QVn') 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 -? - help with examples -V - version qconvex . Qhull 2020.2.r 2020/08/31 Except for 'F.' and 'PG', upper-case options take an argument. facet-dump Geomview incidences mathematica normals off-format points summary Farea FArea-total Fcoplanars FCentrums Fd-cdd-in FD-cdd-out FFacets-xridge Finner FIDs Fmerges FMaple Fneighbors FNeigh-vertex Fouter FOptions FPoint-near FQhull Fsummary FSize Ftriangles Fvertices FVertex-ave Fxtremes Gall-points Gcentrums GDrop-dim Ghyperplanes Ginner Gno-planes Gouter Gpoints Gridges Gvertices PArea-keep Pdrop-d0:0D0 PFacet-area-keep Pgood PGood-neighbors PMerge-keep Poutput-forced Pprecision-not Qallow-short QbBound-0:0.5 QbB-scale-box Qcoplanar QGood-point Qinterior QJoggle QRotate Qsearch-all Qtriangulate QVertex-good Qwarn-allow Q12-allow-wide Q14-merge-pinched TFacet-log TInput-file TOutput-file Tstatistics Tverify Tz-stdout T4-trace Tannotate TAdd-stop Tcheck-often TCone-stop Tflush TMerge-trace TPoint-trace TVertex-stop TWide-trace Angle-max Centrum-size Random-dist Ucoplanar-max Wide-outside qconvex -? # [mar'19] isatty does not work for Git for Windows qconvex -- compute the convex hull. Qhull 2020.2.r 2020/08/31 input (stdin): dimension, number of points, point coordinates comments start with a non-numeric character options (qconvex.htm): Qt - triangulated output QJ - joggled input instead of merged facets Tv - verify result: structure, convexity, and point inclusion . - concise list of all options - - one-line description of each option -? - this message -V - version output options (subset): s - summary of results (default) i - vertices incident to each facet n - normals with offsets p - vertex coordinates (if 'Qc', includes coplanar points) FA - report total area and volume FS - total area and volume Fx - extreme points (convex hull vertices) G - Geomview output (2-d, 3-d, and 4-d) m - Mathematica output (2-d and 3-d) o - OFF format (dim, n, points, facets) QVn - print facets that include point n, -n if not TI file - input file, may be enclosed in single quotes TO file - output 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 Qc s n rbox y 1000 W0 | qconvex s QJ rbox d G1 D12 | qconvex QR0 FA Pp rbox c D7 | qconvex FA TF1000 rbox c D3 | qconvex s n Qt Convex hull of 8 points in 3-d: Number of vertices: 8 Number of facets: 12 Number of triangulated facets: 6 Statistics for: rbox c D3 | qconvex s n Qt Number of points processed: 8 Number of hyperplanes created: 11 Number of distance tests for qhull: 34 Number of distance tests for merging: 90 Number of distance tests for checking: 48 Number of merged facets: 6 CPU seconds to compute hull (after input): 0.000115 4 12 -0 -0 -1 -0.5 -0 -0 -1 -0.5 0 -1 0 -0.5 0 -1 0 -0.5 1 -0 -0 -0.5 1 -0 -0 -0.5 -1 -0 -0 -0.5 -1 -0 -0 -0.5 0 1 -0 -0.5 0 1 -0 -0.5 -0 -0 1 -0.5 -0 -0 1 -0.5 rbox c D2 | qconvex s i Convex hull of 4 points in 2-d: Number of vertices: 4 Number of facets: 4 Statistics for: rbox c D2 | qconvex s i Number of points processed: 4 Number of hyperplanes created: 6 Number of distance tests for qhull: 5 CPU seconds to compute hull (after input): 4.6e-05 4 0 2 1 0 2 3 3 1 rbox c D2 | qconvex s n Convex hull of 4 points in 2-d: Number of vertices: 4 Number of facets: 4 Statistics for: rbox c D2 | qconvex s n Number of points processed: 4 Number of hyperplanes created: 6 Number of distance tests for qhull: 5 CPU seconds to compute hull (after input): 7.6e-05 3 4 -0 -1 -0.5 -1 0 -0.5 1 -0 -0.5 0 1 -0.5 rbox c D2 | qconvex o 2 4 4 4 -0.5 -0.5 -0.5 0.5 0.5 -0.5 0.5 0.5 2 0 2 2 1 0 2 2 3 2 3 1 rbox 1000 s | qconvex s Tv FA Convex hull of 1000 points in 3-d: Number of vertices: 1000 Number of facets: 1996 Statistics for: rbox 1000 s | qconvex s Tv FA Number of points processed: 1000 Number of hyperplanes created: 5544 Number of distance tests for qhull: 25487 CPU seconds to compute hull (after input): 0.01232 Total facet area: 3.1201951 Total volume: 0.51650274 qhull output completed. Verifying that 1000 points are below 2.1e-15 of the nearest facet. rbox c d D2 | qconvex s Qc Fx Convex hull of 8 points in 2-d: Number of vertices: 4 Number of coplanar points: 4 Number of facets: 4 Statistics for: rbox c d D2 | qconvex s Qc Fx Number of points processed: 4 Number of hyperplanes created: 6 Number of distance tests for qhull: 35 CPU seconds to compute hull (after input): 5e-05 4 0 2 3 1 rbox y 1000 W0 | qconvex Qc s n Convex hull of 1004 points in 3-d: Number of vertices: 4 Number of coplanar points: 1000 Number of facets: 4 Statistics for: rbox y 1000 W0 | qconvex Qc s n Number of points processed: 4 Number of hyperplanes created: 4 Number of distance tests for qhull: 11000 CPU seconds to compute hull (after input): 0.000612 4 4 0.2135848119563837 0.1168704340428168 0.9699086708284446 -0.09806074564261894 0.08553875579270347 -0.8316435307282575 -0.5486822022403076 -0.1234144150397865 -0.749541668500822 -0.02779445272382575 -0.6613733859014791 -0.2159556159595279 0.3120013537900506 0.9498158823230658 -0.02247097950761911 -0.02453689035981485 rbox y 1000 W0 | qconvex s QJ Convex hull of 1004 points in 3-d: Number of vertices: 51 Number of facets: 98 Statistics for: rbox y 1000 W0 | qconvex s QJ Number of points processed: 52 Number of hyperplanes created: 180 Number of distance tests for qhull: 6420 CPU seconds to compute hull (after input): 0.000445 Input joggled by: 2.1e-11 rbox d G1 D12 | qconvex QR0 FA Convex hull of 24 points in 12-d: Number of vertices: 24 Number of facets: 4096 Statistics for: rbox d G1 D12 | qconvex QR0 FA QR1633474211 Number of points processed: 24 Number of hyperplanes created: 4107 Number of distance tests for qhull: 4215 Number of distance tests for merging: 121142 Number of distance tests for checking: 98304 Number of merged facets: 2036 CPU seconds to compute hull (after input): 0.0359 Approximate facet area: 0.00035546337 Approximate volume: 8.5511197e-06 rbox c D6 | qconvex s FA TF500 At 22:50:11 & 0.00135 CPU secs, qhull has created 543 facets and merged 289. The current hull contains 91 facets and 23 vertices. There are 41 outside points. Next is point p27(v24), 0.64 above f107. At 22:50:11 & 0.00267 CPU secs, qhull has created 1061 facets and merged 737. The current hull contains 69 facets and 33 vertices. There are 31 outside points. Next is point p22(v34), 0.52 above f610. At 22:50:11 & 0.003968 CPU secs, qhull has created 1567 facets and merged 1216. The current hull contains 37 facets and 48 vertices. There are 16 outside points. Next is point p9(v49), 0.45 above f1061. At 22:50:11 & 0.004756 CPU secs, qhull has created 1819 facets and merged 1462. The current hull contains 12 facets and 64 vertices. Last point was p11 Convex hull of 64 points in 6-d: Number of vertices: 64 Number of facets: 12 Number of non-simplicial facets: 12 Statistics for: rbox c D6 | qconvex s FA TF500 Number of points processed: 64 Number of hyperplanes created: 358 Number of distance tests for qhull: 2515 Number of distance tests for merging: 14300 Number of distance tests for checking: 0 Number of merged facets: 1462 First post-merge with 'C3.5e-15' and 'A1.8e+308' At 22:50:11 & 0.004933 CPU secs, qhull has created 1819 facets and merged 1462. The current hull contains 12 facets and 64 vertices. Last point was p11 Testing all coplanar points. computing area of each facet and volume of the convex hull Convex hull of 64 points in 6-d: Number of vertices: 64 Number of facets: 12 Number of non-simplicial facets: 12 Statistics for: rbox c D6 | qconvex s FA TF500 Number of points processed: 64 Number of hyperplanes created: 358 Number of distance tests for qhull: 2515 Number of distance tests for merging: 14420 Number of distance tests for checking: 768 Number of merged facets: 1462 CPU seconds to compute hull (after input): 0.004981 Approximate facet area: 12 Approximate volume: 1 rbox c D7 | qconvex s FA TF1000 At 22:50:11 & 0.002832 CPU secs, qhull has created 1048 facets and merged 469. The current hull contains 230 facets and 24 vertices. There are 104 outside points. Next is point p79(v25), 0.66 above f145. At 22:50:11 & 0.006398 CPU secs, qhull has created 2146 facets and merged 1272. The current hull contains 273 facets and 31 vertices. There are 97 outside points. Next is point p120(v32), 0.54 above f437. At 22:50:11 & 0.010339 CPU secs, qhull has created 3310 facets and merged 2244. The current hull contains 243 facets and 36 vertices. There are 92 outside points. Next is point p60(v37), 0.54 above f1338. At 22:50:11 & 0.013956 CPU secs, qhull has created 4322 facets and merged 3099. The current hull contains 249 facets and 42 vertices. There are 86 outside points. Next is point p30(v43), 0.54 above f2005. At 22:50:11 & 0.020622 CPU secs, qhull has created 5491 facets and merged 4196. The current hull contains 186 facets and 48 vertices. There are 80 outside points. Next is point p21(v49), 0.5 above f2995. At 22:50:11 & 0.027579 CPU secs, qhull has created 6589 facets and merged 5175. The current hull contains 194 facets and 53 vertices. There are 75 outside points. Next is point p56(v54), 0.28 above f3731. At 22:50:11 & 0.035338 CPU secs, qhull has created 7867 facets and merged 6337. The current hull contains 203 facets and 60 vertices. There are 68 outside points. Next is point p76(v61), 0.29 above f5879. At 22:50:11 & 0.041837 CPU secs, qhull has created 8971 facets and merged 7362. The current hull contains 179 facets and 67 vertices. There are 61 outside points. Next is point p80(v68), 0.23 above f7175. At 22:50:11 & 0.048348 CPU secs, qhull has created 9984 facets and merged 8352. The current hull contains 104 facets and 77 vertices. There are 51 outside points. Next is point p96(v78), 0.41 above f6748. At 22:50:11 & 0.054563 CPU secs, qhull has created 10990 facets and merged 9326. The current hull contains 54 facets and 90 vertices. There are 38 outside points. Next is point p18(v91), 0.41 above f10178. At 22:50:11 & 0.059227 CPU secs, qhull has created 11996 facets and merged 10295. The current hull contains 34 facets and 114 vertices. There are 14 outside points. Next is point p19(v115), 0.38 above f11792. At 22:50:11 & 0.062889 CPU secs, qhull has created 12860 facets and merged 11072. The current hull contains 14 facets and 128 vertices. Last point was p77 Convex hull of 128 points in 7-d: Number of vertices: 128 Number of facets: 14 Number of non-simplicial facets: 14 Statistics for: rbox c D7 | qconvex s FA TF1000 Number of points processed: 128 Number of hyperplanes created: 1789 Number of distance tests for qhull: 10122 Number of distance tests for merging: 87203 Number of distance tests for checking: 0 Number of merged facets: 11072 First post-merge with 'C4.4e-15' and 'A1.8e+308' At 22:50:11 & 0.063473 CPU secs, qhull has created 12860 facets and merged 11072. The current hull contains 14 facets and 128 vertices. Last point was p77 Testing all coplanar points. computing area of each facet and volume of the convex hull Convex hull of 128 points in 7-d: Number of vertices: 128 Number of facets: 14 Number of non-simplicial facets: 14 Statistics for: rbox c D7 | qconvex s FA TF1000 Number of points processed: 128 Number of hyperplanes created: 1789 Number of distance tests for qhull: 10122 Number of distance tests for merging: 87371 Number of distance tests for checking: 1792 Number of merged facets: 11072 CPU seconds to compute hull (after input): 0.06358 Approximate facet area: 14 Approximate volume: 1 rbox d G1 D12 | qconvex QR0 FA Pp Convex hull of 24 points in 12-d: Number of vertices: 24 Number of facets: 4096 Statistics for: rbox d G1 D12 | qconvex QR0 FA Pp QR1633474211 Number of points processed: 24 Number of hyperplanes created: 4107 Number of distance tests for qhull: 4215 Number of distance tests for merging: 121142 Number of distance tests for checking: 98304 Number of merged facets: 2036 CPU seconds to compute hull (after input): 0.03493 Approximate facet area: 0.00035546337 Approximate volume: 8.5511197e-06 rbox c P0 d D2 | qconvex p Fa Fc FP FI Fn FN FS Fv Fx 2 8 -0.5 -0.5 -0.5 0.5 0.5 -0.5 0.5 0.5 0 -0.5 0 0.5 -0.5 0 0.5 0 4 1 1 1 1 4 1 5 1 7 1 8 1 6 4 3 5 1 0.5 2 7 2 0.5 4 8 4 0.5 4 6 5 0.5 4 1 2 4 5 4 2 1 2 2 0 3 2 0 3 2 1 2 9 0 2 0 1 2 1 3 2 2 0 2 3 2 1 0 1 3 1 1 1 2 0 2 4 1 4 2 3 1 2 2 1 2 4 3 2 4 2 4 1 3 4 2 rbox c d D2 | qconvex s i QV0 Convex hull of 8 points in 2-d: Number of vertices: 4 Number of facets: 4 Number of 'good' facets: 2 Statistics for: rbox c d D2 | qconvex s i QV0 Number of points processed: 4 Number of hyperplanes created: 6 Number of distance tests for qhull: 35 CPU seconds to compute hull (after input): 9.1e-05 2 0 2 1 0 rbox c | qconvex Q0 QH6029 qhull option error: option 'Q0' is not used with this program. It may be used with qhull. While executing: | qconvex Q0 Options selected for Qhull 2020.2.r 2020/08/31: run-id 370121029 _maxoutside 0 qvoronoi - qvoronoi -- compute the Voronoi diagram http://www.qhull.org 2020.2.r 2020/08/31 input (stdin): first lines: dimension and number of points (or vice-versa). other lines: point coordinates, best if one point per line comments: start with a non-numeric character options: Qu - compute furthest-site Voronoi diagram Qhull control options: Qa - allow input with fewer or more points than coordinates QRn - random rotation (n=seed, n=0 time, n=-1 time/no rotate) Qs - search all points for the initial simplex Qz - add point-at-infinity to Voronoi diagram Qhull extra options: QGn - Voronoi vertices if visible from point n, -n if not QVn - Voronoi vertices for input point n, -n if not Qw - allow option warnings Q12 - allow wide facets and wide dupridge Q14 - merge pinched vertices that create a dupridge T options: TFn - report summary when n or more facets created TI file - input file, may be enclosed in single quotes TO file - output file, may be enclosed in single quotes Ts - statistics Tv - verify result: structure, convexity, and in-circle test Tz - send all output to stdout Trace options: T4 - trace at level n, 4=all, 5=mem/gauss, -1= events Ta - annotate output with message codes TAn - stop qhull after adding n vertices TCn - stop qhull after building cone for point n TVn - stop qhull after adding point n, -n for before Tc - check frequently during execution Tf - flush each qh_fprintf for debugging segfaults TPn - turn on tracing when point n added to hull TMn - turn on tracing at merge n TWn - trace merge facets when width > n Precision options: Cn - radius of centrum (roundoff added). Merge facets if non-convex An - cosine of maximum angle. Merge facets if cosine > n or non-convex C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge Rn - randomly perturb computations by a factor of [1-n,1+n] Wn - min facet width for non-coincident point (before roundoff) Output formats (may be combined; if none, summary to stdout): p - Voronoi vertices s - summary to stderr f - facet dump i - Delaunay regions (use 'Pp' to avoid warning) o - OFF format (dim, Voronoi vertices, and Voronoi regions) More formats: Fc - count plus coincident points (by Voronoi vertex) Fd - use cdd format for input (homogeneous with offset first) FD - use cdd format for output (offset first) FF - facet dump without ridges Fi - separating hyperplanes for bounded Voronoi regions FI - ID for each Voronoi vertex Fm - merge count for each Voronoi vertex (511 max) Fn - count plus neighboring Voronoi vertices for each Voronoi vertex FN - count and Voronoi vertices for each Voronoi region Fo - separating hyperplanes for unbounded Voronoi regions FO - options and precision constants FP - nearest point and distance for each coincident point FQ - command used for qvoronoi Fs - summary: #int (8), dimension, #points, tot vertices, tot facets, for output: #Voronoi regions, #Voronoi vertices, #coincident points, #non-simplicial regions #real (2), max outer plane and min vertex Fv - Voronoi diagram as Voronoi vertices between adjacent input sites Fx - extreme points of Delaunay triangulation (on convex hull) Geomview output (2-d only) Ga - all points as dots Gp - coplanar points and vertices as radii Gv - vertices as spheres Gc - centrums GDn - drop dimension n in 3-d and 4-d output Gh - hyperplane intersections Gi - inner planes only Gn - no planes Go - outer planes only Gr - ridges Print options: PAn - keep n largest Voronoi vertices by 'area' Pdk:n - drop facet if normal[k] <= n (default 0.0) PDk:n - drop facet if normal[k] >= n PFn - keep Voronoi vertices whose 'area' is at least n Pg - print good Voronoi vertices (needs 'QGn' or 'QVn') PG - print neighbors of good Voronoi vertices PMn - keep n Voronoi vertices with most merges Po - force output. If error, output neighborhood of facet Pp - do not report precision problems . - list of all options - - one line descriptions of all options -? - help with examples -V - version qvoronoi . Qhull 2020.2.r 2020/08/31 Except for 'F.' and 'PG', upper-case options take an argument. facet-dump Geomview i-delaunay off-format p-vertices summary Fcoincident Fd-cdd-in FD-cdd-out FF-dump-xridge Fi-bounded FIDs Fmerges Fneighbors FNeigh-region Fo-unbounded FOptions FPoint-near FQvoronoi Fsummary Fvoronoi Fxtremes Gall-points Gcentrums GDrop-dim Ghyperplanes Ginner Gno-planes Gouter Gpoints Gridges Gvertices PArea-keep Pdrop-d0:0D0 PFacet-area-keep Pgood PGood-neighbors PMerge-keep Poutput-forced Pprecision-not Qallow-short QG-vertex-good QRotate Qsearch-all Qupper-voronoi QV-point-good Qwarn-allow Qzinfinite Q12-allow-wide Q14-merge-pinched TFacet-log TInput-file TOutput-file Tstatistics Tverify Tz-stdout T4-trace Tannotate TAdd-stop Tcheck-often TCone-stop Tflush TMerge-trace TPoint-trace TVertex-stop TWide-trace Angle-max Centrum-size Random-dist Wide-outside qvoronoi -? # [mar'19] isatty does not work for Git for Windows qvoronoi -- compute the Voronoi diagram. Qhull 2020.2.r 2020/08/31 input (stdin): dimension, number of points, point coordinates comments start with a non-numeric character options (qvoronoi.htm): Qu - compute furthest-site Voronoi diagram Tv - verify result: structure, convexity, and in-circle test . - concise list of all options - - one-line description of all options -? - this message -V - version output options (subset): Fi - separating hyperplanes for bounded regions, 'Fo' for unbounded FN - count and Voronoi vertices for each Voronoi region Fv - Voronoi diagram as Voronoi vertices between adjacent input sites G - Geomview output (2-d only) o - OFF file format (dim, Voronoi vertices, and Voronoi regions) p - Voronoi vertices QVn - Voronoi vertices for input point n, -n if not s - summary of results (default) TI file - input file, may be enclosed in single quotes TO file - output file, may be enclosed in single quotes examples: rbox c P0 D2 | qvoronoi s o rbox c P0 D2 | qvoronoi Fi rbox c P0 D2 | qvoronoi Fo rbox c P0 D2 | qvoronoi Fv rbox c P0 D2 | qvoronoi s Qu Fv rbox c P0 D2 | qvoronoi Qu Fo rbox c G1 d D2 | qvoronoi s p rbox c P0 D2 | qvoronoi s Fv QV0 rbox c P0 D2 | qvoronoi s o Voronoi diagram by the convex hull of 5 points in 3-d: Number of Voronoi regions: 5 Number of Voronoi vertices: 4 Statistics for: rbox c P0 D2 | qvoronoi s o Number of points processed: 5 Number of hyperplanes created: 6 Number of facets in hull: 5 Number of distance tests for qhull: 7 Number of distance tests for merging: 34 Number of distance tests for checking: 25 Number of merged facets: 1 CPU seconds to compute hull (after input): 8.9e-05 2 5 5 1 -10.101 -10.101 0 -0.5 -0.5 0 0.5 0 0 0.5 4 4 2 1 3 3 2 0 1 3 4 0 2 3 3 0 1 3 4 0 3 rbox c P0 D2 | qvoronoi Fi Tv 4 5 0 3 0.7071067811865475 -0.7071067811865475 -0.3535533905932737 5 0 1 -0.7071067811865475 -0.7071067811865475 -0.3535533905932737 5 0 2 -0.7071067811865475 0.7071067811865475 -0.3535533905932737 5 0 4 0.7071067811865475 0.7071067811865475 -0.3535533905932737 Voronoi ridge statistics 4 bounded ridges 0 max. distance of midpoint to ridge 4 bounded ridges with ok normal 2.2e-16 ave. angle to ridge 2.2e-16 max. angle to ridge Output completed. Verifying that all points are below outer planes of all facets. Will make 20 distance computations. rbox c P0 D2 | qvoronoi Fo Tv 4 5 1 2 -1 0 -0.5 5 1 3 1 -0 -0 5 2 4 1 -0 -0 5 3 4 -1 0 0.5 Output completed. Verifying that all points are below outer planes of all facets. Will make 20 distance computations. rbox c P0 D2 | qvoronoi Fv 8 4 0 3 1 3 4 0 1 1 2 4 0 2 2 4 4 0 4 3 4 4 1 2 0 2 4 1 3 0 1 4 2 4 0 4 4 3 4 0 3 rbox c P0 D2 | qvoronoi s Qu Fv Furthest-site Voronoi vertices by the convex hull of 5 points in 3-d: Number of Voronoi regions: 5 Number of Voronoi vertices: 1 Number of non-simplicial Voronoi vertices: 1 Statistics for: rbox c P0 D2 | qvoronoi s Qu Fv Number of points processed: 5 Number of hyperplanes created: 6 Number of facets in hull: 5 Number of distance tests for qhull: 7 Number of distance tests for merging: 34 Number of distance tests for checking: 25 Number of merged facets: 1 CPU seconds to compute hull (after input): 7.9e-05 4 4 1 2 0 1 4 1 3 0 1 4 2 4 0 1 4 3 4 0 1 rbox c P0 D2 | qvoronoi s Qu Qt Fv Furthest-site Voronoi vertices by the convex hull of 5 points in 3-d: Number of Voronoi regions: 5 Number of Voronoi vertices: 2 Number of triangulated facets: 1 Statistics for: rbox c P0 D2 | qvoronoi s Qu Qt Fv Number of points processed: 5 Number of hyperplanes created: 6 Number of facets in hull: 6 Number of distance tests for qhull: 7 Number of distance tests for merging: 34 Number of distance tests for checking: 25 Number of merged facets: 1 CPU seconds to compute hull (after input): 8.9e-05 4 4 1 3 0 2 4 1 2 0 1 4 2 4 0 1 4 3 4 0 2 rbox c P0 D2 | qvoronoi Qu Fo 4 5 1 2 -0 1 0 5 1 3 1 -0 -0 5 2 4 1 -0 -0 5 3 4 -0 1 -0 rbox c G1 d D2 | qvoronoi s p Voronoi diagram by the convex hull of 8 points in 3-d: Number of Voronoi regions: 8 Number of Voronoi vertices: 9 Number of non-simplicial Voronoi vertices: 1 Statistics for: rbox c G1 d D2 | qvoronoi s p Number of points processed: 8 Number of hyperplanes created: 16 Number of facets in hull: 10 Number of distance tests for qhull: 41 Number of distance tests for merging: 108 Number of distance tests for checking: 72 Number of merged facets: 3 CPU seconds to compute hull (after input): 9.8e-05 2 9 0 -1.75 -1.75 0 -0.5833333333333334 -0.5833333333333333 0 1.75 -0.5833333333333333 0.5833333333333334 1.75 0 0.5833333333333334 -0.5833333333333333 0.5833333333333334 0.5833333333333333 0 0 rbox c G1 d D2 | qvoronoi QJ p 2 10 -2.57276422388486e-11 1.749999999802917 -2.05463598231932e-11 -1.750000000331276 0.5833333333083517 -0.5833333333052267 1.862254794815499e-11 -7.815052443180038e-11 1.750000000002628 3.498100747664324e-11 0.5833333333132078 0.5833333333796981 -0.5833333332888888 0.5833333333317835 -7.592293460589872e-11 -7.815050692933323e-11 -1.750000000049026 2.293196879294717e-11 -0.5833333333977307 -0.5833333333229861 rbox c P-0.1 P+0.1 P+0.1 D2 | qvoronoi s Fc FP FQ Fn FN Voronoi diagram by the convex hull of 7 points in 3-d: Number of Voronoi regions: 6 Number of nearly incident points: 1 Number of Voronoi vertices: 4 Number of non-simplicial Voronoi vertices: 2 Statistics for: rbox c P-0.1 P+0.1 P+0.1 D2 | qvoronoi s Fc FP FQ Fn FN Number of points processed: 6 Number of hyperplanes created: 7 Number of facets in hull: 5 Number of distance tests for qhull: 31 Number of distance tests for merging: 54 Number of distance tests for checking: 36 Number of merged facets: 3 CPU seconds to compute hull (after input): 7.7e-05 4 0 1 1 0 0 1 2 1 8 0 rbox c P-0.1 P+0.1 P+0.1 D2 | qvoronoi s Fc FP FQ Fn FN 4 3 -1 2 3 3 -1 2 3 4 -1 0 3 1 4 0 -1 2 1 7 3 3 2 0 1 1 3 3 1 2 3 0 -1 2 3 3 -1 0 3 1 -1 2 3 1 -1 3 rbox P0 c D2 | qvoronoi s Fv QV0 Voronoi diagram by the convex hull of 5 points in 3-d: Number of Voronoi regions: 5 Number of 'good' Voronoi vertices: 4 Statistics for: rbox P0 c D2 | qvoronoi s Fv QV0 Number of points processed: 5 Number of hyperplanes created: 6 Number of facets in hull: 5 Number of distance tests for qhull: 7 Number of distance tests for merging: 34 Number of distance tests for checking: 25 Number of merged facets: 1 CPU seconds to compute hull (after input): 5.7e-05 4 4 0 3 1 3 4 0 1 1 2 4 0 2 2 4 4 0 4 3 4 qdelaunay - qdelaunay -- compute the Delaunay triangulation http://www.qhull.org 2020.2.r 2020/08/31 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: QJ - joggled input instead of merged facets Qt - triangulated output Qu - compute furthest-site Delaunay triangulation Qhull control options: Qa - allow input with fewer or more points than coordinates 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 Qz - add point-at-infinity to Delaunay triangulation Qhull extra options: QGn - print Delaunay region if visible from point n, -n if not QVn - print Delaunay regions that include point n, -n if not Qw - allow option warnings Q12 - allow wide facets and wide dupridge Q14 - merge pinched vertices that create a dupridge T options: TFn - report summary when n or more facets created TI file - input file, may be enclosed in single quotes TO file - output file, may be enclosed in single quotes Ts - statistics Tv - verify result: structure, convexity, and in-circle test Tz - send all output to stdout Trace options: T4 - trace at level n, 4=all, 5=mem/gauss, -1= events Ta - annotate output with message codes TAn - stop qhull after adding n vertices TCn - stop qhull after building cone for point n TVn - stop qhull after adding point n, -n for before Tc - check frequently during execution Tf - flush each qh_fprintf for debugging segfaults TPn - turn on tracing when point n added to hull TMn - turn on tracing at merge n TWn - trace merge facets when width > n 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, 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 output (2-d and 3-d points lifted to a paraboloid) Ga - all points as dots Gp - coplanar points and vertices as radii Gv - vertices as spheres Gc - centrums GDn - drop dimension n in 3-d and 4-d output Gh - hyperplane intersections Gi - inner planes only Gn - no planes Go - outer planes only Gr - ridges Gt - transparent outer ridges to view 3-d Delaunay Print options: PAn - keep n largest Delaunay regions by area Pdk:n - drop facet if normal[k] <= n (default 0.0) PDk:n - drop facet if normal[k] >= n PFn - keep Delaunay regions whose area is at least n Pg - print good Delaunay regions (needs 'QGn' or 'QVn') 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 -? - help with examples -V - version qdelaunay . Qhull 2020.2.r 2020/08/31 Except for 'F.' and 'PG', upper-case options take an argument. facet-dump Geomview incidences mathematica off-format points-lifted summary Farea FArea-total Fcoincident Fd-cdd-in FD-cdd-out FF-dump-xridge FIDs Fmerges FMaple Fneighbors FNeigh-vertex FOptions FPoint-near FQdelaun Fsummary FSize Fvertices Fxtremes Gall-points Gcentrums GDrop-dim Ghyperplanes Ginner Gno-planes Gouter Gpoints Gridges Gtransparent Gvertices PArea-keep Pdrop-d0:0D0 PFacet-area-keep Pgood PGood-neighbors PMerge-keep Poutput-forced Pprecision-not Qallow-short QGood-point QJoggle Qrotate Qsearch-all Qtriangulate QupperDelaunay QVertex-good Qwarn-allow Qzinfinite Q12-allow-wide Q14-merge-pinched TFacet-log TInput-file TOutput-file Tstatistics Tverify Tz-stdout T4-trace Tannotate TAdd-stop Tcheck-often TCone-stop Tflush TMerge-trace TPoint-trace TVertex-stop TWide-trace Angle-max Centrum-size Random-dist Wide-outside qdelaunay -? # [mar'19] isatty does not work for Git for Windows qdelaunay -- compute the Delaunay triangulation. Qhull 2020.2.r 2020/08/31 input (stdin): dimension, number of points, point coordinates comments start with a non-numeric character options (qdelaun.htm): Qu - furthest-site Delaunay triangulation Qt - triangulated output QJ - joggled input instead of merged facets Tv - verify result: structure, convexity, and in-circle test . - concise list of all options - - one-line description of each option -? - this message -V - version output options (subset): s - summary of results (default) i - vertices incident to each Delaunay region Fx - extreme points (vertices of the convex hull) G - Geomview output (2-d and 3-d points lifted to a paraboloid) m - Mathematica output (2-d inputs lifted to a paraboloid) o - OFF format (shows the points lifted to a paraboloid) QVn - print Delaunay regions that include point n, -n if not TI file - input file, may be enclosed in single quotes TO file - output file, may be enclosed in single quotes examples: 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 Fv rbox c G1 d D2 | qdelaunay s i rbox c G1 d D2 | qdelaunay Qt rbox M3,4 z 100 D2 | qdelaunay s rbox M3,4 z 100 D2 | qdelaunay s Qt rbox c P0 D2 | qdelaunay s o Delaunay triangulation by the convex hull of 5 points in 3-d: Number of input sites: 5 Number of Delaunay regions: 4 Statistics for: rbox c P0 D2 | qdelaunay s o Number of points processed: 5 Number of hyperplanes created: 6 Number of facets in hull: 5 Number of distance tests for qhull: 7 Number of distance tests for merging: 34 Number of distance tests for checking: 25 Number of merged facets: 1 CPU seconds to compute hull (after input): 6.1e-05 3 5 4 6 0 0 0 -0.5 -0.5 0.5 -0.5 0.5 0.5 0.5 -0.5 0.5 0.5 0.5 0.5 3 3 0 1 3 0 2 1 3 4 0 3 3 0 4 2 rbox c P0 D2 | qdelaunay i 4 3 0 1 0 2 1 4 0 3 0 4 2 rbox c P0 D2 | qdelaunay Fv 4 3 0 3 1 3 0 2 1 3 4 0 3 3 4 0 2 rbox c P0 D2 | qdelaunay s Qu Qt Fv Furthest-site Delaunay triangulation by the convex hull of 5 points in 3-d: Number of input sites: 5 Number of Delaunay regions: 2 Number of triangulated facets: 1 Statistics for: rbox c P0 D2 | qdelaunay s Qu Qt Fv Number of points processed: 5 Number of hyperplanes created: 6 Number of facets in hull: 6 Number of distance tests for qhull: 7 Number of distance tests for merging: 34 Number of distance tests for checking: 25 Number of merged facets: 1 CPU seconds to compute hull (after input): 7.3e-05 2 3 4 2 1 3 4 3 1 rbox c G1 d D2 | qdelaunay s i 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 c G1 d D2 | qdelaunay s i Number of points processed: 8 Number of hyperplanes created: 16 Number of facets in hull: 10 Number of distance tests for qhull: 41 Number of distance tests for merging: 108 Number of distance tests for checking: 72 Number of merged facets: 3 CPU seconds to compute hull (after input): 0.00012 9 2 4 0 6 1 0 4 6 0 5 3 1 6 5 1 3 7 2 7 4 2 5 7 3 4 7 5 6 rbox c G1 d D2 | qhull d Qbb Ft 2 9 12 14 -1 -1 -1 1 1 -1 1 1 0 -0.5 0 0.5 -0.5 0 0.5 0 0 0 3 2 4 0 3 6 1 0 3 4 6 0 3 5 3 1 3 6 5 1 3 3 7 2 3 7 4 2 3 5 7 3 3 8 5 6 3 8 6 4 3 8 7 5 3 8 4 7 rbox c G1 d D2 | qhull d Qbb QJ s Ft Delaunay triangulation by the convex hull of 8 points in 3-d: Number of input sites: 8 Number of Delaunay regions: 10 Statistics for: rbox c G1 d D2 | qhull d Qbb QJ s Ft Number of points processed: 8 Number of hyperplanes created: 19 Number of facets in hull: 12 Number of distance tests for qhull: 31 CPU seconds to compute hull (after input): 6e-05 Input joggled by: 8.3e-11 2 8 10 15 -1.000000000061343 -0.999999999957446 -0.9999999999945448 0.9999999999532114 1.000000000029778 -0.9999999999701502 0.9999999999806051 1.000000000003233 -7.748592400792811e-11 -0.5000000000743411 2.849349704487493e-11 0.49999999991804 -0.5000000000721135 -1.37371989142159e-11 0.5000000000148132 7.166044474310069e-11 3 1 5 3 3 2 4 0 3 7 4 2 3 4 7 5 3 3 7 2 3 5 7 3 3 1 6 5 3 6 4 5 3 6 1 0 3 4 6 0 rbox M3,4 z 100 D2 | qdelaunay s Delaunay triangulation by the convex hull of 100 points in 3-d: Number of input sites: 100 Number of Delaunay regions: 81 Number of non-simplicial Delaunay regions: 81 Statistics for: rbox M3,4 z 100 D2 | qdelaunay s Number of points processed: 100 Number of hyperplanes created: 251 Number of facets in hull: 86 Number of distance tests for qhull: 1650 Number of distance tests for merging: 2765 Number of distance tests for checking: 1248 Number of merged facets: 155 CPU seconds to compute hull (after input): 0.000835 rbox c P-0.1 P+0.1 P+0.1 D2 | qdelaunay s Fx Fa Fc FP FQ Fn FN Delaunay triangulation by the convex hull of 7 points in 3-d: Number of input sites: 6 Number of nearly incident points: 1 Number of Delaunay regions: 4 Number of non-simplicial Delaunay regions: 2 Statistics for: rbox c P-0.1 P+0.1 P+0.1 D2 | qdelaunay s Fx Fa Fc FP FQ Fn FN Number of points processed: 6 Number of hyperplanes created: 7 Number of facets in hull: 5 Number of distance tests for qhull: 31 Number of distance tests for merging: 54 Number of distance tests for checking: 35 Number of merged facets: 3 CPU seconds to compute hull (after input): 7e-05 Approximate facet area: 1 4 4 3 6 5 4 0.2 0.2 0.3 0.3 4 0 1 1 0 0 1 2 1 8 0 rbox c P-0.1 P+0.1 P+0.1 D2 | qdelaunay s Fx Fa Fc FP FQ Fn FN 4 3 -1 2 3 3 -1 2 3 4 -1 0 3 1 4 0 -1 2 1 7 3 3 2 0 1 1 3 3 1 2 3 0 -1 2 3 3 -1 0 3 1 -1 2 3 1 -1 3 rbox P0 P0 c D2 | qdelaunay s FP QV0 Delaunay triangulation by the convex hull of 6 points in 3-d: Number of input sites: 5 Number of nearly incident points: 1 Number of 'good' Delaunay regions: 4 Statistics for: rbox P0 P0 c D2 | qdelaunay s FP QV0 Number of points processed: 5 Number of hyperplanes created: 6 Number of facets in hull: 5 Number of distance tests for qhull: 18 Number of distance tests for merging: 34 Number of distance tests for checking: 30 Number of merged facets: 1 CPU seconds to compute hull (after input): 6.8e-05 1 0 1 2 0 qhalf - qhalf -- compute the intersection of halfspaces about a point http://www.qhull.org 2020.2.r 2020/08/31 input (stdin): optional interior point: dimension, 1, coordinates first lines: dimension+1 and number of halfspaces other lines: halfspace coefficients followed by offset comments: start with a non-numeric character options: Hn,n - specify coordinates of interior point Qc - keep coplanar halfspaces Qi - keep other redundant halfspaces QJ - joggled input instead of merged facets Qt - triangulated output Qhull control options: Qa - allow input with fewer or more points than coordinates 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 halfspaces for the initial simplex Qhull extra options: QGn - print intersection if visible to halfspace n, -n for not QVn - print intersections for halfspace n, -n if not Qw - allow option warnings Q12 - allow wide facets and wide dupridge Q14 - merge pinched vertices that create a dupridge T options: TFn - report summary when n or more facets created TI file - input file, may be enclosed in single quotes TO file - output file, may be enclosed in single quotes Ts - statistics Tv - verify result: structure, convexity, and in-circle test Tz - send all output to stdout Trace options: T4 - trace at level n, 4=all, 5=mem/gauss, -1= events Ta - annotate output with message codes TAn - stop qhull after adding n vertices TCn - stop qhull after building cone for point n TVn - stop qhull after adding point n, -n for before Tc - check frequently during execution Tf - flush each qh_fprintf for debugging segfaults TPn - turn on tracing when point n added to hull TMn - turn on tracing at merge n TWn - trace merge facets when width > n Precision options: Cn - radius of centrum (roundoff added). Merge facets if non-convex An - cosine of maximum angle. Merge facets if cosine > n or non-convex C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge Rn - randomly perturb computations by a factor of [1-n,1+n] Un - max distance below plane for a new, coplanar halfspace Wn - min facet width for outside halfspace (before roundoff) Output formats (may be combined; if none, produces a summary to stdout): f - facet dump G - Geomview output (dual convex hull) i - non-redundant halfspaces incident to each intersection m - Mathematica output (dual convex hull) o - OFF format (dual convex hull: dimension, points, and facets) p - vertex coordinates of dual convex hull (coplanars if 'Qc' or 'Qi') s - summary (stderr) More formats: Fc - count plus redundant halfspaces for each intersection - Qc (default) for coplanar and Qi for other redundant Fd - use cdd format for input (homogeneous with offset first) FF - facet dump without ridges FI - ID of each intersection Fm - merge count for each intersection (511 max) FM - Maple output (dual 2-d or 3-d convex hull) Fn - count plus neighboring intersections for each intersection FN - count plus intersections for each halfspace FO - options and precision constants Fp - dim, count, and intersection coordinates FP - nearest halfspace and distance for each redundant halfspace FQ - command used for qhalf Fs - summary: #int (8), dim, #halfspaces, #non-redundant, #intersections output: #non-redundant, #intersections, #coplanar halfspaces, #non-simplicial intersections #real (2), max outer plane, min vertex Fv - count plus non-redundant halfspaces for each intersection Fx - non-redundant halfspaces Geomview output (2-d, 3-d and 4-d; dual convex hull) Ga - all points (i.e., transformed halfspaces) as dots Gp - coplanar points and vertices as radii Gv - vertices (i.e., non-redundant halfspaces) as spheres Gc - centrums GDn - drop dimension n in 3-d and 4-d output Gh - hyperplane intersections Gi - inner planes (i.e., halfspace intersections) only Gn - no planes Go - outer planes only Gr - ridges Print options: PAn - keep n largest facets (i.e., intersections) by area Pdk:n- drop facet if normal[k] <= n (default 0.0) PDk:n- drop facet if normal[k] >= n PFn - keep facets whose area is at least n Pg - print good facets (needs 'QGn' or 'QVn') 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 -? - help with examples -V - version qhalf . Qhull 2020.2.r 2020/08/31 Except for 'F.' and 'PG', upper_case options take an argument. facet-dump Geomview H0,0-interior incidences mathematica off-format point-dual summary Fc-redundant Fd-cdd-in FF-dump-xridge FIDs Fmerges FMaple Fneighbors FN-intersect FOptions Fp-coordinates FP-nearest FQhalf Fsummary Fv-halfspace Fx-non-redundant Gall-points Gcentrums GDrop-dim Ghyperplanes Ginner Gno-planes Gouter Gpoints Gridges Gvertices PArea-keep Pdrop-d0:0D0 PFacet-area-keep Pgood PGood-neighbors PMerge-keep Poutput-forced Pprecision-not Qallow-short Qbk:0Bk:0-drop Qcoplanar QG-half-good Qi-redundant QJoggle QRotate Qsearch-all Qtriangulate QVertex-good Qwarn-allow Q12-allow-wide Q14-merge-pinched TFacet-log TInput-file TOutput-file Tstatistics Tverify Tz-stdout T4-trace Tannotate TAdd-stop Tcheck-often TCone-stop Tflush TMerge-trace TPoint-trace TVertex-stop TWide-trace Angle-max Centrum-size Random-dist Ucoplanar-max Wide-outside qhalf -? # [mar'19] isatty does not work for Git for Windows qhalf -- halfspace intersection about a point. Qhull 2020.2.r 2020/08/31 input (stdin): [dimension, 1, interior point] dimension+1, number of halfspaces, coefficients+offset comments start with a non-numeric character options (qhalf.htm): Hn,n - specify coordinates of interior point Qt - triangulated output QJ - joggled input instead of merged facets Tv - verify result: structure, convexity, and redundancy . - concise list of all options - - one-line description of each option -? - this message -V - version output options (subset): s - summary of results (default) Fp - intersection coordinates Fv - non-redundant halfspaces incident to each intersection Fx - non-redundant halfspaces G - Geomview output (dual convex hull) m - Mathematica output (dual convex hull) o - OFF file format (dual convex hull) QVn - print intersections for halfspace n, -n if not TI file - input file, may be enclosed in single quotes TO file - output file, may be enclosed in single quotes examples: rbox d | qconvex FQ n | qhalf s H0,0,0 Fp rbox c | qconvex FQ FV n | qhalf s i rbox c | qconvex FQ FV n | qhalf s o rbox d | qhull FQ n | qhalf s Qt H0,0,0 Fp Halfspace intersection by the convex hull of 8 points in 3-d: Number of halfspaces: 8 Number of non-redundant halfspaces: 8 Number of intersection points: 12 Number of triangulated facets: 6 Statistics for: rbox d | qhull FQ n | qhalf s Qt H0,0,0 Fp Number of points processed: 8 Number of hyperplanes created: 11 Number of distance tests for qhull: 32 Number of distance tests for merging: 101 Number of distance tests for checking: 48 Number of merged facets: 7 CPU seconds to compute hull (after input): 8.3e-05 3 12 0 0 -0.5 0 0 -0.5 0 -0.5 0 0 -0.5 0 -0.5 0 0 -0.5 0 0 0.5 0 0 0.5 0 0 0 0.5 0 0 0.5 0 0 0 0.5 0 0 0.5 rbox c | qhull FQ FV n | qhalf s i Halfspace intersection by the convex hull of 6 points in 3-d: Number of halfspaces: 6 Number of non-redundant halfspaces: 6 Number of intersection points: 8 Statistics for: rbox c | qhull FQ FV n | qhalf s i Number of points processed: 6 Number of hyperplanes created: 11 Number of distance tests for qhull: 10 Number of distance tests for merging: 51 Number of distance tests for checking: 48 Number of merged facets: 1 CPU seconds to compute hull (after input): 6.2e-05 8 1 0 3 0 1 2 5 1 3 1 5 2 4 0 2 0 4 3 5 4 2 4 5 3 rbox c | qhull FQ FV n | qhalf o 3 6 8 12 -0 -0 -2 0 -2 0 2 -0 -0 -2 -0 -0 0 2 -0 -0 -0 2 3 1 0 3 3 0 1 2 3 5 1 3 3 1 5 2 3 4 0 2 3 0 4 3 3 5 4 2 3 4 5 3 rbox d D2 | qhull FQ n | qhalf s H0 Fc FP Fn FN FQ Fv Fx Halfspace intersection by the convex hull of 4 points in 2-d: Number of halfspaces: 4 Number of non-redundant halfspaces: 4 Number of intersection points: 4 Statistics for: rbox d D2 | qhull FQ n | qhalf s H0 Fc FP Fn FN FQ Fv Fx Number of points processed: 4 Number of hyperplanes created: 6 Number of distance tests for qhull: 5 CPU seconds to compute hull (after input): 3.8e-05 4 0 0 0 0 0 4 2 1 2 2 0 3 2 0 3 2 1 2 4 2 0 1 2 2 0 2 1 3 2 3 2 rbox d D2 | qhull FQ n | qhalf s H0 Fc FP Fn FN FQ Fv Fx 4 2 1 0 2 2 0 2 3 1 2 3 2 4 0 1 3 2 # qhull - printed at end qhull . Qhull 2020.2.r 2020/08/31 Except for 'F.' and 'PG', upper-case options take an argument. delaunay facet-dump Geomview H0,0-interior Halfspace incidences mathematica normals off-format points summary voronoi Farea FArea-total Fcoplanars FCentrums Fd-cdd-in FD-cdd-out FFacets-xridge Finner FIDs Fmerges FMaple Fneighbors FNeigh-vertex Fouter FOptions Fpoint-intersect FPoint-near FQhull Fsummary FSize Ftriangles Fvertices Fvoronoi FVertex-ave Fxtremes Gall-points Gcentrums GDrop-dim Ghyperplanes Ginner Gno-planes Gouter Gpoints Gridges Gtransparent Gvertices PArea-keep Pdrop-d0:0D0 PFacet-area-keep Pgood PGood-neighbors PMerge-keep Poutput-forced Pprecision-not Qallow-short QbBound-0:0.5 QbB-scale-box Qbb-scale-last Qbk:0Bk:0-drop Qcoplanar Qinterior QJoggle QRotate Qsearch-all Qtriangulate QupperDelaunay Qwarn-allow Qxact-merge Qzinfinite Qfurthest Qgood-only QGood-point Qmax-outside Qrandom Qvneighbors QVertex-good Q0-no-premerge Q1-angle-merge Q2-no-independ Q3-no-redundant Q4-no-old Q5-no-check-out Q6-no-concave Q7-depth-first Q8-no-near-in Q9-pick-furthest Q10-no-narrow Q11-trinormals Q12-allow-wide Q14-merge-pinched Q15-duplicates TFacet-log TInput-file TOutput-file Tstatistics Tverify Tz-stdout T4-trace Tannotate TAdd-stop Tcheck-often TCone-stop Tflush TMerge-trace TPoint-trace TRerun TVertex-stop TWide-trace Angle-max Centrum-size Error-round Random-dist Ucoplanar-max Visible-min Wide-outside qhull -? # [mar'19] isatty does not work for Git for Windows qhull -- compute convex hulls and related structures. Qhull 2020.2.r 2020/08/31 input (stdin): dimension, number of points, point coordinates comments start with a non-numeric character halfspace: use dim+1 and put offsets after coefficients options (qh-quick.htm): d - Delaunay triangulation by lifting points to a paraboloid d Qu - furthest-site Delaunay triangulation (upper convex hull) v - Voronoi diagram as the dual of the Delaunay triangulation v Qu - furthest-site Voronoi diagram H1,1 - Halfspace intersection about [1,1,0,...] via polar duality Qt - triangulated output QJ - joggled input instead of merged facets Tv - verify result: structure, convexity, and point inclusion . - concise list of all options - - one-line description of each option -? - this message -V - version Output options (subset): s - summary of results (default) i - vertices incident to each facet n - normals with offsets p - vertex coordinates (if 'Qc', includes coplanar points) if 'v', Voronoi vertices FA - report total area and volume Fp - halfspace intersections FS - total area and volume Fx - extreme points (convex hull vertices) G - Geomview output (2-d, 3-d and 4-d) m - Mathematica output (2-d and 3-d) o - OFF format (if 'v', outputs Voronoi regions) QVn - print facets that include point n, -n if not TI file - input file, may be enclosed in single quotes TO file - output file, may be enclosed in single quotes examples: rbox D4 | qhull Tv rbox 1000 s | qhull Tv s FA rbox 10 D2 | qhull d QJ s i TO result rbox 10 D2 | qhull v Qbb Qt p rbox 10 D2 | qhull d Qu QJ m rbox 10 D2 | qhull v Qu QJ o rbox c d D2 | qhull Qc s f Fx | more rbox c | qhull FV n | qhull H Fp rbox d D12 | qhull QR0 FA rbox c D7 | qhull FA TF1000 rbox y 1000 W0 | qhull Qc rbox c | qhull n rbox 1000 s | qhull Tv s FA Convex hull of 1000 points in 3-d: Number of vertices: 1000 Number of facets: 1996 Statistics for: rbox 1000 s | qhull Tv s FA Number of points processed: 1000 Number of hyperplanes created: 5544 Number of distance tests for qhull: 25487 CPU seconds to compute hull (after input): 0.005071 Total facet area: 3.1201951 Total volume: 0.51650274 qhull output completed. Verifying that 1000 points are below 2.1e-15 of the nearest facet. rbox 10 D2 | qhull d QJ s i TO q_test.log.1 Delaunay triangulation by the convex hull of 10 points in 3-d: Number of input sites: 10 Number of Delaunay regions: 14 Statistics for: rbox 10 D2 | qhull d QJ s i TO q_test.log.1 Number of points processed: 10 Number of hyperplanes created: 28 Number of facets in hull: 16 Number of distance tests for qhull: 47 CPU seconds to compute hull (after input): 6.8e-05 Input joggled by: 4e-11 cat q_test.log.1 14 9 7 0 8 9 0 3 4 1 3 7 4 7 2 4 0 5 1 7 5 0 5 3 1 3 5 7 6 7 9 6 2 7 8 6 9 6 8 4 2 6 4 rbox 10 D2 | qhull v Qbb Qt p 2 14 -0.1294381801544404 -0.07247409101984714 0.08267689532419747 -0.2397644955865706 0.1295260566906465 1.716033573116837 0.1740355150742391 0.5317519038435655 0.1851415205797575 0.3882545794457364 -0.9065939866848107 -0.2962957610652135 -0.1954805620516266 -0.07111892482963184 -0.1407581310832468 0.7233857048236082 -0.1676297826663962 0.2080621273999375 0.05868313821742954 0.06632066014880154 0.08806341399736994 0.1054080604689985 0.4761588899009253 -0.03168366595227294 3.094213357897477 -0.064721945677682 0.5410515627308725 0.2115615434955919 rbox 10 D2 | qhull d Qu QJ m { Polygon[{{ 0.37903124, 0.37797944, 0.29963416}, { -0.02222276, -0.49797278, 0.23792952}, { -0.42854319, 0.47458265, 0.49797278}}], Polygon[{{ 0.34431227, -0.14373122, 0.06080143}, { -0.02222276, -0.49797278, 0.23792952}, { 0.37903124, 0.37797944, 0.29963416}}]} rbox 10 D2 | qhull v Qu QJ o 2 3 10 1 -10.101 -10.101 -0.06934933488573394 0.05349366577046777 -0.3051278692468022 0.16149850548211 3 0 2 1 2 0 1 0 0 3 0 1 2 0 0 0 2 0 2 0 rbox c d D2 | qhull Qc s f Fx Convex hull of 8 points in 2-d: Number of vertices: 4 Number of coplanar points: 4 Number of facets: 4 Statistics for: rbox c d D2 | qhull Qc s f Fx Number of points processed: 4 Number of hyperplanes created: 6 Number of distance tests for qhull: 35 CPU seconds to compute hull (after input): 4.4e-05 Vertices and facets: - p2(v2): 0.5 -0.5 - p0(v1): -0.5 -0.5 - p1(v3): -0.5 0.5 - p3(v4): 0.5 0.5 - f1 - flags: bottom simplicial - normal: -0 -1 - offset: -0.5 - coplanar set(furthest p4): p4: 0 -0.5 furthest distance= 0 - vertices: p2(v2) p0(v1) - neighboring facets: f2 f4 - f2 - flags: top simplicial - normal: -1 0 - offset: -0.5 - coplanar set(furthest p6): p6: -0.5 0 furthest distance= 0 - vertices: p1(v3) p0(v1) - neighboring facets: f1 f5 - f4 - flags: bottom simplicial - normal: 1 -0 - offset: -0.5 - coplanar set(furthest p7): p7: 0.5 0 furthest distance= 0 - vertices: p3(v4) p2(v2) - neighboring facets: f1 f5 - f5 - flags: top simplicial - normal: 0 1 - offset: -0.5 - coplanar set(furthest p5): p5: 0 0.5 furthest distance= 0 - vertices: p3(v4) p1(v3) - neighboring facets: f2 f4 4 0 2 3 1 rbox c | qhull FV n | qhull H Fp 3 8 -0.5 -0.5 -0.5 0.5 -0.5 -0.5 -0.5 -0.5 0.5 0.5 -0.5 0.5 0.5 0.5 -0.5 -0.5 0.5 -0.5 0.5 0.5 0.5 -0.5 0.5 0.5 rbox d D12 | qhull QR0 FA Convex hull of 24 points in 12-d: Number of vertices: 24 Number of facets: 4096 Statistics for: rbox d D12 | qhull QR0 FA QR1633474211 Number of points processed: 24 Number of hyperplanes created: 4107 Number of distance tests for qhull: 4215 Number of distance tests for merging: 121142 Number of distance tests for checking: 98304 Number of merged facets: 2036 CPU seconds to compute hull (after input): 0.04377 Approximate facet area: 1.735661e-07 Approximate volume: 2.0876757e-09 rbox c D7 | qhull FA TF1000 At 22:50:11 & 0.002916 CPU secs, qhull has created 1048 facets and merged 469. The current hull contains 230 facets and 24 vertices. There are 104 outside points. Next is point p79(v25), 0.66 above f145. At 22:50:11 & 0.006483 CPU secs, qhull has created 2146 facets and merged 1272. The current hull contains 273 facets and 31 vertices. There are 97 outside points. Next is point p120(v32), 0.54 above f437. At 22:50:11 & 0.011981 CPU secs, qhull has created 3310 facets and merged 2244. The current hull contains 243 facets and 36 vertices. There are 92 outside points. Next is point p60(v37), 0.54 above f1338. At 22:50:11 & 0.016841 CPU secs, qhull has created 4322 facets and merged 3099. The current hull contains 249 facets and 42 vertices. There are 86 outside points. Next is point p30(v43), 0.54 above f2005. At 22:50:11 & 0.022442 CPU secs, qhull has created 5491 facets and merged 4196. The current hull contains 186 facets and 48 vertices. There are 80 outside points. Next is point p21(v49), 0.5 above f2995. At 22:50:11 & 0.028005 CPU secs, qhull has created 6589 facets and merged 5175. The current hull contains 194 facets and 53 vertices. There are 75 outside points. Next is point p56(v54), 0.28 above f3731. At 22:50:11 & 0.034571 CPU secs, qhull has created 7867 facets and merged 6337. The current hull contains 203 facets and 60 vertices. There are 68 outside points. Next is point p76(v61), 0.29 above f5879. At 22:50:11 & 0.040664 CPU secs, qhull has created 8971 facets and merged 7362. The current hull contains 179 facets and 67 vertices. There are 61 outside points. Next is point p80(v68), 0.23 above f7175. At 22:50:11 & 0.046934 CPU secs, qhull has created 9984 facets and merged 8352. The current hull contains 104 facets and 77 vertices. There are 51 outside points. Next is point p96(v78), 0.41 above f6748. At 22:50:11 & 0.053771 CPU secs, qhull has created 10990 facets and merged 9326. The current hull contains 54 facets and 90 vertices. There are 38 outside points. Next is point p18(v91), 0.41 above f10178. At 22:50:11 & 0.05999 CPU secs, qhull has created 11996 facets and merged 10295. The current hull contains 34 facets and 114 vertices. There are 14 outside points. Next is point p19(v115), 0.38 above f11792. At 22:50:11 & 0.064919 CPU secs, qhull has created 12860 facets and merged 11072. The current hull contains 14 facets and 128 vertices. Last point was p77 Convex hull of 128 points in 7-d: Number of vertices: 128 Number of facets: 14 Number of non-simplicial facets: 14 Statistics for: rbox c D7 | qhull FA TF1000 Number of points processed: 128 Number of hyperplanes created: 1789 Number of distance tests for qhull: 10122 Number of distance tests for merging: 87203 Number of distance tests for checking: 0 Number of merged facets: 11072 First post-merge with 'C4.4e-15' and 'A1.8e+308' At 22:50:11 & 0.06567 CPU secs, qhull has created 12860 facets and merged 11072. The current hull contains 14 facets and 128 vertices. Last point was p77 Testing all coplanar points. computing area of each facet and volume of the convex hull Convex hull of 128 points in 7-d: Number of vertices: 128 Number of facets: 14 Number of non-simplicial facets: 14 Statistics for: rbox c D7 | qhull FA TF1000 Number of points processed: 128 Number of hyperplanes created: 1789 Number of distance tests for qhull: 10122 Number of distance tests for merging: 87371 Number of distance tests for checking: 1792 Number of merged facets: 11072 CPU seconds to compute hull (after input): 0.06583 Approximate facet area: 14 Approximate volume: 1 rbox y 1000 W0 | qhull Qc Convex hull of 1004 points in 3-d: Number of vertices: 4 Number of coplanar points: 1000 Number of facets: 4 Statistics for: rbox y 1000 W0 | qhull Qc Number of points processed: 4 Number of hyperplanes created: 4 Number of distance tests for qhull: 11000 CPU seconds to compute hull (after input): 0.00039 rbox c | qhull n 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 rbox c | qhull TA1 Early exit due to 'TAn', 'TVn', 'TCn', 'TRn', or precision error with 'QJn'. Convex hull of 8 points in 3-d: Number of vertices: 5 Number of facets: 6 Statistics for: rbox c | qhull TA1 Number of points processed: 5 Number of hyperplanes created: 8 Number of distance tests for qhull: 25 CPU seconds to compute hull (after input): 6.9e-05 rbox 10 s | qhull C1e-5 T1P-1f [QH1008]qh_readpoints: read in 10 3-dimensional points [QH0013]qh_initqhull_globals: for rbox 10 s | qhull C1e-5 T1P-1f Trace level T1, IStracing 0, point TP-1, merge TM0, dist TW1.8e+308, qh.tracefacet_id -1, traceridge_id -1, tracevertex_id -1, last qh.RERUN 0, rbox 10 s | qhull C1e-5 T1P-1f Options selected for Qhull 2020.2.r 2020/08/31: run-id 370121029 Centrum-postmerge 1e-05 Trace-point -1 Tflush _pre-merge _max-width 0.88 Error-roundoff 6.7e-16 _one-merge 3e-05 _near-inside 0.00015 Visible-distance 1.3e-15 U-max-coplanar 1.3e-15 Width-outside 2.7e-15 _wide-facet 8e-15 [QH2112]qh_qhull: finished qh_buildhull and qh_postmerge, start tracing (TP-1) [QH1022]qh_check_maxout: check and update qh.min_vertex -6.7e-16 and qh.max_outside 1.1e-16 [QH1055]qh_check_maxout: determine actual maxoutside [QH1024]qh_check_maxout: p7(v6) is qh.min_vertex -6.7e-16 below facet f4. Point p2 for f4 is qh.max_outside 1.1e-16 above f4. 0 points are outside of not-good facets [QH1036]Qhull: algorithm completed [QH1027]qh_checkpolygon: check all facets from f4, qh.NEWtentative? 0 [QH1062]qh_checkconvex: check that facets are not-flipped and that their centrums are convex by qh.DISTround ('En', 'Rn') Convex hull of 10 points in 3-d: Number of vertices: 10 Number of facets: 16 Statistics for: rbox 10 s | qhull C1e-5 T1P-1f Number of points processed: 10 Number of hyperplanes created: 27 Number of distance tests for qhull: 51 CPU seconds to compute hull (after input): 0.00011 [QH1006]qh_freeqhull: free global memory [QH1005]qh_freebuild: free memory from qh_inithull and qh_buildhull [QH1061]qh_freeqhull: clear qhT except for qh.qhmem and qh.qhstat set +v === check quality of Qhull for edb94518e8da Tue Oct 5 22:50:11 UTC 2021 rbox 1000 W0 | qhull QR2 QJ s Fs Tv Convex hull of 1000 points in 3-d: Number of vertices: 144 Number of facets: 284 Statistics for: rbox 1000 W0 | qhull QR2 QJ s Fs Tv QR2 Number of points processed: 171 Number of hyperplanes created: 1233 Number of distance tests for qhull: 33543 CPU seconds to compute hull (after input): 0.002147 After 1 retries, input joggled by: 2.9e-11 10 3 1000 144 284 144 284 0 0 33 0 2 5.045982607091333e-11 -5.045982607091333e-11 Output completed. Verifying that all points are below 2.9e-15 of all facets. Will make 284000 distance computations. rbox 1000 W0 | qhull QR2 s Fs Tv Convex hull of 1000 points in 3-d: Number of vertices: 84 Number of facets: 98 Number of non-simplicial facets: 6 Statistics for: rbox 1000 W0 | qhull QR2 s Fs Tv QR2 Number of points processed: 97 Number of hyperplanes created: 299 Number of distance tests for qhull: 18050 Number of distance tests for merging: 3163 Number of distance tests for checking: 15481 Number of merged facets: 92 CPU seconds to compute hull (after input): 0.001437 10 3 1000 84 98 84 98 0 6 13 0 2 1.942124858599573e-15 -1.241679291552168e-15 Output completed. Verifying that all points are below outer planes of all facets. Will make 98000 distance computations. rbox 1000 s | qhull C0.02 Qc Tv Convex hull of 1000 points in 3-d: Number of vertices: 110 Number of coplanar points: 890 Number of facets: 57 Number of non-simplicial facets: 57 Statistics for: rbox 1000 s | qhull C0.02 Qc Tv Number of points processed: 1000 Number of hyperplanes created: 5544 Number of distance tests for qhull: 81537 Number of distance tests for merging: 80706 Number of distance tests for checking: 8256 Number of merged facets: 1939 CPU seconds to compute hull (after input): 0.01594 Maximum distance of vertex below facet: -0.079 (1.3x) Output completed. Verifying that all points are below outer planes of all facets. Will make 57000 distance computations. rbox 500 s D4 | qhull C0.01 Qc Tv Convex hull of 500 points in 4-d: Number of vertices: 462 Number of coplanar points: 38 Number of facets: 345 Number of non-simplicial facets: 332 Statistics for: rbox 500 s D4 | qhull C0.01 Qc Tv Number of points processed: 500 Number of hyperplanes created: 11283 Number of distance tests for qhull: 42789 Number of distance tests for merging: 217359 Number of distance tests for checking: 12552 Number of merged facets: 2821 CPU seconds to compute hull (after input): 0.03527 Maximum distance of vertex below facet: -0.08 (2.0x) Output completed. Verifying that all points are below outer planes of all facets. Will make 172500 distance computations. rbox 1000 s | qhull C-0.02 Qc Tv Convex hull of 1000 points in 3-d: Number of vertices: 52 Number of coplanar points: 948 Number of facets: 47 Number of non-simplicial facets: 38 Statistics for: rbox 1000 s | qhull C-0.02 Qc Tv Number of points processed: 53 Number of hyperplanes created: 214 Number of distance tests for qhull: 47445 Number of distance tests for merging: 2943 Number of distance tests for checking: 19555 Number of merged facets: 107 CPU seconds to compute hull (after input): 0.00363 Maximum distance of point above facet: 0.039 (0.7x) Maximum distance of vertex below facet: -0.057 (0.9x) Output completed. Verifying that all points are below outer planes of all facets. Will make 47000 distance computations. rbox 1000 s D4 | qhull C-0.01 Qc Tv Convex hull of 1000 points in 4-d: Number of vertices: 126 Number of coplanar points: 874 Number of facets: 206 Number of non-simplicial facets: 148 Statistics for: rbox 1000 s D4 | qhull C-0.01 Qc Tv Number of points processed: 126 Number of hyperplanes created: 1371 Number of distance tests for qhull: 414344 Number of distance tests for merging: 73447 Number of distance tests for checking: 124140 Number of merged facets: 1331 CPU seconds to compute hull (after input): 0.03026 Maximum distance of point above facet: 0.068 (1.7x) Maximum distance of vertex below facet: -0.1 (2.6x) Output completed. Verifying that all points are below outer planes of all facets. Will make 206000 distance computations. rbox 200 s D5 | qhull C-0.01 Qx Qc Tv Convex hull of 200 points in 5-d: Number of vertices: 161 Number of coplanar points: 39 Number of facets: 416 Number of non-simplicial facets: 365 Statistics for: rbox 200 s D5 | qhull C-0.01 Qx Qc Tv Number of points processed: 161 Number of hyperplanes created: 4552 Number of distance tests for qhull: 229096 Number of distance tests for merging: 309307 Number of distance tests for checking: 54701 Number of merged facets: 6165 CPU seconds to compute hull (after input): 0.06503 Maximum distance of point above facet: 0.059 (1.2x) Maximum distance of vertex below facet: -0.1 (2.1x) QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 83200 distance computations. rbox 100 s D6 | qhull C-0.001 Qx Qc Tv Convex hull of 100 points in 6-d: Number of vertices: 100 Number of facets: 4454 Number of non-simplicial facets: 809 Statistics for: rbox 100 s D6 | qhull C-0.001 Qx Qc Tv Number of points processed: 100 Number of hyperplanes created: 19805 Number of distance tests for qhull: 33228 Number of distance tests for merging: 330047 Number of distance tests for checking: 88758 Number of merged facets: 3862 CPU seconds to compute hull (after input): 0.06839 Maximum distance of point above facet: 0.003 (0.5x) Maximum distance of vertex below facet: -0.014 (2.3x) QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 445400 distance computations. rbox 1000 W1e-4 | qhull C-1e-6 Qc Tv Convex hull of 1000 points in 3-d: Number of vertices: 145 Number of coplanar points: 87 Number of facets: 243 Number of non-simplicial facets: 29 Statistics for: rbox 1000 W1e-4 | qhull C-1e-6 Qc Tv Number of points processed: 185 Number of hyperplanes created: 940 Number of distance tests for qhull: 40788 Number of distance tests for merging: 7744 Number of distance tests for checking: 6136 Number of merged facets: 143 CPU seconds to compute hull (after input): 0.005231 Maximum distance of point above facet: 8.3e-07 (0.3x) Maximum distance of vertex below facet: -3.9e-06 (1.3x) Output completed. Verifying that all points are below outer planes of all facets. Will make 243000 distance computations. rbox 1000 W5e-4 D4 | qhull C-1e-5 Qc Tv Convex hull of 1000 points in 4-d: Number of vertices: 291 Number of coplanar points: 645 Number of facets: 1270 Number of non-simplicial facets: 150 Statistics for: rbox 1000 W5e-4 D4 | qhull C-1e-5 Qc Tv Number of points processed: 365 Number of hyperplanes created: 6253 Number of distance tests for qhull: 173452 Number of distance tests for merging: 91161 Number of distance tests for checking: 56354 Number of merged facets: 1354 CPU seconds to compute hull (after input): 0.01903 Maximum distance of point above facet: 0.00013 (3.3x) Maximum distance of vertex below facet: -0.00021 (5.4x) Output completed. Verifying that all points are below outer planes of all facets. Will make 1270000 distance computations. rbox 400 W1e-3 D5 | qhull C-1e-5 Qx Qc Tv Convex hull of 400 points in 5-d: Number of vertices: 306 Number of coplanar points: 33 Number of facets: 5557 Number of non-simplicial facets: 287 Statistics for: rbox 400 W1e-3 D5 | qhull C-1e-5 Qx Qc Tv Number of points processed: 338 Number of hyperplanes created: 24498 Number of distance tests for qhull: 262194 Number of distance tests for merging: 271068 Number of distance tests for checking: 90075 Number of merged facets: 1472 CPU seconds to compute hull (after input): 0.07379 Maximum distance of point above facet: 5.5e-05 (1.1x) Maximum distance of vertex below facet: -0.0001 (2.1x) QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 2222800 distance computations. set +v === check input format etc. Tue Oct 5 22:50:12 UTC 2021 qhull <r.x qhull TIr.x Convex hull of 10 points in 3-d: Number of vertices: 10 Number of facets: 16 Statistics for: rbox 10 | qhull TIr.x Number of points processed: 10 Number of hyperplanes created: 26 Number of distance tests for qhull: 43 CPU seconds to compute hull (after input): 6.1e-05 qhull p TI r.x TO x.x cat x.x 3 10 -0.374949442106252 0.2247255418679914 -0.03782349642163468 0.3004920247946792 0.3694544596313075 0.4210962191420572 0.3641479121187217 0.2339522165562512 0.03489791698278666 -0.4707134565997063 -0.2810653003687648 0.1354949890035158 0.2642752088273644 -0.3265712199048802 0.3175057017407433 0.3183227589524563 0.05060330969337679 0.4898217078203537 0.4334355904100794 -0.2480392830893763 0.2037671452423252 -0.2855954200826543 -0.002227006947833121 -0.4293096679535784 -0.4075898489985521 -0.3625928418362446 -0.09789381697577781 -0.3013850588364387 -0.3786854184034145 0.4341719447953365 set +v === check qhull output formats Tue Oct 5 22:50:13 UTC 2021 rbox 5 r s D2 | qhull Tcv Convex hull of 5 points in 2-d: Number of vertices: 5 Number of facets: 5 Statistics for: rbox 5 r s D2 | qhull Tcv Number of points processed: 5 Number of hyperplanes created: 8 Number of distance tests for qhull: 7 CPU seconds to compute hull (after input): 4.8e-05 Output completed. Verifying that all points are below 1.3e-15 of all facets. Will make 25 distance computations. rbox 5 r s D2 | qhull s Convex hull of 5 points in 2-d: Number of vertices: 5 Number of facets: 5 Statistics for: rbox 5 r s D2 | qhull s Number of points processed: 5 Number of hyperplanes created: 8 Number of distance tests for qhull: 7 CPU seconds to compute hull (after input): 8.5e-05 rbox 5 r s D2 | qhull s o Convex hull of 5 points in 2-d: Number of vertices: 5 Number of facets: 5 Statistics for: rbox 5 r s D2 | qhull s o Number of points processed: 5 Number of hyperplanes created: 8 Number of distance tests for qhull: 7 CPU seconds to compute hull (after input): 4.6e-05 2 5 5 5 0.1545084971874737 0.4755282581475768 -0.4045084971874737 0.2938926261462366 -0.4045084971874738 -0.2938926261462365 0.1545084971874736 -0.4755282581475768 0.5 -1.224646799147353e-16 2 4 0 2 2 3 2 3 4 2 1 2 2 0 1 rbox 5 r s D2 | qhull f Vertices and facets: - p0(v3): 0.15 0.48 - p4(v2): 0.5 -1.2e-16 - p3(v4): 0.15 -0.48 - p2(v1): -0.4 -0.29 - p1(v5): -0.4 0.29 - f3 - flags: bottom simplicial - normal: 0.809 0.5878 - offset: -0.4045085 - vertices: p0(v3) p4(v2) - neighboring facets: f5 f7 - f4 - flags: bottom simplicial - normal: -0.309 -0.9511 - offset: -0.4045085 - vertices: p3(v4) p2(v1) - neighboring facets: f6 f5 - f5 - flags: top simplicial - normal: 0.809 -0.5878 - offset: -0.4045085 - vertices: p3(v4) p4(v2) - neighboring facets: f3 f4 - f6 - flags: top simplicial - normal: -1 9.444e-17 - offset: -0.4045085 - vertices: p1(v5) p2(v1) - neighboring facets: f4 f7 - f7 - flags: bottom simplicial - normal: -0.309 0.9511 - offset: -0.4045085 - vertices: p1(v5) p0(v3) - neighboring facets: f3 f6 rbox 5 r s D2 | qhull i 5 4 0 2 3 3 4 1 2 0 1 rbox 5 r s D2 | qhull m { Line[{{ 0.50000000, -0.00000000}, { 0.15450850, 0.47552826}}] ,Line[{{ -0.40450850, -0.29389263}, { 0.15450850, -0.47552826}}] ,Line[{{ 0.15450850, -0.47552826}, { 0.50000000, -0.00000000}}] ,Line[{{ -0.40450850, 0.29389263}, { -0.40450850, -0.29389263}}] ,Line[{{ 0.15450850, 0.47552826}, { -0.40450850, 0.29389263}}] } rbox 5 r s D2 | qhull FM PLOT(CURVES( [[ 0.50000000, -0.00000000], [ 0.15450850, 0.47552826]] ,[[ -0.40450850, -0.29389263], [ 0.15450850, -0.47552826]] ,[[ 0.15450850, -0.47552826], [ 0.50000000, -0.00000000]] ,[[ -0.40450850, 0.29389263], [ -0.40450850, -0.29389263]] ,[[ 0.15450850, 0.47552826], [ -0.40450850, 0.29389263]] )); rbox 5 r s D2 | qhull n 3 5 0.8090169943749476 0.587785252292473 -0.4045084971874737 -0.3090169943749476 -0.9510565162951536 -0.4045084971874738 0.8090169943749472 -0.5877852522924732 -0.4045084971874737 -1 9.444121133484361e-17 -0.4045084971874738 -0.3090169943749474 0.9510565162951536 -0.4045084971874738 rbox 5 r s D2 | qhull p 2 5 0.1545084971874737 0.4755282581475768 -0.4045084971874737 0.2938926261462366 -0.4045084971874738 -0.2938926261462365 0.1545084971874736 -0.4755282581475768 0.5 -1.224646799147353e-16 rbox 5 r s D2 | qhull o 2 5 5 5 0.1545084971874737 0.4755282581475768 -0.4045084971874737 0.2938926261462366 -0.4045084971874738 -0.2938926261462365 0.1545084971874736 -0.4755282581475768 0.5 -1.224646799147353e-16 2 4 0 2 2 3 2 3 4 2 1 2 2 0 1 rbox 5 r s D2 | qhull Ft 2 5 5 5 0.1545084971874737 0.4755282581475768 -0.4045084971874737 0.2938926261462366 -0.4045084971874738 -0.2938926261462365 0.1545084971874736 -0.4755282581475768 0.5 -1.224646799147353e-16 2 4 0 2 2 3 2 3 4 2 1 2 2 0 1 rbox 5 r s D2 | qhull Fx 5 4 0 1 2 3 rbox 5 r s D2 | qhull p n i p p 2 5 0.1545084971874737 0.4755282581475768 -0.4045084971874737 0.2938926261462366 -0.4045084971874738 -0.2938926261462365 0.1545084971874736 -0.4755282581475768 0.5 -1.224646799147353e-16 3 5 0.8090169943749476 0.587785252292473 -0.4045084971874737 -0.3090169943749476 -0.9510565162951536 -0.4045084971874738 0.8090169943749472 -0.5877852522924732 -0.4045084971874737 -1 9.444121133484361e-17 -0.4045084971874738 -0.3090169943749474 0.9510565162951536 -0.4045084971874738 5 4 0 2 3 3 4 1 2 0 1 rbox 10 D3 | qhull f Tcv Vertices and facets: - p0(v5): -0.022 -0.37 0.33 - p9(v3): 0.38 -0.47 -0.22 - p6(v1): -0.31 -0.011 -0.49 - p1(v4): -0.067 -0.16 0.46 - p7(v2): 0.39 0.045 0.12 - p3(v6): 0.31 0.084 -0.1 - p4(v7): 0.18 0.12 0.049 - p5(v8): -0.12 0.015 -0.14 - p2(v9): 0.028 0.042 0.058 - f5 - flags: top simplicial - normal: -0.4934 -0.8471 -0.1973 - offset: -0.2568231 - vertices: p0(v5) p9(v3) p6(v1) - neighboring facets: f9 f6 f7 - f6 - flags: bottom simplicial - normal: -0.9301 -0.3157 0.1877 - offset: -0.1977325 - vertices: p0(v5) p1(v4) p6(v1) - neighboring facets: f17 f5 f8 - f7 - flags: bottom simplicial - normal: 0.7008 -0.3956 0.5936 - offset: -0.323519 - vertices: p0(v5) p9(v3) p7(v2) - neighboring facets: f10 f8 f5 - f8 - flags: top simplicial - normal: 0.6544 -0.298 0.6949 - offset: -0.3219447 - vertices: p0(v5) p1(v4) p7(v2) - neighboring facets: f13 f7 f6 - f9 - flags: bottom simplicial - normal: 0.4866 0.2316 -0.8424 - offset: -0.2582907 - vertices: p3(v6) p9(v3) p6(v1) - neighboring facets: f5 f16 f10 - f10 - flags: top simplicial - normal: 0.943 0.1711 -0.2855 - offset: -0.3386013 - vertices: p3(v6) p9(v3) p7(v2) - neighboring facets: f7 f14 f9 - f13 - flags: bottom simplicial - normal: 0.08536 0.8035 0.5892 - offset: -0.1388354 - vertices: p4(v7) p1(v4) p7(v2) - neighboring facets: f8 f14 f20 - f14 - flags: top simplicial - normal: 0.3121 0.948 0.06295 - offset: -0.1707289 - vertices: p4(v7) p3(v6) p7(v2) - neighboring facets: f10 f13 f16 - f16 - flags: bottom simplicial - normal: -0.008104 0.9738 -0.2271 - offset: -0.1026508 - vertices: p4(v7) p3(v6) p6(v1) - neighboring facets: f9 f18 f14 - f17 - flags: top simplicial - normal: -0.6179 0.7381 0.2709 - offset: -0.04995414 - vertices: p5(v8) p1(v4) p6(v1) - neighboring facets: f6 f18 f21 - f18 - flags: bottom simplicial - normal: -0.3978 0.9064 0.1423 - offset: -0.04320607 - vertices: p5(v8) p4(v7) p6(v1) - neighboring facets: f16 f17 f22 - f20 - flags: top simplicial - normal: -0.4124 0.8514 0.3242 - offset: -0.04294297 - vertices: p2(v9) p4(v7) p1(v4) - neighboring facets: f13 f21 f22 - f21 - flags: bottom simplicial - normal: -0.5086 0.8133 0.2826 - offset: -0.03620543 - vertices: p2(v9) p5(v8) p1(v4) - neighboring facets: f17 f20 f22 - f22 - flags: top simplicial - normal: -0.432 0.8759 0.2148 - offset: -0.03703814 - vertices: p2(v9) p5(v8) p4(v7) - neighboring facets: f18 f20 f21 Output completed. Verifying that all points are below 2e-15 of all facets. Will make 140 distance computations. rbox 10 D3 | qhull i 14 0 9 6 1 0 6 9 0 7 0 1 7 9 3 6 3 9 7 1 4 7 4 3 7 3 4 6 5 1 6 4 5 6 2 4 1 5 2 1 2 5 4 rbox 10 D3 | qhull p 3 9 -0.0222149361131852 -0.366434993563625 0.3270621312102882 -0.06676722137887703 -0.1566931052661437 0.4589771055234383 0.02820502736438535 0.04189077954915421 0.05832764185809314 0.3126723396709863 0.08400649026409401 -0.1029227018383543 0.1781470954214661 0.1182274414396169 0.04860343742054274 -0.1220315663349177 0.01546165115708642 -0.1360330368727753 -0.3072535691850387 -0.01073880122111998 -0.4870359524963758 0.3867462923626847 0.04492879989084675 0.118335500935405 0.3789805913148268 -0.4732086509216658 -0.2177962499836425 rbox 10 D3 | qhull o 3 10 14 21 -0.0222149361131852 -0.366434993563625 0.3270621312102882 -0.06676722137887703 -0.1566931052661437 0.4589771055234383 0.02820502736438535 0.04189077954915421 0.05832764185809314 0.3126723396709863 0.08400649026409401 -0.1029227018383543 0.1781470954214661 0.1182274414396169 0.04860343742054274 -0.1220315663349177 0.01546165115708642 -0.1360330368727753 -0.3072535691850387 -0.01073880122111998 -0.4870359524963758 0.3867462923626847 0.04492879989084675 0.118335500935405 -0.1352406177997967 0.01093378431250691 -0.2358910583293913 0.3789805913148268 -0.4732086509216658 -0.2177962499836425 3 0 9 6 3 1 0 6 3 9 0 7 3 0 1 7 3 9 3 6 3 3 9 7 3 1 4 7 3 4 3 7 3 3 4 6 3 5 1 6 3 4 5 6 3 2 4 1 3 5 2 1 3 2 5 4 rbox 10 D3 | qhull Fx 9 0 1 2 3 4 5 6 7 9 rbox 27 M1,0,1 | qhull Qc Convex hull of 27 points in 3-d: Number of vertices: 8 Number of coplanar points: 18 Number of facets: 6 Number of non-simplicial facets: 6 Statistics for: rbox 27 M1,0,1 | qhull Qc Number of points processed: 8 Number of hyperplanes created: 11 Number of distance tests for qhull: 297 Number of distance tests for merging: 90 Number of distance tests for checking: 168 Number of merged facets: 6 CPU seconds to compute hull (after input): 0.000105 rbox 50 D3 s | qhull C0.1 Qc Pd0d1d2 Pg s p Tcv Convex hull of 50 points in 3-d: Number of vertices: 17 Number of coplanar points: 33 Number of facets: 11 Number of 'good' facets: 1 Statistics for: rbox 50 D3 s | qhull C0.1 Qc Pd0d1d2 Pg s p Tcv Number of points processed: 50 Number of hyperplanes created: 236 Number of distance tests for qhull: 1191 Number of distance tests for merging: 3250 Number of distance tests for checking: 1146 Number of merged facets: 85 CPU seconds to compute hull (after input): 0.001224 Maximum distance of vertex below facet: -0.24 (0.8x) 3 4 0.4995640899182717 0.005583735684776723 0.02011322848106416 0.3642936952899509 -0.2163723184172344 -0.2654677445467591 0.39379735093457 0.04855022442420501 -0.3042474685273066 0.397166795352245 -0.07497301400429786 -0.2943426300092109 Output completed. Verifying that all points are below outer planes of all facets. Will make 50 distance computations. rbox 10 D2 P0 P1e-15 | qhull d Qc FP s Tcv Delaunay triangulation by the convex hull of 12 points in 3-d: Number of input sites: 11 Number of nearly incident points: 1 Number of Delaunay regions: 16 Statistics for: rbox 10 D2 P0 P1e-15 | qhull d Qc FP s Tcv Number of points processed: 11 Number of hyperplanes created: 33 Number of facets in hull: 18 Number of distance tests for qhull: 107 CPU seconds to compute hull (after input): 0.0001 1 0 1 12 1e-15 Output completed. Verifying that all points are below outer planes of all facets. Will make 192 distance computations. rbox 100 s | qhull C-0.003 Qc FP s Convex hull of 100 points in 3-d: Number of vertices: 90 Number of coplanar points: 10 Number of facets: 118 Number of non-simplicial facets: 46 Statistics for: rbox 100 s | qhull C-0.003 Qc FP s Number of points processed: 90 Number of hyperplanes created: 404 Number of distance tests for qhull: 1996 Number of distance tests for merging: 3783 Number of distance tests for checking: 1381 Number of merged facets: 105 CPU seconds to compute hull (after input): 0.001237 Maximum distance of point above facet: 0.0057 (0.6x) Maximum distance of vertex below facet: -0.0087 (1.0x) 10 29 92 222 0.05221620842441997 49 2 292 0.03790045221711884 99 9 336 0.02993864679572162 54 84 340 0.06479664045626413 54 72 226 0.03827167959574595 96 6 368 0.02282529175708784 19 1 372 0.01048228658130246 69 26 409 0.04998878658421259 19 66 371 0.008281093788857875 19 45 371 0.04608027722786196 rbox 100 s D2 | qhull C0.1 i Fx Tcv 6 4 28 77 70 6 68 70 6 68 4 28 77 6 4 28 77 70 6 68 Output completed. Verifying that all points are below outer planes of all facets. Will make 600 distance computations. rbox 4 s D3 | qhull Qc Ghipv Tcv {appearance {+edge -evert linewidth 2} LIST # rbox 4 s D3 | qhull Qc Ghipv Tcv {appearance {-edge -normal normscale 0} { INST geom {define vsphere OFF 18 32 48 0 0 1 1 0 0 0 1 0 -1 0 0 0 -1 0 0 0 -1 0.707107 0 0.707107 0 -0.707107 0.707107 0.707107 -0.707107 0 -0.707107 0 0.707107 -0.707107 -0.707107 0 0 0.707107 0.707107 -0.707107 0.707107 0 0.707107 0.707107 0 0.707107 0 -0.707107 0 0.707107 -0.707107 -0.707107 0 -0.707107 0 -0.707107 -0.707107 3 0 6 11 3 0 7 6 3 0 9 7 3 0 11 9 3 1 6 8 3 1 8 14 3 1 13 6 3 1 14 13 3 2 11 13 3 2 12 11 3 2 13 15 3 2 15 12 3 3 9 12 3 3 10 9 3 3 12 16 3 3 16 10 3 4 7 10 3 4 8 7 3 4 10 17 3 4 17 8 3 5 14 17 3 5 15 14 3 5 16 15 3 5 17 16 3 6 13 11 3 7 8 6 3 9 10 7 3 11 12 9 3 14 8 17 3 15 13 14 3 16 12 15 3 17 10 16 } transforms { TLIST 0.009951 0 0 0 # v3 0 0.009951 0 0 0 0 0.009951 0 -0.04234 -0.2077 -0.4529 # p3 1 0.009951 0 0 0 # v2 0 0.009951 0 0 0 0 0.009951 0 0.004313 -0.4976 0.04904 # p2 1 0.009951 0 0 0 # v1 0 0.009951 0 0 0 0 0.009951 0 -0.4876 0.03313 -0.1055 # p0 1 0.009951 0 0 0 # v4 0 0.009951 0 0 0 0 0.009951 0 -0.3939 -0.1068 -0.2889 # p1 1 }}} { OFF 3 1 1 # f1 -0.04933 -0.2152 -0.4566 -0.002675 -0.5051 0.04532 -0.4946 0.02557 -0.1092 3 0 1 2 0.1808 0.1547 0.3302 1.0 } VECT 1 2 1 2 1 # intersect f1 f2 0.004313 -0.4976 0.04904 # projected p2 -0.4876 0.03313 -0.1055 # projected p0 0 0 0 1.0 VECT 1 2 1 2 1 # intersect f1 f3 -0.04234 -0.2077 -0.4529 # projected p3 -0.4876 0.03313 -0.1055 # projected p0 0 0 0 1.0 VECT 1 2 1 2 1 # intersect f1 f4 -0.04234 -0.2077 -0.4529 # projected p3 0.004313 -0.4976 0.04904 # projected p2 0 0 0 1.0 { OFF 3 1 1 # f2 0.01247 -0.4904 0.04773 -0.3857 -0.09961 -0.2902 -0.4795 0.04031 -0.1068 3 0 1 2 0.8726 0.828 0.4402 1.0 } VECT 1 2 1 2 1 # intersect f2 f3 -0.3939 -0.1068 -0.2889 # projected p1 -0.4876 0.03313 -0.1055 # projected p0 0 0 0 1.0 VECT 1 2 1 2 1 # intersect f2 f4 -0.3939 -0.1068 -0.2889 # projected p1 0.004313 -0.4976 0.04904 # projected p2 0 0 0 1.0 { OFF 3 1 1 # f3 -0.3931 -0.1153 -0.282 -0.04157 -0.2162 -0.446 -0.4869 0.02464 -0.09863 3 0 1 2 0.5351 0.1123 0.8138 1.0 } VECT 1 2 1 2 1 # intersect f3 f4 -0.3939 -0.1068 -0.2889 # projected p1 -0.04234 -0.2077 -0.4529 # projected p3 0 0 0 1.0 { OFF 3 1 1 # f4 -0.03767 -0.1989 -0.4482 -0.3892 -0.09803 -0.2843 0.008983 -0.4888 0.05366 3 0 1 2 0.7133 0.8999 0.7112 1.0 } } Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 16 distance computations. rbox 6 D4 | qhull f Tcv Vertices and facets: - p3(v5): 0.1 -0.13 -0.17 -0.42 - p0(v4): -0.33 -0.43 -0.46 0.15 - p2(v3): 0.11 0.4 -0.063 -0.18 - p1(v1): -0.35 -0.24 0.14 -0.18 - p4(v2): 0.14 -0.34 -0.084 0.087 - p5(v6): -0.25 -0.5 0.22 -0.033 - f4 - flags: bottom simplicial - normal: -0.6536 0.3379 -0.424 -0.5281 - offset: -0.1850304 - vertices: p3(v5) p0(v4) p2(v3) p1(v1) - neighboring facets: f6 f8 f10 f5 - f5 - flags: top simplicial - normal: 0.6142 0.09488 -0.7743 0.1197 - offset: -0.1313181 - vertices: p3(v5) p0(v4) p2(v3) p4(v2) - neighboring facets: f7 f9 f11 f4 - f6 - flags: top simplicial - normal: -0.4209 0.3853 0.2879 0.7691 - offset: 0.04819078 - vertices: p5(v6) p0(v4) p2(v3) p1(v1) - neighboring facets: f4 f8 f10 f7 - f7 - flags: bottom simplicial - normal: -0.1759 0.3066 0.2842 0.8912 - offset: 0.07466537 - vertices: p5(v6) p0(v4) p2(v3) p4(v2) - neighboring facets: f5 f9 f11 f6 - f8 - flags: bottom simplicial - normal: 0.2584 0.07433 0.814 -0.515 - offset: -0.09844114 - vertices: p5(v6) p3(v5) p2(v3) p1(v1) - neighboring facets: f4 f6 f10 f9 - f9 - flags: top simplicial - normal: 0.6576 -0.06072 0.7252 -0.195 - offset: -0.03612816 - vertices: p5(v6) p3(v5) p2(v3) p4(v2) - neighboring facets: f5 f7 f11 f8 - f10 - flags: top simplicial - normal: -0.3537 -0.6003 -0.2017 -0.6883 - offset: -0.3651888 - vertices: p5(v6) p3(v5) p0(v4) p1(v1) - neighboring facets: f4 f6 f8 f11 - f11 - flags: bottom simplicial - normal: 0.2962 -0.865 -0.2123 -0.3449 - offset: -0.3220787 - vertices: p5(v6) p3(v5) p0(v4) p4(v2) - neighboring facets: f5 f7 f9 f10 Output completed. Verifying that all points are below 3e-15 of all facets. Will make 48 distance computations. rbox 6 D4 | qhull i 8 0 3 2 1 3 0 2 4 5 0 2 1 0 5 2 4 3 5 2 1 5 3 2 4 5 3 0 1 3 5 0 4 rbox 6 D4 | qhull p 4 6 -0.3257826863096865 -0.4296101703584289 -0.4581337649916613 0.1458114577883961 -0.3468340047139991 -0.2391184267952278 0.1365988111464296 -0.1837860440684352 0.1079548672847029 0.397449696341017 -0.062960620096848 -0.1791453880063681 0.1034612661259819 -0.1265049433582509 -0.1685859450777862 -0.4239815160855479 0.1426585555473888 -0.3376619446442108 -0.08430490557505277 0.08744874697872318 -0.2489141260729303 -0.4997188728300099 0.224904344160952 -0.03269336003129686 rbox 6 D4 | qhull o 4 6 8 16 -0.3257826863096865 -0.4296101703584289 -0.4581337649916613 0.1458114577883961 -0.3468340047139991 -0.2391184267952278 0.1365988111464296 -0.1837860440684352 0.1079548672847029 0.397449696341017 -0.062960620096848 -0.1791453880063681 0.1034612661259819 -0.1265049433582509 -0.1685859450777862 -0.4239815160855479 0.1426585555473888 -0.3376619446442108 -0.08430490557505277 0.08744874697872318 -0.2489141260729303 -0.4997188728300099 0.224904344160952 -0.03269336003129686 4 0 3 2 1 4 3 0 2 4 4 5 0 2 1 4 0 5 2 4 4 3 5 2 1 4 5 3 2 4 4 5 3 0 1 4 3 5 0 4 rbox 1000 s D2 | qhull FA Tcv Convex hull of 1000 points in 2-d: Number of vertices: 1000 Number of facets: 1000 Statistics for: rbox 1000 s D2 | qhull FA Tcv Number of points processed: 1000 Number of hyperplanes created: 1997 Number of distance tests for qhull: 13977 CPU seconds to compute hull (after input): 0.108 Total facet area: 3.1415592 Total volume: 0.7853647 qhull output completed. Verifying that 1000 points are below 1.3e-15 of the nearest facet. rbox 1000 s | qhull FA Tcv Convex hull of 1000 points in 3-d: Number of vertices: 1000 Number of facets: 1996 Statistics for: rbox 1000 s | qhull FA Tcv Number of points processed: 1000 Number of hyperplanes created: 5544 Number of distance tests for qhull: 25487 CPU seconds to compute hull (after input): 0.0876 Total facet area: 3.1201951 Total volume: 0.51650274 qhull output completed. Verifying that 1000 points are below 2.1e-15 of the nearest facet. rbox c D4 | qhull FA Tcv Convex hull of 16 points in 4-d: Number of vertices: 16 Number of facets: 8 Number of non-simplicial facets: 8 Statistics for: rbox c D4 | qhull FA Tcv Number of points processed: 16 Number of hyperplanes created: 25 Number of distance tests for qhull: 167 Number of distance tests for merging: 510 Number of distance tests for checking: 412 Number of merged facets: 36 CPU seconds to compute hull (after input): 0.00045 Approximate facet area: 8 Approximate volume: 1 Output completed. Verifying that all points are below outer planes of all facets. Will make 128 distance computations. rbox c D5 | qhull FA Tcv Convex hull of 32 points in 5-d: Number of vertices: 32 Number of facets: 10 Number of non-simplicial facets: 10 Statistics for: rbox c D5 | qhull FA Tcv Number of points processed: 32 Number of hyperplanes created: 86 Number of distance tests for qhull: 721 Number of distance tests for merging: 2702 Number of distance tests for checking: 400 Number of merged facets: 210 CPU seconds to compute hull (after input): 0.00569 Approximate facet area: 10 Approximate volume: 1 QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 320 distance computations. rbox c D5 | qhull FA Qt Tcv Convex hull of 32 points in 5-d: Number of vertices: 32 Number of facets: 316 Number of triangulated facets: 10 Statistics for: rbox c D5 | qhull FA Qt Tcv Number of points processed: 32 Number of hyperplanes created: 86 Number of distance tests for qhull: 721 Number of distance tests for merging: 2702 Number of distance tests for checking: 400 Number of merged facets: 210 CPU seconds to compute hull (after input): 0.005653 Approximate facet area: 10 Approximate volume: 1 QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 10112 distance computations. rbox 10 D2 | qhull d FA Tcv Delaunay triangulation by the convex hull of 10 points in 3-d: Number of input sites: 10 Number of Delaunay regions: 14 Statistics for: rbox 10 D2 | qhull d FA Tcv Number of points processed: 10 Number of hyperplanes created: 28 Number of facets in hull: 16 Number of distance tests for qhull: 47 CPU seconds to compute hull (after input): 0.000136 Total facet area: 0.46254269 Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 140 distance computations. rbox 10 D2 | qhull d Qu FA Tcv Furthest-site Delaunay triangulation by the convex hull of 10 points in 3-d: Number of input sites: 10 Number of Delaunay regions: 2 Statistics for: rbox 10 D2 | qhull d Qu FA Tcv Number of points processed: 10 Number of hyperplanes created: 28 Number of facets in hull: 16 Number of distance tests for qhull: 47 CPU seconds to compute hull (after input): 8.1e-05 Total facet area: 0.46254269 Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 20 distance computations. rbox 10 D2 | qhull FA Tcv Convex hull of 10 points in 2-d: Number of vertices: 4 Number of facets: 4 Statistics for: rbox 10 D2 | qhull FA Tcv Number of points processed: 4 Number of hyperplanes created: 5 Number of distance tests for qhull: 51 CPU seconds to compute hull (after input): 5e-05 Total facet area: 2.8999576 Total volume: 0.46254269 Output completed. Verifying that all points are below 1.3e-15 of all facets. Will make 40 distance computations. rbox 10 c D2 | qhull Fx Tcv 4 10 12 13 11 Output completed. Verifying that all points are below 1.3e-15 of all facets. Will make 56 distance computations. rbox 1000 s | qhull FS Tcv 0 2 3.120195135077461 0.516502736886338 qhull output completed. Verifying that 1000 points are below 2.1e-15 of the nearest facet. rbox 10 W0 D2 | qhull p Qc FcC Tcv 2 10 -0.3863076515368257 0.5 -0.05259535978789942 0.5 0.2626424396993987 0.5 0.3748708151978168 0.5 -0.01474997775140219 0.5 0.1582814042067914 0.5 -0.5 0.4508927962285399 -0.5 -0.003085198815060031 -0.3688616616361418 -0.5 -0.2798755283280048 0.5 5 0 0 0 0 5 2 4 5 9 1 2 5 0.003004576780837498 -8.023127287351645e-18 -0.5 0.2239037987067399 -0.4344308308180709 -0.25154259940753 -0.4431538257684129 0.4754463981142699 -0.005718418169504469 0.5 Output completed. Verifying that all points are below outer planes of all facets. Will make 50 distance computations. rbox 4 z h s D2 | qhull Fd s n FD Tcv Convex hull of 4 points in 2-d: Number of vertices: 4 Number of facets: 4 Statistics for: rbox 4 z h s D2 | qhull Fd s n FD Tcv Number of points processed: 4 Number of hyperplanes created: 5 Number of distance tests for qhull: 4 CPU seconds to compute hull (after input): 3.9e-05 rbox 4 z h s D2 | qhull Fd s n FD Tcv begin 4 3 real 107643.7343385944 -0.2650304141580589 -0.964240052876465 797791.7732245289 -0.6912673062074456 0.7225991360143615 874890.2679778723 0.9916265954087946 0.1291382796771071 864878.4439653738 0.3984446264475182 0.9171923896626583 end Output completed. Verifying that all points are below 2.6e-09 of all facets. Will make 16 distance computations. 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 Options selected for Qhull 2020.2.r 2020/08/31: run-id 370154643 Centrum-premerge- 0.1 Qcoplanar-keep FFacets-xridge summary FQhull Finner normals Fouter FQhull FIDs Fmerges Fneighbors FNeighbors-vertex FOptions FQhull Fsummary FSize FVertex-average Tcheck-frequently Tverify Fvertices _max-width 0.86 Error-roundoff 6.6e-16 _one-merge 0.3 _near-inside 1.5 Visible-distance 0.1 U-max-coplanar 0.1 Width-outside 0.2 _wide-facet 0.6 Convex hull of 6 points in 3-d: Number of vertices: 4 Number of coplanar points: 2 Number of facets: 4 Statistics for: 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 Number of points processed: 4 Number of hyperplanes created: 4 Number of distance tests for qhull: 22 CPU seconds to compute hull (after input): 8e-05 Total facet area: 0.82966766 Total volume: 0.010511079 Maximum distance of point above facet: 0.11 (0.4x) Vertices and facets: - p1(v3): -0.3 0.39 -0.092 - p5(v2): 0.4 -0.22 -0.2 - p4(v1): -0.46 -0.19 -0.018 - p2(v4): 0.25 0.28 -0.33 - f1 - flags: top simplicial isarea - area: 0.26 - normal: 0.2054 0.06987 0.9762 - offset: 0.125398 - center: -0.1205015151724569 -0.008790385787885074 -0.1024776532548504 - vertices: p1(v3) p5(v2) p4(v1) - neighboring facets: f2 f3 f4 - f2 - flags: bottom simplicial isarea - area: 0.23 - normal: -0.2032 -0.3001 -0.932 - offset: -0.1680571 - center: 0.06430144219370747 -0.04270356053094847 -0.1805812707066012 - maxoutside: 0.1132672 - coplanar set(furthest p3): p0: 0.07025 -0.4742 -0.142 p3: 0.2976 -0.2965 -0.2712 furthest distance= 0.11 - vertices: p2(v4) p5(v2) p4(v1) - neighboring facets: f1 f3 f4 - f3 - flags: top simplicial isarea - area: 0.18 - normal: -0.3912 -0.01238 -0.9202 - offset: -0.1989549 - center: -0.1715856748140029 0.1590825675964338 -0.1454013928109104 - vertices: p2(v4) p1(v3) p4(v1) - neighboring facets: f1 f2 f4 - f4 - flags: bottom simplicial isarea - area: 0.16 - normal: 0.4184 0.3424 0.8413 - offset: 0.07254957 - center: 0.116549362001881 0.1503252206347392 -0.2053893818610149 - vertices: p2(v4) p1(v3) p5(v2) - neighboring facets: f1 f2 f3 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 4 4 0.205360378770873 0.06987429109559466 0.976188864039624 0.1253980026939646 -0.2031613339148238 -0.3001304507855299 -0.9320124381751694 -0.1680570625036091 -0.3911895500493898 -0.01238286325891905 -0.9202268202077502 -0.1989548866041478 0.4183781509471984 0.3424157187037644 0.8412557271095321 0.07254956874669725 4 4 0.205360378770873 0.06987429109559466 0.976188864039624 0.125398002693964 -0.2031613339148238 -0.3001304507855299 -0.9320124381751694 -0.1680570625036098 -0.3911895500493898 -0.01238286325891905 -0.9202268202077502 -0.1989548866041485 0.4183781509471984 0.3424157187037644 0.8412557271095321 0.0725495687466966 4 4 0.205360378770873 0.06987429109559466 0.976188864039624 0.1253980026939626 -0.2031613339148238 -0.3001304507855299 -0.9320124381751694 -0.2813242952138535 -0.3911895500493898 -0.01238286325891905 -0.9202268202077502 -0.1989548866041498 0.4183781509471984 0.3424157187037644 0.8412557271095321 0.07254956874669528 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 4 1 2 3 4 4 0 0 0 0 4 3 1 2 3 3 0 2 3 3 0 1 3 3 0 1 2 6 1 1 3 3 0 2 3 3 1 2 1 1 3 2 0 1 3 3 0 1 Options selected for Qhull 2020.2.r 2020/08/31: run-id 370154643 Centrum-premerge- 0.1 Qcoplanar-keep FFacets-xridge summary FQhull Finner normals Fouter FQhull FIDs Fmerges Fneighbors FNeighbors-vertex FOptions FQhull Fsummary FSize FVertex-average Tcheck-frequently Tverify Fvertices _max-width 0.86 Error-roundoff 6.6e-16 _one-merge 0.3 _near-inside 1.5 Visible-distance 0.1 U-max-coplanar 0.1 Width-outside 0.2 _wide-facet 0.6 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 10 3 6 4 4 4 4 2 0 0 0 2 0.1132672327102437 -1.315898280434284e-15 0 2 0.8296676646636063 0.01051107893821417 3 1 -0.02780909644771785 0.06447846047808484 -0.1584624246583442 4 3 1 5 4 3 2 5 4 3 2 1 4 3 2 1 5 Output completed. Verifying that all points are below outer planes of all facets. Will make 24 distance computations. rbox P0.5,0.5 P0.5,0.5 W0 5 D2 | qhull d FN Qc 7 5 3 1 0 -4 -8 1 1 5 -10 2 -3 -4 -8 4 2 -3 0 1 3 -4 0 -3 3 -10 -8 3 4 -10 2 1 3 rbox 10 D3 | qhull Fa PA5 5 0.2844546842397038 0.1170134053930415 0.1758021655943633 0.07490600482805046 0.2087585943133527 rbox 10 D3 | qhull Fa PF0.4 QH7055 qhull warning: no facets printed 0 set +v === test Qt Tue Oct 5 22:50:13 UTC 2021 rbox c | qhull Qt s o Tcv Convex hull of 8 points in 3-d: Number of vertices: 8 Number of facets: 12 Number of triangulated facets: 6 Statistics for: rbox c | qhull Qt s o Tcv Number of points processed: 8 Number of hyperplanes created: 11 Number of distance tests for qhull: 34 Number of distance tests for merging: 96 Number of distance tests for checking: 100 Number of merged facets: 6 CPU seconds to compute hull (after input): 0.000242 3 8 12 18 -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 3 6 2 0 3 4 6 0 3 5 4 0 3 1 5 0 3 5 6 4 3 6 5 7 3 2 3 0 3 3 1 0 3 6 3 2 3 3 6 7 3 3 5 1 3 5 3 7 Output completed. Verifying that all points are below outer planes of all facets. Will make 96 distance computations. rbox c | qhull Qt f i Vertices and facets: - p6(v6): 0.5 0.5 -0.5 neighbors: f17 f18 f25 f27 f33 f34 - p2(v3): -0.5 0.5 -0.5 neighbors: f17 f29 f33 - p0(v1): -0.5 -0.5 -0.5 neighbors: f17 f18 f21 f22 f29 f30 - p4(v2): 0.5 -0.5 -0.5 neighbors: f18 f21 f25 - p5(v7): 0.5 -0.5 0.5 neighbors: f21 f22 f25 f27 f37 f38 - p1(v4): -0.5 -0.5 0.5 neighbors: f22 f30 f37 - p7(v5): 0.5 0.5 0.5 neighbors: f27 f34 f38 - p3(v8): -0.5 0.5 0.5 neighbors: f29 f30 f33 f34 f37 f38 - f17 - flags: top simplicial tricoplanar keepcentrum - owner of normal & centrum is facet f17 - normal: -0 -0 -1 - offset: -0.5 - center: 0 0 -0.5 - vertices: p6(v6) p2(v3) p0(v1) - neighboring facets: f29 f18 f33 - f18 - flags: bottom simplicial tricoplanar - owner of normal & centrum is facet f17 - normal: -0 -0 -1 - offset: -0.5 - center: 0 0 -0.5 - vertices: p6(v6) p4(v2) p0(v1) - neighboring facets: f21 f17 f25 - f21 - flags: top simplicial tricoplanar keepcentrum - owner of normal & centrum is facet f21 - normal: 0 -1 0 - offset: -0.5 - center: 0 -0.5 0 - vertices: p5(v7) p4(v2) p0(v1) - neighboring facets: f18 f22 f25 - f22 - flags: bottom simplicial tricoplanar - owner of normal & centrum is facet f21 - normal: 0 -1 0 - offset: -0.5 - center: 0 -0.5 0 - vertices: p5(v7) p1(v4) p0(v1) - neighboring facets: f30 f21 f37 - f25 - flags: top simplicial tricoplanar keepcentrum - owner of normal & centrum is facet f25 - normal: 1 -0 -0 - offset: -0.5 - center: 0.5 0 0 - vertices: p5(v7) p6(v6) p4(v2) - neighboring facets: f18 f21 f27 - f27 - flags: bottom simplicial tricoplanar - owner of normal & centrum is facet f25 - normal: 1 -0 -0 - offset: -0.5 - center: 0.5 0 0 - vertices: p5(v7) p6(v6) p7(v5) - neighboring facets: f34 f38 f25 - f29 - flags: bottom simplicial tricoplanar keepcentrum - owner of normal & centrum is facet f29 - normal: -1 -0 -0 - offset: -0.5 - center: -0.5 0 0 - vertices: p3(v8) p2(v3) p0(v1) - neighboring facets: f17 f30 f33 - f30 - flags: top simplicial tricoplanar - owner of normal & centrum is facet f29 - normal: -1 -0 -0 - offset: -0.5 - center: -0.5 0 0 - vertices: p3(v8) p1(v4) p0(v1) - neighboring facets: f22 f29 f37 - f33 - flags: bottom simplicial tricoplanar keepcentrum - owner of normal & centrum is facet f33 - normal: 0 1 -0 - offset: -0.5 - center: 0 0.5 0 - vertices: p3(v8) p6(v6) p2(v3) - neighboring facets: f17 f29 f34 - f34 - flags: top simplicial tricoplanar - owner of normal & centrum is facet f33 - normal: 0 1 -0 - offset: -0.5 - center: 0 0.5 0 - vertices: p3(v8) p6(v6) p7(v5) - neighboring facets: f27 f38 f33 - f37 - flags: top simplicial tricoplanar keepcentrum - owner of normal & centrum is facet f37 - normal: -0 -0 1 - offset: -0.5 - center: 0 0 0.5 - vertices: p3(v8) p5(v7) p1(v4) - neighboring facets: f22 f30 f38 - f38 - flags: bottom simplicial tricoplanar - owner of normal & centrum is facet f37 - normal: -0 -0 1 - offset: -0.5 - center: 0 0 0.5 - vertices: p3(v8) p5(v7) p7(v5) - neighboring facets: f27 f34 f37 12 6 2 0 4 6 0 5 4 0 1 5 0 5 6 4 6 5 7 2 3 0 3 1 0 6 3 2 3 6 7 3 5 1 5 3 7 rbox c | qhull Qt m FM n { Polygon[{{ 0.50000000, 0.50000000, -0.50000000}, { -0.50000000, 0.50000000, -0.50000000}, { -0.50000000, -0.50000000, -0.50000000}}], Polygon[{{ 0.50000000, -0.50000000, -0.50000000}, { 0.50000000, 0.50000000, -0.50000000}, { -0.50000000, -0.50000000, -0.50000000}}], Polygon[{{ 0.50000000, -0.50000000, 0.50000000}, { 0.50000000, -0.50000000, -0.50000000}, { -0.50000000, -0.50000000, -0.50000000}}], Polygon[{{ -0.50000000, -0.50000000, 0.50000000}, { 0.50000000, -0.50000000, 0.50000000}, { -0.50000000, -0.50000000, -0.50000000}}], Polygon[{{ 0.50000000, -0.50000000, 0.50000000}, { 0.50000000, 0.50000000, -0.50000000}, { 0.50000000, -0.50000000, -0.50000000}}], Polygon[{{ 0.50000000, 0.50000000, -0.50000000}, { 0.50000000, -0.50000000, 0.50000000}, { 0.50000000, 0.50000000, 0.50000000}}], Polygon[{{ -0.50000000, 0.50000000, -0.50000000}, { -0.50000000, 0.50000000, 0.50000000}, { -0.50000000, -0.50000000, -0.50000000}}], Polygon[{{ -0.50000000, 0.50000000, 0.50000000}, { -0.50000000, -0.50000000, 0.50000000}, { -0.50000000, -0.50000000, -0.50000000}}], Polygon[{{ 0.50000000, 0.50000000, -0.50000000}, { -0.50000000, 0.50000000, 0.50000000}, { -0.50000000, 0.50000000, -0.50000000}}], Polygon[{{ -0.50000000, 0.50000000, 0.50000000}, { 0.50000000, 0.50000000, -0.50000000}, { 0.50000000, 0.50000000, 0.50000000}}], Polygon[{{ -0.50000000, 0.50000000, 0.50000000}, { 0.50000000, -0.50000000, 0.50000000}, { -0.50000000, -0.50000000, 0.50000000}}], Polygon[{{ 0.50000000, -0.50000000, 0.50000000}, { -0.50000000, 0.50000000, 0.50000000}, { 0.50000000, 0.50000000, 0.50000000}}]} PLOT3D(POLYGONS( [[ 0.50000000, 0.50000000, -0.50000000], [ -0.50000000, 0.50000000, -0.50000000], [ -0.50000000, -0.50000000, -0.50000000]], [[ 0.50000000, -0.50000000, -0.50000000], [ 0.50000000, 0.50000000, -0.50000000], [ -0.50000000, -0.50000000, -0.50000000]], [[ 0.50000000, -0.50000000, 0.50000000], [ 0.50000000, -0.50000000, -0.50000000], [ -0.50000000, -0.50000000, -0.50000000]], [[ -0.50000000, -0.50000000, 0.50000000], [ 0.50000000, -0.50000000, 0.50000000], [ -0.50000000, -0.50000000, -0.50000000]], [[ 0.50000000, -0.50000000, 0.50000000], [ 0.50000000, 0.50000000, -0.50000000], [ 0.50000000, -0.50000000, -0.50000000]], [[ 0.50000000, 0.50000000, -0.50000000], [ 0.50000000, -0.50000000, 0.50000000], [ 0.50000000, 0.50000000, 0.50000000]], [[ -0.50000000, 0.50000000, -0.50000000], [ -0.50000000, 0.50000000, 0.50000000], [ -0.50000000, -0.50000000, -0.50000000]], [[ -0.50000000, 0.50000000, 0.50000000], [ -0.50000000, -0.50000000, 0.50000000], [ -0.50000000, -0.50000000, -0.50000000]], [[ 0.50000000, 0.50000000, -0.50000000], [ -0.50000000, 0.50000000, 0.50000000], [ -0.50000000, 0.50000000, -0.50000000]], [[ -0.50000000, 0.50000000, 0.50000000], [ 0.50000000, 0.50000000, -0.50000000], [ 0.50000000, 0.50000000, 0.50000000]], [[ -0.50000000, 0.50000000, 0.50000000], [ 0.50000000, -0.50000000, 0.50000000], [ -0.50000000, -0.50000000, 0.50000000]], [[ 0.50000000, -0.50000000, 0.50000000], [ -0.50000000, 0.50000000, 0.50000000], [ 0.50000000, 0.50000000, 0.50000000]])); 4 12 -0 -0 -1 -0.5 -0 -0 -1 -0.5 0 -1 0 -0.5 0 -1 0 -0.5 1 -0 -0 -0.5 1 -0 -0 -0.5 -1 -0 -0 -0.5 -1 -0 -0 -0.5 0 1 -0 -0.5 0 1 -0 -0.5 -0 -0 1 -0.5 -0 -0 1 -0.5 rbox c | qhull Qt p o 3 8 -0.5 -0.5 -0.5 -0.5 -0.5 0.5 -0.5 0.5 -0.5 -0.5 0.5 0.5 0.5 -0.5 -0.5 0.5 -0.5 0.5 0.5 0.5 -0.5 0.5 0.5 0.5 3 8 12 18 -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 3 6 2 0 3 4 6 0 3 5 4 0 3 1 5 0 3 5 6 4 3 6 5 7 3 2 3 0 3 3 1 0 3 6 3 2 3 3 6 7 3 3 5 1 3 5 3 7 rbox c | qhull Qt Fx 8 0 1 2 3 4 5 6 7 rbox c | qhull Qt FA s Fa Convex hull of 8 points in 3-d: Number of vertices: 8 Number of facets: 12 Number of triangulated facets: 6 Statistics for: rbox c | qhull Qt FA s Fa Number of points processed: 8 Number of hyperplanes created: 11 Number of distance tests for qhull: 34 Number of distance tests for merging: 90 Number of distance tests for checking: 48 Number of merged facets: 6 CPU seconds to compute hull (after input): 0.000144 Approximate facet area: 6 Approximate volume: 1 12 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 rbox 6 r s c G0.1 D2 | qhull Qt d FA Tcv Delaunay triangulation by the convex hull of 10 points in 3-d: Number of input sites: 10 Number of Delaunay regions: 12 Number of triangulated facets: 3 Statistics for: rbox 6 r s c G0.1 D2 | qhull Qt d FA Tcv Number of points processed: 10 Number of hyperplanes created: 19 Number of facets in hull: 16 Number of distance tests for qhull: 48 Number of distance tests for merging: 170 Number of distance tests for checking: 164 Number of merged facets: 7 CPU seconds to compute hull (after input): 0.0002 Approximate facet area: 0.64951905 Output completed. Verifying that all points are below outer planes of all facets. Will make 120 distance computations. rbox 6 r s c G0.1 D2 | qhull d FA Tcv Delaunay triangulation by the convex hull of 10 points in 3-d: Number of input sites: 10 Number of Delaunay regions: 9 Number of non-simplicial Delaunay regions: 3 Statistics for: rbox 6 r s c G0.1 D2 | qhull d FA Tcv Number of points processed: 10 Number of hyperplanes created: 19 Number of facets in hull: 10 Number of distance tests for qhull: 48 Number of distance tests for merging: 170 Number of distance tests for checking: 164 Number of merged facets: 7 CPU seconds to compute hull (after input): 0.000162 Approximate facet area: 0.64951905 Output completed. Verifying that all points are below outer planes of all facets. Will make 90 distance computations. rbox 6 r s c G0.1 D2 | qhull Qt v p Tcv 2 12 -0.3359969878447703 -0.1939879513790814 -0.3359969878447704 0.1939879513790817 -0.2875 0 0.3359969878447702 -0.1939879513790819 0.3359969878447707 0.1939879513790815 0.2875 0 -2.220446049250313e-16 -0.3453321730569308 -2.220446049250313e-16 -0.3453321730569308 1.110223024625157e-16 0.3453321730569308 1.110223024625157e-16 0.3453321730569308 0 0 0 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 120 distance computations. 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 Options selected for Qhull 2020.2.r 2020/08/31: run-id 370154643 Qtriangulate Centrum-premerge- 0.1 Qcoplanar-keep FFacets-xridge summary FQhull Finner normals Fouter FQhull FIDs Fmerges Fneighbors FNeighbors-vertex FOptions FQhull Fsummary FSize FVertex-average Tcheck-frequently Tverify Fvertices _max-width 1 Error-roundoff 6.9e-16 _one-merge 0.3 _near-inside 1.5 Visible-distance 0.1 U-max-coplanar 0.1 Width-outside 0.2 _wide-facet 0.6 Convex hull of 8 points in 3-d: Number of vertices: 8 Number of facets: 12 Number of triangulated facets: 6 Statistics for: 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 Number of points processed: 8 Number of hyperplanes created: 11 Number of distance tests for qhull: 34 Number of distance tests for merging: 102 Number of distance tests for checking: 126 Number of merged facets: 6 CPU seconds to compute hull (after input): 0.000193 Approximate facet area: 6 Approximate volume: 1 Vertices and facets: - p6(v6): 0.5 0.5 -0.5 neighbors: f17 f18 f25 f27 f33 f34 - p2(v3): -0.5 0.5 -0.5 neighbors: f17 f29 f33 - p0(v1): -0.5 -0.5 -0.5 neighbors: f17 f18 f21 f22 f29 f30 - p4(v2): 0.5 -0.5 -0.5 neighbors: f18 f21 f25 - p5(v7): 0.5 -0.5 0.5 neighbors: f21 f22 f25 f27 f37 f38 - p1(v4): -0.5 -0.5 0.5 neighbors: f22 f30 f37 - p7(v5): 0.5 0.5 0.5 neighbors: f27 f34 f38 - p3(v8): -0.5 0.5 0.5 neighbors: f29 f30 f33 f34 f37 f38 - f17 - flags: top simplicial tricoplanar isarea keepcentrum - area: 0.5 - normal: -0 -0 -1 - offset: -0.5 - center: 0 0 -0.5 - vertices: p6(v6) p2(v3) p0(v1) - neighboring facets: f29 f18 f33 - f18 - flags: bottom simplicial tricoplanar isarea - area: 0.5 - normal: -0 -0 -1 - offset: -0.5 - center: 0 0 -0.5 - vertices: p6(v6) p4(v2) p0(v1) - neighboring facets: f21 f17 f25 - f21 - flags: top simplicial tricoplanar isarea keepcentrum - area: 0.5 - normal: 0 -1 0 - offset: -0.5 - center: 0 -0.5 0 - vertices: p5(v7) p4(v2) p0(v1) - neighboring facets: f18 f22 f25 - f22 - flags: bottom simplicial tricoplanar isarea - area: 0.5 - normal: 0 -1 0 - offset: -0.5 - center: 0 -0.5 0 - vertices: p5(v7) p1(v4) p0(v1) - neighboring facets: f30 f21 f37 - f25 - flags: top simplicial tricoplanar isarea keepcentrum - area: 0.5 - normal: 1 -0 -0 - offset: -0.5 - center: 0.5 0 0 - vertices: p5(v7) p6(v6) p4(v2) - neighboring facets: f18 f21 f27 - f27 - flags: bottom simplicial tricoplanar isarea - area: 0.5 - normal: 1 -0 -0 - offset: -0.5 - center: 0.5 0 0 - vertices: p5(v7) p6(v6) p7(v5) - neighboring facets: f34 f38 f25 - f29 - flags: bottom simplicial tricoplanar isarea keepcentrum - area: 0.5 - normal: -1 -0 -0 - offset: -0.5 - center: -0.5 0 0 - vertices: p3(v8) p2(v3) p0(v1) - neighboring facets: f17 f30 f33 - f30 - flags: top simplicial tricoplanar isarea - area: 0.5 - normal: -1 -0 -0 - offset: -0.5 - center: -0.5 0 0 - vertices: p3(v8) p1(v4) p0(v1) - neighboring facets: f22 f29 f37 - f33 - flags: bottom simplicial tricoplanar isarea keepcentrum - area: 0.5 - normal: 0 1 -0 - offset: -0.5 - center: 0 0.5 0 - vertices: p3(v8) p6(v6) p2(v3) - neighboring facets: f17 f29 f34 - f34 - flags: top simplicial tricoplanar isarea - area: 0.5 - normal: 0 1 -0 - offset: -0.5 - center: 0 0.5 0 - vertices: p3(v8) p6(v6) p7(v5) - neighboring facets: f27 f38 f33 - f37 - flags: top simplicial tricoplanar isarea keepcentrum - area: 0.5 - normal: -0 -0 1 - offset: -0.5 - center: 0 0 0.5 - vertices: p3(v8) p5(v7) p1(v4) - neighboring facets: f22 f30 f38 - f38 - flags: bottom simplicial tricoplanar isarea - area: 0.5 - normal: -0 -0 1 - offset: -0.5 - center: 0 0 0.5 - vertices: p3(v8) p5(v7) p7(v5) - neighboring facets: f27 f34 f37 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 4 12 -0 -0 -1 -0.4999999999999993 -0 -0 -1 -0.4999999999999993 0 -1 0 -0.4999999999999993 0 -1 0 -0.4999999999999993 1 -0 -0 -0.4999999999999993 1 -0 -0 -0.4999999999999993 -1 -0 -0 -0.4999999999999993 -1 -0 -0 -0.4999999999999993 0 1 -0 -0.4999999999999993 0 1 -0 -0.4999999999999993 -0 -0 1 -0.4999999999999993 -0 -0 1 -0.4999999999999993 4 12 -0 -0 -1 -0.5 -0 -0 -1 -0.5 0 -1 0 -0.5 0 -1 0 -0.5 1 -0 -0 -0.5 1 -0 -0 -0.5 -1 -0 -0 -0.5 -1 -0 -0 -0.5 0 1 -0 -0.5 0 1 -0 -0.5 -0 -0 1 -0.5 -0 -0 1 -0.5 4 12 -0 -0 -1 -0.5000000000000013 -0 -0 -1 -0.5000000000000013 0 -1 0 -0.5000000000000013 0 -1 0 -0.5000000000000013 1 -0 -0 -0.5000000000000013 1 -0 -0 -0.5000000000000013 -1 -0 -0 -0.5000000000000013 -1 -0 -0 -0.5000000000000013 0 1 -0 -0.5000000000000013 0 1 -0 -0.5000000000000013 -0 -0 1 -0.5000000000000013 -0 -0 1 -0.5000000000000013 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 12 17 18 21 22 25 27 29 30 33 34 37 38 12 0 0 0 0 0 0 0 0 0 0 0 0 12 3 6 1 8 3 2 0 4 3 1 3 4 3 7 2 10 3 1 2 5 3 9 11 4 3 0 7 8 3 3 6 10 3 0 6 9 3 5 11 8 3 3 7 11 3 5 9 10 8 6 7 3 2 1 0 6 3 10 3 7 3 8 0 6 6 11 9 8 6 7 10 3 4 1 2 6 11 5 4 2 3 10 6 9 5 4 1 0 8 3 11 5 9 Options selected for Qhull 2020.2.r 2020/08/31: run-id 370154643 Qtriangulate Centrum-premerge- 0.1 Qcoplanar-keep FFacets-xridge summary FQhull Finner normals Fouter FQhull FIDs Fmerges Fneighbors FNeighbors-vertex FOptions FQhull Fsummary FSize FVertex-average Tcheck-frequently Tverify Fvertices _max-width 1 Error-roundoff 6.9e-16 _one-merge 0.3 _near-inside 1.5 Visible-distance 0.1 U-max-coplanar 0.1 Width-outside 0.2 _wide-facet 0.6 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 10 3 8 8 12 8 12 0 0 0 6 2 1.387359992873471e-15 -6.936799964367356e-16 0 2 6 1 3 1 0 0 0 12 3 6 2 0 3 6 4 0 3 5 4 0 3 5 1 0 3 5 6 4 3 5 6 7 3 3 2 0 3 3 1 0 3 3 6 2 3 3 6 7 3 3 5 1 3 3 5 7 Output completed. Verifying that all points are below outer planes of all facets. Will make 96 distance computations. rbox 6 r s c G0.1 D2 P0.1,0.1 | qhull s FP d FO Qt Options selected for Qhull 2020.2.r 2020/08/31: run-id 370154643 summary FPoint-nearest delaunay Qtriangulate _pre-merge _zero-centrum Pgood Qcoplanar _max-width 1 Error-roundoff 6.9e-16 _one-merge 4.9e-15 _near-inside 2.4e-14 Visible-distance 1.4e-15 U-max-coplanar 1.4e-15 Width-outside 2.8e-15 _wide-facet 8.3e-15 Delaunay triangulation by the convex hull of 11 points in 3-d: Number of input sites: 10 Number of nearly incident points: 1 Number of Delaunay regions: 12 Number of triangulated facets: 3 Statistics for: rbox 6 r s c G0.1 D2 P0.1,0.1 | qhull s FP d FO Qt Number of points processed: 10 Number of hyperplanes created: 19 Number of facets in hull: 16 Number of distance tests for qhull: 79 Number of distance tests for merging: 153 Number of distance tests for checking: 100 Number of merged facets: 6 CPU seconds to compute hull (after input): 0.00012 1 0 10 36 0 rbox 100 W0 | qhull Tv Q11 FO Options selected for Qhull 2020.2.r 2020/08/31: run-id 370154643 Tverify Q11-trinormals Qtriangulate _pre-merge _zero-centrum _max-width 1 Error-roundoff 6.9e-16 _one-merge 4.9e-15 _near-inside 2.4e-14 Visible-distance 1.4e-15 U-max-coplanar 1.4e-15 Width-outside 2.8e-15 _wide-facet 8.3e-15 Convex hull of 100 points in 3-d: Number of vertices: 45 Number of facets: 86 Number of triangulated facets: 33 Statistics for: rbox 100 W0 | qhull Tv Q11 FO Number of points processed: 52 Number of hyperplanes created: 171 Number of distance tests for qhull: 1575 Number of distance tests for merging: 1368 Number of distance tests for checking: 1131 Number of merged facets: 41 CPU seconds to compute hull (after input): 0.000457 Output completed. Verifying that all points are below outer planes of all facets. Will make 8600 distance computations. set +v === test unbounded intersection Tue Oct 5 22:50:13 UTC 2021 rbox c | qhull PD0:0.5 n | qhull H0 Fp Tcv 3 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 -10.101 -10.101 -10.101 Output completed. Verifying that all points are below outer planes of all facets. Will make 25 distance computations. rbox 1000 W1e-3 D3 | qhull PA8 Fa FS s n Tcv Convex hull of 1000 points in 3-d: Number of vertices: 156 Number of facets: 308 Number of 'good' facets: 8 Statistics for: rbox 1000 W1e-3 D3 | qhull PA8 Fa FS s n Tcv Number of points processed: 203 Number of hyperplanes created: 1043 Number of distance tests for qhull: 21452 CPU seconds to compute hull (after input): 0.008436 Total facet area: 5.8817432 Total volume: 0.99685163 8 0.1446087232094601 0.1622198334884075 0.2057158590759608 0.1567143851824352 0.188985866819172 0.1580674614313252 0.1616733826473111 0.1767351337533958 0 2 5.881743214947513 0.9968516315221345 4 8 1.009144997325421e-05 0.9999999999463923 2.319049754624652e-06 -0.4999875785488853 -1.229609861584452e-05 8.587946880918045e-05 0.9999999962367613 -0.500004859549355 -1.383340239672454e-05 -0.9999999998842694 6.332306547224586e-06 -0.4999917156571327 1.802476239613105e-05 -1.901476191096464e-05 0.9999999996567733 -0.4999909156385879 0.9999999996788914 1.780140020603311e-05 -1.803683546259361e-05 -0.4999971349013697 3.470111681088057e-06 -3.668365732095583e-05 -0.9999999993211337 -0.4999893476858696 -1.633273154317779e-05 -0.9999999998072314 1.08985791646657e-05 -0.4999921708899001 -0.9999999997878146 -2.055073082985623e-05 -1.427680287303445e-06 -0.4999990322171605 Output completed. Verifying that all points are below outer planes of all facets. Will make 8000 distance computations. rbox 1000 W1e-3 D3 | qhull C-0.01 PM10 Fm n Tcv Qc 10 1 1 5 8 6 6 2 0 7 10 4 10 0.6345454980886096 0.2737427089707436 0.7227841587506171 -0.7458921924784656 -0.00253733560834815 0.666653414016696 0.7453635270845322 -0.6767722083805112 -0.003237401631533091 0.002761552371517554 -0.9999909464886048 -0.4969398742962436 -0.0004022623770974538 0.9999997831336711 0.0005214571799133833 -0.5000167453415887 -0.999601787347817 0.0214081839262726 0.01838359029211947 -0.4985486000821885 -0.005480509661076107 -0.9999701072857251 0.005454223027194169 -0.4992904789191579 -0.9987007292177809 -0.05077399000218431 -0.004342280406757339 -0.5182179901342427 0.6755431502353132 -0.2163920762108173 0.7048517017950092 -0.7475007704997935 0.001196850675493193 0.0003334814784797861 0.9999992281689842 -0.4989807987213126 0.9999992961453315 0.00118637926097064 1.459763172590229e-05 -0.4998611663332402 Output completed. Verifying that all points are below outer planes of all facets. Will make 10000 distance computations. rbox 1000 W1e-3 D3 | qhull C-0.01 PA8 PG n Tcv Qc 4 12 0.6345454980886096 0.2737427089707436 0.7227841587506171 -0.7458921924784656 -0.00253733560834815 0.666653414016696 0.7453635270845322 -0.6767722083805112 -0.9785529186794025 -0.009694358843403266 -0.2057673558916428 -0.5832522471275383 0.8278306348810541 -0.3414688798813042 -0.4450791435520636 -0.7665474225756105 0.7383776593319754 -0.4655216164679661 0.4879426777814019 -0.7788991125303445 0.2008161614085187 -0.8823413491644904 0.4256132198037728 -0.6982307124493007 0.41932306725662 0.6721295192910486 -0.6102541065524131 -0.7755692997856908 -0.3210285130221472 0.4863414284958994 -0.8126578054478755 -0.7591490151594069 -0.4745617604911457 -0.2935495843214587 0.8298311738084099 -0.7523676152838523 -0.8238864443814345 -0.556605789918439 0.1067760337987315 -0.695666244857558 -0.5357402012449896 -0.5359428531021374 -0.6524934443952053 -0.811263040246498 0.6755431502353132 -0.2163920762108173 0.7048517017950092 -0.7475007704997935 Output completed. Verifying that all points are below outer planes of all facets. Will make 8000 distance computations. rbox 10 | qhull FO Tz TO q_test.log.1 cat q_test.log.1 Options selected for Qhull 2020.2.r 2020/08/31: run-id 370154643 Tz-stdout TOutput-file q_test.log.1 _pre-merge _zero-centrum _max-width 0.92 Error-roundoff 6.8e-16 _one-merge 4.8e-15 _near-inside 2.4e-14 Visible-distance 1.4e-15 U-max-coplanar 1.4e-15 Width-outside 2.7e-15 _wide-facet 8.2e-15 Convex hull of 10 points in 3-d: Number of vertices: 10 Number of facets: 16 Statistics for: rbox 10 | qhull FO Tz TO q_test.log.1 Number of points processed: 10 Number of hyperplanes created: 26 Number of distance tests for qhull: 43 CPU seconds to compute hull (after input): 6.7e-05 set +v === check Delaunay/Voronoi Tue Oct 5 22:50:13 UTC 2021 rbox 10 D2 | qhull d Tcv Delaunay triangulation by the convex hull of 10 points in 3-d: Number of input sites: 10 Number of Delaunay regions: 14 Statistics for: rbox 10 D2 | qhull d Tcv Number of points processed: 10 Number of hyperplanes created: 28 Number of facets in hull: 16 Number of distance tests for qhull: 47 CPU seconds to compute hull (after input): 8.1e-05 Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 140 distance computations. rbox 10 D2 | qhull d Qz Tcv Delaunay triangulation by the convex hull of 11 points in 3-d: Number of input sites and at-infinity: 11 Number of Delaunay regions: 14 Statistics for: rbox 10 D2 | qhull d Qz Tcv Number of points processed: 11 Number of hyperplanes created: 30 Number of facets in hull: 18 Number of distance tests for qhull: 55 CPU seconds to compute hull (after input): 8.6e-05 Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 154 distance computations. rbox 10 D3 | qhull d Tcv Delaunay triangulation by the convex hull of 10 points in 4-d: Number of input sites: 10 Number of Delaunay regions: 18 Statistics for: rbox 10 D3 | qhull d Tcv Number of points processed: 10 Number of hyperplanes created: 43 Number of facets in hull: 27 Number of distance tests for qhull: 66 CPU seconds to compute hull (after input): 0.000227 Output completed. Verifying that all points are below 2.9e-15 of all facets. Will make 180 distance computations. rbox c | qhull d Qz Ft Tcv 3 10 12 3 -0.5 -0.5 -0.5 -0.5 -0.5 0.5 -0.5 0.5 -0.5 -0.5 0.5 0.5 0.5 -0.5 -0.5 0.5 -0.5 0.5 0.5 0.5 -0.5 0.5 0.5 0.5 0 0 0 0 0 0 4 9 1 2 0 4 9 2 4 0 4 9 4 1 0 4 9 7 5 4 4 9 6 7 4 4 9 7 6 2 4 9 2 6 4 4 9 5 7 1 4 9 5 1 4 4 9 7 3 1 4 9 1 3 2 4 9 3 7 2 Output completed. Verifying that all points are below outer planes of all facets. Will make 9 distance computations. rbox 10 s D2 c | qhull d Tcv Delaunay triangulation by the convex hull of 14 points in 3-d: Number of input sites: 14 Number of Delaunay regions: 15 Number of non-simplicial Delaunay regions: 1 Statistics for: rbox 10 s D2 c | qhull d Tcv Number of points processed: 14 Number of hyperplanes created: 32 Number of facets in hull: 16 Number of distance tests for qhull: 115 Number of distance tests for merging: 296 Number of distance tests for checking: 272 Number of merged facets: 8 CPU seconds to compute hull (after input): 0.000281 Output completed. Verifying that all points are below outer planes of all facets. Will make 210 distance computations. rbox 10 s D2 | qhull d Tcv Qz Q8 Delaunay triangulation by the convex hull of 11 points in 3-d: Number of input sites and at-infinity: 11 Number of Delaunay regions: 1 Number of non-simplicial Delaunay regions: 1 Statistics for: rbox 10 s D2 | qhull d Tcv Qz Q8 Number of points processed: 11 Number of hyperplanes created: 19 Number of facets in hull: 11 Number of distance tests for qhull: 54 Number of distance tests for merging: 201 Number of distance tests for checking: 204 Number of merged facets: 7 CPU seconds to compute hull (after input): 0.000216 QH7077 qhull input warning: no outer plane check ('Q5') or no processing of near-inside points ('Q8'). Verify may report that a point is outside of a facet. Output completed. Verifying that all points are below outer planes of all facets. Will make 11 distance computations. rbox 10 D2 | qhull d Tcv p 3 10 -0.02222276248244826 -0.4979727817680433 0.2484707425541546 -0.4285431913366012 0.4745826469497594 0.4088779556267987 0.3105396575392593 0.2400179190933871 0.1540434803905201 -0.01883958887200765 0.3630260628303755 0.13214285240299 0.3790312361708201 0.3779794437605696 0.2865331378987296 -0.2994955874043476 0.3776609263174803 0.2323253821416525 0.3471817493878135 0.08365533089605659 0.1275333814953112 -0.00485819764887746 0.3482682405489201 0.121314369459436 0.3443122672329771 -0.1437312230875075 0.1392096018573439 0.309330780347186 -0.07758103877080702 0.1017043492469565 Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 140 distance computations. rbox 10 D2 | qhull d Tcv i 14 9 7 0 8 9 0 3 4 1 3 7 4 7 2 4 0 5 1 7 5 0 5 3 1 3 5 7 6 7 9 6 2 7 8 6 9 6 8 4 2 6 4 Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 140 distance computations. rbox 10 D2 | qhull d Tcv o 3 10 14 21 -0.02222276248244826 -0.4979727817680433 0.2484707425541546 -0.4285431913366012 0.4745826469497594 0.4088779556267987 0.3105396575392593 0.2400179190933871 0.1540434803905201 -0.01883958887200765 0.3630260628303755 0.13214285240299 0.3790312361708201 0.3779794437605696 0.2865331378987296 -0.2994955874043476 0.3776609263174803 0.2323253821416525 0.3471817493878135 0.08365533089605659 0.1275333814953112 -0.00485819764887746 0.3482682405489201 0.121314369459436 0.3443122672329771 -0.1437312230875075 0.1392096018573439 0.309330780347186 -0.07758103877080702 0.1017043492469565 3 9 7 0 3 8 9 0 3 3 4 1 3 3 7 4 3 7 2 4 3 0 5 1 3 7 5 0 3 5 3 1 3 3 5 7 3 6 7 9 3 6 2 7 3 8 6 9 3 6 8 4 3 2 6 4 Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 140 distance computations. rbox 10 D2 | qhull v Tcv o 2 15 10 1 -10.101 -10.101 -0.1294381801544404 -0.07247409101984714 0.08267689532419747 -0.2397644955865706 0.1295260566906465 1.716033573116837 0.1740355150742391 0.5317519038435655 0.1851415205797575 0.3882545794457364 -0.9065939866848107 -0.2962957610652135 -0.1954805620516266 -0.07111892482963184 -0.1407581310832468 0.7233857048236082 -0.1676297826663962 0.2080621273999375 0.05868313821742954 0.06632066014880154 0.08806341399736994 0.1054080604689985 0.4761588899009253 -0.03168366595227294 3.094213357897477 -0.064721945677682 0.5410515627308725 0.2115615434955919 5 7 1 2 0 6 4 8 3 0 6 3 14 5 11 4 9 4 3 8 6 14 5 4 3 0 13 4 9 7 6 8 5 14 11 10 12 13 7 11 5 4 9 7 1 10 4 13 0 2 12 4 12 2 1 10 Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 140 distance computations. rbox 10 D2 | qhull v Tcv p 2 14 -0.1294381801544404 -0.07247409101984714 0.08267689532419747 -0.2397644955865706 0.1295260566906465 1.716033573116837 0.1740355150742391 0.5317519038435655 0.1851415205797575 0.3882545794457364 -0.9065939866848107 -0.2962957610652135 -0.1954805620516266 -0.07111892482963184 -0.1407581310832468 0.7233857048236082 -0.1676297826663962 0.2080621273999375 0.05868313821742954 0.06632066014880154 0.08806341399736994 0.1054080604689985 0.4761588899009253 -0.03168366595227294 3.094213357897477 -0.064721945677682 0.5410515627308725 0.2115615434955919 Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 140 distance computations. rbox 10 D2 | qhull v Tcv G {appearance {linewidth 3} LIST # rbox 10 D2 | qhull v Tcv G {appearance {+edge -face} OFF 15 10 1 # Voronoi centers and cells 0 0 0 # infinity not used # 1 f8 -0.1294381801544404 -0.07247409101984714 0 # 2 f11 0.08267689532419747 -0.2397644955865706 0 # 3 f12 0.1295260566906465 1.716033573116837 0 # 4 f14 0.1740355150742391 0.5317519038435655 0 # 5 f15 0.1851415205797575 0.3882545794457364 0 # 6 f19 -0.9065939866848107 -0.2962957610652135 0 # 7 f20 -0.1954805620516266 -0.07111892482963184 0 # 8 f21 -0.1407581310832468 0.7233857048236082 0 # 9 f22 -0.1676297826663962 0.2080621273999375 0 # 10 f23 0.05868313821742954 0.06632066014880154 0 # 11 f24 0.08806341399736994 0.1054080604689985 0 # 12 f25 0.4761588899009253 -0.03168366595227294 0 # 13 f26 3.094213357897477 -0.064721945677682 0 # 14 f27 0.5410515627308725 0.2115615434955919 0 4 7 1 2 6 # p0(v3) 3 8 3 6 # p1(v1) 3 14 5 11 # p2(v8) 4 9 4 3 8 # p3(v7) 5 14 5 4 3 13 # p4(v2) 4 9 7 6 8 # p5(v9) 5 14 11 10 12 13 # p6(v10) 7 11 5 4 9 7 1 10 # p7(v5) 3 13 2 12 # p8(v6) 4 12 2 1 10 # p9(v4) } } Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 140 distance computations. rbox 10 D2 | qhull v Tcv Fv 23 4 0 1 0 6 4 0 7 1 7 4 0 9 1 2 4 0 8 0 2 4 0 5 6 7 4 1 4 0 3 4 1 3 3 8 4 1 5 6 8 4 2 7 5 11 4 2 4 5 14 4 2 6 11 14 4 3 4 3 4 4 3 7 4 9 4 3 5 8 9 4 4 8 0 13 4 4 7 4 5 4 4 6 13 14 4 5 7 7 9 4 6 7 10 11 4 6 9 10 12 4 6 8 12 13 4 7 9 1 10 4 8 9 2 12 Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 140 distance computations. rbox 10 D2 | qhull v Tcv Fi 19 5 0 7 0.02051532578114336 0.9997895385570373 0.07511430445246037 5 0 9 0.619259133056969 0.7851866823409139 0.1370614663104577 5 0 5 -0.301880639203215 0.9533457293522944 0.008789126238507583 5 1 3 0.9648718030091262 -0.2627211520946079 0.3258622775065156 5 1 5 0.7995952824356682 -0.6005392446015695 0.5469710423089692 5 2 7 -0.9458410914974847 0.3246299888101017 0.04907537812572171 5 2 4 0.444671031232542 0.8956939622340812 -0.4300843534994401 5 2 6 0.2281595097543261 -0.9736237661995858 0.08253528745668784 5 3 4 0.9992944873266901 0.03755699133966539 -0.1938837324602516 5 3 7 0.6877523324625971 -0.7259454037269313 0.2663295190946441 5 3 5 -0.9986432053419565 0.05207445078292259 -0.1782370644858237 5 4 7 -0.9970183790688238 -0.07716444646969993 0.2145489484590235 5 4 6 -0.1075842248297359 -0.9941959739245502 0.2685422477498993 5 5 7 0.9950609206245129 -0.09926612839179765 0.187455367716064 5 6 7 -0.7993641842155074 0.6008468199079334 0.007060641163779212 5 6 9 -0.2285415587894342 -0.973534157544611 0.07797696388863314 5 6 8 -0.01261839651625044 -0.9999203848653946 -0.02567278177543585 5 7 9 0.5936952885926361 -0.8046899429612046 0.01852766555277016 5 8 9 -0.4674785097727932 0.8840044360186256 0.2506025495170936 Voronoi ridge statistics 19 bounded ridges 4.2e-17 ave. distance of midpoint to ridge 1.7e-16 max. distance of midpoint to ridge 19 bounded ridges with ok normal 5.8e-17 ave. angle to ridge 2.2e-16 max. angle to ridge Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 140 distance computations. rbox 10 D2 | qhull v Tcv Fo 4 5 0 1 -0.3854955578888161 0.922709691532494 -0.07609298438083822 5 0 8 0.719062520784207 0.6949453872092842 0.1071733734620186 5 1 4 0.9929212365203526 -0.1187746524595787 0.07521211888503937 5 4 8 -0.06640144810487483 -0.9977929883946747 0.1408811441173877 Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 140 distance computations. rbox 10 D2 | qhull v Qu o Fv Fi Fo Tcv 2 3 10 1 -10.101 -10.101 -0.06934933486244874 0.05349366577784781 -0.3051278694340224 0.161498505581022 3 0 2 1 2 0 1 0 0 3 0 1 2 0 0 0 2 0 2 0 5 4 0 8 0 2 4 0 4 1 2 4 0 1 0 1 4 1 4 0 1 4 4 8 0 2 1 5 0 4 0.4164624817835529 0.9091529031283372 -0.01975252543405325 4 5 0 8 0.7190625207842071 0.6949453872092841 0.1071733734620185 5 0 1 -0.3854955578888162 0.922709691532494 -0.07609298438083828 5 1 4 0.9929212365203528 -0.1187746524595786 0.07521211888503934 5 4 8 -0.06640144810487485 -0.9977929883946747 0.1408811441173877 Voronoi ridge statistics 1 bounded ridges 1.2e-16 ave. distance of midpoint to ridge 1.2e-16 max. distance of midpoint to ridge 1 bounded ridges with ok normal 0 max. angle to ridge Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 20 distance computations. rbox 10 D3 | qhull v Fv Tcv 32 6 0 1 0 17 15 3 7 0 9 0 7 12 11 2 6 0 6 0 7 18 17 5 0 7 0 2 3 6 0 2 2 3 15 11 5 0 8 7 18 12 7 0 5 11 12 18 17 15 5 1 7 0 5 3 6 1 2 3 5 0 15 5 1 5 15 0 17 6 2 3 1 4 13 9 6 2 9 1 2 11 9 7 2 7 1 2 3 5 4 6 2 4 4 5 0 13 7 2 5 9 11 15 0 13 7 3 9 0 6 10 9 1 5 3 7 0 4 1 5 3 6 0 8 6 7 3 4 0 8 14 13 4 6 3 8 6 8 14 10 6 3 5 9 10 14 13 5 4 7 0 5 4 5 4 6 0 16 8 5 4 8 8 16 14 6 4 5 13 0 16 14 6 5 9 9 11 12 10 7 5 8 10 12 18 16 14 6 5 6 0 17 18 16 5 6 9 0 6 7 7 6 8 6 7 18 16 8 5 7 9 0 1 2 6 8 9 6 7 12 10 Output completed. Verifying that all points are below 2.9e-15 of all facets. Will make 180 distance computations. rbox 10 D3 | qhull v Fi Tcv 13 6 0 2 0.1026012494065408 0.8309156055795224 -0.5468566905731632 0.2399036185798246 6 0 8 -0.1644981128676535 0.549224308046351 -0.8193247404503221 0.1220237399030437 6 0 5 -0.1640386761614813 0.6276090456203122 -0.7610507201092116 0.1709974344854015 6 2 3 0.8628264983391892 0.127742449234631 -0.4890933453107607 -0.1660057988150948 6 2 9 0.5146151495466437 -0.7556910962035636 -0.4050953159143434 -0.3000434746332832 6 2 7 0.9862472983740704 0.008356748990702902 0.1650649302430821 -0.2195655184060844 6 3 8 -0.9471370887617877 -0.1545163381156413 -0.2811690529684558 0.04372902199764667 6 3 5 -0.9850113492204077 -0.1553182373520528 -0.07502590921037623 0.09265233510028284 6 4 8 -0.7177135399298967 -0.245721536677967 -0.65154293873383 -0.02974683605231299 6 5 9 0.7110332662678562 -0.693517783370965 -0.116037831799318 -0.2706062861955821 6 5 8 -0.1310037283001485 -0.04490613421135446 -0.9903643078593113 -0.2004293237314498 6 6 8 0.563653077615962 0.07101685912338832 0.8229531054770393 0.4221671959133705 6 8 9 0.7278413449934529 -0.6852671087526033 0.02561183671604023 -0.2412830130907243 Voronoi ridge statistics 15 non-simplicial Voronoi vertices for all ridges 6.9e-17 ave. distance to ridge 1.9e-16 max. distance to ridge 13 bounded ridges 7.8e-17 ave. distance of midpoint to ridge 3e-16 max. distance of midpoint to ridge 13 bounded ridges with ok normal 8.5e-17 ave. angle to ridge 2.2e-16 max. angle to ridge Output completed. Verifying that all points are below 2.9e-15 of all facets. Will make 180 distance computations. rbox 10 D3 | qhull v Fo Tcv 19 6 0 1 -0.1769702595802885 0.8331351847724077 0.5239916899325134 0.004105600879712498 6 0 9 0.5856843296472444 -0.1558732679166009 -0.7954102025713885 -0.1264594278193164 6 0 6 -0.305501768024369 0.3812318858994052 -0.8725427891556765 -0.04822326899809234 6 0 7 0.6633910639781613 0.6672883530766242 -0.3385831509130507 0.06175731395259272 6 1 7 0.7533877382120365 0.334939238848763 -0.5658821628140998 0.06152842458597928 6 1 2 0.2077539373736714 0.4344067294949102 -0.8764297432625574 0.2556318087147513 6 1 5 -0.08886729274769822 0.2768317827550689 -0.9568002760954583 0.1656561460661369 6 2 4 0.8896724708236493 0.4529391082738924 -0.05769799697211265 -0.124969949041603 6 2 5 -0.6080629223625026 -0.1069684332549473 -0.7866493734408965 -0.05602222006342437 6 3 9 0.1157648604151236 -0.9728190902550374 -0.2005530222370839 -0.2615067759720444 6 3 7 0.3131056731324619 -0.1651787990807294 0.9352437125084113 -0.1060546443225209 6 3 6 -0.8429664438017094 -0.1288333013498811 -0.5223117412882753 -0.1470675860428305 6 3 4 -0.6546392846048742 0.1665291828386516 0.7373706247980789 0.1638426312062793 6 4 7 0.8997625993863546 -0.3161631359012113 0.3007792151107228 -0.2534488584590283 6 4 6 -0.6610636619910346 -0.1756381951302929 -0.7294834194184102 -0.1931488689248214 6 4 5 -0.8177140658972858 -0.2799433900977097 -0.5029666040348314 0.01966883326066583 6 5 6 -0.4656867325018191 -0.06587339986788447 -0.8824945112359766 -0.374728122564582 6 6 9 0.7885740013077054 -0.5314391513195501 0.309392102204163 -0.04784058563315544 6 7 9 -0.0125726543874506 -0.8388634914110149 -0.5441966291143082 -0.2018836580171401 Voronoi ridge statistics 14 non-simplicial Voronoi vertices for all ridges 4.3e-17 ave. distance to ridge 9.7e-17 max. distance to ridge Output completed. Verifying that all points are below 2.9e-15 of all facets. Will make 180 distance computations. rbox 10 D3 | qhull v Qu o Fv Fi Fo Tcv 3 10 10 1 -10.101 -10.101 -10.101 -0.04510412048603351 -0.1962229636993575 -0.06746145990413344 -0.2032838761823815 -0.3188041900902701 0.1251484339163768 0.1359785067833994 0.06954805978697726 -0.07249043373758879 -0.9550934192592715 0.3815223390696589 -0.9370156532984113 -0.01637948561987637 -0.8836250780525146 -0.03718065630611937 0.09499885792019704 -0.7038538868165176 -0.181396220925921 2.128743389186444 -4.06034590041635 -1.2162468947864 2.789531685277133 -5.393666229616701 -1.494034092231969 2.640156785601998 -4.796303906482405 -1.459799746992412 3 0 3 4 7 0 1 3 4 6 7 9 4 0 7 8 9 3 0 2 5 5 0 5 6 7 8 3 0 8 9 9 0 1 2 3 5 6 7 8 9 6 0 1 2 4 5 6 0 5 0 1 2 3 4 18 5 0 1 0 3 4 5 0 9 0 3 4 8 1 6 0 3 1 6 7 9 5 1 2 0 7 9 5 1 4 0 6 7 6 1 7 0 4 1 6 5 1 9 1 3 4 5 2 5 0 9 8 5 2 4 0 7 8 5 2 6 7 9 8 5 3 6 0 5 2 5 3 7 0 2 5 7 4 6 0 5 6 7 8 5 4 7 0 6 5 5 5 6 0 9 8 6 6 9 0 3 1 2 6 6 7 1 2 5 6 6 7 9 0 2 1 4 3 6 1 9 0.5123553720802024 -0.363812082853534 -0.7779027838170592 -0.100757404152973 6 2 6 -0.5221667006142685 -0.08192192666458321 -0.8488997200501196 -0.2535440955968309 6 6 7 0.752213645322669 0.06033708575303686 0.6561509489997043 0.09003235761431796 15 6 0 1 -0.1769702595802886 0.8331351847724078 0.5239916899325134 0.004105600879712498 6 0 9 0.5856843296472447 -0.1558732679166012 -0.7954102025713884 -0.1264594278193166 6 1 6 -0.2436653478720986 0.147883680687048 -0.9585184480399009 -0.04663519095132841 6 1 2 0.2077539373736637 0.4344067294949081 -0.8764297432625605 0.255631808714752 6 1 4 0.444220078847362 0.4986447037065236 -0.744326528490203 0.1737545932855555 6 1 7 0.7533877382120362 0.3349392388487629 -0.5658821628141001 0.06152842458597942 6 2 5 -0.6080629223625006 -0.1069684332549458 -0.7866493734408982 -0.05602222006342417 6 2 4 0.8896724708236509 0.4529391082738904 -0.0576979969721034 -0.1249699490416035 6 3 6 -0.8429664438017096 -0.1288333013498811 -0.5223117412882751 -0.1470675860428304 6 3 7 0.3131056731324613 -0.1651787990807291 0.9352437125084115 -0.1060546443225207 6 4 6 -0.6610636619910349 -0.1756381951302929 -0.7294834194184099 -0.1931488689248214 6 4 7 0.8997625993863546 -0.3161631359012115 0.3007792151107228 -0.2534488584590282 6 5 6 -0.4656867325018176 -0.06587339986788343 -0.8824945112359772 -0.374728122564582 6 6 9 0.7885740013077054 -0.5314391513195503 0.3093921022041629 -0.04784058563315553 6 7 9 -0.01257265438745033 -0.8388634914110151 -0.5441966291143079 -0.2018836580171402 Voronoi ridge statistics 9 non-simplicial Voronoi vertices for all ridges 1.5e-16 ave. distance to ridge 4.4e-16 max. distance to ridge 3 bounded ridges 6.4e-16 ave. distance of midpoint to ridge 1.7e-15 max. distance of midpoint to ridge 3 bounded ridges with ok normal 7.4e-17 ave. angle to ridge 2.2e-16 max. angle to ridge Output completed. Verifying that all points are below 2.9e-15 of all facets. Will make 90 distance computations. rbox 5 D2 | qhull v f FnN o Vertices and facets: - p3(v5): 0.43 -0.11 0.19 neighbors: f5 f6 f7 f8 - p2(v2): 0.47 -0.11 0.24 neighbors: f1 f5 f7 - p4(v1): -0.39 0.45 0.36 neighbors: f1 f3 f5 f6 - p0(v4): -0.34 0.23 0.17 neighbors: f3 f6 f8 - p1(v3): 0.32 -0.23 0.16 neighbors: f1 f3 f7 f8 - f5 - flags: top simplicial - normal: 0.437 0.773 -0.4599 - offset: -0.01170704 - center: 0.4751017705052502 0.8404705693422864 - vertices: p3(v5) p2(v2) p4(v1) - neighboring facets: f1 f6 f7 - f6 - flags: bottom simplicial - normal: 0.3235 0.6691 -0.669 - offset: 0.0657 - center: 0.24177356134713 0.5000766029034823 - vertices: p3(v5) p0(v4) p4(v1) - neighboring facets: f3 f5 f8 - f7 - flags: top simplicial - normal: 0.6288 -0.3317 -0.7033 - offset: -0.1682885 - center: 0.4470293595057619 -0.2357835939937328 - vertices: p3(v5) p1(v3) p2(v2) - neighboring facets: f1 f5 f8 - f8 - flags: top simplicial - normal: 0.1177 0.1841 -0.9758 - offset: 0.15929 - center: 0.06029550723695781 0.09433023738340306 - vertices: p3(v5) p0(v4) p1(v3) - neighboring facets: f3 f7 f6 4 3 -1 1 2 3 -3 0 3 3 -1 0 3 3 -3 2 1 5 3 3 -3 1 4 3 -3 -1 2 3 2 -1 0 4 3 1 0 2 4 1 -3 -1 0 2 5 5 1 -10.101 -10.101 0.4751017705052502 0.8404705693422864 0.24177356134713 0.5000766029034823 0.4470293595057619 -0.2357835939937328 0.06029550723695781 0.09433023738340306 3 2 4 0 3 3 4 0 3 1 3 0 4 3 4 2 1 3 1 2 0 set +v === check Halfspace and Qhull identity pipeline, showing the input Tue Oct 5 22:50:13 UTC 2021 === the Qhull pipeline recreates 100 4-D cospherical points with the same area and volume rbox 100 s D4 | qhull FA FV s n | head Convex hull of 100 points in 4-d: Number of vertices: 100 Number of facets: 584 Statistics for: rbox 100 s D4 | qhull FA FV s n Number of points processed: 100 Number of hyperplanes created: 1717 Number of distance tests for qhull: 4090 CPU seconds to compute hull (after input): 0.001892 Total facet area: 1.7919449 Total volume: 0.18640279 4 1 -0.006240661006237819 -0.006198497499885543 -0.0019864189252863 0.03528712962677102 5 584 -0.4728063044129454 -0.06576180062326932 0.3296766529322419 -0.8145200357250598 -0.4001269961794449 0.9350657178932537 -0.116181174817606 -0.009048199757790566 0.3347718147035652 -0.3733488931324643 0.5670388949132408 -0.5323662756300656 -0.3876606744394214 0.4947446227302695 -0.4846392631626165 0.8393609616706702 -0.1089654738688994 -0.05104156673138016 0.530089105710936 -0.4115455431603698 0.6753770108964836 -0.1536990905729236 -0.0485198359900459 0.7196445707605155 -0.4414725485817289 0.20025580309926 0.08170320261530004 0.2334845247641378 0.9480016754748583 -0.4466269780920115 rbox 100 s D4 | qhull FQ FA FV n s | qhull s H Fp | head Convex hull of 100 points in 4-d: Number of vertices: 100 Number of facets: 584 Statistics for: rbox 100 s D4 | qhull FQ FA FV n s Number of points processed: 100 Number of hyperplanes created: 1717 Number of distance tests for qhull: 4090 CPU seconds to compute hull (after input): 0.002265 Total facet area: 1.7919449 Total volume: 0.18640279 Halfspace intersection by the convex hull of 584 points in 4-d: Number of halfspaces: 584 Number of non-redundant halfspaces: 584 Number of intersection points: 100 Number of non-simplicial intersection points: 100 Statistics for: rbox 100 s D4 | qhull FQ FA FV n s | qhull s H Fp Number of points processed: 584 Number of hyperplanes created: 4013 Number of distance tests for qhull: 29717 Number of distance tests for merging: 76931 Number of distance tests for checking: 18265 Number of merged facets: 3444 CPU seconds to compute hull (after input): 0.01716 Maximum distance of point above facet: 2.4e-14 (0.4x) Maximum distance of vertex below facet: -1.7e-14 (0.3x) 4 100 -0.1497820974007844 0.4220759056868791 -0.1730594919621551 0.1395265758865447 -0.1656824599698354 0.2695081565763442 0.2399815540443042 -0.3038478726528215 -0.1287028906527846 0.3274268489457611 0.1066154632455187 -0.3389105597705839 0.2152206390581626 0.2489384546335302 -0.342896351704003 0.1553441801811403 -0.3478218321497436 0.1609400522171699 0.2504669650899252 -0.2009591303498609 -0.2026608048181584 0.132737676060139 -0.4340855448243784 0.05365675464591807 -0.1243914612976075 -0.06208848857682957 -0.4348180038806073 -0.2039732517850684 0.318659177699236 0.2994118752602876 -0.2407753518255607 -0.02891517550426 rbox 100 s D4 | qhull FQ FA FV n s Tcv | qhull FQ s H Fp Tcv | qhull FA Tcv Convex hull of 100 points in 4-d: Number of vertices: 100 Number of facets: 584 Statistics for: rbox 100 s D4 | qhull FQ FA FV n s Tcv Number of points processed: 100 Number of hyperplanes created: 1717 Number of distance tests for qhull: 4090 CPU seconds to compute hull (after input): 0.009323 Total facet area: 1.7919449 Total volume: 0.18640279 Output completed. Verifying that all points are below 2.8e-15 of all facets. Will make 58400 distance computations. Halfspace intersection by the convex hull of 584 points in 4-d: Number of halfspaces: 584 Number of non-redundant halfspaces: 584 Number of intersection points: 100 Number of non-simplicial intersection points: 100 Statistics for: rbox 100 s D4 | qhull FQ FA FV n s Tcv | qhull FQ s H Fp Tcv Number of points processed: 584 Number of hyperplanes created: 4013 Number of distance tests for qhull: 29717 Number of distance tests for merging: 77031 Number of distance tests for checking: 51837 Number of merged facets: 3444 CPU seconds to compute hull (after input): 0.6522 Maximum distance of point above facet: 2.4e-14 (0.4x) Maximum distance of vertex below facet: -1.7e-14 (0.3x) Output completed. Verifying that all points are below outer planes of all facets. Will make 58400 distance computations. Convex hull of 100 points in 4-d: Number of vertices: 100 Number of facets: 584 Statistics for: rbox 100 s D4 | qhull FQ FA FV n s Tcv | qhull FQ s H Fp Tcv | qhull FA Tcv Number of points processed: 100 Number of hyperplanes created: 1717 Number of distance tests for qhull: 4090 CPU seconds to compute hull (after input): 0.01002 Total facet area: 1.7919449 Total volume: 0.18640279 Output completed. Verifying that all points are below 2.8e-15 of all facets. Will make 58400 distance computations. echo === the Qhull pipeline recreates a 3-D tetrahedron === the Qhull pipeline recreates a 3-D tetrahedron rbox d D3 | qhull n FD rbox d D3 | qhull n FD begin 8 4 real 0.2886751345948129 0.5773502691896258 0.5773502691896258 0.5773502691896258 0.2886751345948129 -0.5773502691896258 0.5773502691896258 0.5773502691896258 0.2886751345948129 0.5773502691896258 0.5773502691896258 -0.5773502691896258 0.2886751345948129 -0.5773502691896258 0.5773502691896258 -0.5773502691896258 0.2886751345948129 -0.5773502691896258 -0.5773502691896258 0.5773502691896258 0.2886751345948129 0.5773502691896258 -0.5773502691896258 0.5773502691896258 0.2886751345948129 -0.5773502691896258 -0.5773502691896258 -0.5773502691896258 0.2886751345948129 0.5773502691896258 -0.5773502691896258 -0.5773502691896258 end rbox d D3 | qhull s n FD Tcv | qhull s Fd H0.1,0.1 Fp Tcv Convex hull of 6 points in 3-d: Number of vertices: 6 Number of facets: 8 Statistics for: rbox d D3 | qhull s n FD Tcv Number of points processed: 6 Number of hyperplanes created: 11 Number of distance tests for qhull: 10 Number of distance tests for merging: 59 Number of distance tests for checking: 54 Number of merged facets: 1 CPU seconds to compute hull (after input): 0.000111 Output completed. Verifying that all points are below outer planes of all facets. Will make 48 distance computations. Halfspace intersection by the convex hull of 8 points in 3-d: Number of halfspaces: 8 Number of non-redundant halfspaces: 8 Number of intersection points: 6 Number of non-simplicial intersection points: 6 Statistics for: rbox d D3 | qhull s n FD Tcv | qhull s Fd H0.1,0.1 Fp Tcv Number of points processed: 8 Number of hyperplanes created: 10 Number of distance tests for qhull: 30 Number of distance tests for merging: 95 Number of distance tests for checking: 100 Number of merged facets: 6 CPU seconds to compute hull (after input): 0.000116 3 6 -1.387778780781446e-17 -1.387778780781446e-17 -0.5 -2.775557561562891e-17 0.5 0 -0.5 0 0 0.5 -2.775557561562891e-17 0 0 -0.5 0 -1.387778780781446e-17 1.387778780781446e-17 0.4999999999999999 Output completed. Verifying that all points are below outer planes of all facets. Will make 48 distance computations. echo === the Qhull pipeline recreates a regular 2-D pentagon === the Qhull pipeline recreates a regular 2-D pentagon rbox 5 r D2 | qhull FQ n rbox 5 r D2 | qhull FQ n 3 5 0.8090169943749476 0.587785252292473 -0.4045084971874737 -0.3090169943749476 -0.9510565162951536 -0.4045084971874738 0.8090169943749472 -0.5877852522924732 -0.4045084971874737 -1 9.444121133484361e-17 -0.4045084971874738 -0.3090169943749474 0.9510565162951536 -0.4045084971874738 rbox 5 r D2 | qhull s FQ n Tcv | qhull s H0 Fp Tcv Convex hull of 5 points in 2-d: Number of vertices: 5 Number of facets: 5 Statistics for: rbox 5 r D2 | qhull s FQ n Tcv Number of points processed: 5 Number of hyperplanes created: 8 Number of distance tests for qhull: 7 CPU seconds to compute hull (after input): 7.4e-05 Output completed. Verifying that all points are below 1.3e-15 of all facets. Will make 25 distance computations. Halfspace intersection by the convex hull of 5 points in 2-d: Number of halfspaces: 5 Number of non-redundant halfspaces: 5 Number of intersection points: 5 Statistics for: rbox 5 r D2 | qhull s FQ n Tcv | qhull s H0 Fp Tcv Number of points processed: 5 Number of hyperplanes created: 7 Number of distance tests for qhull: 8 CPU seconds to compute hull (after input): 4.7e-05 2 5 -0.4045084971874738 -0.2938926261462365 0.5 -1.528090898784888e-16 0.1545084971874736 -0.4755282581475768 -0.4045084971874737 0.2938926261462366 0.1545084971874737 0.4755282581475768 Output completed. Verifying that all points are below 6.4e-15 of all facets. Will make 25 distance computations. set +v === check qhull Tue Oct 5 22:50:14 UTC 2021 rbox 10 s D3 | qhull Tcv Convex hull of 10 points in 3-d: Number of vertices: 10 Number of facets: 16 Statistics for: rbox 10 s D3 | qhull Tcv Number of points processed: 10 Number of hyperplanes created: 29 Number of distance tests for qhull: 48 CPU seconds to compute hull (after input): 0.000118 Output completed. Verifying that all points are below 2e-15 of all facets. Will make 160 distance computations. rbox 10 s D3 | qhull f Pd0:0.5 Pd2 Pg Tcv Vertices and facets: - p7(v8): 0.2 0.093 0.45 - p9(v5): 0.29 -0.16 0.38 - p3(v2): 0.48 -0.13 0.022 - p8(v10): 0.32 0.025 -0.38 - f16 - flags: bottom simplicial - normal: 0.858 0.1759 0.4826 - offset: -0.4016457 - vertices: p7(v8) p9(v5) p3(v2) - neighboring facets: f7 f27 f23 - f27 - flags: bottom simplicial - normal: 0.646 0.7625 0.03668 - offset: -0.2138755 - vertices: p8(v10) p7(v8) p3(v2) - neighboring facets: f16 f26 f28 Output completed. Verifying that all points are below 2e-15 of all facets. Will make 20 distance computations. rbox 10 s D3 | qhull f Tcv PD2:-0.5 Pg Vertices and facets: - p4(v7): 0.23 -0.32 -0.31 - p1(v4): -0.072 0.057 -0.49 - p6(v3): -0.13 -0.47 -0.09 - p0(v9): -0.37 -0.27 0.19 - p8(v10): 0.32 0.025 -0.38 - p5(v6): 0.028 0.16 -0.47 - f12 - flags: top simplicial - normal: -0.2354 -0.5691 -0.7879 - offset: -0.3715833 - vertices: p4(v7) p1(v4) p6(v3) - neighboring facets: f21 f11 f25 - f21 - flags: bottom simplicial - normal: -0.8148 -0.2922 -0.5006 - offset: -0.2881945 - vertices: p0(v9) p1(v4) p6(v3) - neighboring facets: f12 f19 f20 - f24 - flags: top simplicial - normal: 0.2636 -0.06941 -0.9621 - offset: -0.4497787 - vertices: p8(v10) p5(v6) p1(v4) - neighboring facets: f9 f25 f28 - f25 - flags: bottom simplicial - normal: 0.2402 -0.2624 -0.9346 - offset: -0.4268812 - vertices: p8(v10) p4(v7) p1(v4) - neighboring facets: f12 f24 f26 Output completed. Verifying that all points are below 2e-15 of all facets. Will make 40 distance computations. rbox 10 s D3 | qhull QR-1 Convex hull of 10 points in 3-d: Number of vertices: 10 Number of facets: 16 Statistics for: rbox 10 s D3 | qhull QR-1 QR-1633474214 Number of points processed: 10 Number of hyperplanes created: 29 Number of distance tests for qhull: 48 CPU seconds to compute hull (after input): 0.000106 rbox 10 s D3 | qhull QR-40 Convex hull of 10 points in 3-d: Number of vertices: 10 Number of facets: 16 Statistics for: rbox 10 s D3 | qhull QR-40 QR-40 Number of points processed: 10 Number of hyperplanes created: 29 Number of distance tests for qhull: 48 CPU seconds to compute hull (after input): 9e-05 rbox 1000 D3 | qhull Tcvs qhull 2020.2.r 2020/08/31 Statistics: rbox 1000 D3 | qhull Tcvs Convex hull of 1000 points in 3-d: Number of vertices: 73 Number of facets: 142 Statistics for: rbox 1000 D3 | qhull Tcvs Number of points processed: 81 Number of hyperplanes created: 367 Number of distance tests for qhull: 12879 CPU seconds to compute hull (after input): 0.002561 qhull invoked by: rbox 1000 D3 | qhull Tcvs 2020.2.r 2020/08/31 with options: run-id 370171450 Tcheck-frequently Tverify Tstatistics _pre-merge _zero-centrum _max-width 1 Error-roundoff 6.9e-16 _one-merge 4.9e-15 _near-inside 2.4e-14 Visible-distance 1.4e-15 U-max-coplanar 1.4e-15 Width-outside 2.8e-15 _wide-facet 8.3e-15 precision constants: 0.5 max. abs. coordinate in the (transformed) input ('Qbd:n') 6.9e-16 max. roundoff error for distance computation ('En') 6.7e-16 max. roundoff error for angle computations 2.8e-15 min. distance for outside points ('Wn') 1.4e-15 min. distance for visible facets ('Vn') 1.4e-15 max. distance for coplanar facets ('Un') 8.3e-15 max. facet width for recomputing centrum and area 2.4e-14 max. distance for near-inside points 1.4e-15 radius of pre-merge centrum 4.9e-15 max. distance for merging two simplicial facets 2.2e-16 max. roundoff error for arithmetic operations 1.1e-308 min. denominator for division zero diagonal for Gauss: 8.88e-15 1.78e-14 2.66e-14 precision statistics 3.8e-17 ave. distance of a new vertex to a facet 1.7e-16 max. distance of a new vertex to a facet 1.4e-16 max. distance of an output vertex to a facet -1.7e-16 min. distance of an output vertex to a facet 0.0026 min. denominator in hyperplane computation summary information 73 number of vertices in output 142 number of facets in output 3 average number of neighbors per facet 3 maximum number of neighbors 3 average number of vertices per facet 3 maximum number of vertices 0.0026 cpu seconds for qhull after input 82 vertices created altogether 367 facets created altogether 0 maximum merges for a facet (at most 511) 0.93 average cosine (angle) of facet normals for all ridges 1 maximum cosine of facet normals (flatest) across a ridge 0.21 minimum cosine of facet normals (sharpest) across a ridge build hull statistics 81 points processed 73 max. vertices at any one time 2.78 ave. visible facets per iteration 0.21 ave. visible facets without an horizon neighbor 2.78 ave. facets deleted per iteration 8 maximum 5.43 ave. visible vertices per iteration 11 maximum 4.38 ave. horizon facets per iteration 4.48 ave. new or merged facets per iteration 10 maximum (includes initial simplex) -0.77 average new facet balance 1.5 standard deviation 77 count 7 determinants for initial hull or voronoi vertices 503 distance tests for facet visibility 73 points checked for facets' outer planes 11.4 ave. distance tests per check 1668 max visit_id/2 3125 max vertex_visit/2 partitioning statistics (see previous for outer planes) 8 total vertices deleted 1 maximum vertices deleted per iteration 132 calls to findbest 2.53 ave. facets tested 6 max. facets tested 2048 calls to findbestnew 4.47 ave. facets tested 13 max. facets tested 36 calls due to qh_sharpnewfacets 927 calls to findhorizon 3.01 ave. facets tested 5 max. facets tested 0.00539 ave. clearly better 5 new bestfacets during qh_findbesthorizon 919 inside points 8 inside points that were coplanar with a facet -2.8e-17 difference in max_outside at final check 3747 distance tests for initial partition 3132 partitions of a point 8553 distance tests for partitioning 518 distance tests for checking flipped facets 1160 distance tests for statistics 16915 total number of distance tests 8 partitions of coplanar points or deleted vertices 76 distance tests for these partitions statistics for matching ridges 726 total lookups for matching ridges of new facets 0.569 average number of tests to match a ridge statistics for determining merges 1089 distance tests for checking simplicial convexity statistics for merging 1.7e-16 max distance of vertex or coplanar point above facet (w/roundoff) -6.9e-16 max distance of vertex below facet (or roundoff) memory usage statistics (in bytes) 31808 for facets and their normals, neighbor and vertex sets 3504 for vertices and their neighbor sets 32768 for input points, outside and coplanar sets, and qhT memory statistics: 1390 quick allocations 687 short allocations 119 long allocations 1421 short frees 119 long frees 36248 bytes of short memory in use 2088 bytes of short memory in freelists 92728 bytes of dropped short memory 520 bytes of unused short memory (estimated) 21640 bytes of long memory allocated (max, except for input) 0 bytes of long memory in use (in 0 pieces) 131064 bytes of short memory buffers (minus links) 65536 bytes per short memory buffer (initially 131072 bytes) 127 calls to qh_setlarger 11 average copy size freelists(bytes->count): 24->4 32->0 40->9 48->0 72->11 120->7 size in bytes: merge 72 ridge 32 vertex 48 facet 120 normal 24 ridge vertices 32 facet vertices or neighbors 40 Output completed. Verifying that all points are below outer planes of all facets. Will make 142000 distance computations. # Test tracing 'Tn', combine stderr/stdout 'Tz', flush fprintf 'Tf' rbox 100 D3 | qhull T1 Tz Tf TA1 TO q_test.log.1 tail -n -10 q_test.log.1 Statistics for: rbox 100 D3 | qhull T1 Tz Tf TA1 TO q_test.log.1 Number of points processed: 5 Number of hyperplanes created: 8 Number of distance tests for qhull: 456 CPU seconds to compute hull (after input): 0.000311 [QH1006]qh_freeqhull: free global memory [QH1005]qh_freebuild: free memory from qh_inithull and qh_buildhull [QH1061]qh_freeqhull: clear qhT except for qh.qhmem and qh.qhstat rm q_test.log.1 rbox 100 s D3 | qhull TcvA10 Early exit due to 'TAn', 'TVn', 'TCn', 'TRn', or precision error with 'QJn'. Convex hull of 100 points in 3-d: Number of vertices: 14 Number of facets: 24 Statistics for: rbox 100 s D3 | qhull TcvA10 Number of points processed: 14 Number of hyperplanes created: 48 Number of distance tests for qhull: 599 CPU seconds to compute hull (after input): 0.000193 rbox 100 s D3 | qhull TcvV-2 Early exit due to 'TAn', 'TVn', 'TCn', 'TRn', or precision error with 'QJn'. Convex hull of 100 points in 3-d: Number of vertices: 78 Number of facets: 152 Statistics for: rbox 100 s D3 | qhull TcvV-2 Number of points processed: 78 Number of hyperplanes created: 390 Number of distance tests for qhull: 1488 CPU seconds to compute hull (after input): 0.001686 rbox 100 s D3 | qhull TcvC2 Early exit due to 'TAn', 'TVn', 'TCn', 'TRn', or precision error with 'QJn'. Convex hull of 100 points in 3-d: Number of vertices: 79 Number of facets: 154 Statistics for: rbox 100 s D3 | qhull TcvC2 Number of points processed: 79 Number of hyperplanes created: 395 Number of distance tests for qhull: 1495 CPU seconds to compute hull (after input): 0.002054 rbox 100 s D3 | qhull TcvV2 Early exit due to 'TAn', 'TVn', 'TCn', 'TRn', or precision error with 'QJn'. Convex hull of 100 points in 3-d: Number of vertices: 79 Number of facets: 154 Statistics for: rbox 100 s D3 | qhull TcvV2 Number of points processed: 79 Number of hyperplanes created: 395 Number of distance tests for qhull: 1495 CPU seconds to compute hull (after input): 0.001678 rbox 100 s D3 | qhull T1cvV2P2 [QH1008]qh_readpoints: read in 100 3-dimensional points [QH0013]qh_initqhull_globals: for rbox 100 s D3 | qhull T1cvV2P2 Trace level T1, IStracing 0, point TP2, merge TM0, dist TW1.8e+308, qh.tracefacet_id -1, traceridge_id -1, tracevertex_id -1, last qh.RERUN 0, rbox 100 s D3 | qhull T1cvV2P2 Options selected for Qhull 2020.2.r 2020/08/31: run-id 370171450 Tcheck-frequently Tverify TV-stop-after-point 2 Trace-point 2 _pre-merge _zero-centrum _max-width 0.94 Error-roundoff 6.7e-16 _one-merge 4.7e-15 _near-inside 2.3e-14 Visible-distance 1.3e-15 U-max-coplanar 1.3e-15 Width-outside 2.7e-15 _wide-facet 8.1e-15 qh_findbest: point p2 starting at f7 isnewfacets? 1, unless 0 exit if > 2.7e-15, testhorizon? 1, noupper? 0, Last qh_addpoint p41, Last merge #0, max_outside 4e-17 qh_findbest: point p2 starting at f15 isnewfacets? 1, unless 0 exit if > 2.7e-15, testhorizon? 1, noupper? 0, Last qh_addpoint p52, Last merge #0, max_outside 1.1e-16 qh_findbest: point p2 starting at f37 isnewfacets? 1, unless 0 exit if > 2.7e-15, testhorizon? 1, noupper? 0, Last qh_addpoint p73, Last merge #0, max_outside 1.1e-16 qh_findbest: point p2 starting at f52 isnewfacets? 1, unless 0 exit if > 2.7e-15, testhorizon? 1, noupper? 0, Last qh_addpoint p87, Last merge #0, max_outside 1.1e-16 qh_findbest: point p2 starting at f72 isnewfacets? 1, unless 0 exit if > 2.7e-15, testhorizon? 1, noupper? 0, Last qh_addpoint p76, Last merge #0, max_outside 1.1e-16 qh_findbest: point p2 starting at f120 isnewfacets? 1, unless 0 exit if > 2.7e-15, testhorizon? 1, noupper? 0, Last qh_addpoint p84, Last merge #0, max_outside 1.1e-16 qh_findbest: point p2 starting at f211 isnewfacets? 1, unless 0 exit if > 2.7e-15, testhorizon? 1, noupper? 0, Last qh_addpoint p10, Last merge #0, max_outside 1.1e-16 qh_findbest: point p2 starting at f289 isnewfacets? 1, unless 0 exit if > 2.7e-15, testhorizon? 1, noupper? 0, Last qh_addpoint p6, Last merge #0, max_outside 1.1e-16 [QH1049]qh_addpoint: add p2(v79) 0.014 above f288 to hull of 152 facets, 0 merges, 22 outside at 0.001831 CPU secs. Previous p56(v78) delta 0.001831 CPU, 152 facets, 0 merges, 390 hyperplanes, 3835 distplanes, 0 retries [QH1040]qh_findhorizon: find horizon for point p2 facet f288 [QH1041]qh_findhorizon: 5 horizon facets(good 5), 3 visible(good 3), 0 coplanar [QH1032]qh_makenewfacets: created 5 new facets f390..f394 from point p2 to horizon [QH1019]qh_matchnewfacets: match neighbors for new facets. [QH1043]qh_partitionvisible: partitioned 0 points from outsidesets, 0 points from coplanarsets, and 0 deleted vertices [QH1018]qh_deletevisible: delete 3 visible facets and 0 vertices [QH1027]qh_checkpolygon: check all facets from f62, qh.NEWtentative? 0 [QH1039]qh_buildhull: completed the hull construction [QH1036]Qhull: algorithm completed [QH1027]qh_checkpolygon: check all facets from f62, qh.NEWtentative? 0 [QH1064]qh_checkconvex: check that facets are not-flipped and for qh.ZEROcentrum that simplicial vertices are below their neighbor (dist<0.0) Early exit due to 'TAn', 'TVn', 'TCn', 'TRn', or precision error with 'QJn'. Convex hull of 100 points in 3-d: Number of vertices: 79 Number of facets: 154 Statistics for: rbox 100 s D3 | qhull T1cvV2P2 Number of points processed: 79 Number of hyperplanes created: 395 Number of distance tests for qhull: 1495 CPU seconds to compute hull (after input): 0.001917 [QH1006]qh_freeqhull: free global memory [QH1005]qh_freebuild: free memory from qh_inithull and qh_buildhull [QH1061]qh_freeqhull: clear qhT except for qh.qhmem and qh.qhstat rbox 100 s D3 | qhull TcvF100 At 22:50:14 & 0.000321 CPU secs, qhull has created 102 facets and merged 0. The current hull contains 46 facets and 25 vertices. There are 75 outside points. Next is point p55(v26), 0.035 above f44. At 22:50:14 & 0.000677 CPU secs, qhull has created 203 facets and merged 0. The current hull contains 86 facets and 45 vertices. There are 55 outside points. Next is point p82(v46), 0.067 above f117. At 22:50:14 & 0.001103 CPU secs, qhull has created 306 facets and merged 0. The current hull contains 122 facets and 63 vertices. There are 37 outside points. Next is point p50(v64), 0.042 above f218. At 22:50:14 & 0.001669 CPU secs, qhull has created 412 facets and merged 0. The current hull contains 160 facets and 82 vertices. There are 18 outside points. Next is point p60(v83), 0.031 above f307. Convex hull of 100 points in 3-d: Number of vertices: 100 Number of facets: 196 Statistics for: rbox 100 s D3 | qhull TcvF100 Number of points processed: 100 Number of hyperplanes created: 514 Number of distance tests for qhull: 1690 CPU seconds to compute hull (after input): 0.002323 Output completed. Verifying that all points are below 2e-15 of all facets. Will make 19600 distance computations. rbox 100 s D3 | qhull Qf Tcv Convex hull of 100 points in 3-d: Number of vertices: 100 Number of facets: 196 Statistics for: rbox 100 s D3 | qhull Qf Tcv Number of points processed: 100 Number of hyperplanes created: 506 Number of distance tests for qhull: 4421 CPU seconds to compute hull (after input): 0.002658 Output completed. Verifying that all points are below 2e-15 of all facets. Will make 19600 distance computations. rbox 100 D3 | qhull Tcv Convex hull of 100 points in 3-d: Number of vertices: 26 Number of facets: 48 Statistics for: rbox 100 D3 | qhull Tcv Number of points processed: 28 Number of hyperplanes created: 109 Number of distance tests for qhull: 1163 CPU seconds to compute hull (after input): 0.000658 Output completed. Verifying that all points are below outer planes of all facets. Will make 4800 distance computations. rbox 100 D3 | qhull Qs Tcv Convex hull of 100 points in 3-d: Number of vertices: 26 Number of facets: 48 Statistics for: rbox 100 D3 | qhull Qs Tcv Number of points processed: 29 Number of hyperplanes created: 105 Number of distance tests for qhull: 1172 CPU seconds to compute hull (after input): 0.000374 Output completed. Verifying that all points are below outer planes of all facets. Will make 4800 distance computations. rbox 100 D5 | qhull Qs Tcv Convex hull of 100 points in 5-d: Number of vertices: 78 Number of facets: 1174 Statistics for: rbox 100 D5 | qhull Qs Tcv Number of points processed: 85 Number of hyperplanes created: 4014 Number of distance tests for qhull: 9050 CPU seconds to compute hull (after input): 0.02048 QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 117400 distance computations. rbox 100 D3 | qhull Qr Tcv Convex hull of 100 points in 3-d: Number of vertices: 26 Number of facets: 48 Statistics for: rbox 100 D3 | qhull Qr Tcv Number of points processed: 56 Number of hyperplanes created: 293 Number of distance tests for qhull: 2135 Output completed. Verifying that all points are below outer planes of all facets. Will make 4800 distance computations. rbox 100 D3 | qhull Qxv Tcv Convex hull of 100 points in 3-d: Number of vertices: 26 Number of facets: 48 Statistics for: rbox 100 D3 | qhull Qxv Tcv Number of points processed: 28 Number of hyperplanes created: 109 Number of distance tests for qhull: 1163 CPU seconds to compute hull (after input): 0.000332 QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 4800 distance computations. rbox 100 D3 | qhull Qi f Pd0 Pd1 Pd2 Pg Tcv Vertices and facets: - p11(v14): -0.31 0.47 0.07 - p59(v8): 0.44 0.42 -0.11 - p33(v3): -0.067 0.49 -0.11 - p48(v25): 0.25 0.24 0.44 - p37(v15): 0.45 0.26 0.04 - p38(v5): 0.42 -0.25 0.42 - f42 - flags: bottom simplicial - normal: 0.1292 0.9495 0.2858 - offset: -0.4221543 - coplanar set(furthest p70): p70: 0.04762 0.3507 -0.06712 furthest distance= -0.1 - vertices: p11(v14) p59(v8) p33(v3) - neighboring facets: f52 f41 f93 - f93 - flags: top simplicial - normal: 0.142 0.9273 0.3463 - offset: -0.4120445 - coplanar set(furthest p28): p27: 0.1182 0.3419 0.068 p25: 0.1663 0.2352 0.3516 p15: 0.2743 0.2665 0.07375 p44: -0.1321 0.3861 0.167 p28: -0.1003 0.4263 0.07335 furthest distance= -0.0056 - vertices: p48(v25) p11(v14) p59(v8) - neighboring facets: f42 f94 f95 - f94 - flags: bottom simplicial - normal: 0.7783 0.4631 0.4241 - offset: -0.4905394 - vertices: p48(v25) p37(v15) p59(v8) - neighboring facets: f47 f93 f97 - f97 - flags: top simplicial - normal: 0.8488 0.2736 0.4523 - offset: -0.4744876 - vertices: p48(v25) p37(v15) p38(v5) - neighboring facets: f46 f99 f94 Output completed. Verifying that all points are below outer planes of all facets. Will make 400 distance computations. rbox c d | qhull Qc f Tcv Vertices and facets: - p6(v6): 0.5 0.5 -0.5 neighbors: f1 f9 f10 - p2(v3): -0.5 0.5 -0.5 neighbors: f1 f3 f10 - p4(v2): 0.5 -0.5 -0.5 neighbors: f1 f2 f9 - p0(v1): -0.5 -0.5 -0.5 neighbors: f1 f2 f3 - p5(v7): 0.5 -0.5 0.5 neighbors: f2 f9 f13 - p1(v4): -0.5 -0.5 0.5 neighbors: f2 f3 f13 - p7(v5): 0.5 0.5 0.5 neighbors: f10 f13 f9 - p3(v8): -0.5 0.5 0.5 neighbors: f3 f10 f13 - f1 - flags: bottom tested - merges: 1 - normal: -0 -0 -1 - offset: -0.5 - center: 0 0 -0.5 - coplanar set(furthest p8): p8: 0 0 -0.5 furthest distance= 0 - vertices: p6(v6) p2(v3) p4(v2) p0(v1) - neighboring facets: f2 f3 f10 f9 - ridges: - r4 tested simplicialtop simplicialbot vertices: p2(v3) p0(v1) between f1 and f3 - r3 tested simplicialtop simplicialbot vertices: p4(v2) p0(v1) between f2 and f1 - r1 tested simplicialtop vertices: p6(v6) p4(v2) between f9 and f1 - r2 tested simplicialbot vertices: p6(v6) p2(v3) between f1 and f10 - f2 - flags: top tested - merges: 1 - normal: 0 -1 0 - offset: -0.5 - center: 0 -0.5 0 - coplanar set(furthest p10): p10: 0 -0.5 0 furthest distance= 0 - vertices: p5(v7) p1(v4) p4(v2) p0(v1) - neighboring facets: f1 f3 f13 f9 - ridges: - r3 tested simplicialtop simplicialbot vertices: p4(v2) p0(v1) between f2 and f1 - r8 tested simplicialtop simplicialbot vertices: p1(v4) p0(v1) between f3 and f2 - r7 tested simplicialtop vertices: p5(v7) p1(v4) between f13 and f2 - r6 tested vertices: p5(v7) p4(v2) between f2 and f9 - f9 - flags: bottom tested - merges: 1 - normal: 1 -0 -0 - offset: -0.5 - center: 0.5 0 0 - coplanar set(furthest p13): p13: 0.5 0 0 furthest distance= 0 - vertices: p5(v7) p6(v6) p7(v5) p4(v2) - neighboring facets: f2 f1 f10 f13 - ridges: - r1 tested simplicialtop vertices: p6(v6) p4(v2) between f9 and f1 - r6 tested vertices: p5(v7) p4(v2) between f2 and f9 - r10 tested simplicialbot vertices: p5(v7) p7(v5) between f9 and f13 - r11 tested simplicialtop simplicialbot vertices: p6(v6) p7(v5) between f10 and f9 - f3 - flags: bottom tested - merges: 1 - normal: -1 -0 -0 - offset: -0.5 - center: -0.5 0 0 - coplanar set(furthest p12): p12: -0.5 0 0 furthest distance= 0 - vertices: p3(v8) p1(v4) p2(v3) p0(v1) - neighboring facets: f1 f2 f13 f10 - ridges: - r4 tested simplicialtop simplicialbot vertices: p2(v3) p0(v1) between f1 and f3 - r13 tested vertices: p3(v8) p2(v3) between f10 and f3 - r14 tested vertices: p3(v8) p1(v4) between f3 and f13 - r8 tested simplicialtop simplicialbot vertices: p1(v4) p0(v1) between f3 and f2 - f10 - flags: top tested - merges: 1 - normal: 0 1 -0 - offset: -0.5 - center: 0 0.5 0 - coplanar set(furthest p11): p11: 0 0.5 0 furthest distance= 0 - vertices: p3(v8) p6(v6) p7(v5) p2(v3) - neighboring facets: f3 f1 f9 f13 - ridges: - r2 tested simplicialbot vertices: p6(v6) p2(v3) between f1 and f10 - r11 tested simplicialtop simplicialbot vertices: p6(v6) p7(v5) between f10 and f9 - r16 tested vertices: p3(v8) p7(v5) between f13 and f10 - r13 tested vertices: p3(v8) p2(v3) between f10 and f3 - f13 - flags: bottom tested - merges: 1 - normal: -0 -0 1 - offset: -0.5 - center: 0 0 0.5 - coplanar set(furthest p9): p9: 0 0 0.5 furthest distance= 0 - vertices: p3(v8) p5(v7) p7(v5) p1(v4) - neighboring facets: f10 f2 f9 f3 - ridges: - r7 tested simplicialtop vertices: p5(v7) p1(v4) between f13 and f2 - r14 tested vertices: p3(v8) p1(v4) between f3 and f13 - r16 tested vertices: p3(v8) p7(v5) between f13 and f10 - r10 tested simplicialbot vertices: p5(v7) p7(v5) between f9 and f13 Output completed. Verifying that all points are below outer planes of all facets. Will make 84 distance computations. rbox c d | qhull Qc p Tcv 3 14 -0.5 -0.5 -0.5 -0.5 -0.5 0.5 -0.5 0.5 -0.5 -0.5 0.5 0.5 0.5 -0.5 -0.5 0.5 -0.5 0.5 0.5 0.5 -0.5 0.5 0.5 0.5 0 0 -0.5 0 0 0.5 0 -0.5 0 0 0.5 0 -0.5 0 0 0.5 0 0 Output completed. Verifying that all points are below outer planes of all facets. Will make 84 distance computations. rbox 100 D3 | qhull QbB FO Tcv Options selected for Qhull 2020.2.r 2020/08/31: run-id 370171450 QbBound-unit-box 0.5 Tcheck-frequently Tverify _pre-merge _zero-centrum _max-width 1 Error-roundoff 6.9e-16 _one-merge 4.9e-15 _near-inside 2.4e-14 Visible-distance 1.4e-15 U-max-coplanar 1.4e-15 Width-outside 2.8e-15 _wide-facet 8.3e-15 Convex hull of 100 points in 3-d: Number of vertices: 26 Number of facets: 48 Statistics for: rbox 100 D3 | qhull QbB FO Tcv Number of points processed: 28 Number of hyperplanes created: 109 Number of distance tests for qhull: 1163 CPU seconds to compute hull (after input): 0.000313 Output completed. Verifying that all points are below outer planes of all facets. Will make 4800 distance computations. rbox 1000 D2 B1e6 | qhull d Qbb FO Tcv Options selected for Qhull 2020.2.r 2020/08/31: run-id 370171450 delaunay Qbbound-last Tcheck-frequently Tverify _pre-merge _zero-centrum Pgood _max-width 2e+06 Error-roundoff 1.4e-09 _one-merge 9.7e-09 _near-inside 4.9e-08 Visible-distance 2.8e-09 U-max-coplanar 2.8e-09 Width-outside 5.5e-09 _wide-facet 1.7e-08 Delaunay triangulation by the convex hull of 1000 points in 3-d: Number of input sites: 1000 Number of Delaunay regions: 1982 Statistics for: rbox 1000 D2 B1e6 | qhull d Qbb FO Tcv Number of points processed: 1000 Number of hyperplanes created: 5457 Number of facets in hull: 1996 Number of distance tests for qhull: 27959 CPU seconds to compute hull (after input): 0.08401 qhull output completed. Verifying that 1000 points are below 4.2e-09 of the nearest facet. rbox 10 D3 | qhull QbB p Tcv 3 9 -0.08928142660407055 -0.3194671263098747 0.3605569202297553 -0.1534778158747162 0.03516440701453921 0.5 -0.01663016790622804 0.3709299907861695 0.0764863283135003 0.3932651765570926 0.4421392241401818 -0.09396622763110282 0.199424728304684 0.5 0.06620718432588452 -0.2331094527352667 0.3262436269787957 -0.128966098672764 -0.5 0.2819439085196089 -0.5 0.4999999999999999 0.3760666748352666 0.1399187075693636 0.4888102268053206 -0.5 -0.2153953634886358 Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 140 distance computations. rbox 10 D3 | qhull Qbb p Tcv QH7040 qhull option warning: option 'Qbb' (scale-last-coordinate) is normally used with 'd' or 'v' 3 9 -0.0222149361131852 -0.366434993563625 0.4072229792632261 -0.06676722137887703 -0.1566931052661437 0.4732086509216659 0.02820502736438535 0.04189077954915421 0.272798317696016 0.3126723396709863 0.08400649026409401 0.1921386936513206 0.1781470954214661 0.1182274414396169 0.2679341378370068 -0.1220315663349177 0.01546165115708642 0.1755764518932639 -0.3072535691850387 -0.01073880122111998 0 0.3867462923626847 0.04492879989084675 0.3028150683084346 0.3789805913148268 -0.4732086509216658 0.1346773760895938 Output completed. Verifying that all points are below 2e-15 of all facets. Will make 140 distance computations. rbox 10 D3 | qhull Qb0:-10B2:20 p Tcv 3 9 -5.733970380575339 -0.366434993563625 17.14322461142018 -6.400761988815288 -0.1566931052661437 20 -4.97936018866004 0.04189077954915421 11.32346018178493 -0.7218812392989191 0.08400649026409401 7.831392539952951 -2.735252796494545 0.1182274414396169 11.11287098934976 -7.227875597731384 0.01546165115708642 7.114348923589702 -10 -0.01073880122111998 -0.4870359524963758 0.3867462923626847 0.04492879989084675 12.62300161615219 0.2705209571204694 -0.4732086509216658 5.343669467959105 Output completed. Verifying that all points are below 7.5e-14 of all facets. Will make 140 distance computations. rbox 10 D3 | qhull Qb0:-10B2:20 p Tcv | qhull QbB p Tcv Output completed. Verifying that all points are below 7.5e-14 of all facets. Will make 140 distance computations. 3 9 -0.08928142660407051 -0.3194671263098747 0.3605569202297555 -0.153477815874716 0.03516440701453921 0.5 -0.01663016790622796 0.3709299907861695 0.07648632831350011 0.3932651765570927 0.4421392241401818 -0.09396622763110274 0.1994247283046841 0.5 0.06620718432588446 -0.2331094527352668 0.3262436269787957 -0.1289660986727639 -0.5 0.2819439085196089 -0.4999999999999999 0.5 0.3760666748352666 0.1399187075693635 0.4888102268053207 -0.5 -0.2153953634886357 Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 126 distance computations. rbox 10 D3 | qhull Qb1:0B1:0 d Tcv Q8 Delaunay triangulation by the convex hull of 10 points in 3-d: Number of input sites: 10 Number of Delaunay regions: 14 Statistics for: rbox 10 D3 | qhull Qb1:0B1:0 d Tcv Q8 Number of points processed: 10 Number of hyperplanes created: 31 Number of facets in hull: 16 Number of distance tests for qhull: 61 CPU seconds to compute hull (after input): 0.000117 QH7077 qhull input warning: no outer plane check ('Q5') or no processing of near-inside points ('Q8'). Verify may report that a point is outside of a facet. Output completed. Verifying that all points are below 2e-15 of all facets. Will make 140 distance computations. rbox 10 D3 | qhull Qb1:0B1:0B2:0 d Tcv Q8 Delaunay triangulation by the convex hull of 10 points in 3-d: Number of input sites: 10 Number of Delaunay regions: 14 Statistics for: rbox 10 D3 | qhull Qb1:0B1:0B2:0 d Tcv Q8 Number of points processed: 10 Number of hyperplanes created: 31 Number of facets in hull: 16 Number of distance tests for qhull: 61 CPU seconds to compute hull (after input): 8.5e-05 QH7077 qhull input warning: no outer plane check ('Q5') or no processing of near-inside points ('Q8'). Verify may report that a point is outside of a facet. Output completed. Verifying that all points are below 2e-15 of all facets. Will make 140 distance computations. rbox 10 D3 | qhull Qb1:0 d Tcv Delaunay triangulation by the convex hull of 10 points in 4-d: Number of input sites: 10 Number of Delaunay regions: 18 Statistics for: rbox 10 D3 | qhull Qb1:0 d Tcv Number of points processed: 10 Number of hyperplanes created: 43 Number of facets in hull: 27 Number of distance tests for qhull: 66 CPU seconds to compute hull (after input): 0.000108 Output completed. Verifying that all points are below 2.9e-15 of all facets. Will make 180 distance computations. rbox 10 D3 | qhull Qb1:0B1:0 Tcv Convex hull of 10 points in 2-d: Number of vertices: 4 Number of facets: 4 Statistics for: rbox 10 D3 | qhull Qb1:0B1:0 Tcv Number of points processed: 4 Number of hyperplanes created: 6 Number of distance tests for qhull: 48 CPU seconds to compute hull (after input): 4.4e-05 Output completed. Verifying that all points are below 1.3e-15 of all facets. Will make 40 distance computations. echo "== next command will error ${d:-`date`} ==" == next command will error Tue Oct 5 22:50:14 UTC 2021 == rbox 10 D2 | qhull Qb1:1B1:1 Tcv QH6154 Qhull precision error: Initial simplex is flat (facet 1 is coplanar with the interior point) While executing: rbox 10 D2 | qhull Qb1:1B1:1 Tcv Options selected for Qhull 2020.2.r 2020/08/31: run-id 370171450 Qbound-dim-low 1 1 QBound-dim-high 1 1 Tcheck-frequently Tverify _pre-merge _zero-centrum _max-width 0.81 Error-roundoff 8.6e-16 _one-merge 4.3e-15 _near-inside 2.1e-14 Visible-distance 1.7e-15 U-max-coplanar 1.7e-15 Width-outside 3.4e-15 _wide-facet 1e-14 _maxoutside 5.1e-15 The input to qhull appears to be less than 2 dimensional, or a computation has overflowed. Qhull could not construct a clearly convex simplex from points: - p0(v3): -0.022 1 - p4(v2): 0.38 1 - p1(v1): -0.43 1 The center point is coplanar with a facet, or a vertex is coplanar with a neighboring facet. The maximum round off error for computing distances is 8.6e-16. The center point, facets and distances to the center point are as follows: center point -0.02391 1 facet p4 p1 distance= 0 facet p0 p1 distance= 0 facet p0 p4 distance= 0 These points either have a maximum or minimum x-coordinate, or they maximize the determinant for k coordinates. Trial points are first selected from points that maximize a coordinate. The min and max coordinates for each dimension are: 0: -0.4285 0.379 difference= 0.8076 1: 1 1 difference= 0 If the input should be full dimensional, you have several options that may determine an initial simplex: - use 'QJ' to joggle the input and make it full dimensional - use 'QbB' to scale the points to the unit cube - use 'QR0' to randomly rotate the input for different maximum points - use 'Qs' to search all points for the initial simplex - use 'En' to specify a maximum roundoff error less than 8.6e-16. - trace execution with 'T3' to see the determinant for each point. If the input is lower dimensional: - use 'QJ' to joggle the input and make it full dimensional - use 'Qbk:0Bk:0' to delete coordinate k from the input. You should pick the coordinate with the least range. The hull will have the correct topology. - determine the flat containing the points, rotate the points into a coordinate plane, and delete the other coordinates. - add one or more points to make the input full dimensional. rbox 200 L20 D2 t | qhull FO Tcv C-0 Options selected for Qhull 2020.2.r 2020/08/31: run-id 370171450 Tcheck-frequently Tverify Centrum-premerge- 0 _zero-centrum _max-width 0.99 Error-roundoff 3.4e-16 _one-merge 1.7e-15 _near-inside 8.5e-15 Visible-distance 6.8e-16 U-max-coplanar 6.8e-16 Width-outside 1.4e-15 _wide-facet 4.1e-15 Convex hull of 200 points in 2-d: Number of vertices: 200 Number of facets: 200 Statistics for: rbox 200 L20 D2 t1633474214 | qhull FO Tcv C-0 Number of points processed: 200 Number of hyperplanes created: 398 Number of distance tests for qhull: 2102 CPU seconds to compute hull (after input): 0.003575 Output completed. Verifying that all points are below 1e-15 of all facets. Will make 40000 distance computations. rbox 1000 L20 t | qhull FO Tcv C-0 Options selected for Qhull 2020.2.r 2020/08/31: run-id 370171450 Tcheck-frequently Tverify Centrum-premerge- 0 _zero-centrum _max-width 1 Error-roundoff 6.9e-16 _one-merge 4.8e-15 _near-inside 2.4e-14 Visible-distance 1.4e-15 U-max-coplanar 1.4e-15 Width-outside 2.8e-15 _wide-facet 8.3e-15 Convex hull of 1000 points in 3-d: Number of vertices: 43 Number of facets: 82 Statistics for: rbox 1000 L20 t1633474214 | qhull FO Tcv C-0 Number of points processed: 62 Number of hyperplanes created: 278 Number of distance tests for qhull: 15440 CPU seconds to compute hull (after input): 0.001298 Output completed. Verifying that all points are below outer planes of all facets. Will make 82000 distance computations. rbox 200 L20 D4 t | qhull FO Tcv C-0 Options selected for Qhull 2020.2.r 2020/08/31: run-id 370171450 Tcheck-frequently Tverify Centrum-premerge- 0 _zero-centrum _max-width 1 Error-roundoff 1e-15 _one-merge 9e-15 _near-inside 4.5e-14 Visible-distance 6e-15 U-max-coplanar 6e-15 Width-outside 1.2e-14 _wide-facet 3.6e-14 Convex hull of 200 points in 4-d: Number of vertices: 59 Number of facets: 260 Statistics for: rbox 200 L20 D4 t1633474214 | qhull FO Tcv C-0 Number of points processed: 69 Number of hyperplanes created: 731 Number of distance tests for qhull: 6345 CPU seconds to compute hull (after input): 0.003351 Output completed. Verifying that all points are below outer planes of all facets. Will make 52000 distance computations. rbox 200 L20 D5 t | qhull FO Tcv Qx Options selected for Qhull 2020.2.r 2020/08/31: run-id 370171450 Tcheck-frequently Tverify Qxact-merge _zero-centrum _max-width 1 Error-roundoff 1.4e-15 _one-merge 1.5e-14 _near-inside 7.5e-14 Visible-distance 8.2e-15 U-max-coplanar 8.2e-15 Width-outside 1.6e-14 _wide-facet 4.9e-14 Convex hull of 200 points in 5-d: Number of vertices: 98 Number of facets: 1380 Statistics for: rbox 200 L20 D5 t1633474214 | qhull FO Tcv Qx Number of points processed: 121 Number of hyperplanes created: 5324 Number of distance tests for qhull: 19784 CPU seconds to compute hull (after input): 0.03282 QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 276000 distance computations. rbox 1000 W1e-3 s D2 t | qhull d FO Tcv Qu Q0 Options selected for Qhull 2020.2.r 2020/08/31: run-id 370171450 delaunay Tcheck-frequently Tverify QupperDelaunay Q0-no-premerge Pgood _max-width 1 Error-roundoff 6.9e-16 Visible-distance 6.9e-16 U-max-coplanar 6.9e-16 Width-outside 1.4e-15 _wide-facet 4.2e-15 Furthest-site Delaunay triangulation by the convex hull of 1000 points in 3-d: Number of input sites: 1000 Number of Delaunay regions: 257 Statistics for: rbox 1000 W1e-3 s D2 t1633474214 | qhull d FO Tcv Qu Q0 Number of points processed: 1000 Number of hyperplanes created: 4577 Number of facets in hull: 1996 Number of distance tests for qhull: 27046 CPU seconds to compute hull (after input): 0.05441 Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 257000 distance computations. rbox 1000 W1e-3 s D2 t | qhull d FO Tcv Qu C-0 Options selected for Qhull 2020.2.r 2020/08/31: run-id 370171450 delaunay Tcheck-frequently Tverify QupperDelaunay Centrum-premerge- 0 _zero-centrum Pgood _max-width 1 Error-roundoff 6.9e-16 _one-merge 4.9e-15 _near-inside 2.4e-14 Visible-distance 1.4e-15 U-max-coplanar 1.4e-15 Width-outside 2.8e-15 _wide-facet 8.3e-15 Furthest-site Delaunay triangulation by the convex hull of 1000 points in 3-d: Number of input sites: 1000 Number of Delaunay regions: 257 Statistics for: rbox 1000 W1e-3 s D2 t1633474214 | qhull d FO Tcv Qu C-0 Number of points processed: 1000 Number of hyperplanes created: 4577 Number of facets in hull: 1996 Number of distance tests for qhull: 27046 CPU seconds to compute hull (after input): 0.06773 Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 257000 distance computations. set +v === check joggle and TRn Tue Oct 5 22:50:14 UTC 2021 rbox 100 W0 | qhull QJ1e-14 Qc TR100 Tv Early exit due to 'TAn', 'TVn', 'TCn', 'TRn', or precision error with 'QJn'. Convex hull of 100 points in 3-d: Number of vertices: 15 Number of coplanar points: 4 Number of facets: 25 Statistics for: rbox 100 W0 | qhull QJ1e-14 Qc TR100 Tv Number of points processed: 15 Number of hyperplanes created: 11218 Number of distance tests for qhull: 119030 CPU seconds to compute hull (after input): 0.018 Percentage of runs with precision errors: 100.0 precision problems (corrected unless 'Q0' or an error) 100 coplanar horizon facets for new vertices 400 coplanar points during partitioning rbox 100 W0 | qhull QJ1e-13 Qc TR100 Tv Early exit due to 'TAn', 'TVn', 'TCn', 'TRn', or precision error with 'QJn'. Convex hull of 100 points in 3-d: Number of vertices: 28 Number of coplanar points: 12 Number of facets: 50 Statistics for: rbox 100 W0 | qhull QJ1e-13 Qc TR100 Tv Number of points processed: 28 Number of hyperplanes created: 24747 Number of distance tests for qhull: 195826 CPU seconds to compute hull (after input): 0.02555 Percentage of runs with precision errors: 63.0 precision problems (corrected unless 'Q0' or an error) 10 coplanar half ridges in output 53 coplanar horizon facets for new vertices 119 coplanar points during partitioning rbox 100 W0 | qhull QJ1e-12 Qc TR100 Tv Early exit due to 'TAn', 'TVn', 'TCn', 'TRn', or precision error with 'QJn'. Convex hull of 100 points in 3-d: Number of vertices: 40 Number of coplanar points: 16 Number of facets: 75 Statistics for: rbox 100 W0 | qhull QJ1e-12 Qc TR100 Tv Number of points processed: 40 Number of hyperplanes created: 29152 Number of distance tests for qhull: 216487 CPU seconds to compute hull (after input): 0.03889 Percentage of runs with precision errors: 8.0 precision problems (corrected unless 'Q0' or an error) 2 coplanar half ridges in output 6 coplanar horizon facets for new vertices 17 coplanar points during partitioning rbox 100 W0 | qhull QJ1e-11 Qc TR100 Tv Convex hull of 100 points in 3-d: Number of vertices: 66 Number of coplanar points: 34 Number of facets: 128 Statistics for: rbox 100 W0 | qhull QJ1e-11 Qc TR100 Tv Number of points processed: 75 Number of hyperplanes created: 29577 Number of distance tests for qhull: 218409 CPU seconds to compute hull (after input): 0.03008 Percentage of runs with precision errors: 0.0 precision problems (corrected unless 'Q0' or an error) 3 coplanar points during partitioning Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 12800 distance computations. rbox 100 W0 | qhull QJ1e-10 Qc TR100 Tv Convex hull of 100 points in 3-d: Number of vertices: 66 Number of coplanar points: 34 Number of facets: 128 Statistics for: rbox 100 W0 | qhull QJ1e-10 Qc TR100 Tv Number of points processed: 75 Number of hyperplanes created: 29583 Number of distance tests for qhull: 218315 CPU seconds to compute hull (after input): 0.03212 Percentage of runs with precision errors: 0.0 Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 12800 distance computations. rbox 100 | qhull d QJ Qb0:1e4 QB0:1e5 Qb1:1e4 QB1:1e6 Qb2:1e5 QB2:1e7 FO Tv Options selected for Qhull 2020.2.r 2020/08/31: run-id 370171450 delaunay Qbound-dim-low 0 1e+04 QBound-dim-high 0 1e+05 Qbound-dim-low 1 1e+04 QBound-dim-high 1 1e+06 Qbound-dim-low 2 1e+05 QBound-dim-high 2 1e+07 Tverify Pgood _run 1 QJoggle 6.7e+03 _joggle-seed 16807 _max-width 1e+14 Error-roundoff 0.11 Visible-distance 0.11 U-max-coplanar 0.11 Width-outside 0.23 _wide-facet 0.68 Delaunay triangulation by the convex hull of 100 points in 4-d: Number of input sites: 100 Number of Delaunay regions: 488 Statistics for: rbox 100 | qhull d QJ Qb0:1e4 QB0:1e5 Qb1:1e4 QB1:1e6 Qb2:1e5 QB2:1e7 FO Tv Number of points processed: 100 Number of hyperplanes created: 1477 Number of facets in hull: 560 Number of distance tests for qhull: 3418 CPU seconds to compute hull (after input): 0.001233 Input joggled by: 6.7e+03 Output completed. Verifying that all points are below 0.34 of all facets. Will make 48800 distance computations. set +v === check precision options Tue Oct 5 22:50:14 UTC 2021 rbox 100 D3 s | qhull E0.01 Qx Tcv FO Options selected for Qhull 2020.2.r 2020/08/31: run-id 370171450 Distance-roundoff 0.01 Qxact-merge Tcheck-frequently Tverify _zero-centrum _max-width 0.98 _one-merge 0.07 _near-inside 0.35 Visible-distance 0.02 U-max-coplanar 0.02 Width-outside 0.04 _wide-facet 0.12 Convex hull of 100 points in 3-d: Number of vertices: 46 Number of facets: 41 Number of non-simplicial facets: 29 Statistics for: rbox 100 D3 s | qhull E0.01 Qx Tcv FO Number of points processed: 46 Number of hyperplanes created: 162 Number of distance tests for qhull: 3834 Number of distance tests for merging: 1887 Number of distance tests for checking: 1989 Number of merged facets: 60 CPU seconds to compute hull (after input): 0.001268 Maximum distance of point above facet: 0.048 (0.6x) Maximum distance of vertex below facet: -0.072 (0.9x) QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 4100 distance computations. rbox 100 D3 W1e-1 | qhull W1e-3 Tcv Convex hull of 100 points in 3-d: Number of vertices: 33 Number of facets: 62 Statistics for: rbox 100 D3 W1e-1 | qhull W1e-3 Tcv Number of points processed: 37 Number of hyperplanes created: 169 Number of distance tests for qhull: 1565 CPU seconds to compute hull (after input): 0.000971 Maximum distance of point above facet: 0.00084 Output completed. Verifying that all points are below outer planes of all facets. Will make 6200 distance computations. rbox 100 D3 W1e-1 | qhull W1e-2 Tcv Q0 Convex hull of 100 points in 3-d: Number of vertices: 28 Number of facets: 52 Statistics for: rbox 100 D3 W1e-1 | qhull W1e-2 Tcv Q0 Number of points processed: 29 Number of hyperplanes created: 127 Number of distance tests for qhull: 1691 CPU seconds to compute hull (after input): 0.000331 precision problems (corrected unless 'Q0' or an error) 23 coplanar points during partitioning Output completed. Verifying that all points are below outer planes of all facets. Will make 5200 distance computations. rbox 100 D3 W1e-1 | qhull W1e-2 Tcv Convex hull of 100 points in 3-d: Number of vertices: 29 Number of facets: 54 Statistics for: rbox 100 D3 W1e-1 | qhull W1e-2 Tcv Number of points processed: 30 Number of hyperplanes created: 131 Number of distance tests for qhull: 1720 CPU seconds to compute hull (after input): 0.000451 Maximum distance of point above facet: 0.0057 Output completed. Verifying that all points are below outer planes of all facets. Will make 5400 distance computations. rbox 100 D3 W1e-1 | qhull W1e-1 Tcv Convex hull of 100 points in 3-d: Number of vertices: 13 Number of facets: 22 Statistics for: rbox 100 D3 W1e-1 | qhull W1e-1 Tcv Number of points processed: 13 Number of hyperplanes created: 45 Number of distance tests for qhull: 2377 CPU seconds to compute hull (after input): 0.00033 Maximum distance of point above facet: 0.098 Output completed. Verifying that all points are below outer planes of all facets. Will make 2200 distance computations. rbox 15 D2 P0 P1e-14,1e-14 | qhull d Quc Tcv Furthest-site Delaunay triangulation by the convex hull of 17 points in 3-d: Number of input sites: 17 Number of Delaunay regions: 5 Statistics for: rbox 15 D2 P0 P1e-14,1e-14 | qhull d Quc Tcv Number of points processed: 17 Number of hyperplanes created: 63 Number of facets in hull: 28 Number of distance tests for qhull: 141 Number of distance tests for merging: 474 Number of distance tests for checking: 236 Number of merged facets: 7 CPU seconds to compute hull (after input): 0.000419 Maximum distance of point above facet: 1.6e-15 (0.3x) Output completed. Verifying that all points are below outer planes of all facets. Will make 85 distance computations. rbox 15 D3 P0 P1e-12,1e-14,1e-14 | qhull d Qcu Tcv Furthest-site Delaunay triangulation by the convex hull of 17 points in 4-d: Number of input sites: 17 Number of Delaunay regions: 14 Statistics for: rbox 15 D3 P0 P1e-12,1e-14,1e-14 | qhull d Qcu Tcv Number of points processed: 17 Number of hyperplanes created: 123 Number of facets in hull: 60 Number of distance tests for qhull: 224 CPU seconds to compute hull (after input): 0.000389 Output completed. Verifying that all points are below 2.8e-15 of all facets. Will make 238 distance computations. rbox 1000 s D3 | qhull C-0.01 Tcv Qc Convex hull of 1000 points in 3-d: Number of vertices: 108 Number of coplanar points: 892 Number of facets: 95 Number of non-simplicial facets: 78 Statistics for: rbox 1000 s D3 | qhull C-0.01 Tcv Qc Number of points processed: 112 Number of hyperplanes created: 464 Number of distance tests for qhull: 62162 Number of distance tests for merging: 6682 Number of distance tests for checking: 24376 Number of merged facets: 264 CPU seconds to compute hull (after input): 0.01151 Maximum distance of point above facet: 0.021 (0.7x) Maximum distance of vertex below facet: -0.029 (1.0x) Output completed. Verifying that all points are below outer planes of all facets. Will make 95000 distance computations. rbox 1000 s D3 | qhull C-0.01 V0 Qc Tcv Convex hull of 1000 points in 3-d: Number of vertices: 137 Number of coplanar points: 863 Number of facets: 87 Number of non-simplicial facets: 82 Statistics for: rbox 1000 s D3 | qhull C-0.01 V0 Qc Tcv Number of points processed: 466 Number of hyperplanes created: 2572 Number of distance tests for qhull: 232428 Number of distance tests for merging: 47390 Number of distance tests for checking: 38513 Number of merged facets: 1818 CPU seconds to compute hull (after input): 0.08562 Maximum distance of point above facet: 0.026 (0.9x) Maximum distance of vertex below facet: -0.075 (2.5x) Output completed. Verifying that all points are below outer planes of all facets. Will make 87000 distance computations. rbox 1000 s D3 | qhull C-0.01 U0 Qc Tcv Convex hull of 1000 points in 3-d: Number of vertices: 108 Number of coplanar points: 892 Number of facets: 97 Number of non-simplicial facets: 77 Statistics for: rbox 1000 s D3 | qhull C-0.01 U0 Qc Tcv Number of points processed: 112 Number of hyperplanes created: 505 Number of distance tests for qhull: 62212 Number of distance tests for merging: 7315 Number of distance tests for checking: 24575 Number of merged facets: 260 CPU seconds to compute hull (after input): 0.01048 Maximum distance of point above facet: 0.021 (0.7x) Maximum distance of vertex below facet: -0.029 (1.0x) Output completed. Verifying that all points are below outer planes of all facets. Will make 97000 distance computations. rbox 1000 s D3 | qhull C-0.01 V0 Qcm Tcv Convex hull of 1000 points in 3-d: Number of vertices: 87 Number of coplanar points: 913 Number of facets: 88 Number of non-simplicial facets: 56 Statistics for: rbox 1000 s D3 | qhull C-0.01 V0 Qcm Tcv Number of points processed: 90 Number of hyperplanes created: 457 Number of distance tests for qhull: 46340 Number of distance tests for merging: 5761 Number of distance tests for checking: 21602 Number of merged facets: 192 CPU seconds to compute hull (after input): 0.006311 Maximum distance of point above facet: 0.032 (1.1x) Maximum distance of vertex below facet: -0.041 (1.4x) Output completed. Verifying that all points are below outer planes of all facets. Will make 88000 distance computations. rbox 1000 s D3 | qhull C-0.01 Qcm Tcv Convex hull of 1000 points in 3-d: Number of vertices: 101 Number of coplanar points: 899 Number of facets: 95 Number of non-simplicial facets: 69 Statistics for: rbox 1000 s D3 | qhull C-0.01 Qcm Tcv Number of points processed: 104 Number of hyperplanes created: 433 Number of distance tests for qhull: 59136 Number of distance tests for merging: 6024 Number of distance tests for checking: 24116 Number of merged facets: 232 CPU seconds to compute hull (after input): 0.008153 Maximum distance of point above facet: 0.023 (0.8x) Maximum distance of vertex below facet: -0.031 (1.0x) Output completed. Verifying that all points are below outer planes of all facets. Will make 95000 distance computations. rbox 1000 s D3 | qhull C-0.01 Q1 FO Tcv Qc Options selected for Qhull 2020.2.r 2020/08/31: run-id 370188257 Centrum-premerge- 0.01 Q1-angle-merge Tcheck-frequently Tverify Qcoplanar-keep _max-width 1 Error-roundoff 6.9e-16 _one-merge 0.03 _near-inside 0.15 Visible-distance 0.01 U-max-coplanar 0.01 Width-outside 0.02 _wide-facet 0.06 Convex hull of 1000 points in 3-d: Number of vertices: 107 Number of coplanar points: 893 Number of facets: 97 Number of non-simplicial facets: 80 Statistics for: rbox 1000 s D3 | qhull C-0.01 Q1 FO Tcv Qc Number of points processed: 111 Number of hyperplanes created: 450 Number of distance tests for qhull: 61776 Number of distance tests for merging: 6387 Number of distance tests for checking: 24594 Number of merged facets: 253 CPU seconds to compute hull (after input): 0.009766 Maximum distance of point above facet: 0.02 (0.7x) Maximum distance of vertex below facet: -0.035 (1.2x) Output completed. Verifying that all points are below outer planes of all facets. Will make 97000 distance computations. rbox 1000 s D3 | qhull C-0.01 Q2 FO Tcv Qc Options selected for Qhull 2020.2.r 2020/08/31: run-id 370188257 Centrum-premerge- 0.01 Q2-no-merge-independent Tcheck-frequently Tverify Qcoplanar-keep _max-width 1 Error-roundoff 6.9e-16 _one-merge 0.03 _near-inside 0.15 Visible-distance 0.01 U-max-coplanar 0.01 Width-outside 0.02 _wide-facet 0.06 Convex hull of 1000 points in 3-d: Number of vertices: 106 Number of coplanar points: 894 Number of facets: 92 Number of non-simplicial facets: 74 Statistics for: rbox 1000 s D3 | qhull C-0.01 Q2 FO Tcv Qc Number of points processed: 110 Number of hyperplanes created: 451 Number of distance tests for qhull: 60312 Number of distance tests for merging: 6396 Number of distance tests for checking: 23893 Number of merged facets: 260 CPU seconds to compute hull (after input): 0.01823 Maximum distance of point above facet: 0.023 (0.8x) Maximum distance of vertex below facet: -0.049 (1.6x) Output completed. Verifying that all points are below outer planes of all facets. Will make 92000 distance computations. rbox 1000 s D3 | qhull C-0.01 Q3 FO Tcv Qc Options selected for Qhull 2020.2.r 2020/08/31: run-id 370188257 Centrum-premerge- 0.01 Q3-no-merge-vertices Tcheck-frequently Tverify Qcoplanar-keep _max-width 1 Error-roundoff 6.9e-16 _one-merge 0.03 _near-inside 0.15 Visible-distance 0.01 U-max-coplanar 0.01 Width-outside 0.02 _wide-facet 0.06 Convex hull of 1000 points in 3-d: Number of vertices: 112 Number of coplanar points: 888 Number of facets: 94 Number of non-simplicial facets: 78 Statistics for: rbox 1000 s D3 | qhull C-0.01 Q3 FO Tcv Qc Number of points processed: 112 Number of hyperplanes created: 468 Number of distance tests for qhull: 61911 Number of distance tests for merging: 6879 Number of distance tests for checking: 24243 Number of merged facets: 268 CPU seconds to compute hull (after input): 0.0138 Maximum distance of point above facet: 0.021 (0.7x) Maximum distance of vertex below facet: -0.03 (1.0x) Output completed. Verifying that all points are below outer planes of all facets. Will make 94000 distance computations. rbox 1000 s D3 | qhull C-0.01 Q4 FO Tcv Qc Options selected for Qhull 2020.2.r 2020/08/31: run-id 370188257 Centrum-premerge- 0.01 Q4-avoid-old-into-new Tcheck-frequently Tverify Qcoplanar-keep _max-width 1 Error-roundoff 6.9e-16 _one-merge 0.03 _near-inside 0.15 Visible-distance 0.01 U-max-coplanar 0.01 Width-outside 0.02 _wide-facet 0.06 Convex hull of 1000 points in 3-d: Number of vertices: 108 Number of coplanar points: 892 Number of facets: 95 Number of non-simplicial facets: 78 Statistics for: rbox 1000 s D3 | qhull C-0.01 Q4 FO Tcv Qc Number of points processed: 112 Number of hyperplanes created: 464 Number of distance tests for qhull: 62162 Number of distance tests for merging: 6682 Number of distance tests for checking: 24376 Number of merged facets: 264 CPU seconds to compute hull (after input): 0.009772 Maximum distance of point above facet: 0.021 (0.7x) Maximum distance of vertex below facet: -0.029 (1.0x) Output completed. Verifying that all points are below outer planes of all facets. Will make 95000 distance computations. echo === this may generate an error ${d:-`date`} === this may generate an error Tue Oct 5 22:50:15 UTC 2021 rbox 1000 s D3 | qhull C-0.01 Q5 FO Tcv Options selected for Qhull 2020.2.r 2020/08/31: run-id 370188257 Centrum-premerge- 0.01 Q5-no-check-outer Tcheck-frequently Tverify _max-width 1 Error-roundoff 6.9e-16 _one-merge 0.03 Visible-distance 0.01 U-max-coplanar 0.01 Width-outside 0.02 _wide-facet 0.06 Convex hull of 1000 points in 3-d: Number of vertices: 108 Number of facets: 95 Number of non-simplicial facets: 78 Statistics for: rbox 1000 s D3 | qhull C-0.01 Q5 FO Tcv Number of points processed: 112 Number of hyperplanes created: 464 Number of distance tests for qhull: 35756 Number of distance tests for merging: 6682 Number of distance tests for checking: 2036 Number of merged facets: 264 CPU seconds to compute hull (after input): 0.009577 Maximum distance of point above facet: 0.022 (0.7x) Maximum distance of vertex below facet: -0.031 (1.0x) QH7077 qhull input warning: no outer plane check ('Q5') or no processing of near-inside points ('Q8'). Verify may report that a point is outside of a facet. Output completed. Verifying that all points are below 0.022 of all facets. Will make 95000 distance computations. echo === this should generate an error ${d:-`date`} === this should generate an error Tue Oct 5 22:50:15 UTC 2021 rbox 1000 s D3 | qhull C-0.01 Q6 FO Po Tcv Qc Options selected for Qhull 2020.2.r 2020/08/31: run-id 370188257 Centrum-premerge- 0.01 Q6-no-concave-merge Poutput-forced Tcheck-frequently Tverify Qcoplanar-keep _max-width 1 Error-roundoff 6.9e-16 _one-merge 0.03 _near-inside 0.15 Visible-distance 0.01 U-max-coplanar 0.01 Width-outside 0.02 _wide-facet 0.06 QH6117 qhull precision error: f328 is concave to f329. Centrum of f328 is 0.001027 above f329 QH6117 qhull precision error: f329 is concave to f328. Centrum of f329 is 0.004134 above f328 QH6117 qhull precision error: f482 is concave to f484. Centrum of f482 is 0.0001795 above f484 QH6117 qhull precision error: f484 is concave to f482. Centrum of f484 is 6.818e-05 above f482 Convex hull of 1000 points in 3-d: Number of vertices: 115 Number of coplanar points: 885 Number of facets: 184 Number of non-simplicial facets: 40 Statistics for: rbox 1000 s D3 | qhull C-0.01 Q6 FO Po Tcv Qc Number of points processed: 115 Number of hyperplanes created: 455 Number of distance tests for qhull: 52081 Number of distance tests for merging: 1190 Number of distance tests for checking: 28981 Number of merged facets: 88 CPU seconds to compute hull (after input): 0.00763 Maximum distance of point above facet: 0.02 (0.7x) Maximum distance of vertex below facet: -0.009 (0.3x) rbox 1000 s D3 | qhull C-0.01 Q7 FO Tcv Qc Options selected for Qhull 2020.2.r 2020/08/31: run-id 370188257 Centrum-premerge- 0.01 Q7-no-breadth-first Tcheck-frequently Tverify Qcoplanar-keep _max-width 1 Error-roundoff 6.9e-16 _one-merge 0.03 _near-inside 0.15 Visible-distance 0.01 U-max-coplanar 0.01 Width-outside 0.02 _wide-facet 0.06 Convex hull of 1000 points in 3-d: Number of vertices: 108 Number of coplanar points: 892 Number of facets: 99 Number of non-simplicial facets: 77 Statistics for: rbox 1000 s D3 | qhull C-0.01 Q7 FO Tcv Qc Number of points processed: 110 Number of hyperplanes created: 449 Number of distance tests for qhull: 55287 Number of distance tests for merging: 6050 Number of distance tests for checking: 22232 Number of merged facets: 242 CPU seconds to compute hull (after input): 0.01657 Maximum distance of point above facet: 0.021 (0.7x) Maximum distance of vertex below facet: -0.031 (1.0x) Output completed. Verifying that all points are below outer planes of all facets. Will make 99000 distance computations. rbox 1000 s D3 | qhull C-0.01 Qx Tcv Qc Convex hull of 1000 points in 3-d: Number of vertices: 115 Number of coplanar points: 885 Number of facets: 101 Number of non-simplicial facets: 76 Statistics for: rbox 1000 s D3 | qhull C-0.01 Qx Tcv Qc Number of points processed: 115 Number of hyperplanes created: 455 Number of distance tests for qhull: 89505 Number of distance tests for merging: 5154 Number of distance tests for checking: 19846 Number of merged facets: 171 CPU seconds to compute hull (after input): 0.01307 Maximum distance of point above facet: 0.02 (0.7x) Maximum distance of vertex below facet: -0.034 (1.1x) QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 101000 distance computations. echo === this may generate an error e.g., t1263080158 ${d:-`date`} === this may generate an error e.g., t1263080158 Tue Oct 5 22:50:15 UTC 2021 rbox 100 s D3 t | qhull R1e-3 Tcv Qc Convex hull of 100 points in 3-d: Number of vertices: 99 Number of coplanar points: 1 Number of facets: 168 Number of non-simplicial facets: 23 Statistics for: rbox 100 s D3 t1633474215 | qhull R1e-3 Tcv Qc Number of points processed: 99 Number of hyperplanes created: 469 Number of distance tests for qhull: 1579 Number of distance tests for merging: 2900 Number of distance tests for checking: 1567 Number of merged facets: 40 CPU seconds to compute hull (after input): 0.00324 Maximum distance of point above facet: 0.0019 (0.5x) Maximum distance of vertex below facet: -0.0045 (1.1x) Output completed. Verifying that all points are below outer planes of all facets. Will make 16800 distance computations. rbox 100 s D3 t | qhull R1e-2 Tcv Qc Convex hull of 100 points in 3-d: Number of vertices: 68 Number of coplanar points: 32 Number of facets: 65 Number of non-simplicial facets: 46 Statistics for: rbox 100 s D3 t1633474215 | qhull R1e-2 Tcv Qc Number of points processed: 72 Number of hyperplanes created: 312 Number of distance tests for qhull: 3300 Number of distance tests for merging: 4120 Number of distance tests for checking: 2789 Number of merged facets: 146 CPU seconds to compute hull (after input): 0.003168 Maximum distance of point above facet: 0.029 (0.7x) Maximum distance of vertex below facet: -0.06 (1.5x) Output completed. Verifying that all points are below outer planes of all facets. Will make 6500 distance computations. rbox 500 s D3 t | qhull R0.05 A-1 Tcv Qc Convex hull of 500 points in 3-d: Number of vertices: 17 Number of coplanar points: 483 Number of facets: 15 Number of non-simplicial facets: 9 Statistics for: rbox 500 s D3 t1633474215 | qhull R0.05 A-1 Tcv Qc Number of points processed: 22 Number of hyperplanes created: 80 Number of distance tests for qhull: 21841 Number of distance tests for merging: 1195 Number of distance tests for checking: 6639 Number of merged facets: 46 CPU seconds to compute hull (after input): 0.002355 Maximum distance of point above facet: 0.19 (0.3x) Maximum distance of vertex below facet: -0.31 (0.5x) Output completed. Verifying that all points are below outer planes of all facets. Will make 7500 distance computations. rbox 100 W0 D3 t | qhull R1e-3 Tcv Qc Convex hull of 100 points in 3-d: Number of vertices: 33 Number of coplanar points: 67 Number of facets: 43 Number of non-simplicial facets: 9 Statistics for: rbox 100 W0 D3 t1633474215 | qhull R1e-3 Tcv Qc Number of points processed: 41 Number of hyperplanes created: 142 Number of distance tests for qhull: 1818 Number of distance tests for merging: 1195 Number of distance tests for checking: 1231 Number of merged facets: 39 CPU seconds to compute hull (after input): 0.000943 Maximum distance of point above facet: 0.0016 (0.4x) Maximum distance of vertex below facet: -0.0049 (1.2x) Output completed. Verifying that all points are below outer planes of all facets. Will make 4300 distance computations. rbox 100 W0 D3 t | qhull R1e-3 Qx Tcv Qc Convex hull of 100 points in 3-d: Number of vertices: 33 Number of coplanar points: 67 Number of facets: 46 Number of non-simplicial facets: 7 Statistics for: rbox 100 W0 D3 t1633474215 | qhull R1e-3 Qx Tcv Qc Number of points processed: 39 Number of hyperplanes created: 132 Number of distance tests for qhull: 2652 Number of distance tests for merging: 1130 Number of distance tests for checking: 1029 Number of merged facets: 33 CPU seconds to compute hull (after input): 0.001245 Maximum distance of point above facet: 0.0014 (0.4x) Maximum distance of vertex below facet: -0.0017 (0.4x) QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 4600 distance computations. rbox 100 W0 D3 t | qhull R1e-2 Tcv Qc Convex hull of 100 points in 3-d: Number of vertices: 18 Number of coplanar points: 82 Number of facets: 17 Number of non-simplicial facets: 8 Statistics for: rbox 100 W0 D3 t1633474215 | qhull R1e-2 Tcv Qc Number of points processed: 24 Number of hyperplanes created: 75 Number of distance tests for qhull: 2218 Number of distance tests for merging: 888 Number of distance tests for checking: 1030 Number of merged facets: 34 CPU seconds to compute hull (after input): 0.000644 Maximum distance of point above facet: 0.023 (0.6x) Maximum distance of vertex below facet: -0.039 (1.0x) Output completed. Verifying that all points are below outer planes of all facets. Will make 1700 distance computations. rbox 100 W0 D3 t | qhull R1e-2 Qx Tcv Qc Convex hull of 100 points in 3-d: Number of vertices: 19 Number of coplanar points: 81 Number of facets: 20 Number of non-simplicial facets: 7 Statistics for: rbox 100 W0 D3 t1633474215 | qhull R1e-2 Qx Tcv Qc Number of points processed: 27 Number of hyperplanes created: 82 Number of distance tests for qhull: 2637 Number of distance tests for merging: 808 Number of distance tests for checking: 880 Number of merged facets: 34 CPU seconds to compute hull (after input): 0.000915 Maximum distance of point above facet: 0.02 (0.5x) Maximum distance of vertex below facet: -0.04 (1.0x) QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 2000 distance computations. rbox 500 W0 D3 t | qhull R0.05 A-1 Tcv Qc Convex hull of 500 points in 3-d: Number of vertices: 8 Number of coplanar points: 492 Number of facets: 6 Number of non-simplicial facets: 6 Statistics for: rbox 500 W0 D3 t1633474215 | qhull R0.05 A-1 Tcv Qc Number of points processed: 12 Number of hyperplanes created: 28 Number of distance tests for qhull: 11591 Number of distance tests for merging: 332 Number of distance tests for checking: 3509 Number of merged facets: 16 CPU seconds to compute hull (after input): 0.001153 Maximum distance of point above facet: 0.12 (0.2x) Maximum distance of vertex below facet: -0.17 (0.3x) Output completed. Verifying that all points are below outer planes of all facets. Will make 3000 distance computations. rbox 500 W0 D3 t | qhull R0.05 Qx Tcv Qc Convex hull of 500 points in 3-d: Number of vertices: 10 Number of coplanar points: 490 Number of facets: 7 Number of non-simplicial facets: 6 Statistics for: rbox 500 W0 D3 t1633474215 | qhull R0.05 Qx Tcv Qc Number of points processed: 18 Number of hyperplanes created: 40 Number of distance tests for qhull: 17515 Number of distance tests for merging: 591 Number of distance tests for checking: 3774 Number of merged facets: 29 CPU seconds to compute hull (after input): 0.001718 Maximum distance of point above facet: 0.12 (0.6x) Maximum distance of vertex below facet: -0.15 (0.8x) QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 3500 distance computations. rbox 1000 W1e-20 t | qhull Tcv Qc Convex hull of 1000 points in 3-d: Number of vertices: 82 Number of coplanar points: 918 Number of facets: 96 Number of non-simplicial facets: 6 Statistics for: rbox 1000 W1e-20 t1633474215 | qhull Tcv Qc Number of points processed: 98 Number of hyperplanes created: 301 Number of distance tests for qhull: 18447 Number of distance tests for merging: 3120 Number of distance tests for checking: 16854 Number of merged facets: 96 CPU seconds to compute hull (after input): 0.005527 Output completed. Verifying that all points are below outer planes of all facets. Will make 96000 distance computations. rbox 1000 W1e-20 D4 t | qhull Tcv Qc Convex hull of 1000 points in 4-d: Number of vertices: 273 Number of coplanar points: 727 Number of facets: 987 Number of non-simplicial facets: 8 Statistics for: rbox 1000 W1e-20 D4 t1633474215 | qhull Tcv Qc Number of points processed: 353 Number of hyperplanes created: 4647 Number of distance tests for qhull: 76781 Number of distance tests for merging: 54085 Number of distance tests for checking: 85395 Number of merged facets: 1065 CPU seconds to compute hull (after input): 0.1675 Output completed. Verifying that all points are below outer planes of all facets. Will make 987000 distance computations. rbox 500 W1e-20 D5 t | qhull Tv Qc Convex hull of 500 points in 5-d: Number of vertices: 344 Number of coplanar points: 156 Number of facets: 5472 Number of non-simplicial facets: 10 Statistics for: rbox 500 W1e-20 D5 t1633474215 | qhull Tv Qc Number of points processed: 402 Number of hyperplanes created: 26920 Number of distance tests for qhull: 124617 Number of distance tests for merging: 295919 Number of distance tests for checking: 119048 Number of merged facets: 3434 CPU seconds to compute hull (after input): 0.08302 QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 2736000 distance computations. rbox 100 W1e-20 D6 t | qhull Tv Qc Convex hull of 100 points in 6-d: Number of vertices: 100 Number of facets: 5785 Number of non-simplicial facets: 9 Statistics for: rbox 100 W1e-20 D6 t1633474215 | qhull Tv Qc Number of points processed: 100 Number of hyperplanes created: 21096 Number of distance tests for qhull: 33371 Number of distance tests for merging: 196616 Number of distance tests for checking: 60546 Number of merged facets: 204 CPU seconds to compute hull (after input): 0.04591 QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 578500 distance computations. rbox 50 W1e-20 D6 t | qhull Qv Tv Qc Convex hull of 50 points in 6-d: Number of vertices: 50 Number of facets: 2122 Number of non-simplicial facets: 2 Statistics for: rbox 50 W1e-20 D6 t1633474215 | qhull Qv Tv Qc Number of points processed: 50 Number of hyperplanes created: 6401 Number of distance tests for qhull: 9416 Number of distance tests for merging: 3590025 Number of distance tests for checking: 21644 Number of merged facets: 7 CPU seconds to compute hull (after input): 0.1451 QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 106100 distance computations. rbox 10000 D4 t | qhull QR0 Qc C-0.01 A0.3 Tv Convex hull of 10000 points in 4-d: Number of vertices: 16 Number of coplanar points: 7896 Number of facets: 8 Number of non-simplicial facets: 8 Statistics for: rbox 10000 D4 t1633474215 | qhull QR0 Qc C-0.01 A0.3 Tv QR1633474215 Number of points processed: 59 Number of hyperplanes created: 378 Number of distance tests for qhull: 1577562 Number of distance tests for merging: 32009 Number of distance tests for checking: 89602 Number of merged facets: 461 CPU seconds to compute hull (after input): 0.06913 Maximum distance of point above facet: 0.058 Maximum distance of vertex below facet: -0.15 Output completed. Verifying that all points are below outer planes of all facets. Will make 80000 distance computations. rbox 1000 D2 t | qhull d QR0 Qc C-1e-8 Qu Tv Furthest-site Delaunay triangulation by the convex hull of 1000 points in 3-d: Number of input sites: 1000 Number of Delaunay regions: 14 Statistics for: rbox 1000 D2 t1633474215 | qhull d QR0 Qc C-1e-8 Qu Tv QR1633474215 Number of points processed: 1000 Number of hyperplanes created: 5506 Number of facets in hull: 1996 Number of distance tests for qhull: 30457 CPU seconds to compute hull (after input): 0.006181 Output completed. Verifying that all points are below outer planes of all facets. Will make 14000 distance computations. rbox 300 D5 t |qhull A-0.999 Qx Qc Tcv Convex hull of 300 points in 5-d: Number of vertices: 157 Number of coplanar points: 41 Number of facets: 1717 Number of non-simplicial facets: 457 Statistics for: rbox 300 D5 t1633474216 | qhull A-0.999 Qx Qc Tcv Number of points processed: 192 Number of hyperplanes created: 11638 Number of distance tests for qhull: 175194 Number of distance tests for merging: 62253 Number of distance tests for checking: 31050 Number of merged facets: 1251 CPU seconds to compute hull (after input): 0.04425 Maximum distance of vertex below facet: -0.026 (0.3x) QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 515100 distance computations. rbox 100 D6 t |qhull A-0.9999 Qx Qc Tcv Convex hull of 100 points in 6-d: Number of vertices: 89 Number of facets: 3794 Number of non-simplicial facets: 235 Statistics for: rbox 100 D6 t1633474216 | qhull A-0.9999 Qx Qc Tcv Number of points processed: 91 Number of hyperplanes created: 13507 Number of distance tests for qhull: 32101 Number of distance tests for merging: 61922 Number of distance tests for checking: 64878 Number of merged facets: 596 CPU seconds to compute hull (after input): 0.06071 Maximum distance of vertex below facet: -0.0082 (0.2x) QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 379400 distance computations. rbox 50 D7 t |qhull A-0.99999 Qx Qc Tcv W0.1 Convex hull of 50 points in 7-d: Number of vertices: 47 Number of coplanar points: 2 Number of facets: 4597 Number of non-simplicial facets: 68 Statistics for: rbox 50 D7 t1633474216 | qhull A-0.99999 Qx Qc Tcv W0.1 Number of points processed: 48 Number of hyperplanes created: 15364 Number of distance tests for qhull: 30167 Number of distance tests for merging: 62443 Number of distance tests for checking: 220327 Number of merged facets: 205 CPU seconds to compute hull (after input): 0.05725 Maximum distance of point above facet: 0.12 Maximum distance of vertex below facet: -0.0022 (0.2x) QH7076 qhull input warning: exact merge ('Qx'). Verify may report that a point is outside of a facet. See qh-optq.htm#Qx Output completed. Verifying that all points are below outer planes of all facets. Will make 229850 distance computations. set +v ======================================================= === The following commands may cause errors Tue Oct 5 22:50:16 UTC 2021 ======================================================= === check bad cases for Qhull Tue Oct 5 22:50:16 UTC 2021 rbox 1000 L100000 s G1e-6 t | qhull Tv QH7089 qhull precision warning: The initial hull is narrow. Is the input lower dimensional (e.g., a square in 3-d instead of a cube)? Cosine of the minimum angle is 1.0000000000000000. If so, Qhull may produce a wide facet. Options 'Qs' (search all points), 'Qbb' (scale last coordinate), or 'QbB' (scale to unit box) may remove this warning. See 'Limitations' in qh-impre.htm. Use 'Pp' to skip this warning. Convex hull of 1000 points in 3-d: Number of vertices: 997 Number of facets: 1521 Number of non-simplicial facets: 2 Statistics for: rbox 1000 L100000 s G1e-6 t1633474216 | qhull Tv Number of points processed: 998 Number of hyperplanes created: 3464 Number of distance tests for qhull: 29009 Number of distance tests for merging: 133185 Number of distance tests for checking: 122167 Number of merged facets: 469 CPU seconds to compute hull (after input): 0.02155 Output completed. Verifying that all points are below outer planes of all facets. Will make 1521000 distance computations. rbox 1000 L100000 s G1e-6 t | qhull Tv Q10 Convex hull of 1000 points in 3-d: Number of vertices: 997 Number of facets: 1521 Number of non-simplicial facets: 2 Statistics for: rbox 1000 L100000 s G1e-6 t1633474216 | qhull Tv Q10 Number of points processed: 998 Number of hyperplanes created: 3464 Number of distance tests for qhull: 29008 Number of distance tests for merging: 133185 Number of distance tests for checking: 122167 Number of merged facets: 469 CPU seconds to compute hull (after input): 0.01603 Output completed. Verifying that all points are below outer planes of all facets. Will make 1521000 distance computations. rbox 1000 s Z1 G1e-13 t | qhull Tv Convex hull of 1001 points in 3-d: Number of vertices: 1001 Number of facets: 1468 Number of non-simplicial facets: 160 Statistics for: rbox 1000 s Z1 G1e-13 t1633474216 | qhull Tv Number of points processed: 1001 Number of hyperplanes created: 4087 Number of distance tests for qhull: 26969 Number of distance tests for merging: 77999 Number of distance tests for checking: 260636 Number of merged facets: 1322 CPU seconds to compute hull (after input): 0.02466 Maximum distance of point above facet: 1.3e-14 (2.3x) Maximum distance of vertex below facet: -1.4e-14 (2.4x) Output completed. Verifying that all points are below outer planes of all facets. Will make 1469468 distance computations. rbox 1000 s W1e-13 P0 t | qhull d Qbb Qc Q12 Tv Delaunay triangulation by the convex hull of 1001 points in 4-d: Number of input sites: 1001 Number of Delaunay regions: 1996 Statistics for: rbox 1000 s W1e-13 P0 t1633474216 | qhull d Qbb Qc Q12 Tv Number of points processed: 1001 Number of hyperplanes created: 114743 Number of facets in hull: 2009 Number of distance tests for qhull: 183566 Number of distance tests for merging: 11819955 Number of distance tests for checking: 2006560 Number of merged facets: 108306 CPU seconds to compute hull (after input): 1.467 Maximum distance of point above facet: 1e-12 (99.0x) Maximum distance of vertex below facet: -1.9e-13 (18.5x) Output completed. Verifying that all points are below outer planes of all facets. Will make 1997996 distance computations. rbox 1000 s W1e-13 t | qhull d Q12 Tv QH7089 qhull precision warning: The initial hull is narrow. Is the input lower dimensional (e.g., a square in 3-d instead of a cube)? Cosine of the minimum angle is 1.0000000000000000. If so, Qhull may produce a wide facet. Options 'Qs' (search all points), 'Qbb' (scale last coordinate), or 'QbB' (scale to unit box) may remove this warning. See 'Limitations' in qh-impre.htm. Use 'Pp' to skip this warning. QH6170 qhull topology error (qh_partitionvisible): all new facets deleted as degenerate facets. Can not continue. While executing: rbox 1000 s W1e-13 t1633474217 | qhull d Q12 Tv Options selected for Qhull 2020.2.r 2020/08/31: run-id 370221871 delaunay Q12-allow-wide Tverify _pre-merge _zero-centrum Pgood _max-width 1 Error-roundoff 1e-15 _one-merge 9.1e-15 _near-inside 4.5e-14 Visible-distance 6e-15 U-max-coplanar 6e-15 Width-outside 1.2e-14 _wide-facet 3.6e-14 _narrow-hull 0 _maxoutside 2.5e-13 Last point added to hull was p495. Last merge was #2640. At error exit: Delaunay triangulation by the convex hull of 1000 points in 4-d: Number of input sites: 22 Total number of deleted points due to merging: 231 Number of nearly incident points: 530 Number of Delaunay regions: 13 Number of non-simplicial Delaunay regions: 5 Statistics for: rbox 1000 s W1e-13 t1633474217 | qhull d Q12 Tv Number of points processed: 261 Number of hyperplanes created: 3252 Number of facets in hull: 27 Number of distance tests for qhull: 969986 Number of distance tests for merging: 278696 Number of distance tests for checking: 0 Number of merged facets: 2735 Maximum distance of point above facet: 2.5e-13 (24.9x) Maximum distance of vertex below facet: -3.8e-12 (378.8x) precision problems (corrected unless 'Q0' or an error) 246 flipped facets 477 coplanar horizon facets for new vertices 530 coplanar points during partitioning 8 dupridges with flip facet into good neighbor A Qhull topology error has occurred. Qhull did not recover from facet merges and vertex merges. This usually occurs when the input is nearly degenerate and substantial merging has occurred. See http://www.qhull.org/html/qh-impre.htm#limit rbox 1000 s W1e-13 t D2 | qhull d Tv QH7089 qhull precision warning: The initial hull is narrow. Is the input lower dimensional (e.g., a square in 3-d instead of a cube)? Cosine of the minimum angle is 1.0000000000000000. If so, Qhull may produce a wide facet. Options 'Qs' (search all points), 'Qbb' (scale last coordinate), or 'QbB' (scale to unit box) may remove this warning. See 'Limitations' in qh-impre.htm. Use 'Pp' to skip this warning. Delaunay triangulation by the convex hull of 1000 points in 3-d: Number of input sites: 969 Total number of deleted points due to merging: 6 Total number of nearly incident points: 25 Number of Delaunay regions: 723 Number of non-simplicial Delaunay regions: 135 Statistics for: rbox 1000 s W1e-13 D2 t1633474218 | qhull d Tv Number of points processed: 975 Number of hyperplanes created: 4138 Number of facets in hull: 1420 Number of distance tests for qhull: 88933 Number of distance tests for merging: 45869 Number of distance tests for checking: 175101 Number of merged facets: 1015 CPU seconds to compute hull (after input): 0.01748 Maximum distance of point above facet: 1.2e-13 (22.3x) Maximum distance of vertex below facet: -1.9e-14 (3.5x) Output completed. Verifying that all points are below outer planes of all facets. Will make 723000 distance computations. set +v === check Qhull without merging Q0 Tue Oct 5 22:50:18 UTC 2021 rbox c D7 | qhull Q0 Tcv Convex hull of 128 points in 7-d: Number of vertices: 128 Number of facets: 8666 Statistics for: rbox c D7 | qhull Q0 Tcv Number of points processed: 128 Number of hyperplanes created: 12287 Number of distance tests for qhull: 26353 CPU seconds to compute hull (after input): 0.0231 precision problems (corrected unless 'Q0' or an error) 41888 coplanar half ridges in output 10185 coplanar horizon facets for new vertices 8389 nearly singular or axis-parallel hyperplanes 8389 zero divisors during back substitute 11903 zero divisors during gaussian elimination qhull output completed. Verifying that 128 points are below 6.6e-15 of the nearest facet. rbox 100 s D3 | qhull Q0 E1e-3 Tc Po QH6115 qhull precision error: f100 is concave to f247, since p44(v13) is 0.002232 above f247 QH6115 qhull precision error: f139 is concave to f274, since p90(v32) is 0.007128 above f274 QH6115 qhull precision error: f163 is concave to f232, since p5(v6) is 0.001226 above f232 QH6115 qhull precision error: f293 is concave to f389, since p11(v61) is 0.002161 above f389 QH6115 qhull precision error: f307 is concave to f459, since p75(v21) is 0.01537 above f459 Convex hull of 100 points in 3-d: Number of vertices: 100 Number of facets: 196 Statistics for: rbox 100 s D3 | qhull Q0 E1e-3 Tc Po Number of points processed: 100 Number of hyperplanes created: 508 Number of distance tests for qhull: 1727 CPU seconds to compute hull (after input): 0.004556 precision problems (corrected unless 'Q0' or an error) 16 coplanar half ridges in output 5 concave half ridges in output 18 coplanar horizon facets for new vertices rbox 100 s D3 | qhull Q0 E1e-2 Tc Po QH6115 qhull precision error: f123 is concave to f235, since p85(v8) is 0.06092 above f235 QH6115 qhull precision error: f177 is concave to f272, since p98(v20) is 0.03571 above f272 QH6115 qhull precision error: f246 is concave to f252, since p7(v57) is 0.02104 above f252 QH6115 qhull precision error: f261 is concave to f305, since p82(v60) is 0.01847 above f305 QH6115 qhull precision error: f266 is concave to f317, since p82(v60) is 0.02592 above f317 Convex hull of 100 points in 3-d: Number of vertices: 72 Number of facets: 140 Statistics for: rbox 100 s D3 | qhull Q0 E1e-2 Tc Po Number of points processed: 72 Number of hyperplanes created: 321 Number of distance tests for qhull: 1664 CPU seconds to compute hull (after input): 0.002499 precision problems (corrected unless 'Q0' or an error) 52 coplanar half ridges in output 5 concave half ridges in output 54 coplanar horizon facets for new vertices 27 coplanar points during partitioning rbox 100 s D3 | qhull Q0 E1e-1 Tc Po Convex hull of 100 points in 3-d: Number of vertices: 10 Number of facets: 16 Statistics for: rbox 100 s D3 | qhull Q0 E1e-1 Tc Po Number of points processed: 10 Number of hyperplanes created: 27 Number of distance tests for qhull: 917 CPU seconds to compute hull (after input): 0.000203 precision problems (corrected unless 'Q0' or an error) 3 coplanar half ridges in output 3 coplanar horizon facets for new vertices 59 coplanar points during partitioning rbox 100 s D3 | qhull Q0 R1e-3 Tc Po QH6115 qhull precision error: f94 is concave to f270, since p44(v13) is 0.003303 above f270 QH6115 qhull precision error: f157 is concave to f255, since p5(v6) is 0.005886 above f255 QH6115 qhull precision error: f289 is concave to f386, since p30(v62) is 0.000726 above f386 QH6115 qhull precision error: f381 is concave to f293, since p56(v79) is 0.0006018 above f293 Convex hull of 100 points in 3-d: Number of vertices: 100 Number of facets: 196 Statistics for: rbox 100 s D3 | qhull Q0 R1e-3 Tc Po Number of points processed: 100 Number of hyperplanes created: 498 Number of distance tests for qhull: 1643 CPU seconds to compute hull (after input): 0.004703 precision problems (corrected unless 'Q0' or an error) 10 coplanar half ridges in output 4 concave half ridges in output 10 coplanar horizon facets for new vertices rbox 100 s D3 | qhull Q0 R1e-2 Tc Po QH6115 qhull precision error: f78 is concave to f147, since p57(v1) is 0.01085 above f147 QH6115 qhull precision error: f89 is concave to f194, since p17(v2) is 0.0111 above f194 QH6115 qhull precision error: f106 is concave to f122, since p74(v27) is 0.01501 above f122 QH6115 qhull precision error: f122 is concave to f106, since p95(v30) is 0.00822 above f106 QH6115 qhull precision error: f126 is concave to f213, since p95(v30) is 0.007437 above f213 QH6115 qhull precision error: f141 is concave to f288, since p81(v34) is 0.007157 above f288 QH6115 qhull precision error: f147 is concave to f227, since p90(v19) is 0.1078 above f227 QH6115 qhull precision error: f161 is concave to f252, since p20(v24) is 0.008976 above f252 QH6115 qhull precision error: f176 is concave to f277, since p38(v22) is 0.008285 above f277 QH6115 qhull precision error: f181 is concave to f276, since p73(v12) is 0.02209 above f276 QH6115 qhull precision error: f186 is concave to f291, since p85(v8) is 0.04316 above f291 QH6115 qhull precision error: f194 is concave to f89, since p82(v45) is 0.009743 above f89 QH6115 qhull precision error: f198 is concave to f273, since p82(v45) is 0.01834 above f273 QH6115 qhull precision error: f213 is concave to f126, since p93(v48) is 0.01071 above f126 QH6115 qhull precision error: f227 is concave to f147, since p37(v51) is 0.007006 above f147 QH6115 qhull precision error: f273 is concave to f198, since p29(v60) is 0.006128 above f198 QH6115 qhull precision error: f288 is concave to f141, since p96(v63) is 0.005493 above f141 QH6115 qhull precision error: f291 is concave to f186, since p34(v64) is 0.008643 above f186 QH6115 qhull precision error: f300 is concave to f355, since p30(v66) is 0.006345 above f355 QH6115 qhull precision error: f324 is concave to f384, since p75(v20) is 0.02388 above f384 QH6115 qhull precision error: f361 is concave to f406, since p41(v5) is 0.009438 above f406 QH6115 qhull precision error: f368 is concave to f367, since p11(v69) is 0.007227 above f367 QH6115 qhull precision error: f390 is concave to f391, since p99(v73) is 0.007279 above f391 QH6115 qhull precision error: f391 is concave to f390, since p43(v74) is 0.01052 above f390 Convex hull of 100 points in 3-d: Number of vertices: 88 Number of facets: 172 Statistics for: rbox 100 s D3 | qhull Q0 R1e-2 Tc Po Number of points processed: 88 Number of hyperplanes created: 413 Number of distance tests for qhull: 1702 CPU seconds to compute hull (after input): 0.003775 precision problems (corrected unless 'Q0' or an error) 49 coplanar half ridges in output 24 concave half ridges in output 53 coplanar horizon facets for new vertices 12 coplanar points during partitioning rbox 100 s D3 | qhull Q0 R0.05 Tc QH6136 qhull precision error: facet f193 is flipped, distance= 0.391655882694 ERRONEOUS FACET: - f193 - flags: top simplicial flipped - normal: -0.2813 -0.9389 0.1981 - offset: 0.2910058 - vertices: p19(v46) p65(v35) p74(v28) - neighboring facets: f183 f194 f195 A flipped facet occurs when its distance to the interior point is greater than or equal to -0.024, the maximum roundoff error. While executing: rbox 100 s D3 | qhull Q0 R0.05 Tc Options selected for Qhull 2020.2.r 2020/08/31: run-id 370238678 Q0-no-premerge Random-perturb 0.05 Tcheck-frequently _max-width 0.94 Error-roundoff 0.024 Visible-distance 0.024 U-max-coplanar 0.024 Width-outside 0.048 _wide-facet 0.15 _maxoutside 0.19 Last point added to hull was p19. Qhull has finished constructing the hull. At error exit: Convex hull of 100 points in 3-d: Number of vertices: 46 Number of facets: 88 Statistics for: rbox 100 s D3 | qhull Q0 R0.05 Tc Number of points processed: 46 Number of hyperplanes created: 196 Number of distance tests for qhull: 2023 CPU seconds to compute hull (after input): 0.00139 precision problems (corrected unless 'Q0' or an error) 1 flipped facets 34 coplanar horizon facets for new vertices 51 coplanar points during partitioning Precision problems were detected during construction of the convex hull. This occurs because convex hull algorithms assume that calculations are exact, but floating-point arithmetic has roundoff errors. To correct for precision problems, do not use 'Q0'. By default, Qhull selects 'C-0' or 'Qx' and merges non-convex facets. With option 'QJ', Qhull joggles the input to prevent precision problems. See "Imprecision in Qhull" (qh-impre.htm). If you use 'Q0', the output may include coplanar ridges, concave ridges, and flipped facets. In 4-d and higher, Qhull may produce a ridge with four neighbors or two facets with the same vertices. Qhull reports these events when they occur. It stops when a concave ridge, flipped facet, or duplicate facet occurs. If you need triangular output: - use option 'Qt' to triangulate the output - use option 'QJ' to joggle the input points and remove precision errors - use option 'Ft'. It triangulates non-simplicial facets with added points. If you must use 'Q0', try one or more of the following options. They can not guarantee an output. - use 'QbB' to scale the input to a cube. - use 'Po' to produce output and prevent partitioning for flipped facets - use 'V0' to set min. distance to visible facet as 0 instead of roundoff - use 'En' to specify a maximum roundoff error less than 0.024. - options 'Qf', 'Qbb', and 'QR0' may also help To guarantee simplicial output: - use option 'Qt' to triangulate the output - use option 'QJ' to joggle the input points and remove precision errors - use option 'Ft' to triangulate the output by adding points - use exact arithmetic (see "Imprecision in Qhull", qh-impre.htm) rbox 100 s D3 | qhull Q0 R0.05 Tc Po QH6136 qhull precision error: facet f193 is flipped, distance= 0.391655882694 QH6115 qhull precision error: f119 is concave to f134, since p31(v31) is 0.05178 above f134 QH6115 qhull precision error: f124 is concave to f131, since p5(v6) is 0.1065 above f131 QH6115 qhull precision error: f147 is concave to f91, since p69(v36) is 0.0354 above f91 QH6113 qhull precision error: f193 is flipped (interior point is outside) Convex hull of 100 points in 3-d: Number of vertices: 46 Number of facets: 88 Statistics for: rbox 100 s D3 | qhull Q0 R0.05 Tc Po Number of points processed: 46 Number of hyperplanes created: 196 Number of distance tests for qhull: 2023 CPU seconds to compute hull (after input): 0.001312 precision problems (corrected unless 'Q0' or an error) 35 coplanar half ridges in output 3 concave half ridges in output 1 flipped facets 34 coplanar horizon facets for new vertices 51 coplanar points during partitioning rbox 1000 W1e-7 | qhull Q0 Tc Po Convex hull of 1000 points in 3-d: Number of vertices: 164 Number of facets: 324 Statistics for: rbox 1000 W1e-7 | qhull Q0 Tc Po Number of points processed: 221 Number of hyperplanes created: 1160 Number of distance tests for qhull: 22590 CPU seconds to compute hull (after input): 0.01839 rbox 50 s | qhull Q0 V0.05 W0.01 Tc Po QH7088 Qhull precision warning: in post-processing (qh_check_maxout) p0 for f36 is 0.061 above hidden facet f70 nearest vertices 0.15 QH7088 Qhull precision warning: in post-processing (qh_check_maxout) p8 for f38 is 0.26 above hidden facet f145 nearest vertices 0.14 QH6297 Qhull precision error (qh_check_maxout): large increase in qh.max_outside during post-processing dist 0.26 (46669910714866.6x). See warning QH0032/QH0033. Allow with 'Q12' (allow-wide) and 'Pp' ERRONEOUS FACET: - f145 - flags: top simplicial - normal: -0.6276 0.1677 -0.7602 - offset: -0.2196772 - maxoutside: 0.2588526 - vertices: p2(v43) p0(v13) p24(v6) - neighboring facets: f39 f146 f147 ERRONEOUS and NEIGHBORING FACETS to output While executing: rbox 50 s | qhull Q0 V0.05 W0.01 Tc Po Options selected for Qhull 2020.2.r 2020/08/31: run-id 370238678 Q0-no-premerge Visible 0.05 W-outside 0.01 Tcheck-frequently Poutput-forced _max-width 0.98 Error-roundoff 6.9e-16 _near-inside 2.4e-14 U-max-coplanar 0.05 _wide-facet 0.3 _maxoutside 0.01 Last point added to hull was p10. At error exit: Convex hull of 50 points in 3-d: Number of vertices: 50 Number of facets: 96 Statistics for: rbox 50 s | qhull Q0 V0.05 W0.01 Tc Po Number of points processed: 50 Number of hyperplanes created: 171 Number of distance tests for qhull: 538 precision problems (corrected unless 'Q0' or an error) 7 flipped facets 82 coplanar horizon facets for new vertices Precision problems were detected during construction of the convex hull. This occurs because convex hull algorithms assume that calculations are exact, but floating-point arithmetic has roundoff errors. To correct for precision problems, do not use 'Q0'. By default, Qhull selects 'C-0' or 'Qx' and merges non-convex facets. With option 'QJ', Qhull joggles the input to prevent precision problems. See "Imprecision in Qhull" (qh-impre.htm). If you use 'Q0', the output may include coplanar ridges, concave ridges, and flipped facets. In 4-d and higher, Qhull may produce a ridge with four neighbors or two facets with the same vertices. Qhull reports these events when they occur. It stops when a concave ridge, flipped facet, or duplicate facet occurs. If you need triangular output: - use option 'Qt' to triangulate the output - use option 'QJ' to joggle the input points and remove precision errors - use option 'Ft'. It triangulates non-simplicial facets with added points. If you must use 'Q0', try one or more of the following options. They can not guarantee an output. - use 'QbB' to scale the input to a cube. - use 'Po' to produce output and prevent partitioning for flipped facets - use 'V0' to set min. distance to visible facet as 0 instead of roundoff - use 'En' to specify a maximum roundoff error less than 6.9e-16. - options 'Qf', 'Qbb', and 'QR0' may also help To guarantee simplicial output: - use option 'Qt' to triangulate the output - use option 'QJ' to joggle the input points and remove precision errors - use option 'Ft' to triangulate the output by adding points - use exact arithmetic (see "Imprecision in Qhull", qh-impre.htm) rbox 100 s D5 | qhull Q0 R1e-2 Tc Po QH6107 qhull topology error: facets f721, f756 and f722 meet at a ridge with more than 2 neighbors. Can not continue due to no qh.PREmerge and no 'Qx' (MERGEexact) ERRONEOUS FACET: - f721 - flags: bottom simplicial newfacet - offset: 0 - vertices: p84(v29) p2(v19) p58(v12) p3(v7) p9(v2) - neighboring facets: f362 f720 f728 f722 f740 ERRONEOUS OTHER FACET: - f756 - flags: top simplicial newfacet - offset: 0 - vertices: p84(v29) p40(v26) p2(v19) p58(v12) p9(v2) - neighboring facets: f566 ERRONEOUS and NEIGHBORING FACETS to output While executing: rbox 100 s D5 | qhull Q0 R1e-2 Tc Po Options selected for Qhull 2020.2.r 2020/08/31: run-id 370238678 Q0-no-premerge Random-perturb 0.01 Tcheck-frequently Poutput-forced _max-width 0.88 Error-roundoff 0.0045 Visible-distance 0.0045 U-max-coplanar 0.0045 Width-outside 0.009 _wide-facet 0.027 _maxoutside 0.054 Last point added to hull was p84. Convex hull of 100 points in 5-d: Number of vertices: 29 Number of facets: 340 Statistics for: rbox 100 s D5 | qhull Q0 R1e-2 Tc Po Number of points processed: 28 Number of hyperplanes created: 720 Number of distance tests for qhull: 2275 precision problems (corrected unless 'Q0' or an error) 1 flipped facets 24 coplanar horizon facets for new vertices Precision problems were detected during construction of the convex hull. This occurs because convex hull algorithms assume that calculations are exact, but floating-point arithmetic has roundoff errors. To correct for precision problems, do not use 'Q0'. By default, Qhull selects 'C-0' or 'Qx' and merges non-convex facets. With option 'QJ', Qhull joggles the input to prevent precision problems. See "Imprecision in Qhull" (qh-impre.htm). If you use 'Q0', the output may include coplanar ridges, concave ridges, and flipped facets. In 4-d and higher, Qhull may produce a ridge with four neighbors or two facets with the same vertices. Qhull reports these events when they occur. It stops when a concave ridge, flipped facet, or duplicate facet occurs. If you need triangular output: - use option 'Qt' to triangulate the output - use option 'QJ' to joggle the input points and remove precision errors - use option 'Ft'. It triangulates non-simplicial facets with added points. If you must use 'Q0', try one or more of the following options. They can not guarantee an output. - use 'QbB' to scale the input to a cube. - use 'Po' to produce output and prevent partitioning for flipped facets - use 'V0' to set min. distance to visible facet as 0 instead of roundoff - use 'En' to specify a maximum roundoff error less than 0.0045. - options 'Qf', 'Qbb', and 'QR0' may also help To guarantee simplicial output: - use option 'Qt' to triangulate the output - use option 'QJ' to joggle the input points and remove precision errors - use option 'Ft' to triangulate the output by adding points - use exact arithmetic (see "Imprecision in Qhull", qh-impre.htm) set +v === check nearly incident points Tue Oct 5 22:50:18 UTC 2021 rbox L100 2000 D4 s C1,1e-13 t2 | qhull Convex hull of 4000 points in 4-d: Number of vertices: 2096 Number of facets: 13614 Number of non-simplicial facets: 52 Statistics for: rbox L100 2000 D4 s C1,1e-13 t2 | qhull Number of points processed: 2111 Number of hyperplanes created: 51581 Number of distance tests for qhull: 585497 Number of distance tests for merging: 267217 Number of distance tests for checking: 152193 Number of merged facets: 129 CPU seconds to compute hull (after input): 0.1188 Maximum distance of point above facet: 1.8e-14 (1.9x) Maximum distance of vertex below facet: -8.9e-15 (0.9x) rbox L100 2000 D4 s C1,1e-13 t2 | qhull Q12 Convex hull of 4000 points in 4-d: Number of vertices: 2096 Number of facets: 13614 Number of non-simplicial facets: 52 Statistics for: rbox L100 2000 D4 s C1,1e-13 t2 | qhull Q12 Number of points processed: 2111 Number of hyperplanes created: 51581 Number of distance tests for qhull: 585497 Number of distance tests for merging: 267217 Number of distance tests for checking: 152193 Number of merged facets: 129 CPU seconds to compute hull (after input): 0.08867 Maximum distance of point above facet: 1.8e-14 (1.9x) Maximum distance of vertex below facet: -8.9e-15 (0.9x) rbox 50 C1,1E-13 t1447644703 | qhull d QH6271 qhull topology error (qh_check_dupridge): wide merge (1125070907263.1x wider) due to dupridge between f1143 and f1169 (vertex dist 6.5e-14), merge dist 0.015, while processing p54 - Allow error with option 'Q12' - Experimental option merge-pinched-vertices ('Q14') may avoid this error. It merges nearly adjacent vertices. - A bounding box for the input sites may alleviate this error. ERRONEOUS FACET: - f1143 - flags: bottom upperDelaunay newfacet dupridge mergeridge2 flipped - normal: 0.2935 0.3842 0.4668 0.7405 - offset: 0.05514914 - vertices: p54(v76) p45(v56) p76(v36) p44(v19) - neighboring facets: f405 f1159 f1169 f1144 - ridges: - r576 tested simplicialbot vertices: p45(v56) p76(v36) p44(v19) between f405 and f1143 - r1072 simplicialtop simplicialbot vertices: p54(v76) p76(v36) p44(v19) between f1143 and f1159 - r1073 simplicialbot vertices: p54(v76) p45(v56) p44(v19) between f1169 and f1143 - r1074 simplicialtop simplicialbot vertices: p54(v76) p45(v56) p76(v36) between f1143 and f1144 ERRONEOUS OTHER FACET: - f1169 - flags: bottom upperDelaunay newfacet dupridge mergeridge1 flipped - normal: -0.3214 0.1166 0.5495 0.7623 - offset: 0.114967 - vertices: p54(v76) p45(v56) p44(v19) p92(v11) - neighboring facets: f405 f1159 f1170 f1143 - ridges: - r561 tested simplicialbot vertices: p45(v56) p44(v19) p92(v11) between f405 and f1169 - r1070 simplicialtop simplicialbot vertices: p54(v76) p44(v19) p92(v11) between f1169 and f1159 - r1071 simplicialtop simplicialbot vertices: p54(v76) p45(v56) p92(v11) between f1170 and f1169 - r1073 simplicialbot vertices: p54(v76) p45(v56) p44(v19) between f1169 and f1143 While executing: rbox 50 C1,1E-13 t1447644703 | qhull d Options selected for Qhull 2020.2.r 2020/08/31: run-id 370238678 delaunay _pre-merge _zero-centrum Pgood _max-width 0.94 Error-roundoff 1e-15 _one-merge 9.2e-15 _near-inside 4.6e-14 Visible-distance 6.1e-15 U-max-coplanar 6.1e-15 Width-outside 1.2e-14 _wide-facet 3.7e-14 _maxoutside 1.2e-14 Last point added to hull was p54. Last merge was #247. At error exit: Delaunay triangulation by the convex hull of 100 points in 4-d: Number of input sites: 76 Number of nearly incident points: 1 Number of Delaunay regions: 266 Number of non-simplicial Delaunay regions: 73 Statistics for: rbox 50 C1,1E-13 t1447644703 | qhull d Number of points processed: 76 Number of hyperplanes created: 1087 Number of facets in hull: 303 Number of distance tests for qhull: 5296 Number of distance tests for merging: 10632 Number of distance tests for checking: 0 Number of merged facets: 249 Maximum distance of point above facet: 1.3e-14 (1.3x) Maximum distance of vertex below facet: -1.3e-14 (1.3x) precision problems (corrected unless 'Q0' or an error) 4 flipped facets 73 coplanar horizon facets for new vertices 1 coplanar points during partitioning 213 degenerate hyperplanes recomputed with gaussian elimination 17 nearly singular or axis-parallel hyperplanes 1 dupridges with multiple neighbors A wide merge error has occurred. Qhull has produced a wide facet due to facet merges and vertex merges. This usually occurs when the input is nearly degenerate and substantial merging has occurred. See http://www.qhull.org/html/qh-impre.htm#limit rbox 50 C1,1E-13 t1447644703 | qhull d Q12 QH6271 qhull topology error (qh_check_dupridge): wide merge (1125070907263.1x wider) due to dupridge between f1143 and f1169 (vertex dist 6.5e-14), merge dist 0.015, while processing p54 - Allow error with option 'Q12' - Experimental option merge-pinched-vertices ('Q14') may avoid this error. It merges nearly adjacent vertices. - A bounding box for the input sites may alleviate this error. Delaunay triangulation by the convex hull of 100 points in 4-d: Number of input sites: 99 Total number of nearly incident points: 1 Number of Delaunay regions: 307 Number of non-simplicial Delaunay regions: 133 Statistics for: rbox 50 C1,1E-13 t1447644703 | qhull d Q12 Number of points processed: 99 Number of hyperplanes created: 1504 Number of facets in hull: 345 Number of distance tests for qhull: 7670 Number of distance tests for merging: 18282 Number of distance tests for checking: 7318 Number of merged facets: 456 CPU seconds to compute hull (after input): 0.008639 Maximum distance of point above facet: 1.3e-14 (1.3x) Maximum distance of vertex below facet: -0.0012 (119810840063.5x) rbox 50 C1,1E-13 t1447644703 | qhull d Q14 Delaunay triangulation by the convex hull of 100 points in 4-d: Number of input sites: 99 Total number of nearly incident points: 1 Number of Delaunay regions: 312 Number of non-simplicial Delaunay regions: 137 Statistics for: rbox 50 C1,1E-13 t1447644703 | qhull d Q14 Number of points processed: 99 Number of hyperplanes created: 1487 Number of facets in hull: 350 Number of distance tests for qhull: 5360 Number of distance tests for merging: 17768 Number of distance tests for checking: 4953 Number of merged facets: 513 CPU seconds to compute hull (after input): 0.003994 Maximum distance of point above facet: 1.3e-14 (1.3x) Maximum distance of vertex below facet: -1.4e-14 (1.4x) set +v ======================================================= === Testing done. Print documentation ======================================================= qhull - qhull -- compute convex hulls and related structures. http://www.qhull.org 2020.2.r 2020/08/31 input (stdin): first lines: dimension and number of points (or vice-versa). other lines: point coordinates, best if one point per line comments: start with a non-numeric character halfspaces: use dim plus one and put offset after coefficients. May be preceded by a single interior point ('H'). options: d - Delaunay triangulation by lifting points to a paraboloid d Qu - furthest-site Delaunay triangulation (upper convex hull) Hn,n,... - halfspace intersection about point [n,n,0,...] Qc - keep coplanar points with nearest facet Qi - keep interior points with nearest facet QJ - joggled input instead of merged facets Qt - triangulated output v - Voronoi diagram (dual of the Delaunay triangulation) v Qu - furthest-site Voronoi diagram Qhull control options: Qa - allow input with fewer or more points than coordinates Qbk:n - scale coord k so that low bound is n QBk:n - scale coord k so that upper bound is n (QBk is 0.5) QbB - scale input to unit cube centered at the origin Qbb - scale last coordinate to [0,m] for Delaunay triangulations Qbk:0Bk:0 - remove k-th coordinate from input QJn - randomly joggle input in range [-n,n] QRn - random rotation (n=seed, n=0 time, n=-1 time/no rotate) Qs - search all points for the initial simplex Qu - for 'd' or 'v', compute upper hull without point at-infinity returns furthest-site Delaunay triangulation QVn - good facet if it includes point n, -n if not Qx - exact pre-merges (skips coplanar and angle-coplanar facets) Qz - add point-at-infinity to Delaunay triangulation Qhull extra options: Qf - partition point to furthest outside facet Qg - only build good facets (needs 'QGn', 'QVn', or 'PdD') QGn - good facet if visible from point n, -n for not visible Qm - only process points that would increase max_outside Qr - process random outside points instead of furthest ones Qv - test vertex neighbors for convexity Qw - allow option warnings Q0 - turn off default premerge with 'C-0'/'Qx' Q1 - merge by mergetype/angle instead of mergetype/distance Q2 - merge all coplanar facets instead of merging independent sets Q3 - do not merge redundant vertices Q4 - avoid old->new merges Q5 - do not correct outer planes at end of qhull Q6 - do not pre-merge concave or coplanar facets Q7 - depth-first processing instead of breadth-first Q8 - do not process near-inside points Q9 - process furthest of furthest points Q10 - no special processing for narrow distributions Q11 - copy normals and recompute centrums for tricoplanar facets Q12 - allow wide facets and wide dupridge Q14 - merge pinched vertices that create a dupridge Q15 - check for duplicate ridges with the same vertices T options: TFn - report summary when n or more facets created TI file - input file, may be enclosed in single quotes TO file - output file, may be enclosed in single quotes Ts - statistics Tv - verify result: structure, convexity, and point inclusion Tz - send all output to stdout Trace options: T4 - trace at level n, 4=all, 5=mem/gauss, -1= events Ta - annotate output with message codes TAn - stop qhull after adding n vertices TCn - stop qhull after building cone for point n TVn - stop qhull after adding point n, -n for before Tc - check frequently during execution Tf - flush each qh_fprintf for debugging segfaults TPn - turn on tracing when point n added to hull TP-1 turn on tracing after qh_buildhull and qh_postmerge TMn - turn on tracing at merge n TWn - trace merge facets when width > n TRn - rerun qhull n times for statistics to adjust 'QJn' Precision options: Cn - radius of centrum (roundoff added). Merge facets if non-convex An - cosine of maximum angle. Merge facets if cosine > n or non-convex C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge En - max roundoff error for distance computation Rn - randomly perturb computations by a factor of [1-n,1+n] Vn - min distance above plane for a visible facet (default 3C-n or En) Un - max distance below plane for a new, coplanar point (default Vn) Wn - min facet width for outside point (before roundoff, default 2Vn) Output formats (may be combined; if none, produces a summary to stdout): f - facet dump G - Geomview output (see below) i - vertices incident to each facet m - Mathematica output (2-d and 3-d) n - normals with offsets o - OFF format (dim, points and facets; Voronoi regions) p - vertex coordinates or Voronoi vertices (coplanar points if 'Qc') s - summary (stderr) More formats: Fa - area for each facet FA - compute total area and volume for option 's' Fc - count plus coplanar points for each facet use 'Qc' (default) for coplanar and 'Qi' for interior FC - centrum or Voronoi center for each facet Fd - use cdd format for input (homogeneous with offset first) FD - use cdd format for numeric output (offset first) FF - facet dump without ridges Fi - inner plane for each facet for 'v', separating hyperplanes for bounded Voronoi regions FI - ID of each facet Fm - merge count for each facet (511 max) FM - Maple output (2-d and 3-d) Fn - count plus neighboring facets for each facet FN - count plus neighboring facets for each point Fo - outer plane (or max_outside) for each facet for 'v', separating hyperplanes for unbounded Voronoi regions FO - options and precision constants Fp - dim, count, and intersection coordinates (halfspace only) FP - nearest vertex and distance for each coplanar point FQ - command used for qhull Fs - summary: #int (8), dimension, #points, tot vertices, tot facets, output: #vertices, #facets, #coplanars, #nonsimplicial #real (2), max outer plane, min vertex FS - sizes: #int (0) #real (2) tot area, tot volume Ft - triangulation with centrums for non-simplicial facets (OFF format) Fv - count plus vertices for each facet for 'v', Voronoi diagram as Voronoi vertices for pairs of sites FV - average of vertices (a feasible point for 'H') Fx - extreme points (in order for 2-d) Geomview output (2-d, 3-d, and 4-d; 2-d Voronoi) Ga - all points as dots Gp - coplanar points and vertices as radii Gv - vertices as spheres Gc - centrums GDn - drop dimension n in 3-d and 4-d output Gh - hyperplane intersections Gi - inner planes only Gn - no planes Go - outer planes only Gr - ridges Gt - for 3-d 'd', transparent outer ridges Print options: PAn - keep n largest facets by area Pdk:n - drop facet if normal[k] <= n (default 0.0) PDk:n - drop facet if normal[k] >= n PFn - keep facets whose area is at least n Pg - print good facets (needs 'QGn' or 'QVn') 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 -? - help with examples -V - version rbox rbox -- generate various point distributions. Default is random in cube. args (any order, space separated): Version: 2019/11/10 3000 number of random points in cube, lens, spiral, sphere or grid D3 dimension 3-d c add a unit cube to the output ('c G2.0' sets size) d add a unit diamond to the output ('d G2.0' sets size) l generate a regular 3-d spiral r generate a regular polygon, ('r s Z1 G0.1' makes a cone) s generate cospherical points x generate random points in simplex, may use 'r' or 'Wn' y same as 'x', plus simplex Cn,r,m add n nearly adjacent points within radius r of m points Pn,m,r add point [n,m,r] first, pads with 0, maybe repeated Ln lens distribution of radius n. Also 's', 'r', 'G', 'W'. Mn,m,r lattice(Mesh) rotated by [n,-m,0], [m,n,0], [0,0,r], ... '27 M1,0,1' is {0,1,2} x {0,1,2} x {0,1,2}. Try 'M3,4 z'. W0.1 random distribution within 0.1 of the cube's or sphere's surface Z0.5 s random points in a 0.5 disk projected to a sphere Z0.5 s G0.6 same as Z0.5 within a 0.6 gap Bn bounding box coordinates, default 0.5 h output as homogeneous coordinates for cdd n remove command line from the first line of output On offset coordinates by n t use time as the random number seed(default is command line) tn use n as the random number seed z print integer coordinates, default 'Bn' is 1e+06 cat html/qhull.txt html/rbox.txt qhull(1) qhull(1) NAME qhull - convex hull, Delaunay triangulation, Voronoi dia- gram, halfspace intersection about a point, hull volume, facet area SYNOPSIS qhull- compute convex hulls and related structures input (stdin): dimension, #points, point coordinates first comment (non-numeric) is listed in the summary halfspace: use dim plus one with offsets after coefficients options (qh-quick.htm): d - Delaunay triangulation by lifting points to a paraboloid d Qu - furthest-site Delaunay triangulation (upper convex hull) v - Voronoi diagram as the dual of the Delaunay triangulation v Qu - furthest-site Voronoi diagram H1,1 - Halfspace intersection about [1,1,0,...] via polar duality Qt - triangulated output QJ - joggled input instead of merged facets Tv - verify result: structure, convexity, and point inclusion . - concise list of all options - - one-line description of each option -? - this message -V - version Output options (subset): s - summary of results (default) i - vertices incident to each facet n - normals with offsets p - vertex coordinates (if 'Qc', includes coplanar points) if 'v', Voronoi vertices FA - report total area and volume Fp - halfspace intersections FS - total area and volume Fx - extreme points (convex hull vertices) G - Geomview output (2-d, 3-d and 4-d) m - Mathematica output (2-d and 3-d) o - OFF format (if 'v', outputs Voronoi regions) QVn - print facets that include point n, -n if not TI file - input file, may be enclosed in single quotes TO file - output file, may be enclosed in single quotes examples: rbox D4 | qhull Tv rbox 1000 s | qhull Tv s FA rbox 10 D2 | qhull d QJ s i TO result rbox 10 D2 | qhull v Qbb Qt p rbox 10 D2 | qhull d Qu QJ m rbox 10 D2 | qhull v Qu QJ o rbox c d D2 | qhull Qc s f Fx | more rbox c | qhull FV n | qhull H Fp rbox d D12 | qhull QR0 FA rbox c D7 | qhull FA TF1000 rbox y 1000 W0 | qhull Qc rbox c | qhull n - html manual: html/index.htm - installation: README.txt - see also: COPYING.txt, REGISTER.txt, Changes.txt - WWW: - GIT: - news: - Geomview: - news group: - FAQ: - email: qhull@qhull.org - bug reports: qhull_bug@qhull.org Geometry Center 2019/05/03 1 qhull(1) qhull(1) The sections are: - INTRODUCTION - DESCRIPTION, a description of Qhull - IMPRECISION, how Qhull handles imprecision - OPTIONS - Input and output options - Additional input/output formats - Precision options - Geomview options - Print options - Qhull options - Trace options - BUGS - E-MAIL - SEE ALSO - AUTHORS - ACKNOWLEGEMENTS This man page briefly describes all Qhull options. Please report any mismatches with Qhull's html manual (html/index.htm). INTRODUCTION Qhull is a general dimension code for computing convex hulls, Delaunay triangulations, Voronoi diagram, furthest- site Voronoi diagram, furthest-site Delaunay triangula- tions, and halfspace intersections about a point. It implements the Quickhull algorithm for computing the con- vex hull. Qhull handles round-off errors from floating point arithmetic. It can approximate a convex hull. The program includes options for hull volume, facet area, partial hulls, input transformations, randomization, trac- ing, multiple output formats, and execution statistics. The program can be called from within your application. You can view the results in 2-d, 3-d and 4-d with Geomview. DESCRIPTION The format of input is the following: first line contains the dimension, second line contains the number of input points, and point coordinates follow. The dimension and number of points can be reversed. Comments and line breaks are ignored. A comment starts with a non-numeric character and continues to the end of line. The first comment is reported in summaries and statistics. Error reporting is better if there is one point per line. The default printout option is a short summary. There are many other output formats. Geometry Center 2019/05/03 2 qhull(1) qhull(1) Qhull implements the Quickhull algorithm for convex hull. This algorithm combines the 2-d Quickhull algorithm with the n-d beneath-beyond algorithm [c.f., Preparata & Shamos '85]. It is similar to the randomized algorithms of Clarkson and others [Clarkson et al. '93]. The main advantages of Quickhull are output sensitive performance, reduced space requirements, and automatic handling of pre- cision problems. The data structure produced by Qhull consists of vertices, ridges, and facets. A vertex is a point of the input set. A ridge is a set of d vertices and two neighboring facets. For example in 3-d, a ridge is an edge of the polyhedron. A facet is a set of ridges, a set of neighboring facets, a set of incident vertices, and a hyperplane equation. For simplicial facets, the ridges are defined by the vertices and neighboring facets. When Qhull merges two facets, it produces a non-simplicial facet. A non-simplicial facet has more than d neighbors and may share more than one ridge with a neighbor. IMPRECISION Since Qhull uses floating point arithmetic, roundoff error may occur for each calculation. This causes problems for most geometric algorithms. Qhull automatically sets option 'C-0' in 2-d, 3-d, and 4-d, or option 'Qx' in 5-d and higher. These options han- dle precision problems by merging facets. Alternatively, use option 'QJ' to joggle the input. With 'C-0', Qhull merges non-convex facets while con- structing the hull. The remaining facets are clearly con- vex. With 'Qx', Qhull merges coplanar horizon facets, flipped facets, concave facets and duplicated ridges. It merges coplanar facets after constructing the hull. With 'Qx', coplanar points may be missed, but it appears to be unlikely. To guarantee triangular output, joggle the input with option 'QJ'. Facet merging will not occur. OPTIONS To get a list of the most important options, execute 'qhull -?'. To get a complete list of options, execute 'qhull -'. To get a complete, concise list of options, execute 'qhull .'. Options can be in any order. Capitalized options take an argument (except 'PG' and 'F' options). Single letters are used for output formats and precision constants. The other options are grouped into menus: output formats ('F'), Geomview output ('G'), printing ('P'), Qhull control ('Q'), Geometry Center 2019/05/03 3 qhull(1) qhull(1) and tracing ('T'). Main options: default Compute the convex hull of the input points. Report a summary of the result. d Compute the Delaunay triangulation by lifting the input points to a paraboloid. The 'o' option prints the input points and facets. The 'QJ' option guarantees triangular output. The 'Ft' option prints a triangulation. It adds points (the centrums) to non-simplicial facets. v Compute the Voronoi diagram from the Delaunay tri- angulation. The 'p' option prints the Voronoi ver- tices. The 'o' option prints the Voronoi vertices and the vertices in each Voronoi region. It lists regions in site id order. The 'Fv' option prints each ridge of the Voronoi diagram. The first or zero'th vertex indicates the infinity vertex. Its coordinates are qh_INFINITE (-10.101). It indi- cates unbounded Voronoi regions or degenerate Delaunay triangles. Hn,n,... Compute halfspace intersection about [n,n,0,...]. The input is a set of halfspaces defined in the same format as 'n', 'Fo', and 'Fi'. Use 'Fp' to print the intersection points. Use 'Fv' to list the intersection points for each halfspace. The other output formats display the dual convex hull. The point [n,n,n,...] is a feasible point for the halfspaces, i.e., a point that is inside all of the halfspaces (Hx+b <= 0). The default coordinate value is 0. The input may start with a feasible point. If so, use 'H' by itself. The input starts with a feasi- ble point when the first number is the dimension, the second number is "1", and the coordinates com- plete a line. The 'FV' option produces a feasible point for a convex hull. d Qu Compute the furthest-site Delaunay triangulation from the upper convex hull. The 'o' option prints the input points and facets. The 'QJ' option guar- antees triangular otuput. You can also use facets. v Qu Compute the furthest-site Voronoi diagram. The 'p' option prints the Voronoi vertices. The 'o' option prints the Voronoi vertices and the vertices in Geometry Center 2019/05/03 4 qhull(1) qhull(1) each Voronoi region. The 'Fv' option prints each ridge of the Voronoi diagram. The first or zero'th vertex indicates the infinity vertex at infinity. Its coordinates are qh_INFINITE (-10.101). It indicates unbounded Voronoi regions and degenerate Delaunay triangles. Qt Triangulated output. Input/Output options: f Print all facets and all fields of each facet. G Output the hull in Geomview format. For imprecise hulls, Geomview displays the inner and outer hull. Geomview can also display points, ridges, vertices, coplanar points, and facet intersections. See below for a list of options. For Delaunay triangulations, 'G' displays the cor- responding paraboloid. For halfspace intersection, 'G' displays the dual polytope. i Output the incident vertices for each facet. Qhull prints the number of facets followed by the ver- tices of each facet. One facet is printed per line. The numbers are the 0-relative indices of the corresponding input points. The facets are oriented. In 4-d and higher, Qhull triangulates non-simpli- cial facets. Each apex (the first vertex) is a created point that corresponds to the facet's cen- trum. Its index is greater than the indices of the input points. Each base corresponds to a simpli- cial ridge between two facets. To print the ver- tices without triangulation, use option 'Fv'. To print the centrum coordinates, use option 'Ft'. The centrum indices for option 'i' are one more than the centrum indices for option 'Ft'. m Output the hull in Mathematica format. Qhull writes a Mathematica file for 2-d and 3-d convex hulls and for 2-d Delaunay triangulations. Qhull produces a list of objects that you can assign to a variable in Mathematica, for example: "list= << ". If the object is 2-d, it can be visualized by "Show[Graphics[list]] ". For 3-d objects the command is "Show[Graphics3D[list]]". n Output the normal equation for each facet. Qhull prints the dimension (plus one), the number of facets, and the normals for each facet. The facet's offset follows its normal coefficients. o Output the facets in OFF file format. Qhull prints the dimension, number of points, number of facets, and number of ridges. Then it prints the Geometry Center 2019/05/03 5 qhull(1) qhull(1) coordinates of the input points and the vertices for each facet. Each facet is on a separate line. The first number is the number of vertices. The remainder are the indices of the corresponding points. The vertices are oriented in 2-d, 3-d, and in simplicial facets. For 2-d Voronoi diagrams, the vertices are sorted by adjacency, but not oriented. In 3-d and higher, the Voronoi vertices are sorted by index. See the 'v' option for more information. p Output the coordinates of each vertex point. Qhull prints the dimension, the number of points, and the coordinates for each vertex. With the 'Gc' and 'Gi' options, it also prints coplanar and interior points. For Voronoi diagrams, it prints the coor- dinates of each Voronoi vertex. s Print a summary to stderr. If no output options are specified, a summary goes to stdout. The summary lists the number of input points, the dimension, the number of vertices in the convex hull, the number of facets in the convex hull, the number of good facets (if 'Pg'), and statistics. The last two statistics (if needed) measure the maximum distance from a point or vertex to a facet. The number in parenthesis (e.g., 2.1x) is the ratio between the maximum distance and the worst-case distance due to merging two simplicial facets. Precision options An Maximum angle given as a cosine. If the angle between a pair of facet normals is greater than n, Qhull merges one of the facets into a neighbor. If 'n' is negative, Qhull tests angles after adding each point to the hull (pre-merging). If 'n' is posi- tive, Qhull tests angles after constructing the hull (post-merging). Both pre- and post-merging can be defined. Option 'C0' or 'C-0' is set if the corresponding 'Cn' or 'C-n' is not set. If 'Qx' is set, then 'A- n' and 'C-n' are checked after the hull is con- structed and before 'An' and 'Cn' are checked. Cn Centrum radius. If a centrum is less than n below a neighboring facet, Qhull merges one of the facets. If 'n' is negative or '-0', Qhull tests and merges facets after adding each point to the hull. This is called "pre-merging". If 'n' is Geometry Center 2019/05/03 6 qhull(1) qhull(1) positive, Qhull tests for convexity after con- structing the hull ("post-merging"). Both pre- and post-merging can be defined. For 5-d and higher, 'Qx' should be used instead of 'C-n'. Otherwise, most or all facets may be merged together. En Maximum roundoff error for distance computations. Rn Randomly perturb distance computations up to +/- n * max_coord. This option perturbs every distance, hyperplane, and angle computation. To use time as the random number seed, use option 'QR-1'. Vn Minimum distance for a facet to be visible. A facet is visible if the distance from the point to the facet is greater than 'Vn'. Without merging, the default value for 'Vn' is the round-off error ('En'). With merging, the default value is the pre-merge centrum ('C-n') in 2-d or 3--d, or three times that in other dimensions. If the outside width is specified ('Wn'), the maximum, default value for 'Vn' is 'Wn'. Un Maximum distance below a facet for a point to be coplanar to the facet. The default value is 'Vn'. Wn Minimum outside width of the hull. Points are added to the convex hull only if they are clearly outside of a facet. A point is outside of a facet if its distance to the facet is greater than 'Wn'. The normal value for 'Wn' is 'En'. If the user specifies pre-merging and does not set 'Wn', than 'Wn' is set to the premerge 'Cn' and maxco- ord*(1-An). Additional input/output formats Fa Print area for each facet. For Delaunay triangula- tions, the area is the area of the triangle. For Voronoi diagrams, the area is the area of the dual facet. Use 'PAn' for printing the n largest facets, and option 'PFn' for printing facets larger than 'n'. The area for non-simplicial facets is the sum of the areas for each ridge to the centrum. Vertices far below the facet's hyperplane are ignored. The reported area may be significantly less than the actual area. Geometry Center 2019/05/03 7 qhull(1) qhull(1) FA Compute the total area and volume for option 's'. It is an approximation for non-simplicial facets (see 'Fa'). Fc Print coplanar points for each facet. The output starts with the number of facets. Then each facet is printed one per line. Each line is the number of coplanar points followed by the point ids. Option 'Qi' includes the interior points. Each coplanar point (interior point) is assigned to the facet it is furthest above (resp., least below). FC Print centrums for each facet. The output starts with the dimension followed by the number of facets. Then each facet centrum is printed, one per line. Fd Read input in cdd format with homogeneous points. The input starts with comments. The first comment is reported in the summary. Data starts after a "begin" line. The next line is the number of points followed by the dimension+1 and "real" or "integer". Then the points are listed with a leading "1" or "1.0". The data ends with an "end" line. For halfspaces ('Fd Hn,n,...'), the input format is the same. Each halfspace starts with its offset. The sign of the offset is the opposite of Qhull's convention. FD Print normals ('n', 'Fo', 'Fi') or points ('p') in cdd format. The first line is the command line that invoked Qhull. Data starts with a "begin" line. The next line is the number of normals or points followed by the dimension+1 and "real". Then the normals or points are listed with the offset before the coefficients. The offset for points is 1.0. The offset for normals has the opposite sign. The data ends with an "end" line. FF Print facets (as in 'f') without printing the ridges. Fi Print inner planes for each facet. The inner plane is below all vertices. Fi Print separating hyperplanes for bounded, inner regions of the Voronoi diagram. The first line is the number of ridges. Then each hyperplane is printed, one per line. A line starts with the num- ber of indices and floats. The first pair lists adjacent input sites, the next d floats are the normalized coefficients for the hyperplane, and the Geometry Center 2019/05/03 8 qhull(1) qhull(1) last float is the offset. The hyperplane is ori- ented toward 'QVn' (if defined), or the first input site of the pair. Use 'Tv' to verify that the hyperplanes are perpendicular bisectors. Use 'Fo' for unbounded regions, and 'Fv' for the corresponding Voronoi vertices. FI Print facet identifiers. Fm Print number of merges for each facet. At most 511 merges are reported for a facet. See 'PMn' for printing the facets with the most merges. FM Output the hull in Maple format. See 'm' Fn Print neighbors for each facet. The output starts with the number of facets. Then each facet is printed one per line. Each line is the number of neighbors followed by an index for each neighbor. The indices match the other facet output formats. A negative index indicates an unprinted facet due to printing only good facets ('Pg'). It is the negation of the facet's id (option 'FI'). For example, negative indices are used for facets "at infinity" in the Delaunay triangulation. FN Print vertex neighbors or coplanar facet for each point. The first line is the number of points. Then each point is printed, one per line. If the point is coplanar, the line is "1" followed by the facet's id. If the point is not a selected vertex, the line is "0". Otherwise, each line is the num- ber of neighbors followed by the corresponding facet indices (see 'Fn'). Fo Print outer planes for each facet in the same for- mat as 'n'. The outer plane is above all points. Fo Print separating hyperplanes for unbounded, outer regions of the Voronoi diagram. The first line is the number of ridges. Then each hyperplane is printed, one per line. A line starts with the num- ber of indices and floats. The first pair lists adjacent input sites, the next d floats are the normalized coefficients for the hyperplane, and the last float is the offset. The hyperplane is ori- ented toward 'QVn' (if defined), or the first input site of the pair. Use 'Tv' to verify that the hyperplanes are perpendicular bisectors. Use 'Fi' for bounded regions, and 'Fv' for the corresponding Voronoi vertices. FO List all options to stderr, including the default values. Additional 'FO's are printed to stdout. Fp Print points for halfspace intersections (option 'Hn,n,...'). Each intersection corresponds to a Geometry Center 2019/05/03 9 qhull(1) qhull(1) facet of the dual polytope. The "infinity" point [-10.101,-10.101,...] indicates an unbounded intersection. FP For each coplanar point ('Qc') print the point id of the nearest vertex, the point id, the facet id, and the distance. FQ Print command used for qhull and input. Fs Print a summary. The first line consists of the number of integers ("7"), followed by the dimen- sion, the number of points, the number of vertices, the number of facets, the number of vertices selected for output, the number of facets selected for output, the number of coplanar points selected for output. The second line consists of the number of reals ("2"), followed by the maxmimum offset to an outer plane and and minimum offset to an inner plane. Roundoff is included. Later versions of Qhull may produce additional integers or reals. FS Print the size of the hull. The first line con- sists of the number of integers ("0"). The second line consists of the number of reals ("2"), fol- lowed by the total facet area, and the total vol- ume. Later versions of Qhull may produce addi- tional integers or reals. The total volume measures the volume of the inter- section of the halfspaces defined by each facet. Both area and volume are approximations for non- simplicial facets. See option 'Fa'. Ft Print a triangulation with added points for non- simplicial facets. The first line is the dimension and the second line is the number of points and the number of facets. The points follow, one per line, then the facets follow as a list of point indices. With option points include the point-at-infinity. Fv Print vertices for each facet. The first line is the number of facets. Then each facet is printed, one per line. Each line is the number of vertices followed by the corresponding point ids. Vertices are listed in the order they were added to the hull (the last one is first). Fv Print all ridges of a Voronoi diagram. The first line is the number of ridges. Then each ridge is printed, one per line. A line starts with the num- ber of indices. The first pair lists adjacent Geometry Center 2019/05/03 10 qhull(1) qhull(1) input sites, the remaining indices list Voronoi vertices. Vertex '0' indicates the vertex-at- infinity (i.e., an unbounded ray). In 3-d, the vertices are listed in order. See 'Fi' and 'Fo' for separating hyperplanes. FV Print average vertex. The average vertex is a fea- sible point for halfspace intersection. Fx List extreme points (vertices) of the convex hull. The first line is the number of points. The other lines give the indices of the corresponding points. The first point is '0'. In 2-d, the points occur in counter-clockwise order; otherwise they occur in input order. For Delaunay triangulations, 'Fx' lists the extreme points of the input sites. The points are unordered. Geomview options G Produce a file for viewing with Geomview. Without other options, Qhull displays edges in 2-d, outer planes in 3-d, and ridges in 4-d. A ridge can be explicit or implicit. An explicit ridge is a dim-1 dimensional simplex between two facets. In 4-d, the explicit ridges are triangles. When displaying a ridge in 4-d, Qhull projects the ridge's vertices to one of its facets' hyperplanes. Use 'Gh' to project ridges to the intersection of both hyper- planes. Ga Display all input points as dots. Gc Display the centrum for each facet in 3-d. The centrum is defined by a green radius sitting on a blue plane. The plane corresponds to the facet's hyperplane. The radius is defined by 'C-n' or 'Cn'. GDn Drop dimension n in 3-d or 4-d. The result is a 2-d or 3-d object. Gh Display hyperplane intersections in 3-d and 4-d. In 3-d, the intersection is a black line. It lies on two neighboring hyperplanes (c.f., the blue squares associated with centrums ('Gc')). In 4-d, the ridges are projected to the intersection of both hyperplanes. Gi Display inner planes in 2-d and 3-d. The inner plane of a facet is below all of its vertices. It is parallel to the facet's hyperplane. The inner plane's color is the opposite (1-r,1-g,1-b) of the Geometry Center 2019/05/03 11 qhull(1) qhull(1) outer plane. Its edges are determined by the ver- tices. Gn Do not display inner or outer planes. By default, Geomview displays the precise plane (no merging) or both inner and output planes (merging). Under merging, Geomview does not display the inner plane if the the difference between inner and outer is too small. Go Display outer planes in 2-d and 3-d. The outer plane of a facet is above all input points. It is parallel to the facet's hyperplane. Its color is determined by the facet's normal, and its edges are determined by the vertices. Gp Display coplanar points and vertices as radii. A radius defines a ball which corresponds to the imprecision of the point. The imprecision is the maximum of the roundoff error, the centrum radius, and maxcoord * (1-An). It is at least 1/20'th of the maximum coordinate, and ignores post-merging if pre-merging is done. Gr Display ridges in 3-d. A ridge connects the two vertices that are shared by neighboring facets. Ridges are always displayed in 4-d. Gt A 3-d Delaunay triangulation looks like a convex hull with interior facets. Option 'Gt' removes the outside ridges to reveal the outermost facets. It automatically sets options 'Gr' and 'GDn'. Gv Display vertices as spheres. The radius of the sphere corresponds to the imprecision of the data. See 'Gp' for determining the radius. Print options PAn Only the n largest facets are marked good for printing. Unless 'PG' is set, 'Pg' is automati- cally set. Pdk:n Drop facet from output if normal[k] <= n. The option 'Pdk' uses the default value of 0 for n. PDk:n Drop facet from output if normal[k] >= n. The option 'PDk' uses the default value of 0 for n. PFn Only facets with area at least 'n' are marked good for printing. Unless 'PG' is set, 'Pg' is automat- ically set. Geometry Center 2019/05/03 12 qhull(1) qhull(1) Pg Print only good facets. A good facet is either visible from a point (the 'QGn' option) or includes a point (the 'QVn' option). It also meets the requirements of 'Pdk' and 'PDk' options. Option 'Pg' is automatically set for options 'd', 'PAn', 'PFn', and 'PMn' PG Print neighbors of good facets. PMn Only the n facets with the most merges are marked good for printing. Unless 'PG' is set, 'Pg' is automatically set. Po Force output despite precision problems. Verify ('Tv') does not check coplanar points. Flipped facets are reported and concave facets are counted. If 'Po' is used, points are not partitioned into flipped facets and a flipped facet is always visible to a point. Also, if an error occurs before the completion of Qhull and tracing is not active, 'Po' outputs a neighborhood of the erroneous facets (if any). Pp Do not report precision problems. Qhull control options Qa Allow input with fewer or more points than coordinates Qbk:0Bk:0 Drop dimension k from the input points. This allows the user to take convex hulls of sub-dimen- sional objects. It happens before the Delaunay and Voronoi transformation. QbB Scale the input points to fit the unit cube. After scaling, the lower bound will be -0.5 and the upper bound +0.5 in all dimensions. For Delaunay and Voronoi diagrams, scaling happens after projection to the paraboloid. Under precise arithmetic, scal- ing does not change the topology of the convex hull. Qbb Scale the last coordinate to [0, m] where m is the maximum absolute value of the other coordinates. For Delaunay and Voronoi diagrams, scaling happens after projection to the paraboloid. It reduces roundoff error for inputs with integer coordinates. Under precise arithmetic, scaling does not change the topology of the convex hull. Qbk:n Scale the k'th coordinate of the input points. After scaling, the lower bound of the input points will be n. 'Qbk' scales to -0.5. Geometry Center 2019/05/03 13 qhull(1) qhull(1) QBk:n Scale the k'th coordinate of the input points. After scaling, the upper bound will be n. 'QBk' scales to +0.5. Qc Keep coplanar points with the nearest facet. Out- put formats 'p', 'f', 'Gp', 'Fc', 'FN', and 'FP' will print the points. Qf Partition points to the furthest outside facet. Qg Only build good facets. With the 'Qg' option, Qhull will only build those facets that it needs to determine the good facets in the output. See 'QGn', 'QVn', and 'PdD' for defining good facets, and 'Pg' and 'PG' for printing good facets and their neighbors. QGn A facet is good (see 'Qg' and 'Pg') if it is visi- ble from point n. If n < 0, a facet is good if it is not visible from point n. Point n is not added to the hull (unless 'TCn' or 'TPn'). With rbox, use the 'Pn,m,r' option to define your point; it will be point 0 (QG0). Qi Keep interior points with the nearest facet. Out- put formats 'p', 'f', 'Gp', 'FN', 'FP', and 'Fc' will print the points. QJn Joggle each input coordinate by adding a random number in [-n,n]. If a precision error occurs, then qhull increases n and tries again. It does not increase n beyond a certain value, and it stops after a certain number of attempts [see user.h]. Option 'QJ' selects a default value for n. The output will be simplicial. For Delaunay triangula- tions, 'QJn' sets 'Qbb' to scale the last coordi- nate (not if 'Qbk:n' or 'QBk:n' is set). 'QJn' is deprecated for Voronoi diagrams. See also 'Qt'. Qm Only process points that would otherwise increase max_outside. Other points are treated as coplanar or interior points. Qr Process random outside points instead of furthest ones. This makes Qhull equivalent to the random- ized incremental algorithms. CPU time is not reported since the randomization is inefficient. QRn Randomly rotate the input points. If n=0, use time as the random number seed. If n>0, use n as the random number seed. If n=-1, don't rotate but use time as the random number seed. For Delaunay tri- angulations ('d' and 'v'), rotate about the last axis. Geometry Center 2019/05/03 14 qhull(1) qhull(1) Qs Search all points for the initial simplex. Qt Triangulated output. Triangulate non-simplicial facets. 'Qt' is deprecated for Voronoi diagrams. See also 'QJn' Qv Test vertex neighbors for convexity after post- merging. To use the 'Qv' option, you also need to set a merge option (e.g., 'Qx' or 'C-0'). QVn A good facet (see 'Qg' and 'Pg') includes point n. If n<0, then a good facet does not include point n. The point is either in the initial simplex or it is the first point added to the hull. Option 'QVn' may not be used with merging. Qw Allow option warnings. Otherwise Qhull returns an error after most option warnings. Qx Perform exact merges while building the hull. The "exact" merges are merging a point into a coplanar facet (defined by 'Vn', 'Un', and 'C-n'), merging concave facets, merging duplicate ridges, and merg- ing flipped facets. Coplanar merges and angle coplanar merges ('A-n') are not performed. Concav- ity testing is delayed until a merge occurs. After the hull is built, all coplanar merges are performed (defined by 'C-n' and 'A-n'), then post- merges are performed (defined by 'Cn' and 'An'). Qz Add a point "at infinity" that is above the paraboloid for Delaunay triangulations and Voronoi diagrams. This reduces precision problems and allows the triangulation of cospherical points. Qhull experiments and speedups Q0 Turn off pre-merging as a default option. With 'Q0'/'Qx' and without explicit pre-merge options, Qhull ignores precision issues while constructing the convex hull. This may lead to precision errors. If so, a descriptive warning is generated. Q1 With 'Q1', Qhull merges by mergetype/angle instead of mergetype/distance. Q2 With 'Q2', Qhull merges all facets at once instead of using independent sets of merges and then retesting. Q3 With 'Q3', Qhull does not remove redundant ver- tices. Q4 With 'Q4', Qhull avoids merges of an old facet into a new facet. Q5 With 'Q5', Qhull does not correct outer planes at the end. The maximum outer plane is used instead. Geometry Center 2019/05/03 15 qhull(1) qhull(1) Q6 With 'Q6', Qhull does not pre-merge concave or coplanar facets. Q7 With 'Q7', Qhull processes facets in depth-first order instead of breadth-first order. Q8 With 'Q8' and merging, Qhull does not retain near- interior points for adjusting outer planes. 'Qc' will probably retain all points that adjust outer planes. Q9 With 'Q9', Qhull processes the furthest of all out- side sets at each iteration. Q10 With 'Q10', Qhull does not use special processing for narrow distributions. Q11 With 'Q11', Qhull copies normals and recomputes centrums for tricoplanar facets. Q12 With 'Q12', Qhull allows wide facets and wide dupridge Q14 With 'Q14', Qhull merges pinched vertices that create a dupridge. Q15 With 'Q15', Qhull checks for duplicate ridges with the same vertices. Trace options Tn Trace at level n. Qhull includes full execution tracing. 'T-1' traces events. 'T1' traces the overall execution of the program. 'T2' and 'T3' trace overall execution and geometric and topologi- cal events. 'T4' traces the algorithm. 'T5' includes information about memory allocation and Gaussian elimination. Ta Annotate output with codes that identify the corresponding qh_fprintf() statement. TAn Stop Qhull after adding n vertices. Tc Check frequently during execution. This will catch most inconsistency errors. TCn Stop Qhull after building the cone of new facets for point n. The output for 'f' includes the cone and the old hull. See also 'TVn'. Tf Flush output after each qh_fprintf. Use 'Tf' for debugging segfaults. See 'Tz' for redirecting stderr. TFn Report progress whenever more than n facets are created During post-merging, 'TFn' reports progress after more than n/2 merges. TI file Input data from 'file'. The filename may not include spaces or quotes. TMn Turn on tracing at n'th merge. TO file Output results to 'file'. The name may be enclosed in single quotes. TPn Turn on tracing when point n is added to the hull. Trace partitions of point n. If used with TWn, turn off tracing after adding point n to the hull. TP-1 Turn on tracing after qh_buildhull and qh_postmerge. TRn Rerun qhull n times. Usually used with 'QJn' to determine the probability that a given joggle will fail. Ts Collect statistics and print to stderr at the end of execution. Tv Verify the convex hull. This checks the topologi- cal structure, facet convexity, and point inclu- sion. If precision problems occurred, facet con- vexity is tested whether or not 'Tv' is selected. Option 'Tv' does not check point inclusion if Geometry Center 2019/05/03 16 qhull(1) qhull(1) forcing output with 'Po', or if 'Q5' is set. For point inclusion testing, Qhull verifies that all points are below all outer planes (facet->max- outside). Point inclusion is exhaustive if merging or if the facet-point product is small enough; oth- erwise Qhull verifies each point with a directed search (qh_findbest). Point inclusion testing occurs after producing out- put. It prints a message to stderr unless option 'Pp' is used. This allows the user to interrupt Qhull without changing the output. TVn Stop Qhull after adding point n. If n < 0, stop Qhull before adding point n. Output shows the hull at this time. See also 'TCn' TWn Trace merge facets when the width is greater than n. Tz Redirect stderr to stdout. See 'Tf' for flushing writes. BUGS Please report bugs to Brad Barber at qhull_bug@qhull.org. If Qhull does not compile, it is due to an incompatibility between your system and ours. The first thing to check is that your compiler is ANSI standard. If it is, check the man page for the best options, or find someone to help you. If you locate the cause of your problem, please send email since it might help others. If Qhull compiles but crashes on the test case (rbox D4), there's still incompatibility between your system and ours. Typically it's been due to mem.c and memory align- ment. You can use qh_NOmem in mem.h to turn off memory management. Please let us know if you figure out how to fix these problems. If you do find a problem, try to simplify it before reporting the error. Try different size inputs to locate the smallest one that causes an error. You're welcome to hunt through the code using the execution trace as a guide. This is especially true if you're incorporating Qhull into your own program. When you do report an error, please attach a data set to the end of your message. This allows us to see the error for ourselves. Qhull is maintained part-time. Geometry Center 2019/05/03 17 qhull(1) qhull(1) E-MAIL Please send correspondence to qhull@qhull.org and report bugs to qhull_bug@qhull.org. Let us know how you use Qhull. If you mention it in a paper, please send the reference and an abstract. If you would like to get Qhull announcements (e.g., a new version) and news (any bugs that get fixed, etc.), let us know and we will add you to our mailing list. If you would like to communicate with other Qhull users, we will add you to the qhull_users alias. For Internet news about geometric algorithms and convex hulls, look at comp.graph- ics.algorithms and sci.math.num-analysis SEE ALSO rbox(1) Barber, C. B., D.P. Dobkin, and H.T. Huhdanpaa, "The Quickhull Algorithm for Convex Hulls," ACM Trans. on Math- ematical Software, 22(4):469-483, Dec. 1996. http://portal.acm.org/citation.cfm?doid=235815.235821 http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405 Clarkson, K.L., K. Mehlhorn, and R. Seidel, "Four results on randomized incremental construction," Computational Geometry: Theory and Applications, vol. 3, p. 185-211, 1993. Preparata, F. and M. Shamos, Computational Geometry, Springer-Verlag, New York, 1985. AUTHORS C. Bradford Barber Hannu Huhdanpaa bradb@shore.net hannu@qhull.org ACKNOWLEDGEMENTS A special thanks to Albert Marden, Victor Milenkovic, the Geometry Center, Harvard University, and Endocardial Solu- tions, Inc. for supporting this work. Qhull 1.0 and 2.0 were developed under National Science Foundation grants NSF/DMS-8920161 and NSF-CCR-91-15793 750-7504. David Dobkin Geometry Center 2019/05/03 18 qhull(1) qhull(1) guided the original work at Princeton University. If you find it useful, please let us know. 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. Qhull is available from http://www.qhull.org Geometry Center 2019/05/03 19 rbox(1) rbox(1) NAME rbox - generate point distributions for qhull SYNOPSIS Command "rbox" (w/o arguments) lists the options. DESCRIPTION rbox generates random or regular points according to the options given, and outputs the points to stdout. The points are generated in a cube, unless 's' or given. The format of the output is the following: first line contains the dimension and a comment, second line contains the num- ber of points, and the following lines contain the points, one point per line. Points are represented by their coor- dinate values. EXAMPLES rbox 10 10 random points in the unit cube centered at the origin. rbox 10 s D2 10 random points on a 2-d circle. rbox 100 W0 100 random points on the surface of a cube. rbox 1000 s D4 1000 random points on a 4-d sphere. rbox c D5 O0.5 a 5-d hypercube with one corner at the origin. rbox d D10 a 10-d diamond. rbox x 1000 r W0 100 random points on the surface of a fixed simplex rbox y D12 a 12-d simplex. rbox l 10 10 random points along a spiral rbox l 10 r 10 regular points along a spiral plus two end points rbox 1000 L10000 D4 s 1000 random points on the surface of a narrow lens. rbox c G2 d G3 a cube with coordinates +2/-2 and a diamond with Geometry Center August 10, 1998 1 rbox(1) rbox(1) coordinates +3/-3. rbox 64 M3,4 z a rotated, {0,1,2,3} x {0,1,2,3} x {0,1,2,3} lat- tice (Mesh) of integer points. rbox P0 P0 P0 P0 P0 5 copies of the origin in 3-d. Try 'rbox P0 P0 P0 P0 P0 | qhull QJ'. r 100 s Z1 G0.1 two cospherical 100-gons plus another cospherical point. 100 s Z1 a cone of points. 100 s Z1e-7 a narrow cone of points with many precision errors. OPTIONS n number of points Dn dimension n-d (default 3-d) Bn bounding box coordinates (default 0.5) l spiral distribution, available only in 3-d Ln lens distribution of radius n. May be used with 's', 'r', 'G', and 'W'. Mn,m,r lattice (Mesh) rotated by {[n,-m,0], [m,n,0], [0,0,r], ...}. Use 'Mm,n' for a rigid rotation with r = sqrt(n^2+m^2). 'M1,0' is an orthogonal lattice. For example, '27 M1,0' is {0,1,2} x {0,1,2} x {0,1,2}. s cospherical points randomly generated in a cube and projected to the unit sphere x simplicial distribution. It is fixed for option 'r'. May be used with 'W'. y simplicial distribution plus a simplex. Both 'x' and 'y' generate the same points. Wn restrict points to distance n of the surface of a sphere or a cube c add a unit cube to the output c Gm add a cube with all combinations of +m and -m to the output Geometry Center August 10, 1998 2 rbox(1) rbox(1) d add a unit diamond to the output. d Gm add a diamond made of 0, +m and -m to the output Cn,r,m add n nearly coincident points within radius r of m points Pn,m,r add point [n,m,r] to the output first. Pad coordi- nates with 0.0. n Remove the command line from the first line of out- put. On offset the data by adding n to each coordinate. t use time in seconds as the random number seed (default is command line). tn set the random number seed to n. z generate integer coordinates. Use 'Bn' to change the range. The default is 'B1e6' for six-digit coordinates. In R^4, seven-digit coordinates will overflow hyperplane normalization. Zn s restrict points to a disk about the z+ axis and the sphere (default Z1.0). Includes the opposite pole. 'Z1e-6' generates degenerate points under single precision. Zn Gm s same as Zn with an empty center (default G0.5). r s D2 generate a regular polygon r s Z1 G0.1 generate a regular cone BUGS Some combinations of arguments generate odd results. Report bugs to qhull_bug@qhull.org, other correspon- dence to qhull@qhull.org SEE ALSO qhull(1) AUTHOR C. Bradford Barber bradb@shore.net Geometry Center August 10, 1998 3 # end of q_test make[1]: Leaving directory '/build/qhull-vzozxV/qhull-2020.2' create-stamp debian/debhelper-build-stamp dh_testroot -i -O--buildsystem=cmake dh_prep -i -O--buildsystem=cmake debian/rules override_dh_auto_install make[1]: Entering directory '/build/qhull-vzozxV/qhull-2020.2' dh_auto_install --buildsystem=cmake cd obj-x86_64-linux-gnu && make -j4 install DESTDIR=/build/qhull-vzozxV/qhull-2020.2/debian/tmp AM_UPDATE_INFO_DIR=no "INSTALL=install --strip-program=true" make[2]: Entering directory '/build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu' /usr/bin/cmake -S/build/qhull-vzozxV/qhull-2020.2 -B/build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu --check-build-system CMakeFiles/Makefile.cmake 0 make -f CMakeFiles/Makefile2 preinstall make[3]: Entering directory '/build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu' make[3]: Nothing to be done for 'preinstall'. make[3]: Leaving directory 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/build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhull_r/libqhull_r.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhull_r/geom_r.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhull_r/io_r.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhull_r/mem_r.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhull_r/merge_r.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhull_r/poly_r.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhull_r/qhull_ra.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhull_r/qset_r.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhull_r/random_r.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhull_r/stat_r.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhull_r/user_r.h -- 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/build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullLinkedList.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullPoint.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullPoints.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullPointSet.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullQh.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullRidge.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullSet.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullSets.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullStat.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullUser.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullVertex.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullVertexSet.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/RboxPoints.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/RoadError.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/RoadLogEvent.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/RoadTest.h -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/man/man1/qhull.1 -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/man/man1/rbox.1 -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/README.txt -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/REGISTER.txt -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/Announce.txt -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/COPYING.txt -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/index.htm -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-quick.htm -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/rbox.txt -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-optp.htm -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-faq.htm -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qhull.man -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qhull.txt -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qconvex.htm -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qdelaun.htm -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh--4d.gif -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh--dt.gif -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qvoron_f.htm -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qhull-cpp.xml -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-get.htm -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/rbox.man -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-optc.htm -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/rbox.htm -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-optf.htm -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-code.htm -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-opto.htm -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/index.htm -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-eg.htm -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/normal_voronoi_knauss_oesterle.jpg -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-impre.htm -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qvoronoi.htm -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh--cone.gif -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qdelau_f.htm -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qhull.htm -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh--rand.gif -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-optt.htm -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-optg.htm -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh--geom.gif -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qhalf.htm -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-optq.htm -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh_findbestfacet-drielsma.pdf -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh--half.gif -- Installing: /build/qhull-vzozxV/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/src/Changes.txt make[2]: Leaving directory '/build/qhull-vzozxV/qhull-2020.2/obj-x86_64-linux-gnu' make[1]: Leaving directory '/build/qhull-vzozxV/qhull-2020.2' debian/rules execute_after_dh_auto_install make[1]: Entering directory '/build/qhull-vzozxV/qhull-2020.2' No need for extra copy of license rm --verbose debian/tmp/usr/share/doc/libqhull-dev/qhull/COPYING.txt removed 'debian/tmp/usr/share/doc/libqhull-dev/qhull/COPYING.txt' No need for doc/ copies of man pages in ../../man/man1/ or for other formats. removed 'debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qhull.man' removed 'debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qhull.txt' removed 'debian/tmp/usr/share/doc/libqhull-dev/qhull/html/rbox.man' removed 'debian/tmp/usr/share/doc/libqhull-dev/qhull/html/rbox.txt' rm --verbose debian/tmp/usr/share/doc/libqhull-dev/qhull/src/Changes.txt removed 'debian/tmp/usr/share/doc/libqhull-dev/qhull/src/Changes.txt' make[1]: Leaving directory '/build/qhull-vzozxV/qhull-2020.2' dh_install -i -O--buildsystem=cmake dh_installdocs -i -O--buildsystem=cmake debian/rules override_dh_installchangelogs make[1]: Entering directory '/build/qhull-vzozxV/qhull-2020.2' dh_installchangelogs src/Changes.txt make[1]: Leaving directory '/build/qhull-vzozxV/qhull-2020.2' dh_installexamples -i -O--buildsystem=cmake dh_installman -i -O--buildsystem=cmake dh_installsystemduser -i -O--buildsystem=cmake dh_perl -i -O--buildsystem=cmake debian/rules execute_before_dh_link-indep make[1]: Entering directory '/build/qhull-vzozxV/qhull-2020.2' mkdir -p debian/libqhull-doc/usr/share/doc/libqhull-dev/qhull/src/libqhull_r 'debian/libqhull-doc/usr/share/doc/libqhull-dev/qhull/src/libqhull_r/geom_r.h' -> '/usr/include/libqhull_r/geom_r.h' 'debian/libqhull-doc/usr/share/doc/libqhull-dev/qhull/src/libqhull_r/io_r.h' -> '/usr/include/libqhull_r/io_r.h' 'debian/libqhull-doc/usr/share/doc/libqhull-dev/qhull/src/libqhull_r/libqhull_r.h' -> '/usr/include/libqhull_r/libqhull_r.h' 'debian/libqhull-doc/usr/share/doc/libqhull-dev/qhull/src/libqhull_r/mem_r.h' -> '/usr/include/libqhull_r/mem_r.h' 'debian/libqhull-doc/usr/share/doc/libqhull-dev/qhull/src/libqhull_r/merge_r.h' -> '/usr/include/libqhull_r/merge_r.h' 'debian/libqhull-doc/usr/share/doc/libqhull-dev/qhull/src/libqhull_r/poly_r.h' -> '/usr/include/libqhull_r/poly_r.h' 'debian/libqhull-doc/usr/share/doc/libqhull-dev/qhull/src/libqhull_r/qhull_ra.h' -> '/usr/include/libqhull_r/qhull_ra.h' 'debian/libqhull-doc/usr/share/doc/libqhull-dev/qhull/src/libqhull_r/qset_r.h' -> '/usr/include/libqhull_r/qset_r.h' 'debian/libqhull-doc/usr/share/doc/libqhull-dev/qhull/src/libqhull_r/random_r.h' -> '/usr/include/libqhull_r/random_r.h' 'debian/libqhull-doc/usr/share/doc/libqhull-dev/qhull/src/libqhull_r/stat_r.h' -> '/usr/include/libqhull_r/stat_r.h' 'debian/libqhull-doc/usr/share/doc/libqhull-dev/qhull/src/libqhull_r/user_r.h' -> '/usr/include/libqhull_r/user_r.h' make[1]: Leaving directory '/build/qhull-vzozxV/qhull-2020.2' dh_link -i -O--buildsystem=cmake dh_strip_nondeterminism -i -O--buildsystem=cmake debian/rules override_dh_compress make[1]: Entering directory '/build/qhull-vzozxV/qhull-2020.2' dh_compress -X.c -X.h -X.txt make[1]: Leaving directory '/build/qhull-vzozxV/qhull-2020.2' dh_fixperms -i -O--buildsystem=cmake dh_missing -i -O--buildsystem=cmake dh_installdeb -i -O--buildsystem=cmake dh_gencontrol -i -O--buildsystem=cmake dh_md5sums -i -O--buildsystem=cmake dh_builddeb -i -O--buildsystem=cmake dpkg-deb: building package 'libqhull-doc' in '../libqhull-doc_2020.2-3_all.deb'. dpkg-genbuildinfo --build=all dpkg-genchanges --build=all >../qhull_2020.2-3_all.changes dpkg-genchanges: info: binary-only arch-indep upload (source code and arch-specific packages not included) dpkg-source --after-build . dpkg-buildpackage: info: binary-only upload (no source included) I: running special hook: sync-out /build/qhull-vzozxV /tmp/qhull-2020.2-3lpc432br I: cleaning package lists and apt cache... I: creating tarball... I: done I: removing tempdir /tmp/mmdebstrap.tZ1KXmBowC... I: success in 394.2914 seconds md5: libqhull-doc_2020.2-3_all.deb: OK sha1: libqhull-doc_2020.2-3_all.deb: OK sha256: libqhull-doc_2020.2-3_all.deb: OK Checksums: OK