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<p><a name="TOP"><b>Up:</b></a> <a
href="http://www.qhull.org">Home page</a> for Qhull<br>
<b>Up:</b><a
href="http://www.qhull.org/news">News</a> about Qhull<br>
<b>Up:</b> <a href="http://www.qhull.org/html/qh-faq.htm">FAQ</a> about Qhull<br>
<b>To:</b> <a href="#TOC">Qhull manual: Table of Contents</a>
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<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
• <a href="qh-quick.htm#options">Options</a>
• <a href="qh-opto.htm#output">Output</a>
• <a href="qh-optf.htm#format">Formats</a>
• <a href="qh-optg.htm#geomview">Geomview</a>
• <a href="qh-optp.htm#print">Print</a>
• <a href="qh-optq.htm#qhull">Qhull</a>
• <a href="qh-optc.htm#prec">Precision</a>
• <a href="qh-optt.htm#trace">Trace</a><br>
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<h1><a
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/fixed.html"><img
src="qh--rand.gif" alt="[random-fixed]" align="middle"
width="100" height="100"></a> Qhull manual </h1>
<p>Qhull is a general dimension code for computing convex hulls,
Delaunay triangulations, halfspace intersections about a point, Voronoi
diagrams, furthest-site Delaunay triangulations, and
furthest-site Voronoi diagrams. These structures have
applications in science, engineering, statistics, and
mathematics. See <a
href="http://www.ifor.math.ethz.ch/staff/fukuda/polyfaq/polyfaq.html">Fukuda's
introduction</a> to convex hulls, Delaunay triangulations,
Voronoi diagrams, and linear programming. For a detailed
introduction, see O'Rourke [<a href="#orou94">'94</a>], <i>Computational
Geometry in C</i>.
</p>
<p>There are six programs. Except for rbox, they use
the same code.
<blockquote>
<ul>
<li><a href="qconvex.htm">qconvex</a> -- convex hulls
<li><a href="qdelaun.htm">qdelaunay</a> -- Delaunay triangulations and
furthest-site Delaunay triangulations
<li><a href="qhalf.htm">qhalf</a> -- halfspace intersections about a point
<li><a href="qhull.htm">qhull</a> -- all structures with additional options
<li><a href="qvoronoi.htm">qvoronoi</a> -- Voronoi diagrams and
furthest-site Voronoi diagrams
<li><a href="rbox.htm">rbox</a> -- generate point distributions for qhull
</ul>
</blockquote>
<p>Qhull implements the Quickhull algorithm for computing the
convex hull. Qhull includes options
for hull volume, facet area, multiple output formats, and
graphical output. It can approximate a convex hull. </p>
<p>Qhull handles roundoff errors from floating point
arithmetic. It generates a convex hull with "thick" facets.
A facet's outer plane is clearly above all of the points;
its inner plane is clearly below the facet's vertices. Any
exact convex hull must lie between the inner and outer plane.
<p>Qhull uses merged facets, triangulated output, or joggled
input. Triangulated output triangulates non-simplicial, merged
facets. Joggled input also
guarantees simplicial output, but it
is less accurate than merged facets. For merged facets, Qhull
reports the maximum outer and inner plane.
<p><i>Brad Barber, Cambridge MA, 2003/12/30</i></p>
<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
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