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285 lines
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<head>
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<title>Qhull code for Convex Hull, Delaunay Triangulation, Voronoi Diagram, and Halfspace Intersection about a Point</title>
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</head>
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<body>
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<!-- Navigation links -->
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<b>URL:</b> <a href="http://www.qhull.org">http://www.qhull.org</a>
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<br><b>To:</b>
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<a href="http://www.qhull.org/news">News</a>
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• <a href="http://www.qhull.org/download">Download</a>
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• <a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405">CiteSeer</a>
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• <a href=http://images.google.com/images?q=qhull&num=100>Images</a>
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• <a href="html/index.htm#TOC">Manual</a>
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• <a href="http://www.qhull.org/html/qh-faq.htm">FAQ</a>
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• <a href="html/qh-quick.htm#programs">Programs</a>
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• <a href="html/qh-quick.htm#options">Options</a>
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</p>
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<hr>
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<!-- Main text of document -->
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<table>
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<tr><td valign=top>
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<h1>Qhull</h1>
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<a
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href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html"><img
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src="html/qh--cone.gif" alt="[CONE]" align="middle" width="100"
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height="100"></a>
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</td><td>
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Qhull computes the convex hull, Delaunay triangulation, Voronoi diagram,
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halfspace intersection about a point, furthest-site Delaunay
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triangulation, and furthest-site Voronoi diagram. The source code runs in
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2-d, 3-d, 4-d, and higher dimensions. Qhull implements the Quickhull
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algorithm for computing the convex hull. It handles roundoff
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errors from floating point arithmetic. It computes volumes,
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surface areas, and approximations to the convex hull.</p>
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<!-- duplicated in index.htm and html/index.htm -->
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<p>Qhull does <i>not</i> support triangulation of non-convex surfaces, mesh
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generation of non-convex objects, medium-sized inputs in 9-D
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and higher, alpha shapes, weighted Voronoi diagrams, Voronoi volumes, or
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constrained Delaunay triangulations, </p>
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<p>Qhull 2015.2 introduces reentrant Qhull. It allows concurrent Qhull runs and simplifies the C++ interface to Qhull.
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If you call Qhull from your program, you should use reentrant Qhull (libqhull_r) instead of qh_QHpointer (libqhull).
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If you use Qhull 2003.1. please upgrade or apply <a href="http://www.qhull.org/download/poly.c-qh_gethash.patch">poly.c-qh_gethash.patch</a>.
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</p>
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</td></tr></table>
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<hr>
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<form method=get action=http://www.google.com/search>
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<input type=hidden name=sitesearch value=www.qhull.org>
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<input type=hidden name=num value=100>
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<ul>
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<li><a href="http://www.qhull.org/news">News</a> and
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<a href="http://www.qhull.org/news/qhull-news.html#bugs">Bugs</a>
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about Qhull 2015.2 2016/01/18</li>
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<li><a href="http://www.qhull.org/download">Download</a> Qhull (<a href="http://www.qhull.org/src/Changes.txt">changes</a>)</li>
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<li><a href=http://github.com/qhull/qhull/wiki>GitHub</a> C++ interface to Qhull
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<li><a href="html/index.htm">Manual</a> for Qhull and rbox
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<li><a href="html/index.htm#geomview">Geomview</a> for 3-D and 4-D visualization of Qhull output
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<li><input name=as_q size=10 value="">
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<input type="submit" value="Search">
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www.qhull.org
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<p>
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<li><a href="http://www.qhull.org/news/qhull-news.html#users">How</a> is Qhull used?</li>
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<li><a href="http://scholar.google.com/scholar?cites=13151392091060773178&as_sdt=40000005">Google Scholar</a>,
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<a href="http://libra.msra.cn/Publication/232063/the-quickhull-algorithm-for-convex-hulls">Microsoft Academic</a>,
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and <a href="http://citeseerx.ist.psu.edu/showciting?doi=10.1.1.117.405&sort=cite">CiteSeer</a>
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references to Qhull
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<li>
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<a href=http://www.google.com/search?as_q=qhull+-debian+-cvs+-gentoo+-pool+-mirrors&num=100>Google</a> Qhull,
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<a href="http://images.google.com/images?q=qhull&num=100">Images</a>,
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<a href="http://www.google.com/#q=qhull&tbm=bks">Books</a>,
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<a href="http://www.google.com/search?q=qhull&tbm=pts">Patents</a>,
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<a href="http://groups.google.com/groups?as_q=qhull&num=100&as_scoring=d">Newsgroups</a>,
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<a href="http://www.google.com/search?q=qhull&tbm=blg">Blogs</a>,
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and <a href=http://www.googlism.com/who_is/q/qhull/>Who is</a> Qhull?
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<p>
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<li><a href=http://www.mathworks.com/>MATLAB</a> uses Qhull for their n-d computational geometry functions:
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<a href=http://www.mathworks.com/help/techdoc/ref/convhulln.html>convhulln</a>
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<a href=http://www.mathworks.com/help/techdoc/ref/delaunayn.html>delaunayn</a>
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<a href=http://www.mathworks.com/help/techdoc/ref/griddatan.html>griddatan</a>
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<a href=http://www.mathworks.com/help/techdoc/ref/voronoin.html>voronoin</a>.
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</li>
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<li>The <a href="http://cran.r-project.org/web/packages/geometry/geometry.pdf">geometry</a> package of <a href="http://www.r-project.org/">R</a> provides <a href="http://geometry.r-forge.r-project.org/">Qhull in R</a>.
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<li>The <a href="http://packages.debian.org/sid/octave3.2">Debian build</a> of
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<a href=http://www.octave.org/>GNU Octave</a> includes Qhull for <a href="http://www.gnu.org/software/octave/doc/interpreter/Geometry.html">computational geometry<a>.
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<li><a href=http://www.wolfram.com/products/mathematica/>Mathematica</a>'s Delaunay interface <a href=http://library.wolfram.com/infocenter/MathSource/1160/>qh-math</a>
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and <a href="http://portal.uni-freiburg.de/imteksimulation/downloads/ims">QHullInterface</a>
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<li>The <a href="http://docs.scipy.org/doc/scipy/reference/tutorial/spatial.html">scipy.spatial</a> of <a href="http://scipy.org/">SciPy</a> is implemented with Qhull. It includes
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support for Delaunay triangulations,
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</ul>
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</form>
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<p><b>Introduction</b>
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<ul>
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<li><a
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href="http://www.cs.mcgill.ca/~fukuda/soft/polyfaq/polyfaq.html"
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>Fukuda's introduction</a> to convex hulls, Delaunay
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triangulations, Voronoi diagrams, and linear programming</li>
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<li><a
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href="http://www.cse.unsw.edu.au/~lambert/java/3d/hull.html"
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>Lambert's Java</a> visualization of convex hull algorithms </li>
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<li><a
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href="http://www.algorithmic-solutions.info/leda_guide/geometryalgorithms.html"
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>LEDA Guide</a> to geometry algorithms
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<li><a
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href="http://mathworld.wolfram.com/ComputationalGeometry.html"
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>MathWorld's</a> Computational Geometry from Wolfram Research
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<li><a
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href="http://www.cs.sunysb.edu/~algorith/major_section/1.6.shtml"
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>Skiena's</a> Computational Geometry from his <i>Algorithm Design Manual</i>.
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<li><a
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href="http://www.cs.sunysb.edu/~algorith/major_section/1.6.shtml"
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>Stony Brook</a> Algorithm Repository, computational geometry</li>
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</ul>
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<p><b>Qhull Documentation and Support</b>
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<ul>
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<li><a href="html/index.htm">Manual</a> for Qhull and rbox
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<table><tr><td>
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<ul>
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<li><a href="html/index.htm#description">Description</a> of Qhull
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<li><a href="html/qh-impre.htm">Imprecision</a> in Qhull
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<li><a href="html/qh-quick.htm#programs">Programs</a> and <a href="html/qh-quick.htm#options">Options</a>
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quick reference
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<li><a href="html/qconvex.htm">qconvex</a> -- convex hull
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<li><a href="html/qdelaun.htm">qdelaunay</a> -- Delaunay triangulation
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<li><a href="html/qvoronoi.htm">qvoronoi</a> -- Voronoi diagram
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<li><a href="html/qhalf.htm">qhalf</a> -- halfspace intersection about a point
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<li><a href="html/rbox.htm">rbox</a> -- generate point distributions
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</ul></td><td><ul>
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<li><a href="http://www.qhull.org/html/qh-faq.htm">Frequently</a> asked
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questions about Qhull</li>
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<li><a href="html/index.htm#geomview">Geomview</a> for visualizing Qhull
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<li><a href="COPYING.txt">COPYING.txt</a> - copyright notice<br>
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<li><a href="REGISTER.txt">REGISTER.txt</a> - registration<br>
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<li><a href="README.txt">README.txt</a> - installation
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instructions<br>
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<li><a href="src/Changes.txt">Changes.txt</a> - change history <br>
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<li><a href="html/qh-code.htm">Calling Qhull</a> from your program
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<li><a href="src/libqhull_r/index.htm">Reentrant</a> Qhull functions, macros, and data structures with source
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</ul>
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</td></tr></table>
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<li>Send e-mail to <a href=mailto:qhull@qhull.org>qhull@qhull.org</a> </li>
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<li>Report bugs to <a
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href="mailto:qhull_bug@qhull.org">qhull_bug@qhull.org</a>
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</ul>
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<p><b>Related URLs</b>
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<ul>
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<li><a href="http://www.geom.uiuc.edu/software/cglist">Amenta's directory</a> of
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computational geometry software </li>
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<li><a href=http://www.boost.org/libs/graph/doc/table_of_contents.html>BGL</a>
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Boost Graph Library provides C++ classes for graph data structures
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and algorithms,
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<li><a
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href="http://www.netlib.org/voronoi/hull.html">Clarkson's
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hull </a>program with exact arithmetic for convex hulls, Delaunay triangulations,
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Voronoi volumes, and alpha shapes. </li>
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<li><a href="http://compgeom.cs.uiuc.edu/~jeffe/compgeom/compgeom.html">Erickson's
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Computational</a> Geometry Pages and
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<a href="http://compgeom.cs.uiuc.edu/~jeffe/compgeom/code.html">Software</a>
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<li><a
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href="http://www.cs.mcgill.ca/~fukuda/soft/cdd_home/cdd.html">Fukuda's
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cdd</a> program for halfspace intersection and convex hulls (<a
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href="http://www.csb.ethz.ch/tools/polco">Polco/Java</a>)</li>
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<li><a href="http://www.inf.ethz.ch/personal/gaertner/miniball.html">Gartner's
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Miniball</a> for fast and robust smallest enclosing balls (up to 20-d)
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<li><a href=http://www.algorithmic-solutions.com/enleda.htm>Leda</a>
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and <a href=http://www.cgal.org/>CGAL</a> libraries for writing computational
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geometry programs and other combinatorial algorithms
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<li><a href=http://www.mathtools.net/>Mathtools.net</a> of scientific and engineering
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software
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<li><a href="http://www.imr.sandia.gov/papers/topics.html">Owen's International Meshing</a> Roundtable
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<li><a
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href="http://www.robertschneiders.de/meshgeneration/meshgeneration.html">Schneiders'
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Finite Element</a> Mesh Generation page</li>
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<li><a href="http://www.cs.cmu.edu/~quake/triangle.html">Shewchuk's
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triangle </a>program for 2-d Delaunay</li>
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<li><a href=http://www.voronoi.com>Voronoi Web Site</a> for all things Voronoi
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<li>Young's <a href="http://homepage.usask.ca/~ijm451/finite/fe_resources/">Internet Finite Element Resources</a>
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<li><a href="http://www.uic.nnov.ru/~zny/skeleton/">Zolotykh's Skeleton</a> generates all extreme rays of a polyhedral cone using the Double Description Method</li>
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<li><a href="https://github.com/tomilov/quickhull/blob/master/include/quickhull.hpp">Tomilov's quickhull.hpp</a> (<a href="http://habrahabr.ru/post/245221/">doc-ru</a>) implements the Quickhull algorithm for points in general position.
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</ul>
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<p><b>FAQs and Newsgroups</b>
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<ul>
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<li><a
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href="http://www.faqs.org/faqs/graphics/algorithms-faq/">FAQ</a>
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for computer graphics algorithms
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(Exaflop.org: <a href="http://exaflop.org/docs/cgafaq/cga6.html">geometric</a> structures)
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</li>
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<li><a
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href="http://www-unix.mcs.anl.gov/otc/Guide/faq/linear-programming-faq.html">FAQ
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</a>for linear programming </li>
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<li><a href="news:comp.graphics.algorithms">Newsgroup</a>:
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comp.graphics.algorithms </li>
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<li><a href="news:comp.soft-sys.matlab">Newsgroup</a>:
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comp.soft-sys.matlab</li>
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<li><a href="news:sci.math.num-analysis">Newsgroup</a>:
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sci.math.num-analysis </li>
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<li><a href="news:sci.op-research">Newsgroup</a>:
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sci.op-research </li>
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</ul>
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</blockquote>
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<hr>
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<p>The program includes options for input transformations,
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randomization, tracing, multiple output formats, and execution
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statistics. The program can be called from within your
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application. </p>
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<p>You can view the results in 2-d, 3-d and 4-d with <a
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href="http://www.geomview.org">Geomview</a>. An alternative
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is <a href=http://www.vtk.org/>VTK</a>.</p>
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<p>For an article about Qhull, download from
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<a href="http://dl.acm.org/authorize?89250">ACM</a> or <a
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href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405">CiteSeer</a>:
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</p>
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<blockquote>
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<p>Barber, C.B., Dobkin, D.P., and Huhdanpaa, H.T., "The
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Quickhull algorithm for convex hulls," <i>ACM Trans. on
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Mathematical Software</i>, 22(4):469-483, Dec 1996, http://www.qhull.org</p>
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</blockquote>
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<p>Abstract: </p>
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<blockquote>
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<p>The convex hull of a set of points is the smallest convex
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set that contains the points. This article presents a
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practical convex hull algorithm that combines the
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two-dimensional Quickhull Algorithm with the general
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dimension Beneath-Beyond Algorithm. It is similar to the
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randomized, incremental algorithms for convex hull and
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Delaunay triangulation. We provide empirical evidence that
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the algorithm runs faster when the input contains non-extreme
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points, and that it uses less memory. </p>
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<p>Computational geometry algorithms have traditionally
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assumed that input sets are well behaved. When an algorithm
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is implemented with floating point arithmetic, this
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assumption can lead to serious errors. We briefly describe a
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solution to this problem when computing the convex hull in
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two, three, or four dimensions. The output is a set of
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"thick" facets that contain all possible exact convex hulls
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of the input. A variation is effective in five or more
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dimensions. </p>
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</blockquote>
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<!-- Navigation links -->
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<hr>
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<p><b>Up:</b> <a href="http://www.geom.uiuc.edu/software/past-projects.html"><i>Past Software
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Projects of the Geometry Center</i></a> <br>
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<b>URL:</b> <a href="http://www.qhull.org">http://www.qhull.org</a>
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<br><b>To:</b>
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<a href="http://www.qhull.org/news">News</a>
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• <a href="http://www.qhull.org/download">Download</a>
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• <a href="http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.117.405">CiteSeer</a>
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• <a href=http://images.google.com/images?q=qhull&num=100>Images</a>
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• <a href="html/index.htm#TOC">Manual</a>
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• <a href="http://www.qhull.org/html/qh-faq.htm">FAQ</a>
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• <a href="html/qh-quick.htm#programs">Programs</a>
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• <a href="html/qh-quick.htm#options">Options</a>
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<!-- GC common information --></p>
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<hr>
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<p><a href="http://www.geom.uiuc.edu/"><img src="html/qh--geom.gif" alt="[HOME]"
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align="middle"></a> <i>The Geometry Center Home Page</i> </p>
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<p>Comments to: <a href="mailto:qhull@qhull.org">qhull@qhull.org</a>
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<br>
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Created: May 17 1995 --- <!-- hhmts start -->
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</body>
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</html>
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