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			<title>qhull.c -- top-level functions and basic data types</title>
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			<p><a name="TOP"><b>Up:</b></a> <a
			href="http://www.geom.umn.edu/locate/qhull">Home page</a> for Qhull<br>
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			<h2>qhull.c -- top-level functions and basic data types</h2>
			<blockquote>
			<p>Qhull implements the Quickhull algorithm for computing
			the convex hull. The Quickhull algorithm combines two
			well-known algorithms: the 2-d quickhull algorithm and
			the n-d beneath-beyond algorithm. See
			<a href="index.htm#description">Description of Qhull</a>. </p>
			<p>This section provides an index to the top-level
			functions and base data types. The top-level header file, <tt>qhull.h</tt>,
			contains prototypes for these functions.</p>
			</blockquote>
			<p><b>Copyright ｩ 1995-2001 The Geometry Center, Minneapolis MN</b></p>
			<hr>
			<p><a href="#TOP">ｻ</a> <a href="qh-geom.htm#TOC">Geom</a>
			<a name="TOC"></a> <a href="qh-globa.htm#TOC">Global</a>
			<a href="qh-io.htm#TOC">Io</a> <a href="qh-mem.htm#TOC">Mem</a>
			<a href="qh-merge.htm#TOC">Merge</a> <a href="qh-poly.htm#TOC">Poly</a>
			<b>Qhull</b> <a href="qh-set.htm#TOC">Set</a>
			<a href="qh-stat.htm#TOC">Stat</a> <a href="qh-user.htm#TOC">User</a>
			</p>
			<h3>Index to <a href="qhull.c#TOP">qhull.c</a>,
			<a href="qhull.h#TOP">qhull.h</a>, and
			<a href="unix.c#TOP">unix.c</a></h3>
			<ul>
			<li><a href="#qtype">qhull.h and unix.c data types and
			constants</a> </li>
			<li><a href="#qmacro">qhull.h other macros</a> </li>
			<li><a href="#qfunc">Quickhull routines in call order</a> </li>
			<li><a href=="#qinit">Top-level routines for initializing and terminating Qhull</a></li>
			<li><a href="#qin">Top-level routines for reading and modifying the input</a></li>
			<li><a href="#qcall">Top-level routines for calling Qhull</a></li>
			<li><a href="#qout">Top-level routines for returning results</a></li>
			<li><a href="#qtest">Top-level routines for testing and debugging</a></li>
			</ul>

			<h3><a href="qh-qhull.htm#TOC">ｻ</a><a name="qtype">qhull.h and unix.c
			data types and constants</a></h3>
			<ul>
			<li><a href="qhull.h#flagT">flagT</a> Boolean flag as
			a bit </li>
			<li><a href="qhull.h#boolT">boolT</a> boolean value,
			either True or False </li>
			<li><a href="qhull.h#CENTERtype">CENTERtype</a> to
			distinguish facet->center </li>
			<li><a href="qhull.h#qh_PRINT">qh_PRINT</a> output
			formats for printing (qh.PRINTout) </li>
			<li><a href="qhull.h#qh_ALL">qh_ALL</a> argument flag
			for selecting everything </li>
			<li><a href="qhull.h#qh_ERR">qh_ERR</a> Qhull exit
			codes for indicating errors </li>
			<li><a href="unix.c#prompt">qh_prompt</a> version and long prompt for Qhull</li>
			<li><a href="unix.c#prompt2">qh_prompt2</a> synopsis for Qhull</li>
			<li><a href="unix.c#prompt3">qh_prompt3</a> concise prompt for Qhull</li>
			</ul>

			<h3><a href="qh-qhull.htm#TOC">ｻ</a><a name="qmacro">qhull.h other
			macros</a></h3>
			<ul>
			<li><a href="qhull.h#traceN">traceN</a> print trace
			message if <em>qh.IStracing >= N</em>. </li>
			</ul>

			<h3><a href="qh-qhull.htm#TOC">ｻ</a><a name="qfunc">Quickhull
			routines in call order</a></h3>
			<ul>
			<li><a href="unix.c#main">main</a> processes the
			command line, calls qhull() to do the work, and
			exits </li>
			<li><a href="qhull.c#qhull">qh_qhull</a> construct
			the convex hull of a set of points </li>
			<li><a href="qhull.c#build_withrestart">qh_build_withrestart</a>
			allow restarts while calling qh_buildhull</li>
			<li><a href="poly2.c#initbuild">qh_initbuild</a>
			initialize hull and outside sets with point array</li>
			<li><a href="qhull.c#partitionall">qh_partitionall</a>
			partition all points into outside sets </li>
			<li><a href="qhull.c#buildhull">qh_buildhull</a>
			construct a convex hull by adding points one at a
			time </li>
			<li><a href="qhull.c#nextfurthest">qh_nextfurthest</a>
			return next furthest point for processing </li>
			<li><a href="qhull.c#buildtracing">qh_buildtracing</a>
			trace an iteration of buildhull </li>
			<li><a href="qhull.c#addpoint">qh_addpoint</a> add a
			point to the convex hull </li>
			<li><a href="qhull.c#findhorizon">qh_findhorizon</a>
			find the horizon and visible facets for a point </li>
			<li><a href="qhull.c#partitionvisible">qh_partitionvisible</a>
			partition points from facets in qh.visible_list
			to facets in qh.newfacet_list </li>
			<li><a href="qhull.c#partitionpoint">qh_partitionpoint</a>
			partition a point as inside, coplanar with, or
			outside a facet </li>
			<li><a href="qhull.c#partitioncoplanar">qh_partitioncoplanar</a>
			partition coplanar point into a facet </li>
			<li><a href="qhull.c#precision">qh_precision</a> restart on precision errors if not merging and if 'QJn'</li>
			</ul>

			<h3><a href="qh-qhull.htm#TOC">ｻ</a><a name="qinit">Top-level routines for initializing and terminating Qhull (in other modules)</a></h3>
			<ul>
			<li><a href="global.c#freebuild">qh_freebuild</a>
			free memory used by qh_initbuild and qh_buildhull
			</li>
			<li><a href="global.c#checkflags">qh_checkflags</a>
			check flags for multiple frontends to qhull
			<li><a href="global.c#freeqhull">qh_freeqhull</a>
			free memory used by qhull </li>
			<li><a href="global.c#init_A">qh_init_A</a> called
			before error handling initialized </li>
			<li><a href="global.c#init_B">qh_init_B</a> called
			after points are defined </li>
			<li><a href="global.c#initflags">qh_initflags</a> set
			flags and constants from command line </li>
			<li><a href="qhull.c#restore_qhull">qh_restore_qhull</a>
			restores a saved qhull </li>
			<li><a href="qhull.c#save_qhull">qh_save_qhull</a>
			saves qhull for later restoring </li>
			<li><a href="qhull.c#user_memsizes">qh_user_memsizes</a>
			define additional quick allocation sizes
			</li>
			</ul>

			<h3><a href="qh-qhull.htm#TOC">ｻ</a><a name="qin">Top-level routines for reading and modifying the input (in other modules)</a></h3>
			<ul>
			<li><a href="geom2.c#gram_schmidt">qh_gram_schmidt</a>
			implements Gram-Schmidt orthogonalization by rows </li>
			<li><a href="qhull.c#projectinput">qh_projectinput</a>
			project input along one or more dimensions +
			Delaunay projection </li>
			<li><a href="geom2.c#randommatrix">qh_randommatrix</a>
			generate a random dimXdim matrix in range (-1,1) </li>
			<li><a href="io.c#readpoints">qh_readpoints</a> read
			points from input </li>
			<li><a href="geom2.c#rotateinput">qh_rotateinput</a> rotate
			input points using row matrix </li>
			<li><a href="geom2.c#scaleinput">qh_scaleinput</a> scale
			input points using qh low_bound/high_bound </li>
			<li><a href="geom2.c#setdelaunay">qh_setdelaunay</a> project
			points to paraboloid for Delaunay triangulation </li>
			<li><a href="geom2.c#sethalfspace_all">qh_sethalfspace_all</a>
			generate dual for halfspace intersection with interior
			point </li>
			</ul>

			<h3><a href="qh-qhull.htm#TOC">ｻ</a><a name="qcall">Top-level routines for calling Qhull (in other modules)</a></h3>
			<ul>
			<li><a href="qhull.c#addpoint">qh_addpoint</a> add
			point to convex hull </li>
			<li><a href="poly2.c#findbestfacet">qh_findbestfacet</a>
			find facet that is furthest below a point </li>
			<li><a href="poly2.c#findfacet_all">qh_findfacet_all</a>
			exhaustive search for facet below a point </li>
			<li><a href="qhull.c#qhull">qh_qhull</a> construct
			the convex hull of a set of points </li>
			</ul>

			<h3><a href="qh-qhull.htm#TOC">ｻ</a><a name="qout">Top-level routines for returning results (in other modules)</a></h3>
			<ul>
			<li><a href="stat.c#collectstatistics">qh_collectstatistics</a>
			collect statistics for qh.facet_list </li>
			<li><a href="geom2.c#nearvertex">qh_nearvertex</a>
			return nearest vertex to point </li>
			<li><a href="poly2.c#point">qh_point</a> return point
			for a point ID </li>
			<li><a href="poly2.c#pointfacet">qh_pointfacet</a>
			return temporary set of facets indexed by point
			ID </li>
			<li><a href="poly.c#pointid">qh_pointid</a> return ID
			for a point</li>
			<li><a href="poly2.c#pointvertex">qh_pointvertex</a>
			return vertices (if any) for all points</li>
			<li><a href="stat.c#printallstatistics">qh_printallstatistics</a>
			print all statistics </li>
			<li><a href="io.c#printneighborhood">qh_printneighborhood</a>
			print neighborhood of one or two facets </li>
			<li><a href="qhull.c#printsummary">qh_printsummary</a>
			print summary </li>
			<li><a href="io.c#produce_output">qh_produce_output</a>
			print the results of qh_qhull() </li>
			<li><a href="qhull.c#setvoronoi_all">qh_setvoronoi_all</a>
			compute Voronoi centers for all facets </li>
			</ul>

			<h3><a href="qh-qhull.htm#TOC">ｻ</a><a name="qtest">Top-level routines for testing and debugging (in other modules)</a></h3>
			<ul>
			<li><a href="io.c#dfacet">dfacet</a> print facet by
			ID from debugger </li>
			<li><a href="io.c#dvertex">dvertex</a> print vertex
			by ID from debugger </li>
			<li><a href="poly2.c#check_output">qh_check_output</a>
			check output </li>
			<li><a href="poly2.c#check_points">qh_check_points</a>
			verify that all points are inside the convex hull
			</li>
			<li><a href="user.c#errexit">qh_errexit</a> report
			error with a facet and a ridge</li>
			<li><a href="qhull.c#errexit2">qh_errexit2</a> report
			error with two facets </li>
			<li><a href="user.c#errprint">qh_errprint</a> print
			erroneous facets, ridge, and vertex </li>
			<li><a href="user.c#printfacetlist">qh_printfacetlist</a>
			print all fields for a list of facets </li>
			</ul>

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			<p><b>Up:</b>
			<a href="http://www.geom.umn.edu/locate/qhull">Home page for
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			<b>To:</b> <a href="qh-geom.htm">Geom</a>
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			<a href="qh-poly.htm">Poly</a> <a href="qh-qhull.htm#TOC">Qhull</a>
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			<p><a href="http://www.geom.umn.edu/"><img
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			Geometry Center Home Page </i></p>
			<p>Comments to:
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			Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
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