Sat Nov 23 02:30:38 UTC 2024 I: starting to build qhull/trixie/i386 on jenkins on '2024-11-23 02:30' Sat Nov 23 02:30:38 UTC 2024 I: The jenkins build log is/was available at https://jenkins.debian.net/userContent/reproducible/debian/build_service/i386_20/33505/console.log Sat Nov 23 02:30:38 UTC 2024 I: Downloading source for trixie/qhull=2020.2-6 --2024-11-23 02:30:39-- http://deb.debian.org/debian/pool/main/q/qhull/qhull_2020.2-6.dsc Connecting to 46.16.76.132:3128... connected. Proxy request sent, awaiting response... 200 OK Length: 2199 (2.1K) [text/prs.lines.tag] Saving to: ‘qhull_2020.2-6.dsc’ 0K .. 100% 290M=0s 2024-11-23 02:30:39 (290 MB/s) - ‘qhull_2020.2-6.dsc’ saved [2199/2199] Sat Nov 23 02:30:39 UTC 2024 I: qhull_2020.2-6.dsc -----BEGIN PGP SIGNED MESSAGE----- Hash: SHA512 Format: 3.0 (quilt) Source: qhull Binary: libqhull8.0, libqhull-r8.0, libqhullcpp8.0, libqhull-dev, libqhull-doc, qhull-bin Architecture: any all Version: 2020.2-6 Maintainer: Debian Science Maintainers Uploaders: Barak A. Pearlmutter , Timo Röhling Homepage: https://www.qhull.org Standards-Version: 4.6.1 Vcs-Browser: https://salsa.debian.org/science-team/qhull Vcs-Git: https://salsa.debian.org/science-team/qhull.git Testsuite: autopkgtest Testsuite-Triggers: c++-compiler, c-compiler, cmake, g++, gcc, pkg-config Build-Depends: debhelper-compat (= 13), cmake, pkg-kde-tools Package-List: libqhull-dev deb libdevel optional arch=any libqhull-doc deb doc optional arch=all libqhull-r8.0 deb libs optional arch=any libqhull8.0 deb libs optional arch=any libqhullcpp8.0 deb libs optional arch=any qhull-bin deb math optional arch=any Checksums-Sha1: 2dbc240919560ac008a92363984754a70677b353 1298874 qhull_2020.2.orig.tar.gz 02944f8f59be1933e0af11a548e901665dd0910a 18648 qhull_2020.2-6.debian.tar.xz Checksums-Sha256: b5c2d7eb833278881b952c8a52d20179eab87766b00b865000469a45c1838b7e 1298874 qhull_2020.2.orig.tar.gz e9c46af8bfb7f372ef5758f4da99292d774a8a05e0247936a913ee8dff276c33 18648 qhull_2020.2-6.debian.tar.xz Files: 295f7332269a38279478f555cc185296 1298874 qhull_2020.2.orig.tar.gz 3fb27e8c0943aeb84727c87da5921307 18648 qhull_2020.2-6.debian.tar.xz -----BEGIN PGP SIGNATURE----- iQHIBAEBCgAyFiEEJvtDgpxjkjCIVtam+C8H+466LVkFAmSrKpQUHHJvZWhsaW5n QGRlYmlhbi5vcmcACgkQ+C8H+466LVnnMQwA4Fg7DFlLYigk0fGd5rjekEnY1VZs 6sP1xXXsFk7Y6TQkvgknfTyxCtH225lyx+Qv3fCRP2+1U7I0DquucjkiwJrv/2Jc wAb3CfGceTOo0CpNyMND4ISZ+IZxUSQAFQh3NMIRfg7ZwebDRMrWlOM0luO3RohL FjnpyobHnXrETdrwBPctWJgVITIBe2FXmKj3D9F2pFjexhVRisgGYhUdyt/skhL2 tH3HRVgQjEppc4VFPiiFiAQiqLJWaFseQj4A+5wT19hoh4+YqT2BvoYqbARUx/Xn ZliIdsHLtBC6p9f0Jswxn1YuniPrrXyuUR4ov7sIDWbxi6nmSp2TFFzp1hJ2vqBl QVeLJDJTtYta/3Tn0Nidwvp3fj7r5WztEg6uHkr9yNhfRFU0ZIICFnHlfOKa8vC+ KQzvmEAT/nE252WZSZIVlLvAdReDTMcZ+375KF5OkqM/WQ/v8vZjzuDD2EYtUU0X xIeQVzYtogIC1DxHWWCXuroUGLY5WIiWITsd =8I5V -----END PGP SIGNATURE----- Sat Nov 23 02:30:39 UTC 2024 I: Checking whether the package is not for us Sat Nov 23 02:30:39 UTC 2024 I: Starting 1st build on remote node infom08-i386.debian.net. Sat Nov 23 02:30:39 UTC 2024 I: Preparing to do remote build '1' on infom08-i386.debian.net. Sat Nov 23 02:31:59 UTC 2024 I: Deleting $TMPDIR on infom08-i386.debian.net. I: pbuilder: network access will be disabled during build I: Current time: Thu Dec 25 20:53:40 -12 2025 I: pbuilder-time-stamp: 1766739220 I: Building the build Environment I: extracting base tarball [/var/cache/pbuilder/trixie-reproducible-base.tgz] I: copying local configuration W: --override-config is not set; not updating apt.conf Read the manpage for details. I: mounting /proc filesystem I: mounting /sys filesystem I: creating /{dev,run}/shm I: mounting /dev/pts filesystem I: redirecting /dev/ptmx to /dev/pts/ptmx I: policy-rc.d already exists I: using eatmydata during job I: Copying source file I: copying [qhull_2020.2-6.dsc] I: copying [./qhull_2020.2.orig.tar.gz] I: copying [./qhull_2020.2-6.debian.tar.xz] I: Extracting source gpgv: Signature made Sun Jul 9 21:45:56 2023 gpgv: using RSA key 26FB43829C6392308856D6A6F82F07FB8EBA2D59 gpgv: issuer "roehling@debian.org" gpgv: Can't check signature: No public key dpkg-source: warning: cannot verify inline signature for ./qhull_2020.2-6.dsc: no acceptable signature found dpkg-source: info: extracting qhull in qhull-2020.2 dpkg-source: info: unpacking qhull_2020.2.orig.tar.gz dpkg-source: info: unpacking qhull_2020.2-6.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: Not using root during the build. I: Installing the build-deps I: user script /srv/workspace/pbuilder/29269/tmp/hooks/D02_print_environment starting I: set BUILDDIR='/build/reproducible-path' BUILDUSERGECOS='first user,first room,first work-phone,first home-phone,first other' BUILDUSERNAME='pbuilder1' BUILD_ARCH='i386' DEBIAN_FRONTEND='noninteractive' DEB_BUILD_OPTIONS='buildinfo=+all reproducible=+all parallel=6 ' DISTRIBUTION='trixie' HOME='/root' HOST_ARCH='i386' IFS=' ' INVOCATION_ID='41179ad5eea7478dab6ff7cd312a2eb9' LANG='C' LANGUAGE='en_US:en' LC_ALL='C' LD_LIBRARY_PATH='/usr/lib/libeatmydata' LD_PRELOAD='libeatmydata.so' MAIL='/var/mail/root' OPTIND='1' PATH='/usr/sbin:/usr/bin:/sbin:/bin:/usr/games' PBCURRENTCOMMANDLINEOPERATION='build' PBUILDER_OPERATION='build' PBUILDER_PKGDATADIR='/usr/share/pbuilder' PBUILDER_PKGLIBDIR='/usr/lib/pbuilder' PBUILDER_SYSCONFDIR='/etc' PPID='29269' PS1='# ' PS2='> ' PS4='+ ' PWD='/' SHELL='/bin/bash' SHLVL='2' SUDO_COMMAND='/usr/bin/timeout -k 18.1h 18h /usr/bin/ionice -c 3 /usr/bin/nice /usr/sbin/pbuilder --build --configfile /srv/reproducible-results/rbuild-debian/r-b-build.ntlCLPQU/pbuilderrc_RxfF --distribution trixie --hookdir /etc/pbuilder/first-build-hooks --debbuildopts -b --basetgz /var/cache/pbuilder/trixie-reproducible-base.tgz --buildresult /srv/reproducible-results/rbuild-debian/r-b-build.ntlCLPQU/b1 --logfile b1/build.log qhull_2020.2-6.dsc' SUDO_GID='111' SUDO_UID='104' SUDO_USER='jenkins' TERM='unknown' TZ='/usr/share/zoneinfo/Etc/GMT+12' USER='root' _='/usr/bin/systemd-run' I: uname -a Linux infom08-i386 6.11.5+bpo-amd64 #1 SMP PREEMPT_DYNAMIC Debian 6.11.5-1~bpo12+1 (2024-11-11) x86_64 GNU/Linux I: ls -l /bin lrwxrwxrwx 1 root root 7 Aug 4 2024 /bin -> usr/bin I: user script /srv/workspace/pbuilder/29269/tmp/hooks/D02_print_environment finished -> Attempting to satisfy build-dependencies -> Creating pbuilder-satisfydepends-dummy package Package: pbuilder-satisfydepends-dummy Version: 0.invalid.0 Architecture: i386 Maintainer: Debian Pbuilder Team Description: Dummy package to satisfy dependencies with aptitude - created by pbuilder This package was created automatically by pbuilder to satisfy the build-dependencies of the package being currently built. Depends: debhelper-compat (= 13), cmake, pkg-kde-tools dpkg-deb: building package 'pbuilder-satisfydepends-dummy' in '/tmp/satisfydepends-aptitude/pbuilder-satisfydepends-dummy.deb'. Selecting previously unselected package pbuilder-satisfydepends-dummy. (Reading database ... 19956 files and directories currently installed.) Preparing to unpack .../pbuilder-satisfydepends-dummy.deb ... Unpacking pbuilder-satisfydepends-dummy (0.invalid.0) ... dpkg: pbuilder-satisfydepends-dummy: dependency problems, but configuring anyway as you requested: pbuilder-satisfydepends-dummy depends on debhelper-compat (= 13); however: Package debhelper-compat is not installed. pbuilder-satisfydepends-dummy depends on cmake; however: Package cmake is not installed. pbuilder-satisfydepends-dummy depends on pkg-kde-tools; however: Package pkg-kde-tools is not installed. Setting up pbuilder-satisfydepends-dummy (0.invalid.0) ... Reading package lists... Building dependency tree... Reading state information... Initializing package states... Writing extended state information... Building tag database... pbuilder-satisfydepends-dummy is already installed at the requested version (0.invalid.0) pbuilder-satisfydepends-dummy is already installed at the requested version (0.invalid.0) The following NEW packages will be installed: autoconf{a} automake{a} autopoint{a} autotools-dev{a} bsdextrautils{a} cmake{a} cmake-data{a} debhelper{a} dh-autoreconf{a} dh-strip-nondeterminism{a} dwz{a} file{a} gettext{a} gettext-base{a} groff-base{a} intltool-debian{a} libarchive-zip-perl{a} libarchive13t64{a} libbrotli1{a} libcom-err2{a} libcurl4t64{a} libdebhelper-perl{a} libelf1t64{a} libexpat1{a} libfile-stripnondeterminism-perl{a} libgssapi-krb5-2{a} libicu72{a} libjsoncpp26{a} libk5crypto3{a} libkeyutils1{a} libkrb5-3{a} libkrb5support0{a} libldap-2.5-0{a} libmagic-mgc{a} libmagic1t64{a} libnghttp2-14{a} libnsl2{a} libpipeline1{a} libproc2-0{a} libpsl5t64{a} libpython3-stdlib{a} libpython3.12-minimal{a} libpython3.12-stdlib{a} libreadline8t64{a} librhash1{a} librtmp1{a} libsasl2-2{a} libsasl2-modules-db{a} libssh2-1t64{a} libtirpc-common{a} libtirpc3t64{a} libtool{a} libuchardet0{a} libuv1t64{a} libxml2{a} libyaml-0-2{a} m4{a} man-db{a} media-types{a} netbase{a} pkg-kde-tools{a} po-debconf{a} procps{a} python3{a} python3-autocommand{a} python3-chardet{a} python3-debian{a} python3-inflect{a} python3-jaraco.context{a} python3-jaraco.functools{a} python3-minimal{a} python3-more-itertools{a} python3-pkg-resources{a} python3-typeguard{a} python3-typing-extensions{a} python3-yaml{a} python3.12{a} python3.12-minimal{a} readline-common{a} sensible-utils{a} tzdata{a} The following packages are RECOMMENDED but will NOT be installed: ca-certificates curl krb5-locales libarchive-cpio-perl libldap-common libltdl-dev libmail-sendmail-perl libsasl2-modules libwww-perl linux-sysctl-defaults lynx psmisc publicsuffix python3-apt wget zstd 0 packages upgraded, 81 newly installed, 0 to remove and 0 not upgraded. Need to get 46.1 MB of archives. After unpacking 171 MB will be used. Writing extended state information... Get: 1 http://deb.debian.org/debian trixie/main i386 libpython3.12-minimal i386 3.12.7-3 [814 kB] Get: 2 http://deb.debian.org/debian trixie/main i386 libexpat1 i386 2.6.4-1 [107 kB] Get: 3 http://deb.debian.org/debian trixie/main i386 python3.12-minimal i386 3.12.7-3 [2236 kB] Get: 4 http://deb.debian.org/debian trixie/main i386 python3-minimal i386 3.12.6-1 [26.7 kB] Get: 5 http://deb.debian.org/debian trixie/main i386 media-types all 10.1.0 [26.9 kB] Get: 6 http://deb.debian.org/debian trixie/main i386 netbase all 6.4 [12.8 kB] Get: 7 http://deb.debian.org/debian trixie/main i386 tzdata all 2024b-3 [255 kB] Get: 8 http://deb.debian.org/debian trixie/main i386 libkrb5support0 i386 1.21.3-3 [34.9 kB] Get: 9 http://deb.debian.org/debian trixie/main i386 libcom-err2 i386 1.47.1-1+b1 [23.4 kB] Get: 10 http://deb.debian.org/debian trixie/main i386 libk5crypto3 i386 1.21.3-3 [83.6 kB] Get: 11 http://deb.debian.org/debian trixie/main i386 libkeyutils1 i386 1.6.3-4 [9600 B] Get: 12 http://deb.debian.org/debian trixie/main i386 libkrb5-3 i386 1.21.3-3 [350 kB] Get: 13 http://deb.debian.org/debian trixie/main i386 libgssapi-krb5-2 i386 1.21.3-3 [146 kB] Get: 14 http://deb.debian.org/debian trixie/main i386 libtirpc-common all 1.3.4+ds-1.3 [10.9 kB] Get: 15 http://deb.debian.org/debian trixie/main i386 libtirpc3t64 i386 1.3.4+ds-1.3+b1 [90.5 kB] Get: 16 http://deb.debian.org/debian trixie/main i386 libnsl2 i386 1.3.0-3+b3 [42.7 kB] Get: 17 http://deb.debian.org/debian trixie/main i386 readline-common all 8.2-5 [69.3 kB] Get: 18 http://deb.debian.org/debian trixie/main i386 libreadline8t64 i386 8.2-5 [173 kB] Get: 19 http://deb.debian.org/debian trixie/main i386 libpython3.12-stdlib i386 3.12.7-3 [1964 kB] Get: 20 http://deb.debian.org/debian trixie/main i386 python3.12 i386 3.12.7-3 [671 kB] Get: 21 http://deb.debian.org/debian trixie/main i386 libpython3-stdlib i386 3.12.6-1 [9692 B] Get: 22 http://deb.debian.org/debian trixie/main i386 python3 i386 3.12.6-1 [27.8 kB] Get: 23 http://deb.debian.org/debian trixie/main i386 libproc2-0 i386 2:4.0.4-6 [65.7 kB] Get: 24 http://deb.debian.org/debian trixie/main i386 procps i386 2:4.0.4-6 [876 kB] Get: 25 http://deb.debian.org/debian trixie/main i386 sensible-utils all 0.0.24 [24.8 kB] Get: 26 http://deb.debian.org/debian trixie/main i386 libmagic-mgc i386 1:5.45-3+b1 [314 kB] Get: 27 http://deb.debian.org/debian trixie/main i386 libmagic1t64 i386 1:5.45-3+b1 [115 kB] Get: 28 http://deb.debian.org/debian trixie/main i386 file i386 1:5.45-3+b1 [43.2 kB] Get: 29 http://deb.debian.org/debian trixie/main i386 gettext-base i386 0.22.5-2 [201 kB] Get: 30 http://deb.debian.org/debian trixie/main i386 libuchardet0 i386 0.0.8-1+b2 [69.2 kB] Get: 31 http://deb.debian.org/debian trixie/main i386 groff-base i386 1.23.0-5 [1196 kB] Get: 32 http://deb.debian.org/debian trixie/main i386 bsdextrautils i386 2.40.2-11 [95.6 kB] Get: 33 http://deb.debian.org/debian trixie/main i386 libpipeline1 i386 1.5.8-1 [41.2 kB] Get: 34 http://deb.debian.org/debian trixie/main i386 man-db i386 2.13.0-1 [1428 kB] Get: 35 http://deb.debian.org/debian trixie/main i386 m4 i386 1.4.19-4 [293 kB] Get: 36 http://deb.debian.org/debian trixie/main i386 autoconf all 2.72-3 [493 kB] Get: 37 http://deb.debian.org/debian trixie/main i386 autotools-dev all 20220109.1 [51.6 kB] Get: 38 http://deb.debian.org/debian trixie/main i386 automake all 1:1.16.5-1.3 [823 kB] Get: 39 http://deb.debian.org/debian trixie/main i386 autopoint all 0.22.5-2 [723 kB] Get: 40 http://deb.debian.org/debian trixie/main i386 cmake-data all 3.30.5-1 [2223 kB] Get: 41 http://deb.debian.org/debian trixie/main i386 libicu72 i386 72.1-5+b1 [9583 kB] Get: 42 http://deb.debian.org/debian trixie/main i386 libxml2 i386 2.12.7+dfsg+really2.9.14-0.2+b1 [734 kB] Get: 43 http://deb.debian.org/debian trixie/main i386 libarchive13t64 i386 3.7.4-1.1 [390 kB] Get: 44 http://deb.debian.org/debian trixie/main i386 libbrotli1 i386 1.1.0-2+b6 [308 kB] Get: 45 http://deb.debian.org/debian trixie/main i386 libsasl2-modules-db i386 2.1.28+dfsg1-8 [20.6 kB] Get: 46 http://deb.debian.org/debian trixie/main i386 libsasl2-2 i386 2.1.28+dfsg1-8 [61.0 kB] Get: 47 http://deb.debian.org/debian trixie/main i386 libldap-2.5-0 i386 2.5.18+dfsg-3+b1 [200 kB] Get: 48 http://deb.debian.org/debian trixie/main i386 libnghttp2-14 i386 1.64.0-1 [82.4 kB] Get: 49 http://deb.debian.org/debian trixie/main i386 libpsl5t64 i386 0.21.2-1.1+b1 [57.7 kB] Get: 50 http://deb.debian.org/debian trixie/main i386 librtmp1 i386 2.4+20151223.gitfa8646d.1-2+b5 [62.4 kB] Get: 51 http://deb.debian.org/debian trixie/main i386 libssh2-1t64 i386 1.11.1-1 [256 kB] Get: 52 http://deb.debian.org/debian trixie/main i386 libcurl4t64 i386 8.11.0-1 [392 kB] Get: 53 http://deb.debian.org/debian trixie/main i386 libjsoncpp26 i386 1.9.6-2 [90.0 kB] Get: 54 http://deb.debian.org/debian trixie/main i386 librhash1 i386 1.4.5-1 [144 kB] Get: 55 http://deb.debian.org/debian trixie/main i386 libuv1t64 i386 1.48.0-7 [157 kB] Get: 56 http://deb.debian.org/debian trixie/main i386 cmake i386 3.30.5-1 [12.5 MB] Get: 57 http://deb.debian.org/debian trixie/main i386 libdebhelper-perl all 13.20 [89.7 kB] Get: 58 http://deb.debian.org/debian trixie/main i386 libtool all 2.4.7-8 [517 kB] Get: 59 http://deb.debian.org/debian trixie/main i386 dh-autoreconf all 20 [17.1 kB] Get: 60 http://deb.debian.org/debian trixie/main i386 libarchive-zip-perl all 1.68-1 [104 kB] Get: 61 http://deb.debian.org/debian trixie/main i386 libfile-stripnondeterminism-perl all 1.14.0-1 [19.5 kB] Get: 62 http://deb.debian.org/debian trixie/main i386 dh-strip-nondeterminism all 1.14.0-1 [8448 B] Get: 63 http://deb.debian.org/debian trixie/main i386 libelf1t64 i386 0.192-4 [195 kB] Get: 64 http://deb.debian.org/debian trixie/main i386 dwz i386 0.15-1+b1 [116 kB] Get: 65 http://deb.debian.org/debian trixie/main i386 gettext i386 0.22.5-2 [1631 kB] Get: 66 http://deb.debian.org/debian trixie/main i386 intltool-debian all 0.35.0+20060710.6 [22.9 kB] Get: 67 http://deb.debian.org/debian trixie/main i386 po-debconf all 1.0.21+nmu1 [248 kB] Get: 68 http://deb.debian.org/debian trixie/main i386 debhelper all 13.20 [915 kB] Get: 69 http://deb.debian.org/debian trixie/main i386 libyaml-0-2 i386 0.2.5-1+b2 [56.0 kB] Get: 70 http://deb.debian.org/debian trixie/main i386 python3-autocommand all 2.2.2-3 [13.6 kB] Get: 71 http://deb.debian.org/debian trixie/main i386 python3-more-itertools all 10.5.0-1 [63.8 kB] Get: 72 http://deb.debian.org/debian trixie/main i386 python3-typing-extensions all 4.12.2-2 [73.0 kB] Get: 73 http://deb.debian.org/debian trixie/main i386 python3-typeguard all 4.4.1-1 [37.0 kB] Get: 74 http://deb.debian.org/debian trixie/main i386 python3-inflect all 7.3.1-2 [32.4 kB] Get: 75 http://deb.debian.org/debian trixie/main i386 python3-jaraco.context all 6.0.0-1 [7984 B] Get: 76 http://deb.debian.org/debian trixie/main i386 python3-jaraco.functools all 4.1.0-1 [12.0 kB] Get: 77 http://deb.debian.org/debian trixie/main i386 python3-pkg-resources all 74.1.2-2 [213 kB] Get: 78 http://deb.debian.org/debian trixie/main i386 python3-chardet all 5.2.0+dfsg-1 [107 kB] Get: 79 http://deb.debian.org/debian trixie/main i386 python3-debian all 0.1.49 [115 kB] Get: 80 http://deb.debian.org/debian trixie/main i386 python3-yaml i386 6.0.2-1+b1 [173 kB] Get: 81 http://deb.debian.org/debian trixie/main i386 pkg-kde-tools all 0.18.5 [87.6 kB] Fetched 46.1 MB in 1s (35.9 MB/s) debconf: delaying package configuration, since apt-utils is not installed Selecting previously unselected package libpython3.12-minimal:i386. (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 ... 19956 files and directories currently installed.) Preparing to unpack .../libpython3.12-minimal_3.12.7-3_i386.deb ... Unpacking libpython3.12-minimal:i386 (3.12.7-3) ... Selecting previously unselected package libexpat1:i386. Preparing to unpack .../libexpat1_2.6.4-1_i386.deb ... Unpacking libexpat1:i386 (2.6.4-1) ... Selecting previously unselected package python3.12-minimal. Preparing to unpack .../python3.12-minimal_3.12.7-3_i386.deb ... Unpacking python3.12-minimal (3.12.7-3) ... Setting up libpython3.12-minimal:i386 (3.12.7-3) ... Setting up libexpat1:i386 (2.6.4-1) ... Setting up python3.12-minimal (3.12.7-3) ... Selecting previously unselected package python3-minimal. (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 ... 20276 files and directories currently installed.) Preparing to unpack .../00-python3-minimal_3.12.6-1_i386.deb ... Unpacking python3-minimal (3.12.6-1) ... Selecting previously unselected package media-types. Preparing to unpack .../01-media-types_10.1.0_all.deb ... Unpacking media-types (10.1.0) ... Selecting previously unselected package netbase. Preparing to unpack .../02-netbase_6.4_all.deb ... Unpacking netbase (6.4) ... Selecting previously unselected package tzdata. Preparing to unpack .../03-tzdata_2024b-3_all.deb ... Unpacking tzdata (2024b-3) ... Selecting previously unselected package libkrb5support0:i386. Preparing to unpack .../04-libkrb5support0_1.21.3-3_i386.deb ... Unpacking libkrb5support0:i386 (1.21.3-3) ... Selecting previously unselected package libcom-err2:i386. Preparing to unpack .../05-libcom-err2_1.47.1-1+b1_i386.deb ... Unpacking libcom-err2:i386 (1.47.1-1+b1) ... Selecting previously unselected package libk5crypto3:i386. Preparing to unpack .../06-libk5crypto3_1.21.3-3_i386.deb ... Unpacking libk5crypto3:i386 (1.21.3-3) ... 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Adding 'diversion of /lib/i386-linux-gnu/libtirpc.so.3 to /lib/i386-linux-gnu/libtirpc.so.3.usr-is-merged by libtirpc3t64' Adding 'diversion of /lib/i386-linux-gnu/libtirpc.so.3.0.0 to /lib/i386-linux-gnu/libtirpc.so.3.0.0.usr-is-merged by libtirpc3t64' Unpacking libtirpc3t64:i386 (1.3.4+ds-1.3+b1) ... Selecting previously unselected package libnsl2:i386. Preparing to unpack .../12-libnsl2_1.3.0-3+b3_i386.deb ... Unpacking libnsl2:i386 (1.3.0-3+b3) ... Selecting previously unselected package readline-common. Preparing to unpack .../13-readline-common_8.2-5_all.deb ... Unpacking readline-common (8.2-5) ... Selecting previously unselected package libreadline8t64:i386. Preparing to unpack .../14-libreadline8t64_8.2-5_i386.deb ... Adding 'diversion of /lib/i386-linux-gnu/libhistory.so.8 to /lib/i386-linux-gnu/libhistory.so.8.usr-is-merged by libreadline8t64' Adding 'diversion of /lib/i386-linux-gnu/libhistory.so.8.2 to /lib/i386-linux-gnu/libhistory.so.8.2.usr-is-merged by libreadline8t64' Adding 'diversion of /lib/i386-linux-gnu/libreadline.so.8 to /lib/i386-linux-gnu/libreadline.so.8.usr-is-merged by libreadline8t64' Adding 'diversion of /lib/i386-linux-gnu/libreadline.so.8.2 to /lib/i386-linux-gnu/libreadline.so.8.2.usr-is-merged by libreadline8t64' Unpacking libreadline8t64:i386 (8.2-5) ... Selecting previously unselected package libpython3.12-stdlib:i386. Preparing to unpack .../15-libpython3.12-stdlib_3.12.7-3_i386.deb ... Unpacking libpython3.12-stdlib:i386 (3.12.7-3) ... Selecting previously unselected package python3.12. Preparing to unpack .../16-python3.12_3.12.7-3_i386.deb ... Unpacking python3.12 (3.12.7-3) ... Selecting previously unselected package libpython3-stdlib:i386. 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Setting up librtmp1:i386 (2.4+20151223.gitfa8646d.1-2+b5) ... Setting up libjsoncpp26:i386 (1.9.6-2) ... Setting up libproc2-0:i386 (2:4.0.4-6) ... Setting up autopoint (0.22.5-2) ... Setting up libk5crypto3:i386 (1.21.3-3) ... Setting up libsasl2-2:i386 (2.1.28+dfsg1-8) ... Setting up autoconf (2.72-3) ... Setting up dwz (0.15-1+b1) ... Setting up sensible-utils (0.0.24) ... Setting up libuchardet0:i386 (0.0.8-1+b2) ... Setting up procps (2:4.0.4-6) ... Setting up netbase (6.4) ... Setting up cmake-data (3.30.5-1) ... Setting up librhash1:i386 (1.4.5-1) ... Setting up libkrb5-3:i386 (1.21.3-3) ... Setting up libssh2-1t64:i386 (1.11.1-1) ... Setting up readline-common (8.2-5) ... Setting up libxml2:i386 (2.12.7+dfsg+really2.9.14-0.2+b1) ... Setting up automake (1:1.16.5-1.3) ... update-alternatives: using /usr/bin/automake-1.16 to provide /usr/bin/automake (automake) in auto mode Setting up libfile-stripnondeterminism-perl (1.14.0-1) ... Setting up gettext (0.22.5-2) ... 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Setting up python3-more-itertools (10.5.0-1) ... Setting up python3-jaraco.functools (4.1.0-1) ... Setting up python3-jaraco.context (6.0.0-1) ... Setting up python3-typeguard (4.4.1-1) ... Setting up python3-yaml (6.0.2-1+b1) ... Setting up python3-inflect (7.3.1-2) ... Setting up python3-pkg-resources (74.1.2-2) ... Setting up python3-chardet (5.2.0+dfsg-1) ... Setting up python3-debian (0.1.49) ... Setting up pkg-kde-tools (0.18.5) ... Processing triggers for libc-bin (2.40-3) ... Reading package lists... Building dependency tree... Reading state information... Reading extended state information... Initializing package states... Writing extended state information... Building tag database... -> Finished parsing the build-deps I: Building the package I: Running cd /build/reproducible-path/qhull-2020.2/ && env PATH="/usr/sbin:/usr/bin:/sbin:/bin:/usr/games" HOME="/nonexistent/first-build" dpkg-buildpackage -us -uc -b && env PATH="/usr/sbin:/usr/bin:/sbin:/bin:/usr/games" HOME="/nonexistent/first-build" dpkg-genchanges -S > ../qhull_2020.2-6_source.changes dpkg-buildpackage: info: source package qhull dpkg-buildpackage: info: source version 2020.2-6 dpkg-buildpackage: info: source distribution unstable dpkg-buildpackage: info: source changed by Timo Röhling dpkg-source --before-build . dpkg-buildpackage: info: host architecture i386 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 dh binary --buildsystem=cmake --with pkgkde_symbolshelper dh_update_autotools_config -O--buildsystem=cmake dh_autoreconf -O--buildsystem=cmake debian/rules override_dh_auto_configure make[1]: Entering directory '/build/reproducible-path/qhull-2020.2' dh_auto_configure \ --buildsystem=cmake \ --builddir=/build/reproducible-path/qhull-2020.2/obj-i686-linux-gnu \ -- \ -DCMAKE_SKIP_RPATH=ON \ -DINCLUDE_INSTALL_DIR=include \ -DLINK_APPS_SHARED=ON \ -DLIB_INSTALL_DIR=lib/i386-linux-gnu \ -DBIN_INSTALL_DIR=bin \ -DMAN_INSTALL_DIR=share/man/man1 \ -DDOC_INSTALL_DIR=share/doc/libqhull-dev/qhull cd obj-i686-linux-gnu && DEB_PYTHON_INSTALL_LAYOUT=deb PKG_CONFIG=/usr/bin/pkg-config 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_USE_PACKAGE_REGISTRY=OFF -DCMAKE_FIND_PACKAGE_NO_PACKAGE_REGISTRY=ON -DFETCHCONTENT_FULLY_DISCONNECTED=ON -DCMAKE_INSTALL_RUNSTATEDIR=/run -DCMAKE_SKIP_INSTALL_ALL_DEPENDENCY=ON "-GUnix Makefiles" -DCMAKE_VERBOSE_MAKEFILE=ON -DCMAKE_INSTALL_LIBDIR=lib/i386-linux-gnu -DCMAKE_SKIP_RPATH=ON -DINCLUDE_INSTALL_DIR=include -DLINK_APPS_SHARED=ON -DLIB_INSTALL_DIR=lib/i386-linux-gnu -DBIN_INSTALL_DIR=bin -DMAN_INSTALL_DIR=share/man/man1 -DDOC_INSTALL_DIR=share/doc/libqhull-dev/qhull .. CMake Warning (dev) at CMakeLists.txt:70 (project): cmake_minimum_required() should be called prior to this top-level project() call. Please see the cmake-commands(7) manual for usage documentation of both commands. This warning is for project developers. Use -Wno-dev to suppress it. -- The C compiler identification is GNU 14.2.0 -- The CXX compiler identification is GNU 14.2.0 -- 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 CMake Deprecation Warning at CMakeLists.txt:71 (cmake_minimum_required): Compatibility with CMake < 3.5 will be removed from a future version of CMake. Update the VERSION argument value or use a ... suffix to tell CMake that the project does not need compatibility with older versions. -- 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/i386-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 (2.8s) -- Generating done (0.1s) CMake Warning: Manually-specified variables were not used by the project: CMAKE_EXPORT_NO_PACKAGE_REGISTRY CMAKE_FIND_PACKAGE_NO_PACKAGE_REGISTRY CMAKE_FIND_USE_PACKAGE_REGISTRY CMAKE_INSTALL_LIBDIR CMAKE_INSTALL_LOCALSTATEDIR CMAKE_INSTALL_RUNSTATEDIR CMAKE_INSTALL_SYSCONFDIR FETCHCONTENT_FULLY_DISCONNECTED -- Build files have been written to: /build/reproducible-path/qhull-2020.2/obj-i686-linux-gnu make[1]: Leaving directory '/build/reproducible-path/qhull-2020.2' dh_auto_build -O--buildsystem=cmake cd obj-i686-linux-gnu && make -j6 "INSTALL=install --strip-program=true" 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CMakeFiles/libqhull.dir/src/libqhull/poly2.c.o.d -o CMakeFiles/libqhull.dir/src/libqhull/poly2.c.o -c /build/reproducible-path/qhull-2020.2/src/libqhull/poly2.c [ 17%] Built target testqset_r [ 18%] Building C object CMakeFiles/qhullstatic_r.dir/src/libqhull_r/merge_r.c.o /usr/bin/cc -I/build/reproducible-path/qhull-2020.2/src -g -O2 -Werror=implicit-function-declaration -ffile-prefix-map=/build/reproducible-path/qhull-2020.2=. -flto=auto -ffat-lto-objects -fstack-protector-strong -Wformat -Werror=format-security -D_LARGEFILE_SOURCE -D_FILE_OFFSET_BITS=64 -Wdate-time -D_FORTIFY_SOURCE=2 -MD -MT CMakeFiles/qhullstatic_r.dir/src/libqhull_r/merge_r.c.o -MF CMakeFiles/qhullstatic_r.dir/src/libqhull_r/merge_r.c.o.d -o CMakeFiles/qhullstatic_r.dir/src/libqhull_r/merge_r.c.o -c /build/reproducible-path/qhull-2020.2/src/libqhull_r/merge_r.c [ 18%] Building C object CMakeFiles/qhullstatic_r.dir/src/libqhull_r/libqhull_r.c.o /usr/bin/cc -I/build/reproducible-path/qhull-2020.2/src -g -O2 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/build/reproducible-path/qhull-2020.2/obj-i686-linux-gnu/CMakeFiles/user_eg3.dir/DependInfo.cmake "--color=" make[3]: Leaving directory '/build/reproducible-path/qhull-2020.2/obj-i686-linux-gnu' make -f CMakeFiles/user_eg3.dir/build.make CMakeFiles/user_eg3.dir/build make[3]: Entering directory '/build/reproducible-path/qhull-2020.2/obj-i686-linux-gnu' [ 98%] Building CXX object CMakeFiles/user_eg3.dir/src/user_eg3/user_eg3_r.cpp.o /usr/bin/c++ -I/build/reproducible-path/qhull-2020.2/src -g -O2 -ffile-prefix-map=/build/reproducible-path/qhull-2020.2=. -flto=auto -ffat-lto-objects -fstack-protector-strong -Wformat -Werror=format-security -D_LARGEFILE_SOURCE -D_FILE_OFFSET_BITS=64 -Wdate-time -D_FORTIFY_SOURCE=2 -MD -MT CMakeFiles/user_eg3.dir/src/user_eg3/user_eg3_r.cpp.o -MF CMakeFiles/user_eg3.dir/src/user_eg3/user_eg3_r.cpp.o.d -o CMakeFiles/user_eg3.dir/src/user_eg3/user_eg3_r.cpp.o -c /build/reproducible-path/qhull-2020.2/src/user_eg3/user_eg3_r.cpp [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/reproducible-path/qhull-2020.2=. -flto=auto -ffat-lto-objects -fstack-protector-strong -Wformat -Werror=format-security -D_LARGEFILE_SOURCE -D_FILE_OFFSET_BITS=64 -Wdate-time -D_FORTIFY_SOURCE=2 -flto=auto -ffat-lto-objects -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 [100%] 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/reproducible-path/qhull-2020.2=. -flto=auto -ffat-lto-objects -fstack-protector-strong -Wformat -Werror=format-security -D_LARGEFILE_SOURCE -D_FILE_OFFSET_BITS=64 -Wdate-time -D_FORTIFY_SOURCE=2 -flto=auto -ffat-lto-objects -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 /usr/bin/cmake -E cmake_symlink_library libqhullcpp.so.8.0.2 libqhullcpp.so.8.0 libqhullcpp.so make[3]: Leaving directory '/build/reproducible-path/qhull-2020.2/obj-i686-linux-gnu' [100%] Built target qhullcpp make[3]: Leaving directory '/build/reproducible-path/qhull-2020.2/obj-i686-linux-gnu' [100%] Built target user_eg3 make[2]: Leaving directory '/build/reproducible-path/qhull-2020.2/obj-i686-linux-gnu' /usr/bin/cmake -E cmake_progress_start /build/reproducible-path/qhull-2020.2/obj-i686-linux-gnu/CMakeFiles 0 make[1]: Leaving directory '/build/reproducible-path/qhull-2020.2/obj-i686-linux-gnu' debian/rules execute_after_dh_auto_build make[1]: Entering directory '/build/reproducible-path/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 > $comm.1 && \ echo " done"; \ done Building man page for qconvex... done Building man page for qdelaunay... done Building man page for qhalf... done Building man page for qvoronoi... done make[1]: Leaving directory '/build/reproducible-path/qhull-2020.2' debian/rules override_dh_auto_test make[1]: Entering directory '/build/reproducible-path/qhull-2020.2' env LD_LIBRARY_PATH=/build/reproducible-path/qhull-2020.2/obj-i686-linux-gnu \ PATH=/build/reproducible-path/qhull-2020.2/obj-i686-linux-gnu:$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): 9.2e-05 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: 14 Statistics for: | qhull s d Tcv Number of points processed: 8 Number of hyperplanes created: 29 Number of facets in hull: 18 Number of distance tests for qhull: 28 CPU seconds to compute hull (after input): 3.9e-05 Output completed. Verifying that all points are below 1.3e-14 of all facets. Will make 112 distance computations. Delaunay triangulation by the convex hull of 8 points in 4-d: Number of input sites: 8 Number of Delaunay regions: 11 Statistics for: | qhull s d Tcv Number of points processed: 8 Number of hyperplanes created: 26 Number of facets in hull: 16 Number of distance tests for qhull: 43 CPU seconds to compute hull (after input): 3.1e-05 Output completed. Verifying that all points are below 1.5e-14 of all facets. Will make 88 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): 4.7e-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 pbuilder1 pbuilder1 45640 Dec 25 20:54 /build/reproducible-path/qhull-2020.2/obj-i686-linux-gnu/qconvex -rwxr-xr-x 1 pbuilder1 pbuilder1 45356 Dec 25 20:54 /build/reproducible-path/qhull-2020.2/obj-i686-linux-gnu/qdelaunay -rwxr-xr-x 1 pbuilder1 pbuilder1 45616 Dec 25 20:54 /build/reproducible-path/qhull-2020.2/obj-i686-linux-gnu/qhalf -rwxr-xr-x 1 pbuilder1 pbuilder1 49168 Dec 25 20:54 /build/reproducible-path/qhull-2020.2/obj-i686-linux-gnu/qhull -rwxr-xr-x 1 pbuilder1 pbuilder1 44768 Dec 25 20:54 /build/reproducible-path/qhull-2020.2/obj-i686-linux-gnu/qvoronoi -rwxr-xr-x 1 pbuilder1 pbuilder1 40168 Dec 25 20:54 /build/reproducible-path/qhull-2020.2/obj-i686-linux-gnu/user_eg -rwxr-xr-x 1 pbuilder1 pbuilder1 1325068 Dec 25 20:54 /build/reproducible-path/qhull-2020.2/obj-i686-linux-gnu/user_eg2 -rwxr-xr-x 1 pbuilder1 pbuilder1 4030548 Dec 25 20:54 /build/reproducible-path/qhull-2020.2/obj-i686-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): 8.4e-05 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: 1766739287 input -0.692 -0.925 -0.623 -0.886 -0.675 0.471 0.416 0.699 0.419 0.0769 0.895 0.687 -0.775 0.807 0.961 0.793 -0.41 -0.964 -0.121 -0.89 0.692 -0.666 -0.879 -0.412 Delaunay triangulation by the convex hull of 8 points in 4-d: Number of input sites: 8 Number of Delaunay regions: 14 Statistics for: | qhull s d Tcv Number of points processed: 8 Number of hyperplanes created: 29 Number of facets in hull: 18 Number of distance tests for qhull: 28 CPU seconds to compute hull (after input): 4.1e-05 Output completed. Verifying that all points are below 1.3e-14 of all facets. Will make 112 distance computations. 8 vertices and 18 facets with normals: -0.32 0.45 -0.72 -0.42 -0.91 0.25 -0.27 -0.2 -0.036 -0.49 0.3 0.82 0.19 -0.41 0.22 0.86 -0.32 -0.94 0.14 -0.062 0.28 -0.92 -0.17 -0.21 -0.28 -0.16 0.05 -0.94 0.24 -0.37 -0.2 -0.87 0.7 -0.074 0.5 0.51 0.79 -0.085 0.5 0.34 -0.37 0.63 -0.68 -0.085 -0.37 0.61 -0.68 -0.14 -0.34 0.038 0.76 -0.55 -0.34 0.037 0.66 -0.67 -0.56 0.55 -0.54 -0.31 -0.54 0.55 -0.56 -0.32 -0.7 0.39 -0.22 -0.56 -0.69 0.39 -0.21 -0.57 find 3-d Delaunay triangle or adjacent triangle closest to [0.5, 0.5, ...] -0.12 -0.89 0.69 -0.67 -0.88 -0.41 0.42 0.70 0.42 0.79 -0.41 -0.96 ======== Compute a new triangulation as a separate instance of Qhull seed: 1766739288 input -0.692 -0.662 0.888 0.0311 0.391 0.909 0.51 0.0565 -0.223 -0.0537 -0.338 -0.274 0.886 0.876 -0.932 -0.147 0.933 -0.949 0.646 -0.756 -0.473 0.707 0.299 -0.551 Delaunay triangulation by the convex hull of 8 points in 4-d: Number of input sites: 8 Number of Delaunay regions: 11 Statistics for: | qhull s d Tcv Number of points processed: 8 Number of hyperplanes created: 26 Number of facets in hull: 16 Number of distance tests for qhull: 43 CPU seconds to compute hull (after input): 3.2e-05 Output completed. Verifying that all points are below 1.5e-14 of all facets. Will make 88 distance computations. 8 vertices and 16 facets with normals: -0.37 -0.52 -0.53 0.57 0.7 -0.23 0.56 0.38 -0.32 0.6 0.46 0.57 -0.61 -0.49 -0.61 0.1 0.41 -0.57 0.59 -0.4 -0.87 0.37 0.05 -0.33 0.42 -0.56 0.58 -0.41 -0.37 0.71 -0.017 -0.6 0.91 -0.02 0.42 0.0063 0.9 -0.037 0.42 -0.052 0.13 -0.14 -0.96 -0.2 0.26 0.9 0.085 -0.35 0.2 0.89 0.062 -0.41 0.038 -0.16 -0.95 -0.27 0.33 -0.22 -0.79 -0.47 -0.01 0.29 -0.78 -0.56 ======== Free memory allocated by the new instance of Qhull, and redisplay the old results. 8 vertices and 18 facets with normals: -0.32 0.45 -0.72 -0.42 -0.91 0.25 -0.27 -0.2 -0.036 -0.49 0.3 0.82 0.19 -0.41 0.22 0.86 -0.32 -0.94 0.14 -0.062 0.28 -0.92 -0.17 -0.21 -0.28 -0.16 0.05 -0.94 0.24 -0.37 -0.2 -0.87 0.7 -0.074 0.5 0.51 0.79 -0.085 0.5 0.34 -0.37 0.63 -0.68 -0.085 -0.37 0.61 -0.68 -0.14 -0.34 0.038 0.76 -0.55 -0.34 0.037 0.66 -0.67 -0.56 0.55 -0.54 -0.31 -0.54 0.55 -0.56 -0.32 -0.7 0.39 -0.22 -0.56 -0.69 0.39 -0.21 -0.57 ======== 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): 4.7e-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: 10 Number of distance tests for qhull: 24 Number of distance tests for merging: 106 Number of distance tests for checking: 109 Number of merged facets: 7 CPU seconds to compute hull (after input): 0.0001 3 8 0.9124763375291642 1.390833937612012 -0.4826674750136242 -0.5764091147442416 0.565375258822974 -1.532352227508615 -0.1847368907548404 1.250953879569599 1.183632828365285 -1.673622343028246 0.4254952007805603 0.1339480758702938 1.673622343028246 -0.4254952007805603 -0.1339480758702938 0.1847368907548404 -1.250953879569599 -1.183632828365285 0.5764091147442416 -0.565375258822974 1.532352227508615 -0.9124763375291642 -1.390833937612012 0.4826674750136242 4 12 0.5486066141420023 0.06994002902120681 -0.8331501516894545 -1 0.5486066141420023 0.06994002902120681 -0.8331501516894545 -1 -0.7444427261367029 -0.4127293393945192 -0.5248423762474955 -1 -0.7444427261367029 -0.4127293393945192 -0.5248423762474955 -1 -0.380573002749541 0.9081645691962864 -0.1743596995716652 -1 -0.380573002749541 0.9081645691962864 -0.1743596995716652 -1 0.380573002749541 -0.9081645691962864 0.1743596995716651 -0.9999999999999999 0.380573002749541 -0.9081645691962864 0.1743596995716651 -0.9999999999999999 0.7444427261367029 0.4127293393945192 0.5248423762474956 -1 0.7444427261367029 0.4127293393945192 0.5248423762474956 -1 -0.5486066141420023 -0.0699400290212068 0.8331501516894545 -1 -0.5486066141420023 -0.0699400290212068 0.8331501516894545 -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: 0.55 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 0.38 -0.91 0.17 0.38 -0.91 0.17 0.74 0.41 0.52 0.74 0.41 0.52 -0.55 -0.07 0.83 -0.55 -0.07 0.83 ======== compute 3-d Delaunay triangulation seed: 1766739287 input -0.692 -0.925 -0.623 -0.886 -0.675 0.471 0.416 0.699 0.419 0.0769 0.895 0.687 -0.775 0.807 0.961 0.793 -0.41 -0.964 -0.121 -0.89 0.692 -0.666 -0.879 -0.412 Voronoi diagram by the convex hull of 8 points in 4-d: Number of Voronoi regions: 8 Number of Voronoi vertices: 14 Statistics for: | qhull s d Tcv v p Number of points processed: 8 Number of hyperplanes created: 29 Number of facets in hull: 18 Number of distance tests for qhull: 28 CPU seconds to compute hull (after input): 4.2e-05 3 14 -0.3869505631966547 0.5473367628686248 -0.8662092363740432 -2.239746465244463 0.6261096162184633 -0.6595238829827973 -2.570300939306273 -7.550100288819971 1.148568197987627 0.6732190995763587 -2.201719563011769 -0.3997142115193174 -0.1476489221547988 -0.0868056365381262 0.02669473842967882 0.1398740080253711 -0.2086671764327446 -0.1164933655201657 -2.188453276446459 3.676129782026723 -3.990207994998728 -1.308832755238681 2.176006764767922 -2.423178546358919 -0.3066763051181232 0.03408891517138807 0.6935484991268407 -0.2494179302709941 0.02712849491132616 0.4889605917869493 -0.9005005770368163 0.8911403923996044 -0.8785499024748412 -0.8451010962813648 0.8691215620756347 -0.8804774889394923 -0.6244942948807374 0.3512057073705355 -0.1934173287255678 -0.6029378135050845 0.3367812029654345 -0.1847099626363767 Output completed. Verifying that all points are below 1.3e-14 of all facets. Will make 112 distance computations. 8 vertices and 18 facets with normals: -0.32 0.45 -0.72 -0.42 -0.91 0.25 -0.27 -0.2 -0.036 -0.49 0.3 0.82 0.19 -0.41 0.22 0.86 -0.32 -0.94 0.14 -0.062 0.28 -0.92 -0.17 -0.21 -0.28 -0.16 0.05 -0.94 0.24 -0.37 -0.2 -0.87 0.7 -0.074 0.5 0.51 0.79 -0.085 0.5 0.34 -0.37 0.63 -0.68 -0.085 -0.37 0.61 -0.68 -0.14 -0.34 0.038 0.76 -0.55 -0.34 0.037 0.66 -0.67 -0.56 0.55 -0.54 -0.31 -0.54 0.55 -0.56 -0.32 -0.7 0.39 -0.22 -0.56 -0.69 0.39 -0.21 -0.57 find 3-d Delaunay triangle or adjacent triangle closest to [0.5, 0.5, ...] -0.12 -0.89 0.69 -0.67 -0.88 -0.41 0.42 0.70 0.42 0.79 -0.41 -0.96 ======== Compute a new triangulation as a separate instance of Qhull seed: 1766739288 input -0.692 -0.662 0.888 0.0311 0.391 0.909 0.51 0.0565 -0.223 -0.0537 -0.338 -0.274 0.886 0.876 -0.932 -0.147 0.933 -0.949 0.646 -0.756 -0.473 0.707 0.299 -0.551 Voronoi diagram by the convex hull of 8 points in 4-d: Number of Voronoi regions: 8 Number of Voronoi vertices: 11 Statistics for: | qhull s d Tcv v p Number of points processed: 8 Number of hyperplanes created: 26 Number of facets in hull: 16 Number of distance tests for qhull: 43 CPU seconds to compute hull (after input): 3.4e-05 3 11 0.5123810883923262 -0.7113038087510328 0.7340451404363041 -1.335723356362483 0.5715327116692873 0.07624744752038291 0.5222156089129758 -0.6875855873471155 0.7187298459312566 -0.311135821854325 0.5989453591627577 -0.01406142310608471 8.733813367775333 -0.3596569258326869 4.098561045686695 0.3242211775804149 -0.3454091304777254 -2.373984227789903 0.3737215292420546 1.289870038519164 0.1218001184264083 0.2509167814873434 1.096139994988469 0.07706371800421163 0.069389423560146 -0.2828225907999108 -1.727567403075561 0.3485038335437028 -0.2342085909871188 -0.8473369641746458 -0.009292190075530286 0.2574920584462871 -0.6989966821133822 Output completed. Verifying that all points are below 1.5e-14 of all facets. Will make 88 distance computations. 8 vertices and 16 facets with normals: -0.37 -0.52 -0.53 0.57 0.7 -0.23 0.56 0.38 -0.32 0.6 0.46 0.57 -0.61 -0.49 -0.61 0.1 0.41 -0.57 0.59 -0.4 -0.87 0.37 0.05 -0.33 0.42 -0.56 0.58 -0.41 -0.37 0.71 -0.017 -0.6 0.91 -0.02 0.42 0.0063 0.9 -0.037 0.42 -0.052 0.13 -0.14 -0.96 -0.2 0.26 0.9 0.085 -0.35 0.2 0.89 0.062 -0.41 0.038 -0.16 -0.95 -0.27 0.33 -0.22 -0.79 -0.47 -0.01 0.29 -0.78 -0.56 ======== Free memory allocated by the new instance of Qhull, and redisplay the old results. 8 vertices and 18 facets with normals: -0.32 0.45 -0.72 -0.42 -0.91 0.25 -0.27 -0.2 -0.036 -0.49 0.3 0.82 0.19 -0.41 0.22 0.86 -0.32 -0.94 0.14 -0.062 0.28 -0.92 -0.17 -0.21 -0.28 -0.16 0.05 -0.94 0.24 -0.37 -0.2 -0.87 0.7 -0.074 0.5 0.51 0.79 -0.085 0.5 0.34 -0.37 0.63 -0.68 -0.085 -0.37 0.61 -0.68 -0.14 -0.34 0.038 0.76 -0.55 -0.34 0.037 0.66 -0.67 -0.56 0.55 -0.54 -0.31 -0.54 0.55 -0.56 -0.32 -0.7 0.39 -0.22 -0.56 -0.69 0.39 -0.21 -0.57 ======== 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): 5.2e-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_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): 9.1e-05 Output completed. Verifying that all points are below outer planes of all facets. Will make 168 distance computations. ======== compute 2-d Delaunay triangulation seed: 1766739287 8 vertices and 12 facets with normals: -0.17 0.038 0.98 -0.99 -0.054 -0.14 0.029 0.99 -0.12 -0.18 0.83 -0.52 -0.14 0.6 -0.78 -0.89 -0.19 -0.42 -0.48 -0.32 -0.82 0.71 -0.7 0.13 0.54 0.74 -0.41 0.72 0.43 -0.55 0.71 -0.69 0.096 0.72 -0.69 0.077 Delaunay triangulation by the convex hull of 8 points in 3-d: Number of input sites: 8 Number of Delaunay regions: 8 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: 30 CPU seconds to compute hull (after input): 2.5e-05 Output completed. Verifying that all points are below 6.5e-15 of all facets. Will make 64 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, ...] 0.89 0.69 0.42 0.70 0.42 0.08 Delaunay triangulation by the convex hull of 14 points in 3-d: Number of input sites: 14 Number of Delaunay regions: 18 Statistics for: user_eg2 Delaunay example | qhull s d Tcv Number of points processed: 14 Number of hyperplanes created: 53 Number of facets in hull: 24 Number of distance tests for qhull: 77 CPU seconds to compute hull (after input): 2.5e-05 Output completed. Verifying that all points are below 6.5e-15 of all facets. Will make 252 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): 4.3e-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): 4.3e-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: 0.55 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 0.38 -0.91 0.17 0.38 -0.91 0.17 0.74 0.41 0.52 0.74 0.41 0.52 -0.55 -0.07 0.83 -0.55 -0.07 0.83 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 -0.63 0.7 0.34 0.1 0.71 -0.7 0.65 0.65 0.41 0.62 0.62 0.49 -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 -0.11 -0.7 0.71 -0.68 -0.29 0.68 0.62 0.49 0.62 0.7 0.13 0.7 -0.66 0.34 0.67 -0.67 0.3 0.67 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: 44 Number of distance tests for qhull: 68 Number of distance tests for merging: 290 Number of distance tests for checking: 253 Number of merged facets: 7 CPU seconds to compute hull (after input): 8.9e-05 3 14 0.9124763375291642 1.390833937612012 -0.4826674750136242 -0.5764091147442416 0.565375258822974 -1.532352227508615 -0.1847368907548404 1.250953879569599 1.183632828365285 -1.673622343028246 0.4254952007805603 0.1339480758702938 1.673622343028246 -0.4254952007805603 -0.1339480758702938 0.1847368907548404 -1.250953879569599 -1.183632828365285 0.5764091147442416 -0.565375258822974 1.532352227508615 -0.9124763375291642 -1.390833937612012 0.4826674750136242 -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: 1766739287 8 vertices and 12 facets with normals: -0.17 0.038 0.98 -0.99 -0.054 -0.14 0.029 0.99 -0.12 -0.18 0.83 -0.52 -0.14 0.6 -0.78 -0.89 -0.19 -0.42 -0.48 -0.32 -0.82 0.71 -0.7 0.13 0.54 0.74 -0.41 0.72 0.43 -0.55 0.71 -0.69 0.096 0.72 -0.69 0.077 Voronoi diagram by the convex hull of 8 points in 3-d: Number of Voronoi regions: 8 Number of Voronoi vertices: 8 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: 30 CPU seconds to compute hull (after input): 2.4e-05 2 8 -3.503717998875223 -0.1926781790361984 0.117428272766606 4.032318485355407 -0.1751771537317628 0.8033496327944323 -0.08783620978549575 0.385466659839739 -1.042434449478703 -0.2226265139799337 -0.2966156836433557 -0.1943516682652714 0.6606862269325582 0.9055604769123614 0.6479026868097931 0.3889426525955554 Output completed. Verifying that all points are below 6.5e-15 of all facets. Will make 64 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, ...] 0.89 0.69 0.42 0.70 0.42 0.08 Voronoi diagram by the convex hull of 14 points in 3-d: Number of Voronoi regions: 14 Number of Voronoi vertices: 18 Statistics for: user_eg2 Delaunay example | qhull s d Tcv v p Number of points processed: 14 Number of hyperplanes created: 53 Number of facets in hull: 24 Number of distance tests for qhull: 77 CPU seconds to compute hull (after input): 2.4e-05 2 18 0.6479026868097931 0.3889426525955554 -0.769963765625807 -0.7062324863727351 0.8584244797252335 0.2246577707324191 5.497977866157113 -2.0883722402692 0.144278982622233 -0.1884284386395805 2.154077140285725 -5.896088604556519 -0.8779328691926779 0.5930580155101515 -0.2060075419458726 0.7941239914280079 -0.1344936684412218 0.6086993918509759 0.6684563872308182 0.900751311191182 0.6599483999585832 0.8757428706501962 0.07375322939002157 0.3862300879017727 -0.1298378668543489 0.5864236970770951 0.1061006352178398 -0.1673174863037235 -0.6261541009757136 0.07863478307944848 -0.4183570102128175 -0.4278646059371435 -0.6249942909664633 -0.3406377709725489 -0.7610842822983078 -0.2060860543432686 Output completed. Verifying that all points are below 6.5e-15 of all facets. Will make 252 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): 4.5e-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. ======== 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): 4.5e-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 -0.5773502691896257 -0.5773502691896257 -0.5773502691896257 -0.2886751345948129 0.5773502691896257 -0.5773502691896257 -0.5773502691896257 -0.2886751345948129 -0.5773502691896257 -0.5773502691896257 0.5773502691896257 -0.2886751345948129 0.5773502691896257 -0.5773502691896257 0.5773502691896257 -0.2886751345948129 0.5773502691896257 0.5773502691896257 -0.5773502691896257 -0.2886751345948129 -0.5773502691896257 0.5773502691896257 -0.5773502691896257 -0.2886751345948129 0.5773502691896257 0.5773502691896257 0.5773502691896257 -0.2886751345948129 -0.5773502691896257 0.5773502691896257 0.5773502691896257 -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 0.07952334739223435 -0.4511049142583319 0.209819606448483 0.2797056779076398 0.01332249167684698 0.07841275503825201 -0.08888640449278654 0.08619647248293875 0.01533062477215728 -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 1.593777193553692e-17 3.225501463144376e-17 0.5856274089010269 4.519767806548947e-17 -2.967377898513707 -0.2290343684408742 -0.2527745420948133 0.956872698664004 1.792237013095374e-17 0.1571419516493774 0.3619977084558905 0.3129256373384355 -0.2763523586794005 0.0530782163393836 -0.1643502208872392 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 1.59378e-17 3.2255e-17 0.585627 4.51977e-17 -2.96738 -0.229034 -0.252775 0.956873 1.79224e-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 1.593777193553692e-17 3.225501463144376e-17 0.5856274089010269 4.519767806548947e-17 -2.967377898513707 -0.2290343684408742 -0.2527745420948133 0.956872698664004 1.792237013095374e-17 0.1571419516493774 0.3619977084558905 0.3129256373384355 -0.2763523586794005 0.0530782163393836 -0.1643502208872392 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 1.59378e-17 3.2255e-17 0.585627 4.51977e-17 -2.96738 -0.229034 -0.252775 0.956873 1.79224e-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 0.9933067158065387 -0.1155065726858348 -0.3427516509210134 5 0 2 -0.2990888272252208 0.9542252739416631 0.1727022360246515 5 0 3 -0.9964596398753636 -0.08407250501478324 -0.2494748932535505 5 1 5 0.3943714145865591 -0.9189511343684148 -0.3773632397513815 5 1 2 -0.9810105005095815 0.1939546284313432 0.08394677360204822 5 1 6 0.4123709353479589 0.9110160326142727 -0.3945864897570009 5 2 6 0.8181972788475074 0.5749375730342681 -0.3366992011759034 5 2 3 -0.5741895716505729 -0.8187223801800777 -0.3384613206611198 5 2 4 -0.7047972640762142 0.709408779583875 -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 1.831810120886449e-17 9.159050604432243e-18 5 3 4 1.781568967028413e-16 1 8.907844835142065e-17 5 4 6 1 -3.766903033201197e-16 1.883451516600599e-16 5 5 6 -3.922836751542099e-17 1 1.96141837577105e-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 1.83181e-17 9.15905e-18 5 3 4 1.78157e-16 1 8.90784e-17 5 4 6 1 -3.7669e-16 1.88345e-16 5 5 6 -3.92284e-17 1 1.96142e-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): 2.8e-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 330809540 _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 5.1e-05 CPU secs. Previous p-1(v3) delta 5.1e-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): 9.3e-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): 6.3e-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): 3.4e-05 2 7 -0.02222276248244826 -0.4979727817680433 -0.4285431913366012 0.4745826469497594 0.3790312361708202 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): 2.4e-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 0.2247255418679915 -0.03782349642163468 0.1925192701852095 0.3004920247946792 0.3694544596313075 0.4210962191420572 0.4041140804824029 0.3641479121187217 0.2339522165562513 0.03489791698278665 0.1885552061417448 -0.4707134565997063 -0.2810653003687647 0.1354949890035158 0.3189277533404903 0.2642752088273644 -0.3265712199048802 0.3175057017407433 0.2773000183087906 0.3183227589524563 0.05060330969337682 0.4898217078203538 0.3438153792710754 0.4334355904100795 -0.2480392830893763 0.2037671452423252 0.2909109464698328 -0.2855954200826543 -0.00222700694783312 -0.4293096679535784 0.2658764945305452 -0.4075898489985521 -0.3625928418362446 -0.0978938169757778 0.3071862533596335 -0.3013850588364387 -0.3786854184034145 0.4341719447953365 0.4227408774485774 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): 0.000709 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): 0.000695 Voronoi vertices and regions for 'qhull v' via C++ classes 5 3 33 1 -10.101 -10.101 -10.101 -10.101 -10.101 -2.77556e-17 -2.77556e-17 -2.77556e-17 2.77556e-17 2.77556e-17 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 -2.775557561562891e-17 -2.775557561562891e-17 -2.775557561562891e-17 2.775557561562891e-17 2.775557561562891e-17 0.9166666666666666 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): 4.8e-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 -0.1294381801544405 -0.07247409101984713 0.08267689532419759 -0.2397644955865706 0.1295260566906467 1.71603357311684 0.1740355150742393 0.5317519038435643 0.1851415205797576 0.3882545794457365 -0.9065939866848103 -0.2962957610652135 -0.1954805620516266 -0.07111892482963197 -0.1407581310832469 0.7233857048236083 -0.1676297826663961 0.2080621273999392 0.05868313821742958 0.06632066014880164 0.08806341399736999 0.1054080604689986 0.4761588899009251 -0.03168366595227298 3.094213357897468 -0.0647219456776819 0.5410515627308727 0.2115615434955919 Results of Fi 19 5 0 5 -0.3018806392032148 0.9533457293522946 0.008789126238507786 5 0 7 0.02051532578114109 0.9997895385570373 0.07511430445246006 5 0 9 0.6192591330569687 0.785186682340914 0.1370614663104578 5 1 5 0.7995952824356685 -0.6005392446015694 0.5469710423089691 5 1 3 0.9648718030091262 -0.2627211520946074 0.3258622775065154 5 2 6 0.2281595097543256 -0.9736237661995858 0.08253528745668798 5 2 4 0.4446710312325421 0.8956939622340812 -0.4300843534994403 5 2 7 -0.9458410914974847 0.3246299888101016 0.04907537812572176 5 3 5 -0.9986432053419565 0.05207445078292232 -0.1782370644858235 5 3 7 0.6877523324625938 -0.7259454037269345 0.2663295190946454 5 3 4 0.99929448732669 0.03755699133966529 -0.1938837324602516 5 4 6 -0.1075842248297362 -0.9941959739245502 0.2685422477498993 5 4 7 -0.9970183790688238 -0.07716444646969929 0.2145489484590233 5 5 7 0.9950609206245129 -0.09926612839179737 0.1874553677160639 5 6 7 -0.7993641842155075 0.6008468199079332 0.007060641163779201 5 6 9 -0.2285415587894346 -0.9735341575446109 0.07797696388863326 5 6 8 -0.01261839651625043 -0.9999203848653945 -0.02567278177543589 5 7 9 0.5936952885926359 -0.8046899429612047 0.01852766555277022 5 8 9 -0.4674785097727934 0.8840044360186256 0.2506025495170937 Results of Fo 4 5 0 8 0.7190625207842074 0.6949453872092837 0.1071733734620183 5 0 1 -0.3854955578888163 0.922709691532494 -0.07609298438083838 5 1 4 0.9929212365203528 -0.1187746524595786 0.07521211888503933 5 4 8 -0.06640144810487504 -0.9977929883946748 0.1408811441173878 set +v === check front ends and examples Thu Dec 25 20:54:47 -12 2025 ================== 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): 6.1e-05 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): 3.5e-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): 2.5e-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): 0.003334 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): 3.4e-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): 0.000263 4 4 0.2135848119563837 0.1168704340428168 0.9699086708284445 -0.09806074564261894 0.08553875579270354 -0.8316435307282576 -0.5486822022403076 -0.1234144150397865 -0.749541668500822 -0.02779445272382572 -0.6613733859014792 -0.2159556159595279 0.3120013537900506 0.9498158823230657 -0.02247097950761923 -0.02453689035981484 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): 0.000267 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 QR1766739288 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): 0.0226 Approximate facet area: 0.00035546337 Approximate volume: 8.5511197e-06 rbox c D6 | qconvex s FA TF500 At 20:54:48 & 0.00094 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 20:54:48 & 0.001914 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 20:54:48 & 0.002792 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 20:54:48 & 0.003273 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 20:54:48 & 0.003448 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): 0.003494 Approximate facet area: 12 Approximate volume: 1 rbox c D7 | qconvex s FA TF1000 At 20:54:48 & 0.001984 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 20:54:48 & 0.004422 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 20:54:48 & 0.00706 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 20:54:48 & 0.009396 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 20:54:48 & 0.012032 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 20:54:48 & 0.014576 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 20:54:48 & 0.017531 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 20:54:48 & 0.020223 CPU secs, qhull has created 8943 facets and merged 7343. The current hull contains 174 facets and 67 vertices. There are 61 outside points. Next is point p80(v68), 0.23 above f7175. At 20:54:48 & 0.023067 CPU secs, qhull has created 10022 facets and merged 8378. The current hull contains 118 facets and 77 vertices. There are 51 outside points. Next is point p12(v78), 0.45 above f7959. At 20:54:48 & 0.025984 CPU secs, qhull has created 11050 facets and merged 9384. The current hull contains 53 facets and 94 vertices. There are 34 outside points. Next is point p15(v95), 0.41 above f10368. At 20:54:48 & 0.028443 CPU secs, qhull has created 12077 facets and merged 10333. The current hull contains 81 facets and 111 vertices. There are 17 outside points. Next is point p82(v112), 0.41 above f10430. At 20:54:48 & 0.030703 CPU secs, qhull has created 12770 facets and merged 11000. The current hull contains 14 facets and 128 vertices. Last point was p37 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: 1771 Number of distance tests for qhull: 10249 Number of distance tests for merging: 90213 Number of distance tests for checking: 0 Number of merged facets: 11000 First post-merge with 'C4.4e-15' and 'A1.8e+308' At 20:54:48 & 0.030947 CPU secs, qhull has created 12770 facets and merged 11000. The current hull contains 14 facets and 128 vertices. Last point was p37 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: 1771 Number of distance tests for qhull: 10249 Number of distance tests for merging: 90381 Number of distance tests for checking: 1792 Number of merged facets: 11000 CPU seconds to compute hull (after input): 0.03104 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 QR1766739288 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): 0.02281 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): 3.5e-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 330826347 _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): 4.8e-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 0.7071067811865476 -0.7071067811865476 -0.3535533905932738 5 0 1 -0.7071067811865476 -0.7071067811865476 -0.3535533905932738 5 0 2 -0.7071067811865476 0.7071067811865476 -0.3535533905932738 5 0 4 0.7071067811865476 0.7071067811865476 -0.3535533905932738 Voronoi ridge statistics 4 bounded ridges 0 max. distance of midpoint to ridge 4 bounded ridges with ok normal 1.4e-16 ave. angle to ridge 1.4e-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): 3.6e-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): 4e-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): 5.6e-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 -2.572789203902914e-11 1.749999999802917 -2.0546373700981e-11 -1.750000000331276 0.5833333333083517 -0.5833333333052267 1.862263126909194e-11 -7.815055220092851e-11 1.750000000002628 3.498097972106761e-11 0.5833333333132078 0.5833333333796981 -0.5833333332888888 0.5833333333317836 -7.592296236147433e-11 -7.815050692933325e-11 -1.750000000049026 2.293199654852279e-11 -0.5833333333977307 -0.583333333322986 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): 5e-05 4 0 0 1 1 0 1 2 1 2 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 2 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): 3.7e-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): 4.1e-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): 3.7e-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): 5.8e-05 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): 4e-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 -7.748592400792809e-11 -0.5000000000743411 2.849349704487492e-11 0.49999999991804 -0.5000000000721135 -1.373719891421591e-11 0.5000000000148132 7.166044474310067e-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: 261 Number of facets in hull: 86 Number of distance tests for qhull: 1733 Number of distance tests for merging: 2778 Number of distance tests for checking: 1248 Number of merged facets: 151 CPU seconds to compute hull (after input): 0.000561 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): 4.7e-05 Approximate facet area: 1 4 4 3 6 5 4 0.2 0.2 0.3 0.3 4 0 0 1 1 0 1 2 1 2 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 2 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): 4.1e-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): 5.4e-05 3 12 0 0 -0.5000000000000001 0 0 -0.5000000000000001 0 -0.5000000000000001 0 0 -0.5000000000000001 0 -0.5000000000000001 0 0 -0.5000000000000001 0 0 0.5000000000000001 0 0 0.5000000000000001 0 0 0 0.5000000000000001 0 0 0.5000000000000001 0 0 0 0.5000000000000001 0 0 0.5000000000000001 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): 3.9e-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): 2.3e-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): 0.003288 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): 5.4e-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 -0.1294381801544405 -0.07247409101984713 0.08267689532419757 -0.2397644955865706 0.1295260566906469 1.71603357311684 0.1740355150742393 0.5317519038435643 0.1851415205797575 0.3882545794457365 -0.9065939866848109 -0.2962957610652137 -0.1954805620516266 -0.07111892482963184 -0.140758131083247 0.723385704823608 -0.1676297826663961 0.2080621273999393 0.05868313821742954 0.06632066014880164 0.0880634139973699 0.1054080604689985 0.4761588899009251 -0.03168366595227296 3.094213357897465 -0.06472194567768184 0.5410515627308723 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 -0.06934933488573389 0.05349366577046778 -0.3051278692468023 0.1614985054821101 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): 2.9e-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 QR1766739288 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): 0.02259 Approximate facet area: 1.735661e-07 Approximate volume: 2.0876757e-09 rbox c D7 | qhull FA TF1000 At 20:54:48 & 0.002107 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 20:54:48 & 0.00447 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 20:54:48 & 0.007148 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 20:54:48 & 0.009414 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 20:54:48 & 0.012024 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 20:54:48 & 0.01459 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 20:54:48 & 0.01752 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 20:54:48 & 0.020115 CPU secs, qhull has created 8943 facets and merged 7343. The current hull contains 174 facets and 67 vertices. There are 61 outside points. Next is point p80(v68), 0.23 above f7175. At 20:54:48 & 0.023045 CPU secs, qhull has created 10022 facets and merged 8378. The current hull contains 118 facets and 77 vertices. There are 51 outside points. Next is point p12(v78), 0.45 above f7959. At 20:54:48 & 0.026093 CPU secs, qhull has created 11050 facets and merged 9384. The current hull contains 53 facets and 94 vertices. There are 34 outside points. Next is point p15(v95), 0.41 above f10368. At 20:54:48 & 0.028581 CPU secs, qhull has created 12077 facets and merged 10333. The current hull contains 81 facets and 111 vertices. There are 17 outside points. Next is point p82(v112), 0.41 above f10430. At 20:54:48 & 0.030834 CPU secs, qhull has created 12770 facets and merged 11000. The current hull contains 14 facets and 128 vertices. Last point was p37 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: 1771 Number of distance tests for qhull: 10249 Number of distance tests for merging: 90213 Number of distance tests for checking: 0 Number of merged facets: 11000 First post-merge with 'C4.4e-15' and 'A1.8e+308' At 20:54:48 & 0.031101 CPU secs, qhull has created 12770 facets and merged 11000. The current hull contains 14 facets and 128 vertices. Last point was p37 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: 1771 Number of distance tests for qhull: 10249 Number of distance tests for merging: 90381 Number of distance tests for checking: 1792 Number of merged facets: 11000 CPU seconds to compute hull (after input): 0.0312 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): 0.000268 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): 2.9e-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 330826347 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 4e-17 [QH1055]qh_check_maxout: determine actual maxoutside [QH1024]qh_check_maxout: p7(v6) is qh.min_vertex -6.7e-16 below facet f4. Point p1 for f4 is qh.max_outside 4e-17 above f16. 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): 0.000135 [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 infom08-i386 Thu Dec 25 20:54:48 -12 2025 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: 33544 CPU seconds to compute hull (after input): 0.001542 After 1 retries, input joggled by: 2.9e-11 10 3 1000 144 284 144 284 0 0 33 0 2 5.045982607091334e-11 -5.045982607091334e-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): 0.001027 10 3 1000 84 98 84 98 0 6 13 0 2 1.942124858599573e-15 -1.036131500307862e-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: 81545 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): 0.01143 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: 344 Number of non-simplicial facets: 331 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: 42727 Number of distance tests for merging: 217801 Number of distance tests for checking: 12557 Number of merged facets: 2822 CPU seconds to compute hull (after input): 0.02145 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 172000 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): 0.00182 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: 73435 Number of distance tests for checking: 124140 Number of merged facets: 1331 CPU seconds to compute hull (after input): 0.0218 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: 4549 Number of distance tests for qhull: 229061 Number of distance tests for merging: 309340 Number of distance tests for checking: 54701 Number of merged facets: 6163 CPU seconds to compute hull (after input): 0.03654 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: 330111 Number of distance tests for checking: 88762 Number of merged facets: 3862 CPU seconds to compute hull (after input): 0.0482 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): 0.002163 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: 290 Number of coplanar points: 646 Number of facets: 1271 Number of non-simplicial facets: 151 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: 173616 Number of distance tests for merging: 91128 Number of distance tests for checking: 56702 Number of merged facets: 1353 CPU seconds to compute hull (after input): 0.0137 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 1271000 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: 5556 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: 262158 Number of distance tests for merging: 271161 Number of distance tests for checking: 90042 Number of merged facets: 1473 CPU seconds to compute hull (after input): 0.04079 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 2222400 distance computations. set +v === check input format etc. Thu Dec 25 20:54:48 -12 2025 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): 6.4e-05 qhull p TI r.x TO x.x cat x.x 3 10 -0.374949442106252 0.2247255418679915 -0.03782349642163468 0.3004920247946792 0.3694544596313075 0.4210962191420572 0.3641479121187217 0.2339522165562513 0.03489791698278665 -0.4707134565997063 -0.2810653003687647 0.1354949890035158 0.2642752088273644 -0.3265712199048802 0.3175057017407433 0.3183227589524563 0.05060330969337682 0.4898217078203538 0.4334355904100795 -0.2480392830893763 0.2037671452423252 -0.2855954200826543 -0.00222700694783312 -0.4293096679535784 -0.4075898489985521 -0.3625928418362446 -0.0978938169757778 -0.3013850588364387 -0.3786854184034145 0.4341719447953365 set +v === check qhull output formats Thu Dec 25 20:54:48 -12 2025 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): 2.8e-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): 2.5e-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): 2.8e-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 -0.9510565162951535 -0.4045084971874737 0.8090169943749473 -0.5877852522924732 -0.4045084971874737 -1 9.444121133484361e-17 -0.4045084971874737 -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 -0.9510565162951535 -0.4045084971874737 0.8090169943749473 -0.5877852522924732 -0.4045084971874737 -1 9.444121133484361e-17 -0.4045084971874737 -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 -0.02221493611318519 -0.366434993563625 0.3270621312102882 -0.06676722137887703 -0.1566931052661437 0.4589771055234383 0.02820502736438534 0.04189077954915425 0.05832764185809311 0.3126723396709862 0.08400649026409396 -0.1029227018383543 0.1781470954214661 0.1182274414396169 0.04860343742054276 -0.1220315663349177 0.01546165115708639 -0.1360330368727753 -0.3072535691850386 -0.01073880122111999 -0.4870359524963758 0.3867462923626847 0.04492879989084676 0.118335500935405 0.3789805913148267 -0.4732086509216658 -0.2177962499836425 rbox 10 D3 | qhull o 3 10 14 21 -0.02221493611318519 -0.366434993563625 0.3270621312102882 -0.06676722137887703 -0.1566931052661437 0.4589771055234383 0.02820502736438534 0.04189077954915425 0.05832764185809311 0.3126723396709862 0.08400649026409396 -0.1029227018383543 0.1781470954214661 0.1182274414396169 0.04860343742054276 -0.1220315663349177 0.01546165115708639 -0.1360330368727753 -0.3072535691850386 -0.01073880122111999 -0.4870359524963758 0.3867462923626847 0.04492879989084676 0.118335500935405 -0.1352406177997967 0.01093378431250694 -0.2358910583293913 0.3789805913148267 -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: 295 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): 6.7e-05 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: 1200 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): 0.00091 Maximum distance of vertex below facet: -0.24 (0.8x) 3 4 0.4995640899182717 0.005583735684776694 0.02011322848106415 0.3642936952899509 -0.2163723184172344 -0.2654677445467591 0.39379735093457 0.048550224424205 -0.3042474685273067 0.3971667953522451 -0.07497301400429786 -0.294342630009211 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): 6.4e-05 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): 0.00069 Maximum distance of point above facet: 0.0057 (0.6x) Maximum distance of vertex below facet: -0.0087 (1.0x) 10 29 92 222 0.05221620842441996 49 2 292 0.03790045221711882 99 9 336 0.02993864679572153 54 84 340 0.06479664045626413 54 72 226 0.03827167959574593 96 6 368 0.02282529175708788 19 1 372 0.01048228658130248 69 26 409 0.04998878658421265 19 66 371 0.008281093788857857 19 45 371 0.04608027722786205 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 -0.2391184267952279 0.1365988111464296 -0.1837860440684352 0.107954867284703 0.397449696341017 -0.062960620096848 -0.1791453880063681 0.1034612661259819 -0.1265049433582509 -0.1685859450777862 -0.4239815160855478 0.1426585555473888 -0.3376619446442108 -0.08430490557505274 0.08744874697872321 -0.2489141260729303 -0.4997188728300099 0.224904344160952 -0.03269336003129684 rbox 6 D4 | qhull o 4 6 8 16 -0.3257826863096865 -0.4296101703584289 -0.4581337649916613 0.1458114577883961 -0.3468340047139991 -0.2391184267952279 0.1365988111464296 -0.1837860440684352 0.107954867284703 0.397449696341017 -0.062960620096848 -0.1791453880063681 0.1034612661259819 -0.1265049433582509 -0.1685859450777862 -0.4239815160855478 0.1426585555473888 -0.3376619446442108 -0.08430490557505274 0.08744874697872321 -0.2489141260729303 -0.4997188728300099 0.224904344160952 -0.03269336003129684 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): 0.04596 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): 0.03231 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): 0.000293 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): 0.00214 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): 0.002087 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): 5.2e-05 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): 5.7e-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): 2.5e-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 3.12019513507746 0.5165027368863381 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 -0.05259535978789941 0.5 0.2626424396993988 0.5 0.3748708151978169 0.5 -0.01474997775140216 0.5 0.1582814042067913 0.5 -0.5 0.4508927962285399 -0.5 -0.003085198815060033 -0.3688616616361418 -0.5 -0.2798755283280048 0.5 5 0 0 0 0 5 2 4 5 9 1 2 5 0.003004576780837543 -5.902852123112957e-19 -0.5 0.2239037987067399 -0.4344308308180709 -0.25154259940753 -0.4431538257684129 0.4754463981142699 -0.005718418169504413 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): 2.7e-05 rbox 4 z h s D2 | qhull Fd s n FD Tcv begin 4 3 real 107643.7343385944 -0.2650304141580589 -0.9642400528764649 797791.7732245286 -0.6912673062074456 0.7225991360143614 874890.2679778723 0.9916265954087946 0.1291382796771071 864878.4439653738 0.3984446264475182 0.9171923896626584 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 330843154 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): 4.3e-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: -0.1205015151724568 -0.008790385787885111 -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: 0.06430144219370749 -0.04270356053094848 -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 0.1590825675964337 -0.1454013928109105 - 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 0.1503252206347391 -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 0.2053603787708732 0.06987429109559468 0.976188864039624 0.1253980026939646 -0.2031613339148239 -0.3001304507855297 -0.9320124381751694 -0.1680570625036092 -0.3911895500493897 -0.01238286325891909 -0.9202268202077502 -0.1989548866041478 0.4183781509471984 0.3424157187037642 0.8412557271095323 0.07254956874669737 4 4 0.2053603787708732 0.06987429109559468 0.976188864039624 0.125398002693964 -0.2031613339148239 -0.3001304507855297 -0.9320124381751694 -0.1680570625036099 -0.3911895500493897 -0.01238286325891909 -0.9202268202077502 -0.1989548866041485 0.4183781509471984 0.3424157187037642 0.8412557271095323 0.0725495687466967 4 4 0.2053603787708732 0.06987429109559468 0.976188864039624 0.1253980026939627 -0.2031613339148239 -0.3001304507855297 -0.9320124381751694 -0.2813242952138534 -0.3911895500493897 -0.01238286325891909 -0.9202268202077502 -0.1989548866041498 0.4183781509471984 0.3424157187037642 0.8412557271095323 0.07254956874669538 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 330843154 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 0.1132672327102436 -1.315898280434284e-15 0 2 0.8296676646636062 0.01051107893821416 3 1 -0.0278090964477178 0.06447846047808481 -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 Thu Dec 25 20:54:49 -12 2025 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): 8.2e-05 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): 5.3e-05 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): 9.9e-05 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): 9.5e-05 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 -0.1939879513790815 -0.3359969878447704 0.1939879513790817 -0.2875 -5.224499218664524e-18 0.3359969878447702 -0.1939879513790819 0.3359969878447707 0.1939879513790815 0.2875 -5.224499218664524e-18 -2.27113250081401e-16 -0.3453321730569307 -2.27113250081401e-16 -0.3453321730569307 1.057503693988049e-16 0.3453321730569308 1.057503693988049e-16 0.3453321730569308 5.224499218664524e-18 -5.224499218664524e-18 5.224499218664524e-18 -5.224499218664524e-18 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 330843154 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): 0.000136 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 330843154 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 330843154 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: 101 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): 7.6e-05 1 0 10 16 0 rbox 100 W0 | qhull Tv Q11 FO Options selected for Qhull 2020.2.r 2020/08/31: run-id 330843154 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): 0.000369 Output completed. Verifying that all points are below outer planes of all facets. Will make 8600 distance computations. set +v === test unbounded intersection Thu Dec 25 20:54:49 -12 2025 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): 0.004652 Total facet area: 5.8817432 Total volume: 0.99685163 8 0.1446087232094602 0.1622198334884075 0.2057158590759608 0.1567143851824352 0.188985866819172 0.1580674614313253 0.1616733826473111 0.1767351337533958 0 2 5.881743214947514 0.9968516315221347 4 8 1.009144997325421e-05 0.9999999999463923 2.319049754624652e-06 -0.4999875785488853 -1.229609861584452e-05 8.587946880918046e-05 0.9999999962367614 -0.5000048595493551 -1.383340239672454e-05 -0.9999999998842695 6.332306547224586e-06 -0.4999917156571328 1.802476239613105e-05 -1.901476191096464e-05 0.9999999996567733 -0.4999909156385879 0.9999999996788913 1.780140020603311e-05 -1.803683546259361e-05 -0.4999971349013697 3.470111681088062e-06 -3.668365732095583e-05 -0.9999999993211338 -0.4999893476858697 -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 0.6345454980886085 0.2737427089707437 0.722784158750618 -0.7458921924784654 -0.002537335608348058 0.6666534140166979 0.7453635270845306 -0.6767722083805113 -0.003237401631533091 0.002761552371517554 -0.9999909464886048 -0.4969398742962436 -0.0004022623770974538 0.9999997831336712 0.0005214571799133834 -0.5000167453415887 -0.999601787347817 0.0214081839262726 0.01838359029211947 -0.4985486000821885 -0.005480509661076107 -0.9999701072857251 0.005454223027194169 -0.4992904789191578 -0.9987007292177809 -0.05077399000218431 -0.004342280406757339 -0.5182179901342427 0.6755431502353134 -0.2163920762108179 0.704851701795009 -0.7475007704997937 0.001196850675493192 0.0003334814784797861 0.9999992281689842 -0.4989807987213126 0.9999992961453315 0.001186379260970641 1.459763172590227e-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 0.6345454980886085 0.2737427089707437 0.722784158750618 -0.7458921924784654 -0.002537335608348058 0.6666534140166979 0.7453635270845306 -0.6767722083805113 -0.9785529186794025 -0.009694358843403238 -0.2057673558916429 -0.5832522471275383 0.827830634881055 -0.3414688798813032 -0.4450791435520626 -0.76654742257561 0.7383776593319755 -0.4655216164679664 0.4879426777814017 -0.7788991125303445 0.2008161614085188 -0.8823413491644905 0.4256132198037725 -0.6982307124493007 0.4193230672566199 0.6721295192910489 -0.610254106552413 -0.7755692997856909 -0.3210285130221474 0.4863414284958983 -0.812657805447876 -0.7591490151594068 -0.4745617604911468 -0.2935495843214608 0.8298311738084084 -0.7523676152838531 -0.8238864443814345 -0.556605789918439 0.1067760337987316 -0.695666244857558 -0.5357402012449896 -0.5359428531021374 -0.6524934443952053 -0.8112630402464979 0.6755431502353134 -0.2163920762108179 0.704851701795009 -0.7475007704997937 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 330843154 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): 4.8e-05 set +v === check Delaunay/Voronoi Thu Dec 25 20:54:49 -12 2025 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): 7.4e-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): 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): 7.3e-05 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): 0.000142 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): 0.000107 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 -0.01883958887200764 0.3630260628303756 0.1321428524029901 0.3790312361708202 0.3779794437605696 0.2865331378987296 -0.2994955874043476 0.3776609263174803 0.2323253821416525 0.3471817493878135 0.08365533089605656 0.1275333814953112 -0.004858197648877462 0.3482682405489201 0.121314369459436 0.3443122672329771 -0.1437312230875075 0.1392096018573439 0.3093307803471859 -0.07758103877080701 0.1017043492469564 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 -0.01883958887200764 0.3630260628303756 0.1321428524029901 0.3790312361708202 0.3779794437605696 0.2865331378987296 -0.2994955874043476 0.3776609263174803 0.2323253821416525 0.3471817493878135 0.08365533089605656 0.1275333814953112 -0.004858197648877462 0.3482682405489201 0.121314369459436 0.3443122672329771 -0.1437312230875075 0.1392096018573439 0.3093307803471859 -0.07758103877080701 0.1017043492469564 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 -0.1294381801544405 -0.07247409101984713 0.08267689532419757 -0.2397644955865706 0.1295260566906469 1.71603357311684 0.1740355150742393 0.5317519038435643 0.1851415205797575 0.3882545794457365 -0.9065939866848109 -0.2962957610652137 -0.1954805620516266 -0.07111892482963184 -0.140758131083247 0.723385704823608 -0.1676297826663961 0.2080621273999393 0.05868313821742954 0.06632066014880164 0.0880634139973699 0.1054080604689985 0.4761588899009251 -0.03168366595227296 3.094213357897465 -0.06472194567768184 0.5410515627308723 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 -0.1294381801544405 -0.07247409101984713 0.08267689532419757 -0.2397644955865706 0.1295260566906469 1.71603357311684 0.1740355150742393 0.5317519038435643 0.1851415205797575 0.3882545794457365 -0.9065939866848109 -0.2962957610652137 -0.1954805620516266 -0.07111892482963184 -0.140758131083247 0.723385704823608 -0.1676297826663961 0.2080621273999393 0.05868313821742954 0.06632066014880164 0.0880634139973699 0.1054080604689985 0.4761588899009251 -0.03168366595227296 3.094213357897465 -0.06472194567768184 0.5410515627308723 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 -0.1294381801544405 -0.07247409101984713 0 # 2 f11 0.08267689532419757 -0.2397644955865706 0 # 3 f12 0.1295260566906469 1.71603357311684 0 # 4 f14 0.1740355150742393 0.5317519038435643 0 # 5 f15 0.1851415205797575 0.3882545794457365 0 # 6 f19 -0.9065939866848109 -0.2962957610652137 0 # 7 f20 -0.1954805620516266 -0.07111892482963184 0 # 8 f21 -0.140758131083247 0.723385704823608 0 # 9 f22 -0.1676297826663961 0.2080621273999393 0 # 10 f23 0.05868313821742954 0.06632066014880164 0 # 11 f24 0.0880634139973699 0.1054080604689985 0 # 12 f25 0.4761588899009251 -0.03168366595227296 0 # 13 f26 3.094213357897465 -0.06472194567768184 0 # 14 f27 0.5410515627308723 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 0.02051532578114318 0.9997895385570373 0.07511430445246034 5 0 9 0.6192591330569687 0.785186682340914 0.1370614663104578 5 0 5 -0.3018806392032151 0.9533457293522944 0.008789126238507562 5 1 3 0.9648718030091262 -0.2627211520946075 0.3258622775065154 5 1 5 0.7995952824356682 -0.6005392446015697 0.5469710423089692 5 2 7 -0.9458410914974847 0.3246299888101017 0.04907537812572171 5 2 4 0.4446710312325426 0.8956939622340808 -0.4300843534994402 5 2 6 0.228159509754326 -0.9736237661995858 0.08253528745668785 5 3 4 0.99929448732669 0.03755699133966514 -0.1938837324602516 5 3 7 0.6877523324625938 -0.7259454037269345 0.2663295190946454 5 3 5 -0.9986432053419565 0.0520744507829223 -0.1782370644858236 5 4 7 -0.9970183790688238 -0.0771644464696991 0.2145489484590232 5 4 6 -0.1075842248297362 -0.9941959739245502 0.2685422477498993 5 5 7 0.9950609206245129 -0.09926612839179749 0.187455367716064 5 6 7 -0.799364184215507 0.6008468199079338 0.00706064116377911 5 6 9 -0.2285415587894346 -0.9735341575446109 0.07797696388863325 5 6 8 -0.01261839651625043 -0.9999203848653945 -0.02567278177543587 5 7 9 0.593695288592636 -0.8046899429612046 0.01852766555277024 5 8 9 -0.4674785097727936 0.8840044360186256 0.2506025495170938 Voronoi ridge statistics 19 bounded ridges 3.8e-17 ave. distance of midpoint to ridge 1.1e-16 max. distance of midpoint to ridge 19 bounded ridges with ok normal 5.5e-17 ave. angle to ridge 1.1e-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 -0.3854955578888162 0.922709691532494 -0.07609298438083832 5 0 8 0.719062520784207 0.6949453872092842 0.1071733734620185 5 1 4 0.9929212365203528 -0.1187746524595787 0.07521211888503934 5 4 8 -0.06640144810487507 -0.9977929883946748 0.1408811441173878 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 -0.06934933486244871 0.05349366577784779 -0.3051278694340226 0.1614985055810222 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 0.4164624817835533 0.9091529031283372 -0.01975252543405322 4 5 0 8 0.7190625207842071 0.6949453872092841 0.1071733734620185 5 0 1 -0.385495557888816 0.9227096915324942 -0.07609298438083825 5 1 4 0.9929212365203528 -0.1187746524595786 0.07521211888503931 5 4 8 -0.06640144810487507 -0.9977929883946748 0.1408811441173878 Voronoi ridge statistics 1 bounded ridges 3.3e-18 ave. distance of midpoint to ridge 3.3e-18 max. distance of midpoint to ridge 1 bounded ridges with ok normal 7.9e-17 ave. angle to ridge 7.9e-17 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 0.1026012494065407 0.8309156055795222 -0.5468566905731636 0.2399036185798246 6 0 8 -0.1644981128676534 0.5492243080463516 -0.8193247404503217 0.1220237399030442 6 0 5 -0.1640386761614814 0.6276090456203117 -0.7610507201092119 0.1709974344854014 6 2 3 0.8628264983391888 0.1277424492346302 -0.4890933453107615 -0.1660057988150948 6 2 9 0.5146151495466439 -0.7556910962035635 -0.4050953159143437 -0.3000434746332832 6 2 7 0.9862472983740704 0.008356748990702162 0.1650649302430824 -0.2195655184060845 6 3 8 -0.9471370887617876 -0.1545163381156412 -0.2811690529684561 0.0437290219976464 6 3 5 -0.9850113492204077 -0.1553182373520524 -0.07502590921037612 0.09265233510028276 6 4 8 -0.7177135399298969 -0.2457215366779669 -0.6515429387338295 -0.02974683605231281 6 5 9 0.7110332662678563 -0.693517783370965 -0.1160378317993187 -0.2706062861955821 6 5 8 -0.1310037283001485 -0.04490613421135385 -0.9903643078593113 -0.2004293237314498 6 6 8 0.563653077615962 0.07101685912338847 0.8229531054770395 0.4221671959133707 6 8 9 0.7278413449934528 -0.6852671087526035 0.0256118367160405 -0.2412830130907242 Voronoi ridge statistics 15 non-simplicial Voronoi vertices for all ridges 2.7e-17 ave. distance to ridge 7.2e-17 max. distance to ridge 13 bounded ridges 3.4e-17 ave. distance of midpoint to ridge 1.2e-16 max. distance of midpoint to ridge 13 bounded ridges with ok normal 2.4e-17 ave. angle to ridge 5e-17 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 -0.1769702595802888 0.8331351847724078 0.5239916899325132 0.004105600879712603 6 0 9 0.5856843296472444 -0.1558732679166011 -0.7954102025713886 -0.1264594278193164 6 0 6 -0.3055017680243689 0.3812318858994053 -0.8725427891556766 -0.04822326899809229 6 0 7 0.6633910639781656 0.667288353076621 -0.3385831509130482 0.06175731395259088 6 1 7 0.7533877382120359 0.3349392388487629 -0.5658821628141006 0.06152842458597964 6 1 2 0.2077539373736713 0.4344067294949112 -0.8764297432625571 0.2556318087147513 6 1 5 -0.08886729274769883 0.2768317827550713 -0.9568002760954576 0.1656561460661369 6 2 4 0.8896724708236494 0.4529391082738923 -0.05769799697211246 -0.1249699490416031 6 2 5 -0.6080629223625024 -0.1069684332549475 -0.7866493734408967 -0.05602222006342435 6 3 9 0.115764860415124 -0.9728190902550374 -0.2005530222370838 -0.2615067759720445 6 3 7 0.313105673132462 -0.1651787990807289 0.9352437125084114 -0.1060546443225209 6 3 6 -0.8429664438017094 -0.1288333013498811 -0.5223117412882754 -0.1470675860428304 6 3 4 -0.6546392846048735 0.1665291828386521 0.7373706247980795 0.1638426312062791 6 4 7 0.8997625993863546 -0.3161631359012114 0.3007792151107228 -0.2534488584590283 6 4 6 -0.6610636619910347 -0.1756381951302929 -0.7294834194184102 -0.1931488689248214 6 4 5 -0.8177140658972857 -0.2799433900977096 -0.5029666040348317 0.01966883326066582 6 5 6 -0.4656867325018189 -0.06587339986788437 -0.8824945112359766 -0.374728122564582 6 6 9 0.7885740013077053 -0.5314391513195502 0.3093921022041632 -0.04784058563315538 6 7 9 -0.01257265438745097 -0.8388634914110146 -0.5441966291143085 -0.2018836580171399 Voronoi ridge statistics 14 non-simplicial Voronoi vertices for all ridges 2.6e-17 ave. distance to ridge 4.7e-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 -0.04510412048603353 -0.1962229636993575 -0.06746145990413341 -0.203283876182382 -0.3188041900902703 0.1251484339163773 0.1359785067833994 0.06954805978697724 -0.07249043373758872 -0.9550934192592698 0.3815223390696578 -0.9370156532984092 -0.0163794856198767 -0.8836250780525153 -0.03718065630611889 0.09499885792019705 -0.7038538868165177 -0.181396220925921 2.128743389186437 -4.060345900416339 -1.216246894786397 2.789531685277144 -5.393666229616723 -1.494034092231972 2.640156785602004 -4.796303906482411 -1.459799746992413 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 0.5123553720802023 -0.3638120828535339 -0.7779027838170596 -0.100757404152973 6 2 6 -0.5221667006142685 -0.0819219266645836 -0.8488997200501196 -0.2535440955968319 6 6 7 0.7522136453226688 0.06033708575303689 0.6561509489997046 0.09003235761431798 15 6 0 1 -0.1769702595802887 0.8331351847724077 0.5239916899325134 0.004105600879712502 6 0 9 0.5856843296472445 -0.1558732679166013 -0.7954102025713885 -0.1264594278193165 6 1 6 -0.2436653478720985 0.1478836806870481 -0.958518448039901 -0.04663519095132838 6 1 2 0.2077539373736704 0.4344067294949107 -0.8764297432625575 0.2556318087147513 6 1 4 0.4442200788473617 0.4986447037065236 -0.7443265284902031 0.1737545932855555 6 1 7 0.7533877382120361 0.334939238848763 -0.5658821628141002 0.06152842458597953 6 2 5 -0.6080629223625013 -0.1069684332549467 -0.7866493734408976 -0.05602222006342442 6 2 4 0.8896724708236501 0.4529391082738915 -0.05769799697210863 -0.1249699490416032 6 3 6 -0.8429664438017094 -0.1288333013498811 -0.5223117412882754 -0.1470675860428305 6 3 7 0.3131056731324615 -0.1651787990807287 0.9352437125084115 -0.1060546443225208 6 4 6 -0.6610636619910347 -0.1756381951302929 -0.7294834194184102 -0.1931488689248214 6 4 7 0.8997625993863546 -0.3161631359012114 0.3007792151107227 -0.2534488584590283 6 5 6 -0.4656867325018176 -0.06587339986788353 -0.8824945112359773 -0.3747281225645819 6 6 9 0.7885740013077053 -0.5314391513195504 0.309392102204163 -0.04784058563315548 6 7 9 -0.01257265438745048 -0.838863491411015 -0.544196629114308 -0.2018836580171402 Voronoi ridge statistics 9 non-simplicial Voronoi vertices for all ridges 5.9e-17 ave. distance to ridge 2.7e-16 max. distance to ridge 3 bounded ridges 2.8e-16 ave. distance of midpoint to ridge 7.3e-16 max. distance of midpoint to ridge 3 bounded ridges with ok normal 4.7e-17 ave. angle to ridge 7.7e-17 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: 0.4751017705052503 0.8404705693422866 - 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: 0.2417735613471299 0.5000766029034821 - 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: 0.06029550723695778 0.09433023738340308 - 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 0.4751017705052503 0.8404705693422866 0.2417735613471299 0.5000766029034821 0.4470293595057619 -0.2357835939937328 0.06029550723695778 0.09433023738340308 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 Thu Dec 25 20:54:49 -12 2025 === 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): 0.000967 Total facet area: 1.7919449 Total volume: 0.18640279 4 1 -0.006240661006237803 -0.006198497499885539 -0.0019864189252863 0.03528712962677102 5 584 -0.4728063044129456 -0.06576180062326954 0.3296766529322424 -0.8145200357250595 -0.400126996179445 0.9350657178932538 -0.1161811748176062 -0.009048199757790365 0.3347718147035647 -0.3733488931324642 0.5670388949132404 -0.5323662756300657 -0.3876606744394215 0.4947446227302696 -0.4846392631626165 0.8393609616706706 -0.1089654738688995 -0.05104156673137999 0.5300891057109354 -0.4115455431603697 0.6753770108964831 -0.1536990905729239 -0.04851983599004574 0.7196445707605158 -0.4414725485817289 0.2002558030992597 0.08170320261529977 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): 0.001034 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: 4014 Number of distance tests for qhull: 29694 Number of distance tests for merging: 77050 Number of distance tests for checking: 18265 Number of merged facets: 3454 CPU seconds to compute hull (after input): 0.01078 Maximum distance of point above facet: 2.9e-14 (0.5x) Maximum distance of vertex below facet: -3.3e-14 (0.6x) 4 100 -0.1497820974007848 0.4220759056868795 -0.1730594919621533 0.1395265758865441 -0.1656824599698354 0.269508156576344 0.2399815540443046 -0.3038478726528215 -0.1287028906527846 0.3274268489457609 0.1066154632455194 -0.3389105597705838 0.2152206390581627 0.2489384546335304 -0.3428963517040029 0.1553441801811402 -0.3478218321497435 0.1609400522171698 0.2504669650899254 -0.200959130349861 -0.2026608048181584 0.1327376760601389 -0.4340855448243787 0.05365675464591765 -0.1243914612976073 -0.06208848857682956 -0.4348180038806074 -0.2039732517850684 0.3186591776992361 0.2994118752602878 -0.2407753518255605 -0.02891517550425976 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): 0.004596 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: 4014 Number of distance tests for qhull: 29694 Number of distance tests for merging: 77150 Number of distance tests for checking: 51827 Number of merged facets: 3454 CPU seconds to compute hull (after input): 0.3184 Maximum distance of point above facet: 2.9e-14 (0.5x) Maximum distance of vertex below facet: -3.3e-14 (0.6x) 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): 0.004514 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 0.5773502691896257 0.5773502691896257 0.5773502691896257 0.2886751345948129 -0.5773502691896257 0.5773502691896257 0.5773502691896257 0.2886751345948129 0.5773502691896257 0.5773502691896257 -0.5773502691896257 0.2886751345948129 -0.5773502691896257 0.5773502691896257 -0.5773502691896257 0.2886751345948129 -0.5773502691896257 -0.5773502691896257 0.5773502691896257 0.2886751345948129 0.5773502691896257 -0.5773502691896257 0.5773502691896257 0.2886751345948129 -0.5773502691896257 -0.5773502691896257 -0.5773502691896257 0.2886751345948129 0.5773502691896257 -0.5773502691896257 -0.5773502691896257 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): 5.1e-05 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): 6.9e-05 3 6 -2.329001791770424e-17 -2.329001791770424e-17 -0.5000000000000001 -2.191443641136326e-17 0.5000000000000001 0 -0.5000000000000001 8.924339132271308e-18 0 0.5000000000000001 -2.191443641136326e-17 0 8.924339132271308e-18 -0.5000000000000001 0 -1.175681730788969e-17 1.708973674380276e-17 0.5000000000000001 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 -0.9510565162951535 -0.4045084971874737 0.8090169943749473 -0.5877852522924732 -0.4045084971874737 -1 9.444121133484361e-17 -0.4045084971874737 -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): 2.6e-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): 2.7e-05 2 5 -0.4045084971874738 -0.2938926261462365 0.5 -1.146068174088666e-16 0.1545084971874737 -0.4755282581475768 -0.4045084971874737 0.2938926261462367 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 Thu Dec 25 20:54:49 -12 2025 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): 5.7e-05 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-1766739289 Number of points processed: 10 Number of hyperplanes created: 29 Number of distance tests for qhull: 48 CPU seconds to compute hull (after input): 4.1e-05 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): 3.9e-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): 0.001466 qhull invoked by: rbox 1000 D3 | qhull Tcvs 2020.2.r 2020/08/31 with options: run-id 330843154 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 2.4e-17 ave. distance of a new vertex to a facet 9e-17 max. distance of a new vertex to a facet 5.9e-17 max. distance of an output vertex to a facet -5.3e-17 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 0.0015 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 -3.1e-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 9e-17 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) 20448 for facets and their normals, neighbor and vertex sets 2044 for vertices and their neighbor sets 31352 for input points, outside and coplanar sets, and qhT memory statistics: 1388 quick allocations 687 short allocations 98 long allocations 1420 short frees 97 long frees 24512 bytes of short memory in use 1416 bytes of short memory in freelists 105136 bytes of dropped short memory 1344 bytes of unused short memory (estimated) 10916 bytes of long memory allocated (max, except for input) 96 bytes of long memory in use (in 1 pieces) 131064 bytes of short memory buffers (minus links) 65536 bytes per short memory buffer (initially 131072 bytes) 104 calls to qh_setlarger 14 average copy size freelists(bytes->count): 16->1 24->13 32->0 48->11 80->7 size in bytes: merge 44 ridge 20 vertex 28 facet 80 normal 24 ridge vertices 16 facet vertices or neighbors 20 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): 0.000111 [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): 9.5e-05 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): 0.000931 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): 0.000857 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): 0.000903 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 330843154 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 6.2e-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 6.2e-17 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 6.2e-17 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 6.2e-17 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 6.2e-17 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 6.2e-17 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 6.2e-17 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 6.2e-17 [QH1049]qh_addpoint: add p2(v79) 0.014 above f288 to hull of 152 facets, 0 merges, 22 outside at 0.000912 CPU secs. Previous p56(v78) delta 0.000912 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): 0.000952 [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 20:54:49 & 0.000198 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 20:54:49 & 0.000401 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 20:54:49 & 0.000649 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 20:54:49 & 0.000975 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): 0.001351 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): 0.001389 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): 0.000211 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): 0.000213 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): 0.009468 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): 0.000229 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 330843154 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): 0.000221 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 330843154 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): 0.03257 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 -0.08928142660407064 -0.3194671263098746 0.3605569202297553 -0.1534778158747163 0.03516440701453923 0.5 -0.01663016790622813 0.3709299907861696 0.07648632831350027 0.3932651765570925 0.4421392241401818 -0.09396622763110282 0.199424728304684 0.5 0.06620718432588453 -0.2331094527352669 0.3262436269787957 -0.128966098672764 -0.5 0.2819439085196089 -0.5 0.5 0.3760666748352666 0.1399187075693636 0.4888102268053205 -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 -0.02221493611318519 -0.366434993563625 0.4072229792632261 -0.06676722137887703 -0.1566931052661437 0.4732086509216659 0.02820502736438534 0.04189077954915425 0.272798317696016 0.3126723396709862 0.08400649026409396 0.1921386936513206 0.1781470954214661 0.1182274414396169 0.2679341378370068 -0.1220315663349177 0.01546165115708639 0.1755764518932638 -0.3072535691850386 -0.01073880122111999 0 0.3867462923626847 0.04492879989084676 0.3028150683084345 0.3789805913148267 -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 -6.40076198881529 -0.1566931052661437 20 -4.979360188660042 0.04189077954915425 11.32346018178493 -0.7218812392989215 0.08400649026409396 7.831392539952951 -2.735252796494545 0.1182274414396169 11.11287098934976 -7.227875597731385 0.01546165115708639 7.114348923589702 -10 -0.01073880122111999 -0.4870359524963758 0.3867462923626843 0.04492879989084676 12.62300161615219 0.2705209571204674 -0.4732086509216658 5.343669467959106 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 -0.08928142660407054 -0.3194671263098746 0.3605569202297554 -0.1534778158747163 0.03516440701453923 0.4999999999999999 -0.01663016790622816 0.3709299907861696 0.07648632831350005 0.3932651765570925 0.4421392241401818 -0.09396622763110278 0.1994247283046841 0.5 0.06620718432588439 -0.2331094527352669 0.3262436269787957 -0.1289660986727639 -0.5 0.2819439085196089 -0.4999999999999999 0.5 0.3760666748352666 0.1399187075693635 0.4888102268053205 -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): 5.5e-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 Qb1:0B1:0B2:0 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): 5.2e-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): 7.9e-05 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): 3.1e-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 Thu Dec 25 20:54:49 -12 2025 == 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 330843154 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 330843154 Tcheck-frequently Tverify Centrum-premerge- 0 _zero-centrum _max-width 0.98 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 t1766739289 | qhull FO Tcv C-0 Number of points processed: 200 Number of hyperplanes created: 398 Number of distance tests for qhull: 2118 CPU seconds to compute hull (after input): 0.002048 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 330843154 Tcheck-frequently Tverify Centrum-premerge- 0 _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 1000 points in 3-d: Number of vertices: 60 Number of facets: 116 Statistics for: rbox 1000 L20 t1766739289 | qhull FO Tcv C-0 Number of points processed: 69 Number of hyperplanes created: 292 Number of distance tests for qhull: 13814 CPU seconds to compute hull (after input): 0.00096 Output completed. Verifying that all points are below outer planes of all facets. Will make 116000 distance computations. rbox 200 L20 D4 t | qhull FO Tcv C-0 Options selected for Qhull 2020.2.r 2020/08/31: run-id 330843154 Tcheck-frequently Tverify Centrum-premerge- 0 _zero-centrum _max-width 0.99 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 Convex hull of 200 points in 4-d: Number of vertices: 57 Number of facets: 266 Statistics for: rbox 200 L20 D4 t1766739289 | qhull FO Tcv C-0 Number of points processed: 70 Number of hyperplanes created: 746 Number of distance tests for qhull: 6216 CPU seconds to compute hull (after input): 0.001911 Output completed. Verifying that all points are below outer planes of all facets. Will make 53200 distance computations. rbox 200 L20 D5 t | qhull FO Tcv Qx Options selected for Qhull 2020.2.r 2020/08/31: run-id 330843154 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: 99 Number of facets: 1406 Statistics for: rbox 200 L20 D5 t1766739289 | qhull FO Tcv Qx Number of points processed: 121 Number of hyperplanes created: 5304 Number of distance tests for qhull: 20993 CPU seconds to compute hull (after input): 0.01349 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 281200 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 330843154 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: 258 Statistics for: rbox 1000 W1e-3 s D2 t1766739289 | qhull d FO Tcv Qu Q0 Number of points processed: 1000 Number of hyperplanes created: 4611 Number of facets in hull: 1996 Number of distance tests for qhull: 27108 CPU seconds to compute hull (after input): 0.03235 Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 258000 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 330843154 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: 258 Statistics for: rbox 1000 W1e-3 s D2 t1766739289 | qhull d FO Tcv Qu C-0 Number of points processed: 1000 Number of hyperplanes created: 4611 Number of facets in hull: 1996 Number of distance tests for qhull: 27108 CPU seconds to compute hull (after input): 0.03216 Output completed. Verifying that all points are below 2.1e-15 of all facets. Will make 258000 distance computations. set +v === check joggle and TRn Thu Dec 25 20:54:49 -12 2025 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: 11197 Number of distance tests for qhull: 118752 CPU seconds to compute hull (after input): 0.008681 Percentage of runs with precision errors: 100.0 precision problems (corrected unless 'Q0' or an error) 100 coplanar horizon facets for new vertices 397 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: 24765 Number of distance tests for qhull: 195967 CPU seconds to compute hull (after input): 0.01607 Percentage of runs with precision errors: 62.0 precision problems (corrected unless 'Q0' or an error) 7 coplanar half ridges in output 55 coplanar horizon facets for new vertices 120 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: 29075 Number of distance tests for qhull: 216082 CPU seconds to compute hull (after input): 0.01859 Percentage of runs with precision errors: 8.0 precision problems (corrected unless 'Q0' or an error) 1 coplanar half ridges in output 7 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: 218403 CPU seconds to compute hull (after input): 0.01896 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): 0.01858 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 330843154 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): 0.000903 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 Thu Dec 25 20:54:49 -12 2025 rbox 100 D3 s | qhull E0.01 Qx Tcv FO Options selected for Qhull 2020.2.r 2020/08/31: run-id 330843154 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): 0.000857 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): 0.000309 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): 0.000237 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): 0.000249 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): 0.000146 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): 0.000175 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): 0.000168 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): 0.005741 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: 232607 Number of distance tests for merging: 47365 Number of distance tests for checking: 38513 Number of merged facets: 1818 CPU seconds to compute hull (after input): 0.03478 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): 0.005775 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): 0.00425 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): 0.005125 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 330859961 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): 0.005616 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 330859961 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): 0.005542 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 330859961 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): 0.005938 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 330859961 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): 0.005898 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 Thu Dec 25 20:54:50 -12 2025 rbox 1000 s D3 | qhull C-0.01 Q5 FO Tcv Options selected for Qhull 2020.2.r 2020/08/31: run-id 330859961 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): 0.004591 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 Thu Dec 25 20:54:50 -12 2025 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 330859961 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): 0.004759 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 330859961 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): 0.005425 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): 0.005189 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 Thu Dec 25 20:54:50 -12 2025 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: 176 Number of non-simplicial facets: 17 Statistics for: rbox 100 s D3 t1766739290 | qhull R1e-3 Tcv Qc Number of points processed: 99 Number of hyperplanes created: 474 Number of distance tests for qhull: 1619 Number of distance tests for merging: 2971 Number of distance tests for checking: 1528 Number of merged facets: 34 CPU seconds to compute hull (after input): 0.001999 Maximum distance of point above facet: 0.0018 (0.5x) Maximum distance of vertex below facet: -0.0041 (1.0x) Output completed. Verifying that all points are below outer planes of all facets. Will make 17600 distance computations. rbox 100 s D3 t | qhull R1e-2 Tcv Qc Convex hull of 100 points in 3-d: Number of vertices: 58 Number of coplanar points: 42 Number of facets: 58 Number of non-simplicial facets: 33 Statistics for: rbox 100 s D3 t1766739290 | qhull R1e-2 Tcv Qc Number of points processed: 59 Number of hyperplanes created: 252 Number of distance tests for qhull: 3481 Number of distance tests for merging: 3231 Number of distance tests for checking: 2759 Number of merged facets: 112 CPU seconds to compute hull (after input): 0.001668 Maximum distance of point above facet: 0.033 (0.8x) Maximum distance of vertex below facet: -0.057 (1.5x) Output completed. Verifying that all points are below outer planes of all facets. Will make 5800 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: 12 Number of non-simplicial facets: 11 Statistics for: rbox 500 s D3 t1766739290 | qhull R0.05 A-1 Tcv Qc Number of points processed: 23 Number of hyperplanes created: 73 Number of distance tests for qhull: 21667 Number of distance tests for merging: 1265 Number of distance tests for checking: 6066 Number of merged facets: 50 CPU seconds to compute hull (after input): 0.001283 Maximum distance of point above facet: 0.22 (0.4x) Maximum distance of vertex below facet: -0.3 (0.5x) Output completed. Verifying that all points are below outer planes of all facets. Will make 6000 distance computations. rbox 100 W0 D3 t | qhull R1e-3 Tcv Qc Convex hull of 100 points in 3-d: Number of vertices: 40 Number of coplanar points: 60 Number of facets: 53 Number of non-simplicial facets: 7 Statistics for: rbox 100 W0 D3 t1766739290 | qhull R1e-3 Tcv Qc Number of points processed: 46 Number of hyperplanes created: 161 Number of distance tests for qhull: 1815 Number of distance tests for merging: 1307 Number of distance tests for checking: 1382 Number of merged facets: 37 CPU seconds to compute hull (after input): 0.000762 Maximum distance of point above facet: 0.0017 (0.4x) Maximum distance of vertex below facet: -0.0048 (1.2x) Output completed. Verifying that all points are below outer planes of all facets. Will make 5300 distance computations. rbox 100 W0 D3 t | qhull R1e-3 Qx Tcv Qc Convex hull of 100 points in 3-d: Number of vertices: 40 Number of coplanar points: 60 Number of facets: 52 Number of non-simplicial facets: 8 Statistics for: rbox 100 W0 D3 t1766739290 | qhull R1e-3 Qx Tcv Qc Number of points processed: 48 Number of hyperplanes created: 166 Number of distance tests for qhull: 2004 Number of distance tests for merging: 1420 Number of distance tests for checking: 1131 Number of merged facets: 40 CPU seconds to compute hull (after input): 0.000773 Maximum distance of point above facet: 0.0019 (0.5x) Maximum distance of vertex below facet: -0.0062 (1.6x) 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 5200 distance computations. rbox 100 W0 D3 t | qhull R1e-2 Tcv Qc Convex hull of 100 points in 3-d: Number of vertices: 28 Number of coplanar points: 72 Number of facets: 32 Number of non-simplicial facets: 7 Statistics for: rbox 100 W0 D3 t1766739290 | qhull R1e-2 Tcv Qc Number of points processed: 35 Number of hyperplanes created: 126 Number of distance tests for qhull: 2431 Number of distance tests for merging: 1507 Number of distance tests for checking: 1408 Number of merged facets: 49 CPU seconds to compute hull (after input): 0.000727 Maximum distance of point above facet: 0.027 (0.7x) Maximum distance of vertex below facet: -0.061 (1.5x) Output completed. Verifying that all points are below outer planes of all facets. Will make 3200 distance computations. rbox 100 W0 D3 t | qhull R1e-2 Qx Tcv Qc Convex hull of 100 points in 3-d: Number of vertices: 28 Number of coplanar points: 72 Number of facets: 29 Number of non-simplicial facets: 10 Statistics for: rbox 100 W0 D3 t1766739290 | qhull R1e-2 Qx Tcv Qc Number of points processed: 36 Number of hyperplanes created: 124 Number of distance tests for qhull: 2824 Number of distance tests for merging: 1398 Number of distance tests for checking: 1080 Number of merged facets: 43 CPU seconds to compute hull (after input): 0.0007 Maximum distance of point above facet: 0.019 (0.5x) Maximum distance of vertex below facet: -0.055 (1.4x) 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 2900 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 t1766739290 | qhull R0.05 A-1 Tcv Qc Number of points processed: 13 Number of hyperplanes created: 35 Number of distance tests for qhull: 13476 Number of distance tests for merging: 421 Number of distance tests for checking: 3612 Number of merged facets: 20 CPU seconds to compute hull (after input): 0.000749 Maximum distance of point above facet: 0.097 (0.2x) Maximum distance of vertex below facet: -0.13 (0.2x) 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 t1766739290 | qhull R0.05 Qx Tcv Qc Number of points processed: 15 Number of hyperplanes created: 45 Number of distance tests for qhull: 16250 Number of distance tests for merging: 463 Number of distance tests for checking: 3793 Number of merged facets: 22 CPU seconds to compute hull (after input): 0.000837 Maximum distance of point above facet: 0.1 (0.5x) Maximum distance of vertex below facet: -0.095 (0.5x) 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: 78 Number of coplanar points: 922 Number of facets: 92 Number of non-simplicial facets: 6 Statistics for: rbox 1000 W1e-20 t1766739290 | qhull Tcv Qc Number of points processed: 104 Number of hyperplanes created: 344 Number of distance tests for qhull: 21252 Number of distance tests for merging: 3368 Number of distance tests for checking: 16367 Number of merged facets: 112 CPU seconds to compute hull (after input): 0.002626 Output completed. Verifying that all points are below outer planes of all facets. Will make 92000 distance computations. rbox 1000 W1e-20 D4 t | qhull Tcv Qc Convex hull of 1000 points in 4-d: Number of vertices: 264 Number of coplanar points: 736 Number of facets: 975 Number of non-simplicial facets: 8 Statistics for: rbox 1000 W1e-20 D4 t1766739290 | qhull Tcv Qc Number of points processed: 342 Number of hyperplanes created: 4596 Number of distance tests for qhull: 74114 Number of distance tests for merging: 53266 Number of distance tests for checking: 82376 Number of merged facets: 1083 CPU seconds to compute hull (after input): 0.06948 Output completed. Verifying that all points are below outer planes of all facets. Will make 975000 distance computations. rbox 500 W1e-20 D5 t | qhull Tv Qc Convex hull of 500 points in 5-d: Number of vertices: 364 Number of coplanar points: 136 Number of facets: 5664 Number of non-simplicial facets: 10 Statistics for: rbox 500 W1e-20 D5 t1766739290 | qhull Tv Qc Number of points processed: 411 Number of hyperplanes created: 27443 Number of distance tests for qhull: 113757 Number of distance tests for merging: 303088 Number of distance tests for checking: 125648 Number of merged facets: 3468 CPU seconds to compute hull (after input): 0.04355 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 2832000 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: 6128 Number of non-simplicial facets: 10 Statistics for: rbox 100 W1e-20 D6 t1766739290 | qhull Tv Qc Number of points processed: 100 Number of hyperplanes created: 21397 Number of distance tests for qhull: 33597 Number of distance tests for merging: 183664 Number of distance tests for checking: 63869 Number of merged facets: 177 CPU seconds to compute hull (after input): 0.03089 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 612800 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: 1944 Number of non-simplicial facets: 3 Statistics for: rbox 50 W1e-20 D6 t1766739290 | qhull Qv Tv Qc Number of points processed: 50 Number of hyperplanes created: 5905 Number of distance tests for qhull: 8568 Number of distance tests for merging: 3186727 Number of distance tests for checking: 19863 Number of merged facets: 7 CPU seconds to compute hull (after input): 0.06108 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 97200 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: 7429 Number of facets: 8 Number of non-simplicial facets: 8 Statistics for: rbox 10000 D4 t1766739290 | qhull QR0 Qc C-0.01 A0.3 Tv QR1766739290 Number of points processed: 39 Number of hyperplanes created: 220 Number of distance tests for qhull: 1055924 Number of distance tests for merging: 17182 Number of distance tests for checking: 89616 Number of merged facets: 252 CPU seconds to compute hull (after input): 0.02144 Maximum distance of point above facet: 0.053 Maximum distance of vertex below facet: -0.13 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 t1766739290 | qhull d QR0 Qc C-1e-8 Qu Tv QR1766739290 Number of points processed: 1000 Number of hyperplanes created: 5554 Number of facets in hull: 1995 Number of distance tests for qhull: 29380 Number of distance tests for merging: 35322 Number of distance tests for checking: 17918 Number of merged facets: 1 CPU seconds to compute hull (after input): 0.004748 Maximum distance of vertex below facet: -1.3e-08 (0.4x) 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: 161 Number of coplanar points: 30 Number of facets: 1763 Number of non-simplicial facets: 434 Statistics for: rbox 300 D5 t1766739290 | qhull A-0.999 Qx Qc Tcv Number of points processed: 186 Number of hyperplanes created: 11237 Number of distance tests for qhull: 169408 Number of distance tests for merging: 57608 Number of distance tests for checking: 31152 Number of merged facets: 1077 CPU seconds to compute hull (after input): 0.02521 Maximum distance of vertex below facet: -0.021 (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 528900 distance computations. rbox 100 D6 t |qhull A-0.9999 Qx Qc Tcv Convex hull of 100 points in 6-d: Number of vertices: 84 Number of coplanar points: 1 Number of facets: 3535 Number of non-simplicial facets: 240 Statistics for: rbox 100 D6 t1766739290 | qhull A-0.9999 Qx Qc Tcv Number of points processed: 90 Number of hyperplanes created: 14476 Number of distance tests for qhull: 32456 Number of distance tests for merging: 59930 Number of distance tests for checking: 60591 Number of merged facets: 577 CPU seconds to compute hull (after input): 0.02614 Maximum distance of vertex below facet: -0.0072 (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 353500 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: 49 Number of facets: 5422 Number of non-simplicial facets: 90 Statistics for: rbox 50 D7 t1766739290 | qhull A-0.99999 Qx Qc Tcv W0.1 Number of points processed: 49 Number of hyperplanes created: 14716 Number of distance tests for qhull: 19459 Number of distance tests for merging: 70632 Number of distance tests for checking: 101591 Number of merged facets: 230 CPU seconds to compute hull (after input): 0.03003 Maximum distance of vertex below facet: -0.0019 (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 271100 distance computations. set +v ======================================================= === The following commands may cause errors Thu Dec 25 20:54:50 -12 2025 ======================================================= === check bad cases for Qhull Thu Dec 25 20:54:50 -12 2025 rbox 1000 L100000 s G1e-6 t | qhull Tv QH6154 Qhull precision error: Initial simplex is flat (facet 1 is coplanar with the interior point) While executing: rbox 1000 L100000 s G1e-6 t1766739290 | qhull Tv Options selected for Qhull 2020.2.r 2020/08/31: run-id 330859961 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 _maxoutside 5.5e-15 The input to qhull appears to be less than 3 dimensional, or a computation has overflowed. Qhull could not construct a clearly convex simplex from points: - p482(v4): 0.00084 0.5 0 - p305(v3): 0.0012 -0.5 0 - p890(v2): 0.5 0.0043 0 - p95(v1): -0.5 0.0012 0 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 6.9e-16. The center point, facets and distances to the center point are as follows: center point 0.0005114 0.001377 0 facet p305 p890 p95 distance= 0 facet p482 p890 p95 distance= 0 facet p482 p305 p95 distance= 0 facet p482 p305 p890 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: -0.5 0.5 difference= 1 1: -0.5 0.5 difference= 1 2: 0 0 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 6.9e-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 1000 L100000 s G1e-6 t | qhull Tv Q10 QH6154 Qhull precision error: Initial simplex is flat (facet 1 is coplanar with the interior point) While executing: rbox 1000 L100000 s G1e-6 t1766739290 | qhull Tv Q10 Options selected for Qhull 2020.2.r 2020/08/31: run-id 330859961 Tverify Q10-no-narrow _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 _maxoutside 5.5e-15 The input to qhull appears to be less than 3 dimensional, or a computation has overflowed. Qhull could not construct a clearly convex simplex from points: - p482(v4): 0.00084 0.5 0 - p305(v3): 0.0012 -0.5 0 - p890(v2): 0.5 0.0043 0 - p95(v1): -0.5 0.0012 0 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 6.9e-16. The center point, facets and distances to the center point are as follows: center point 0.0005114 0.001377 0 facet p305 p890 p95 distance= 0 facet p482 p890 p95 distance= 0 facet p482 p305 p95 distance= 0 facet p482 p305 p890 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: -0.5 0.5 difference= 1 1: -0.5 0.5 difference= 1 2: 0 0 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 6.9e-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 1000 s Z1 G1e-13 t | qhull Tv Convex hull of 1001 points in 3-d: Number of vertices: 1001 Number of facets: 1501 Number of non-simplicial facets: 151 Statistics for: rbox 1000 s Z1 G1e-13 t1766739290 | qhull Tv Number of points processed: 1001 Number of hyperplanes created: 4569 Number of distance tests for qhull: 28796 Number of distance tests for merging: 79288 Number of distance tests for checking: 226635 Number of merged facets: 1628 CPU seconds to compute hull (after input): 0.01099 Maximum distance of point above facet: 1.3e-14 (2.4x) Maximum distance of vertex below facet: -1.4e-14 (2.5x) Output completed. Verifying that all points are below outer planes of all facets. Will make 1502501 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 t1766739290 | qhull d Qbb Qc Q12 Tv Number of points processed: 1001 Number of hyperplanes created: 13668 Number of facets in hull: 3627 Number of distance tests for qhull: 54373 Number of distance tests for merging: 752644 Number of distance tests for checking: 544784 Number of merged facets: 4516 CPU seconds to compute hull (after input): 0.04472 Maximum distance of point above facet: 5.8e-14 (5.8x) Maximum distance of vertex below facet: -8.7e-14 (8.6x) 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 t1766739290 | qhull d Q12 Tv Options selected for Qhull 2020.2.r 2020/08/31: run-id 330859961 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 5.4e-12 Last point added to hull was p302. Last merge was #9272. At error exit: Delaunay triangulation by the convex hull of 1000 points in 4-d: Number of input sites: 131 Total number of deleted points due to merging: 686 Number of nearly incident points: 33 Number of Delaunay regions: 107 Number of non-simplicial Delaunay regions: 39 Statistics for: rbox 1000 s W1e-13 t1766739290 | qhull d Q12 Tv Number of points processed: 824 Number of hyperplanes created: 11247 Number of facets in hull: 223 Number of distance tests for qhull: 2396825 Number of distance tests for merging: 3749150 Number of distance tests for checking: 0 Number of merged facets: 9631 Maximum distance of point above facet: 5.4e-12 (533.3x) Maximum distance of vertex below facet: -8.5e-11 (8460.3x) precision problems (corrected unless 'Q0' or an error) 794 flipped facets 1780 coplanar horizon facets for new vertices 34 coplanar points during partitioning 1 dupridges with multiple neighbors 30 dupridges with flip facet into good neighbor 3 dupridges with flip facet into good flip 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. QH6347 qhull precision error (qh_mergefacet): wide merge for facet f1353 into f845 for mergetype 6 (flip). maxdist 0 (0.0x) mindist -7e-10 (126708.6x) vertexdist 0.0072 Allow with 'Q12' (allow-wide) ERRONEOUS FACET: - f1353 - flags: top simplicial newfacet flipped - normal: -1.188e-13 6.917e-14 -1 - offset: 0.25 - vertices: p423(v231) p926(v103) p636(v22) - neighboring facets: f845 f1354 f1355 ERRONEOUS OTHER FACET: - f845 - flags: bottom simplicial upperDelaunay tested - normal: 1.664e-09 2.925e-10 1 - offset: -0.25 - center: 0.4920917130269191 0.08848566140544455 0.249999999999966 - outside set(furthest p324): p324: 0.4919 0.08982 0.25 - furthest distance= 9.6e-15 - vertices: p259(v165) p926(v103) p636(v22) - neighboring facets: f1353 f843 f844 - ridges: While executing: rbox 1000 s W1e-13 D2 t1766739290 | qhull d Tv Options selected for Qhull 2020.2.r 2020/08/31: run-id 330859961 delaunay Tverify _pre-merge _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 _narrow-hull 0 _maxoutside 2.6e-14 Last point added to hull was p423. Last merge was #519. At error exit: Delaunay triangulation by the convex hull of 1000 points in 3-d: Number of input sites: 231 Total number of nearly incident points: 769 Number of Delaunay regions: 193 Number of non-simplicial Delaunay regions: 21 Statistics for: rbox 1000 s W1e-13 D2 t1766739290 | qhull d Tv Number of points processed: 231 Number of hyperplanes created: 1298 Number of facets in hull: 360 Number of distance tests for qhull: 67594 Number of distance tests for merging: 25455 Number of distance tests for checking: 0 Number of merged facets: 519 Maximum distance of point above facet: 3.4e-14 (6.1x) Maximum distance of vertex below facet: -2.3e-13 (41.0x) precision problems (corrected unless 'Q0' or an error) 85 flipped facets 80 coplanar horizon facets for new vertices 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 set +v === check Qhull without merging Q0 Thu Dec 25 20:54:50 -12 2025 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): 0.01568 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): 0.001445 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): 0.00072 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): 7.2e-05 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): 0.001423 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): 0.001152 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 330859961 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): 0.000449 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): 0.000502 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): 0.00541 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 330859961 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 330859961 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 Thu Dec 25 20:54:50 -12 2025 rbox L100 2000 D4 s C1,1e-13 t2 | qhull Convex hull of 4000 points in 4-d: Number of vertices: 2097 Number of facets: 13620 Number of non-simplicial facets: 55 Statistics for: rbox L100 2000 D4 s C1,1e-13 t2 | qhull Number of points processed: 2111 Number of hyperplanes created: 51531 Number of distance tests for qhull: 587116 Number of distance tests for merging: 267042 Number of distance tests for checking: 152254 Number of merged facets: 133 CPU seconds to compute hull (after input): 0.05204 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: 2097 Number of facets: 13620 Number of non-simplicial facets: 55 Statistics for: rbox L100 2000 D4 s C1,1e-13 t2 | qhull Q12 Number of points processed: 2111 Number of hyperplanes created: 51531 Number of distance tests for qhull: 587116 Number of distance tests for merging: 267042 Number of distance tests for checking: 152254 Number of merged facets: 133 CPU seconds to compute hull (after input): 0.05164 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 (1134760685006.8x wider) due to dupridge between f1169 and f1151 (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: - f1169 - flags: bottom upperDelaunay newfacet dupridge mergeridge2 flipped - normal: -0.3222 0.1164 0.5496 0.7619 - offset: 0.1151858 - vertices: p54(v75) p45(v58) p44(v19) p92(v11) - neighboring facets: f421 f1163 f1170 f1151 - ridges: - r595 tested simplicialbot vertices: p45(v58) p44(v19) p92(v11) between f421 and f1169 - r1063 simplicialtop simplicialbot vertices: p54(v75) p44(v19) p92(v11) between f1169 and f1163 - r1064 simplicialtop simplicialbot vertices: p54(v75) p45(v58) p92(v11) between f1170 and f1169 - r1065 simplicialtop vertices: p54(v75) p45(v58) p44(v19) between f1169 and f1151 ERRONEOUS OTHER FACET: - f1151 - flags: bottom upperDelaunay newfacet dupridge mergeridge1 flipped - normal: 0.3 0.3867 0.4648 0.7379 - offset: 0.05455177 - vertices: p54(v75) p45(v58) p76(v37) p44(v19) - neighboring facets: f421 f1163 f1148 f1169 - ridges: - r610 tested simplicialbot vertices: p45(v58) p76(v37) p44(v19) between f421 and f1151 - r1061 simplicialtop simplicialbot vertices: p54(v75) p76(v37) p44(v19) between f1151 and f1163 - r1062 simplicialtop simplicialbot vertices: p54(v75) p45(v58) p76(v37) between f1151 and f1148 - r1065 simplicialtop vertices: p54(v75) p45(v58) p44(v19) between f1169 and f1151 While executing: rbox 50 C1,1E-13 t1447644703 | qhull d Options selected for Qhull 2020.2.r 2020/08/31: run-id 330876768 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 #242. At error exit: Delaunay triangulation by the convex hull of 100 points in 4-d: Number of input sites: 75 Number of nearly incident points: 1 Number of Delaunay regions: 266 Number of non-simplicial Delaunay regions: 69 Statistics for: rbox 50 C1,1E-13 t1447644703 | qhull d Number of points processed: 75 Number of hyperplanes created: 1091 Number of facets in hull: 303 Number of distance tests for qhull: 5519 Number of distance tests for merging: 10611 Number of distance tests for checking: 0 Number of merged facets: 244 Maximum distance of point above facet: 1.3e-14 (1.3x) Maximum distance of vertex below facet: -9.2e-15 (0.9x) precision problems (corrected unless 'Q0' or an error) 4 flipped facets 69 coplanar horizon facets for new vertices 1 coplanar points during partitioning 221 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 (1134760685006.8x wider) due to dupridge between f1169 and f1151 (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: 306 Number of non-simplicial Delaunay regions: 134 Statistics for: rbox 50 C1,1E-13 t1447644703 | qhull d Q12 Number of points processed: 99 Number of hyperplanes created: 1517 Number of facets in hull: 344 Number of distance tests for qhull: 7905 Number of distance tests for merging: 18547 Number of distance tests for checking: 7314 Number of merged facets: 460 CPU seconds to compute hull (after input): 0.002908 Maximum distance of point above facet: 1.3e-14 (1.3x) Maximum distance of vertex below facet: -0.0012 (117663642506.3x) 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: 308 Number of non-simplicial Delaunay regions: 138 Statistics for: rbox 50 C1,1E-13 t1447644703 | qhull d Q14 Number of points processed: 99 Number of hyperplanes created: 1551 Number of facets in hull: 346 Number of distance tests for qhull: 5680 Number of distance tests for merging: 18779 Number of distance tests for checking: 4940 Number of merged facets: 542 CPU seconds to compute hull (after input): 0.003036 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/reproducible-path/qhull-2020.2' create-stamp debian/debhelper-build-stamp dh_testroot -O--buildsystem=cmake dh_prep -O--buildsystem=cmake debian/rules override_dh_auto_install make[1]: Entering directory '/build/reproducible-path/qhull-2020.2' dh_auto_install --buildsystem=cmake cd obj-i686-linux-gnu && make -j6 install DESTDIR=/build/reproducible-path/qhull-2020.2/debian/tmp AM_UPDATE_INFO_DIR=no "INSTALL=install --strip-program=true" make[2]: Entering directory '/build/reproducible-path/qhull-2020.2/obj-i686-linux-gnu' /usr/bin/cmake -S/build/reproducible-path/qhull-2020.2 -B/build/reproducible-path/qhull-2020.2/obj-i686-linux-gnu --check-build-system CMakeFiles/Makefile.cmake 0 make -f CMakeFiles/Makefile2 preinstall make[3]: Entering directory '/build/reproducible-path/qhull-2020.2/obj-i686-linux-gnu' make[3]: Nothing to be done for 'preinstall'. make[3]: Leaving 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-- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/lib/i386-linux-gnu/libqhull.so -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/lib/i386-linux-gnu/libqhullcpp.a -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/lib/i386-linux-gnu/libqhullstatic.a -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/lib/i386-linux-gnu/libqhullstatic_r.a -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/bin/qhull -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/bin/rbox -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/bin/qconvex -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/bin/qdelaunay -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/bin/qvoronoi -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/bin/qhalf -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/lib/i386-linux-gnu/cmake/Qhull/QhullTargets.cmake -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/lib/i386-linux-gnu/cmake/Qhull/QhullTargets-none.cmake -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/lib/i386-linux-gnu/cmake/Qhull/QhullConfig.cmake -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/lib/i386-linux-gnu/cmake/Qhull/QhullConfigVersion.cmake -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/lib/i386-linux-gnu/pkgconfig/qhull_r.pc -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/lib/i386-linux-gnu/pkgconfig/qhullstatic.pc -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/lib/i386-linux-gnu/pkgconfig/qhull.pc -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/lib/i386-linux-gnu/pkgconfig/qhullstatic_r.pc -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/lib/i386-linux-gnu/pkgconfig/qhullcpp.pc -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhull/libqhull.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhull/geom.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhull/io.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhull/mem.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhull/merge.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhull/poly.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhull/qhull_a.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhull/qset.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhull/random.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhull/stat.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhull/user.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhull/DEPRECATED.txt -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhull_r/libqhull_r.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhull_r/geom_r.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhull_r/io_r.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhull_r/mem_r.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhull_r/merge_r.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhull_r/poly_r.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhull_r/qhull_ra.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhull_r/qset_r.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhull_r/random_r.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhull_r/stat_r.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhull_r/user_r.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/Coordinates.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/functionObjects.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/PointCoordinates.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/Qhull.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullError.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullFacet.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullFacetList.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullFacetSet.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullHyperplane.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullIterator.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullLinkedList.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullPoint.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullPoints.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullPointSet.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullQh.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullRidge.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullSet.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullSets.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullStat.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullUser.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullVertex.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/QhullVertexSet.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/RboxPoints.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/RoadError.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/RoadLogEvent.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/include/libqhullcpp/RoadTest.h -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/man/man1/qhull.1 -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/man/man1/rbox.1 -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/README.txt -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/REGISTER.txt -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/Announce.txt -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/COPYING.txt -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/index.htm -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qhull.htm -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-optf.htm -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-code.htm -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-opto.htm -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/rbox.man -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qvoron_f.htm -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/normal_voronoi_knauss_oesterle.jpg -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qdelau_f.htm -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh--geom.gif -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-quick.htm -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh--half.gif -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-optc.htm -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-optg.htm -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qconvex.htm -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qdelaun.htm -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-optp.htm -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qhalf.htm -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qhull.man -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/rbox.htm -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh--rand.gif -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/index.htm -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-get.htm -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qhull-cpp.xml -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh_findbestfacet-drielsma.pdf -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qvoronoi.htm -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh--cone.gif -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/rbox.txt -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh--dt.gif -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-impre.htm -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-eg.htm -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh--4d.gif -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-optq.htm -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qhull.txt -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-faq.htm -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/html/qh-optt.htm -- Installing: /build/reproducible-path/qhull-2020.2/debian/tmp/usr/share/doc/libqhull-dev/qhull/src/Changes.txt make[2]: Leaving directory '/build/reproducible-path/qhull-2020.2/obj-i686-linux-gnu' make[1]: Leaving directory '/build/reproducible-path/qhull-2020.2' debian/rules execute_after_dh_auto_install make[1]: Entering directory '/build/reproducible-path/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/reproducible-path/qhull-2020.2' dh_install -O--buildsystem=cmake dh_installdocs -O--buildsystem=cmake debian/rules override_dh_installchangelogs make[1]: Entering directory '/build/reproducible-path/qhull-2020.2' dh_installchangelogs src/Changes.txt make[1]: Leaving directory '/build/reproducible-path/qhull-2020.2' dh_installexamples -O--buildsystem=cmake dh_installman -O--buildsystem=cmake dh_installsystemduser -O--buildsystem=cmake dh_perl -O--buildsystem=cmake debian/rules execute_before_dh_link-indep make[1]: Entering directory '/build/reproducible-path/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/reproducible-path/qhull-2020.2' dh_link -O--buildsystem=cmake dh_strip_nondeterminism -O--buildsystem=cmake debian/rules override_dh_compress make[1]: Entering directory '/build/reproducible-path/qhull-2020.2' dh_compress -X.c -X.h -X.txt make[1]: Leaving directory '/build/reproducible-path/qhull-2020.2' dh_fixperms -O--buildsystem=cmake dh_missing -O--buildsystem=cmake dh_dwz -a -O--buildsystem=cmake dh_strip -a -O--buildsystem=cmake dh_makeshlibs -a -O--buildsystem=cmake dpkg-gensymbols: warning: debian/libqhullcpp8.0/DEBIAN/symbols doesn't match completely debian/libqhullcpp8.0.symbols --- debian/libqhullcpp8.0.symbols (libqhullcpp8.0_2020.2-6_i386) +++ dpkg-gensymbolsSlFLO8 2025-12-25 20:54:53.757720075 -1200 @@ -1,9 +1,9 @@ libqhullcpp.so.8.0 libqhullcpp8.0 #MINVER# * Build-Depends-Package: libqhull-dev - (optional=libstdc++|regex)"^_Z(Z|GTt|GV|TI|TS|TT|TV|Thn?\d+_|Tvn?\d+_n?\d+_)?N?r?V?K?[RO]?S[abdiost]" 0~unused - (optional=non-lto)_ZN8orgQhull10QhullErrorD0Ev@Base 2020.1 - (optional=non-lto)_ZN8orgQhull10QhullErrorD1Ev@Base 2020.1 - (optional=non-lto)_ZN8orgQhull10QhullErrorD2Ev@Base 2020.1 +#MISSING: 2020.2-6# (optional=libstdc++|regex)"^_Z(Z|GTt|GV|TI|TS|TT|TV|Thn?\d+_|Tvn?\d+_n?\d+_)?N?r?V?K?[RO]?S[abdiost]" 0~unused +#MISSING: 2020.2-6# (optional=non-lto)_ZN8orgQhull10QhullErrorD0Ev@Base 2020.1 +#MISSING: 2020.2-6# (optional=non-lto)_ZN8orgQhull10QhullErrorD1Ev@Base 2020.1 +#MISSING: 2020.2-6# (optional=non-lto)_ZN8orgQhull10QhullErrorD2Ev@Base 2020.1 _ZN8orgQhull10QhullFacet13s_empty_facetE@Base 2020.1 _ZN8orgQhull10QhullFacet13voronoiVertexEv@Base 2020.1 _ZN8orgQhull10QhullFacet9facetAreaEv@Base 2020.1 @@ -12,12 +12,12 @@ _ZN8orgQhull10QhullFacetC1ERKNS_5QhullEP6facetT@Base 2020.1 _ZN8orgQhull10QhullFacetC2ERKNS_5QhullE@Base 2020.1 _ZN8orgQhull10QhullFacetC2ERKNS_5QhullEP6facetT@Base 2020.1 - (optional=inline-ctor)_ZN8orgQhull10QhullPointC1EPNS_7QhullQhEPd@Base 2020.2 +#MISSING: 2020.2-6# (optional=inline-ctor)_ZN8orgQhull10QhullPointC1EPNS_7QhullQhEPd@Base 2020.2 _ZN8orgQhull10QhullPointC1ERKNS_5QhullE@Base 2020.1 _ZN8orgQhull10QhullPointC1ERKNS_5QhullEPd@Base 2020.1 _ZN8orgQhull10QhullPointC1ERKNS_5QhullERNS_11CoordinatesE@Base 2020.1 _ZN8orgQhull10QhullPointC1ERKNS_5QhullEiPd@Base 2020.1 - (optional=inline-ctor)_ZN8orgQhull10QhullPointC2EPNS_7QhullQhEPd@Base 2020.2 +#MISSING: 2020.2-6# (optional=inline-ctor)_ZN8orgQhull10QhullPointC2EPNS_7QhullQhEPd@Base 2020.2 _ZN8orgQhull10QhullPointC2ERKNS_5QhullE@Base 2020.1 _ZN8orgQhull10QhullPointC2ERKNS_5QhullEPd@Base 2020.1 _ZN8orgQhull10QhullPointC2ERKNS_5QhullERNS_11CoordinatesE@Base 2020.1 @@ -185,9 +185,9 @@ _ZN8orgQhull9RoadErrorC2EiPKciifx@Base 2020.1 _ZN8orgQhull9RoadErrorC2EiRKNSt7__cxx1112basic_stringIcSt11char_traitsIcESaIcEEE@Base 2020.1 _ZN8orgQhull9RoadErrorC2Ev@Base 2020.1 - (optional=non-lto)_ZN8orgQhull9RoadErrorD0Ev@Base 2020.1 - (optional=non-lto)_ZN8orgQhull9RoadErrorD1Ev@Base 2020.1 - (optional=non-lto)_ZN8orgQhull9RoadErrorD2Ev@Base 2020.1 +#MISSING: 2020.2-6# (optional=non-lto)_ZN8orgQhull9RoadErrorD0Ev@Base 2020.1 +#MISSING: 2020.2-6# (optional=non-lto)_ZN8orgQhull9RoadErrorD1Ev@Base 2020.1 +#MISSING: 2020.2-6# (optional=non-lto)_ZN8orgQhull9RoadErrorD2Ev@Base 2020.1 _ZN8orgQhull9RoadErroraSERKS0_@Base 2020.1 _ZNK8orgQhull10QhullFacet10innerplaneEv@Base 2020.1 _ZNK8orgQhull10QhullFacet10outerplaneEv@Base 2020.1 @@ -260,7 +260,7 @@ _ZTIN8orgQhull9RoadErrorE@Base 2020.1 _ZTSN8orgQhull10QhullErrorE@Base 2020.1 _ZTSN8orgQhull9RoadErrorE@Base 2020.1 - (optional=non-lto)_ZTVN8orgQhull10QhullErrorE@Base 2020.1 +#MISSING: 2020.2-6# (optional=non-lto)_ZTVN8orgQhull10QhullErrorE@Base 2020.1 _ZTVN8orgQhull9RoadErrorE@Base 2020.1 _ZlsRSoRKN8orgQhull10QhullFacet10PrintFacetE@Base 2020.1 _ZlsRSoRKN8orgQhull10QhullFacet10PrintFlagsE@Base 2020.1 dh_shlibdeps -a -O--buildsystem=cmake dh_installdeb -O--buildsystem=cmake dh_gencontrol -O--buildsystem=cmake dh_md5sums -O--buildsystem=cmake dh_builddeb -O--buildsystem=cmake dpkg-deb: building package 'libqhull8.0' in '../libqhull8.0_2020.2-6_i386.deb'. dpkg-deb: building package 'libqhull-r8.0' in '../libqhull-r8.0_2020.2-6_i386.deb'. dpkg-deb: building package 'libqhull-dev' in '../libqhull-dev_2020.2-6_i386.deb'. dpkg-deb: building package 'qhull-bin' in '../qhull-bin_2020.2-6_i386.deb'. dpkg-deb: building package 'libqhullcpp8.0' in '../libqhullcpp8.0_2020.2-6_i386.deb'. dpkg-deb: building package 'qhull-bin-dbgsym' in '../qhull-bin-dbgsym_2020.2-6_i386.deb'. dpkg-deb: building package 'libqhullcpp8.0-dbgsym' in '../libqhullcpp8.0-dbgsym_2020.2-6_i386.deb'. dpkg-deb: building package 'libqhull-r8.0-dbgsym' in '../libqhull-r8.0-dbgsym_2020.2-6_i386.deb'. dpkg-deb: building package 'libqhull8.0-dbgsym' in '../libqhull8.0-dbgsym_2020.2-6_i386.deb'. dpkg-deb: building package 'libqhull-doc' in '../libqhull-doc_2020.2-6_all.deb'. dpkg-genbuildinfo --build=binary -O../qhull_2020.2-6_i386.buildinfo dpkg-genchanges --build=binary -O../qhull_2020.2-6_i386.changes dpkg-genchanges: info: binary-only upload (no source code included) dpkg-source --after-build . dpkg-buildpackage: info: binary-only upload (no source included) dpkg-genchanges: info: not including original source code in upload I: copying local configuration I: unmounting dev/ptmx filesystem I: unmounting dev/pts filesystem I: unmounting dev/shm filesystem I: unmounting proc filesystem I: unmounting sys filesystem I: cleaning the build env I: removing directory /srv/workspace/pbuilder/29269 and its subdirectories I: Current time: Thu Dec 25 20:54:57 -12 2025 I: pbuilder-time-stamp: 1766739297 Sat Nov 23 02:31:59 UTC 2024 I: 1st build successful. Starting 2nd build on remote node infom07-i386.debian.net. Sat Nov 23 02:31:59 UTC 2024 I: Preparing to do remote build '2' on infom07-i386.debian.net. Sat Nov 23 02:33:29 UTC 2024 I: Deleting $TMPDIR on infom07-i386.debian.net. Sat Nov 23 02:33:30 UTC 2024 I: qhull_2020.2-6_i386.changes: Format: 1.8 Date: Sun, 09 Jul 2023 23:44:21 +0200 Source: qhull Binary: libqhull-dev libqhull-doc libqhull-r8.0 libqhull-r8.0-dbgsym libqhull8.0 libqhull8.0-dbgsym libqhullcpp8.0 libqhullcpp8.0-dbgsym qhull-bin qhull-bin-dbgsym Architecture: i386 all Version: 2020.2-6 Distribution: unstable Urgency: medium Maintainer: Debian Science Maintainers Changed-By: Timo Röhling Description: libqhull-dev - calculate convex hulls and related structures (development files) libqhull-doc - calculate convex hulls and related structures (documentation file libqhull-r8.0 - calculate convex hulls and related structures (reentrant shared l libqhull8.0 - calculate convex hulls and related structures (shared library) libqhullcpp8.0 - calculate convex hulls and related structures (C++ shared library qhull-bin - calculate convex hulls and related structures (utilities) Closes: 1040724 Changes: qhull (2020.2-6) unstable; urgency=medium . * Avoid deprecation warning with CMake 3.27 (Closes: #1040724) Checksums-Sha1: 23a569d2c4164ef5639ef23e2ffdc4fce154a293 542680 libqhull-dev_2020.2-6_i386.deb bea3bfe05a38910b0508ab330d24c1a48eaa9b55 278208 libqhull-doc_2020.2-6_all.deb 5fcb991d6986bb8f82b034df0a86907ea912e430 263440 libqhull-r8.0-dbgsym_2020.2-6_i386.deb d717b120789ba64e6e84d956ec6e6eb78cca253d 258944 libqhull-r8.0_2020.2-6_i386.deb 0ef9da138f9b44f04bd101cdee5a6903ca81fcd9 258144 libqhull8.0-dbgsym_2020.2-6_i386.deb 7666abafd27234aac2535e69dc4633fb4a4efb4f 257852 libqhull8.0_2020.2-6_i386.deb 007de487c4a8152f85c52e4da26c5500f4ece34b 543048 libqhullcpp8.0-dbgsym_2020.2-6_i386.deb 25872e685edf2b1424fc1f4fcdbed843ef38de84 110532 libqhullcpp8.0_2020.2-6_i386.deb b41c2959143b5217cd76ae5c1088be0900d7bfb7 53952 qhull-bin-dbgsym_2020.2-6_i386.deb 9cc7d9a00a218b818fd0c3728610e7ecb3a9894b 92720 qhull-bin_2020.2-6_i386.deb 3fdb17067826f1f848bbc5a78977625c0affd3e3 9043 qhull_2020.2-6_i386.buildinfo Checksums-Sha256: 652ef95278b4ae17e672ba16e59eef504e00a71fa50cc37812fbe9f7f0c847f2 542680 libqhull-dev_2020.2-6_i386.deb 9b8d02fd12fcf5463d53ce1636be7d472853e2957c030a5c64e32d85e30b8f7c 278208 libqhull-doc_2020.2-6_all.deb a72e705c63e8e8d0004af4630f3c08bbec3c14750c72775714a454c60b857993 263440 libqhull-r8.0-dbgsym_2020.2-6_i386.deb b43c0a491cc00c8e8e47d0536ca37c3e12aaf64d8f3411a92c350ac283c44803 258944 libqhull-r8.0_2020.2-6_i386.deb 3d952d069260faae675ac611f0dda48c11d289cc8bf1ffb373fe08d711f48be4 258144 libqhull8.0-dbgsym_2020.2-6_i386.deb 52db1b063638216b773ee6f93a9f3d7d451d56d733a652aafb79c44f1e36c313 257852 libqhull8.0_2020.2-6_i386.deb d8930d5856478dd36f8330c52e15c5988eca38dd2a96920db051b03f14317f7e 543048 libqhullcpp8.0-dbgsym_2020.2-6_i386.deb 8e86ef00762effc748614710d4e8a7d462422a0e4a1de5a8b7d99d7fc68ac1c6 110532 libqhullcpp8.0_2020.2-6_i386.deb beeb0b0efa1ab59c1f4ea5274ff5f22a341464317238bf7250b1aee68acbe005 53952 qhull-bin-dbgsym_2020.2-6_i386.deb 635caee06bd0db3b2ac65fb7fd8ba240564b2f9a28c4b26bf915454468efe38a 92720 qhull-bin_2020.2-6_i386.deb 302b06c3432a60c3db3fa9ee0174118309764a0b01c065b854d7d6c8ba9a07b9 9043 qhull_2020.2-6_i386.buildinfo Files: b42a1cfea786503bf823ee153dd4aaa8 542680 libdevel optional libqhull-dev_2020.2-6_i386.deb aacfa121760ca4836f6ca79c0ef74555 278208 doc optional libqhull-doc_2020.2-6_all.deb a093460f9546dc7eeb0b51b0a87a0201 263440 debug optional libqhull-r8.0-dbgsym_2020.2-6_i386.deb cf1ddb64f26cdba6ca73498587726b87 258944 libs optional libqhull-r8.0_2020.2-6_i386.deb f7c9b056e1b45f5b670cf51fe24008df 258144 debug optional libqhull8.0-dbgsym_2020.2-6_i386.deb 0f3c06629e299e04b2b9f153deac2485 257852 libs optional libqhull8.0_2020.2-6_i386.deb 9a4be49abae7cec5eeded483dac496f5 543048 debug optional libqhullcpp8.0-dbgsym_2020.2-6_i386.deb fc13c11ecdf587dafe9a3e4881644b77 110532 libs optional libqhullcpp8.0_2020.2-6_i386.deb d85824eded6360ad0450e97e975d8da5 53952 debug optional qhull-bin-dbgsym_2020.2-6_i386.deb 0907b1896cea9888b1969886ad539527 92720 math optional qhull-bin_2020.2-6_i386.deb 6a86175c92204a7af5352f97c66f9127 9043 math optional qhull_2020.2-6_i386.buildinfo Sat Nov 23 02:33:31 UTC 2024 I: diffoscope 283 will be used to compare the two builds: Running as unit: rb-diffoscope-i386_20-33505.service # Profiling output for: /usr/bin/diffoscope --timeout 7200 --html /srv/reproducible-results/rbuild-debian/r-b-build.ntlCLPQU/qhull_2020.2-6.diffoscope.html --text /srv/reproducible-results/rbuild-debian/r-b-build.ntlCLPQU/qhull_2020.2-6.diffoscope.txt --json /srv/reproducible-results/rbuild-debian/r-b-build.ntlCLPQU/qhull_2020.2-6.diffoscope.json --profile=- /srv/reproducible-results/rbuild-debian/r-b-build.ntlCLPQU/b1/qhull_2020.2-6_i386.changes /srv/reproducible-results/rbuild-debian/r-b-build.ntlCLPQU/b2/qhull_2020.2-6_i386.changes ## command (total time: 0.000s) 0.000s 1 call cmp (internal) ## has_same_content_as (total time: 0.000s) 0.000s 1 call abc.DotChangesFile ## main (total time: 0.372s) 0.372s 2 calls outputs 0.000s 1 call cleanup ## recognizes (total time: 0.044s) 0.044s 12 calls diffoscope.comparators.binary.FilesystemFile ## specialize (total time: 0.000s) 0.000s 1 call specialize Finished with result: success Main processes terminated with: code=exited/status=0 Service runtime: 687ms CPU time consumed: 687ms Sat Nov 23 02:33:32 UTC 2024 I: diffoscope 283 found no differences in the changes files, and a .buildinfo file also exists. Sat Nov 23 02:33:32 UTC 2024 I: qhull from trixie built successfully and reproducibly on i386. Sat Nov 23 02:33:33 UTC 2024 I: Submitting .buildinfo files to external archives: Sat Nov 23 02:33:33 UTC 2024 I: Submitting 12K b1/qhull_2020.2-6_i386.buildinfo.asc Sat Nov 23 02:33:34 UTC 2024 I: Submitting 12K b2/qhull_2020.2-6_i386.buildinfo.asc Sat Nov 23 02:33:35 UTC 2024 I: Done submitting .buildinfo files to http://buildinfo.debian.net/api/submit. Sat Nov 23 02:33:35 UTC 2024 I: Done submitting .buildinfo files. Sat Nov 23 02:33:35 UTC 2024 I: Removing signed qhull_2020.2-6_i386.buildinfo.asc files: removed './b1/qhull_2020.2-6_i386.buildinfo.asc' removed './b2/qhull_2020.2-6_i386.buildinfo.asc'