diff options
Diffstat (limited to 'src/qhull/src/libqhull/qh-poly.htm')
| -rw-r--r-- | src/qhull/src/libqhull/qh-poly.htm | 485 |
1 files changed, 485 insertions, 0 deletions
diff --git a/src/qhull/src/libqhull/qh-poly.htm b/src/qhull/src/libqhull/qh-poly.htm new file mode 100644 index 000000000..c8f6b38b0 --- /dev/null +++ b/src/qhull/src/libqhull/qh-poly.htm @@ -0,0 +1,485 @@ +<!-- Do not edit with Front Page, it adds too many spaces --> +<html> +<head> +<meta http-equiv="Content-Type" +content="text/html; charset=iso-8859-1"> +<title>poly.c, poly2.c -- polyhedron operations</title> +</head> + +<body> +<!-- Navigation links --> +<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="../../html/index.htm#TOC">Qhull manual</a>: Table of Contents <br> +<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a> +• <a href="../../html/qh-quick.htm#options">Options</a> +• <a href="../../html/qh-opto.htm#output">Output</a> +• <a href="../../html/qh-optf.htm#format">Formats</a> +• <a href="../../html/qh-optg.htm#geomview">Geomview</a> +• <a href="../../html/qh-optp.htm#print">Print</a> +• <a href="../../html/qh-optq.htm#qhull">Qhull</a> +• <a href="../../html/qh-optc.htm#prec">Precision</a> +• <a href="../../html/qh-optt.htm#trace">Trace</a> +• <a href="index.htm">Functions</a><br> +<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a><br> +<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br> +<b>To:</b> <a href="qh-geom.htm">Geom</a> • <a href="qh-globa.htm">Global</a> +• <a href="qh-io.htm">Io</a> • <a href="qh-mem.htm">Mem</a> +• <a href="qh-merge.htm">Merge</a> • <a href="qh-poly.htm#TOC">Poly</a> +• <a href="qh-qhull.htm">Qhull</a> • <a href="qh-set.htm">Set</a> +• <a href="qh-stat.htm">Stat</a> • <a href="qh-user.htm">User</a> +</p> +<hr> + +<h2>poly.c, poly2.c -- polyhedron operations</h2> +<blockquote> + +<p>Qhull uses dimension-free terminology. Qhull builds a +polyhedron in dimension <em>d. </em>A <em>polyhedron</em> is a +simplicial complex of faces with geometric information for the +top and bottom-level faces. A (<em>d-1</em>)-face is a <em>facet</em>, +a (<em>d-2</em>)-face is a <em>ridge</em>, and a <em>0</em>-face +is a <em>vertex</em>. For example in 3-d, a facet is a polygon +and a ridge is an edge. A facet is built from a ridge (the <em>base</em>) +and a vertex (the <em>apex</em>). See +<a href="../../html/index.htm#structure">Qhull's data structures</a>.</p> + +<p>Qhull's primary data structure is a polyhedron. A +polyhedron is a list of facets. Each facet has a set of +neighboring facets and a set of vertices. Each facet has a +hyperplane. For example, a tetrahedron has four facets. +If its vertices are <em>a, b, c, d</em>, and its facets +are <em>1, 2, 3, 4,</em> the tetrahedron is </p> +<blockquote> +<ul> +<li>facet 1 <ul> + <li>vertices: b c d </li> + <li>neighbors: 2 3 4 </li> +</ul> +</li> +<li>facet 2 <ul> + <li>vertices: a c d </li> + <li>neighbors: 1 3 4 </li> +</ul> +</li> +<li>facet 3 <ul> + <li>vertices: a b d </li> + <li>neighbors: 1 2 4 </li> +</ul> +</li> +<li>facet 4 <ul> + <li>vertices: a b c </li> + <li>neighbors: 1 2 3 </li> +</ul> +</li> +</ul> +</blockquote> +<p>A facet may be simplicial or non-simplicial. In 3-d, a +<i>simplicial facet</i> has three vertices and three +neighbors. A <i>nonsimplicial facet</i> has more than +three vertices and more than three neighbors. A +nonsimplicial facet has a set of ridges and a centrum. </p> +<p> +A simplicial facet has an orientation. An <i>orientation</i> +is either <i>top</i> or <i>bottom</i>. +The flag, <tt>facet->toporient,</tt> +defines the orientation of the facet's vertices. For example in 3-d, +'top' is left-handed orientation (i.e., the vertex order follows the direction +of the left-hand fingers when the thumb is pointing away from the center). +Except for axis-parallel facets in 5-d and higher, topological orientation +determines the geometric orientation of the facet's hyperplane. + +<p>A nonsimplicial facet is due to merging two or more +facets. The facet's ridge set determine a simplicial +decomposition of the facet. Each ridge is a 1-face (i.e., +it has two vertices and two neighboring facets). The +orientation of a ridge is determined by the order of the +neighboring facets. The flag, <tt>facet->toporient,</tt>is +ignored. </p> +<p>A nonsimplicial facet has a centrum for testing +convexity. A <i>centrum</i> is a point on the facet's +hyperplane that is near the center of the facet. Except +for large facets, it is the arithmetic average of the +facet's vertices. </p> +<p>A nonsimplicial facet is an approximation that is +defined by offsets from the facet's hyperplane. When +Qhull finishes, the <i>outer plane</i> is above all +points while the <i>inner plane</i> is below the facet's +vertices. This guarantees that any exact convex hull +passes between the inner and outer planes. The outer +plane is defined by <tt>facet->maxoutside</tt> while +the inner plane is computed from the facet's vertices.</p> + +<p>Qhull 3.1 includes triangulation of non-simplicial facets +('<a href="../../html/qh-optq.htm#Qt">Qt</a>'). +These facets, +called <i>tricoplanar</i>, share the same normal. centrum, and Voronoi center. +One facet (keepcentrum) owns these data structures. +While tricoplanar facets are more accurate than the simplicial facets from +joggled input, they +may have zero area or flipped orientation. + +</blockquote> +<p><b>Copyright © 1995-2015 C.B. Barber</b></p> +<hr> +<p><a href="#TOP">»</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> • <b>Poly</b> +• <a href="qh-qhull.htm#TOC">Qhull</a> • <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="poly.c">poly.c</a>, +<a href="poly2.c">poly2.c</a>, <a href="poly.h">poly.h</a>, +and <a href="libqhull.h">libqhull.h</a></h3> +<ul> +<li><a href="#ptype">Data types and global +lists for polyhedrons</a> </li> +<li><a href="#pconst">poly.h constants</a> </li> +<li><a href="#pgall">Global FORALL macros</a> </li> +<li><a href="#pall">FORALL macros</a> </li> +<li><a href="#peach">FOREACH macros</a> </li> +<li><a href="#pieach">Indexed FOREACH macros</a> </li> +<li><a href="#pmacro">Other macros for polyhedrons</a><p> </li> +<li><a href="#plist">Facetlist functions</a> </li> +<li><a href="#pfacet">Facet functions</a> </li> +<li><a href="#pvertex">Vertex, ridge, and point +functions</a> </li> +<li><a href="#phash">Hashtable functions</a> </li> +<li><a href="#pnew">Allocation and deallocation +functions</a> </li> +<li><a href="#pcheck">Check functions</a> </li> +</ul> +<h3><a href="qh-poly.htm#TOC">»</a><a name="ptype">Data +types and global lists for polyhedrons</a></h3> +<ul> +<li><a href="libqhull.h#facetT">facetT</a> defines a +facet </li> +<li><a href="libqhull.h#ridgeT">ridgeT</a> defines a +ridge </li> +<li><a href="libqhull.h#vertexT">vertexT</a> defines a +vertex </li> +<li><a href="libqhull.h#qh-lists">qh facet and vertex +lists</a> lists of facets and vertices </li> +<li><a href="libqhull.h#qh-set">qh global sets</a> +global sets for merging, hashing, input, etc. </li> +</ul> +<h3><a href="qh-poly.htm#TOC">»</a><a name="pconst">poly.h constants</a></h3> +<ul> +<li><a href="poly.h#ALGORITHMfault">ALGORITHMfault</a> +flag to not report errors in qh_checkconvex() </li> +<li><a href="poly.h#DATAfault">DATAfault</a> flag to +report errors in qh_checkconvex() </li> +<li><a href="poly.h#DUPLICATEridge">DUPLICATEridge</a> +special value for facet->neighbor to indicate +a duplicate ridge </li> +<li><a href="poly.h#MERGEridge">MERGEridge</a> +special value for facet->neighbor to indicate +a merged ridge </li> +</ul> +<h3><a href="qh-poly.htm#TOC">»</a><a name="pgall">Global FORALL +macros</a></h3> +<ul> +<li><a href="libqhull.h#FORALLfacets">FORALLfacets</a> +assign 'facet' to each facet in qh.facet_list </li> +<li><a href="poly.h#FORALLnew_facets">FORALLnew_facets</a> +assign 'facet' to each facet in qh.newfacet_list </li> +<li><a href="poly.h#FORALLvisible_facets">FORALLvisible_facets</a> +assign 'visible' to each visible facet in +qh.visible_list </li> +<li><a href="libqhull.h#FORALLpoints">FORALLpoints</a> +assign 'point' to each point in qh.first_point, +qh.num_points </li> +<li><a href="libqhull.h#FORALLvertices">FORALLvertices</a> +assign 'vertex' to each vertex in qh.vertex_list </li> +</ul> +<h3><a href="qh-poly.htm#TOC">»</a><a name="pall">FORALL macros</a></h3> +<ul> +<li><a href="poly.h#FORALLfacet_">FORALLfacet_</a> +assign 'facet' to each facet in facetlist </li> +<li><a href="libqhull.h#FORALLpoint_">FORALLpoint_</a> +assign 'point' to each point in points array</li> +<li><a href="poly.h#FORALLsame_">FORALLsame_</a> +assign 'same' to each facet in samecycle</li> +<li><a href="poly.h#FORALLsame_cycle_">FORALLsame_cycle_</a> +assign 'same' to each facet in samecycle</li> +<li><a href="poly.h#FORALLvertex_">FORALLvertex_</a> +assign 'vertex' to each vertex in vertexlist </li> +</ul> +<h3><a href="qh-poly.htm#TOC">»</a><a name="peach">FOREACH macros</a></h3> +<ul> +<li><a href="libqhull.h#FOREACHfacet_">FOREACHfacet_</a> +assign 'facet' to each facet in facets </li> +<li><a href="libqhull.h#FOREACHneighbor_">FOREACHneighbor_</a> +assign 'neighbor' to each facet in +facet->neighbors or vertex->neighbors</li> +<li><a href="poly.h#FOREACHnewfacet_">FOREACHnewfacet_</a> +assign 'newfacet' to each facet in facet set </li> +<li><a href="libqhull.h#FOREACHpoint_">FOREACHpoint_</a> +assign 'point' to each point in points set </li> +<li><a href="libqhull.h#FOREACHridge_">FOREACHridge_</a> +assign 'ridge' to each ridge in ridge set </li> +<li><a href="libqhull.h#FOREACHvertex_">FOREACHvertex_</a> +assign 'vertex' to each vertex in vertex set </li> +<li><a href="poly.h#FOREACHvertexA_">FOREACHvertexA_</a> +assign 'vertexA' to each vertex in vertex set</li> +<li><a href="poly.h#FOREACHvisible_">FOREACHvisible_</a> +assign 'visible' to each facet in facet set </li> +</ul> +<h3><a href="qh-poly.htm#TOC">»</a><a name="pieach">Indexed +FOREACH macros</a></h3> +<ul> +<li><a href="libqhull.h#FOREACHfacet_i_">FOREACHfacet_i_</a> +assign 'facet' and 'facet_i' to each facet in +facet set </li> +<li><a href="libqhull.h#FOREACHneighbor_i_">FOREACHneighbor_i_</a> +assign 'neighbor' and 'neighbor_i' to each facet +in facet->neighbors or vertex->neighbors</li> +<li><a href="libqhull.h#FOREACHpoint_i_">FOREACHpoint_i_</a> +assign 'point' and 'point_i' to each point in +points set </li> +<li><a href="libqhull.h#FOREACHridge_i_">FOREACHridge_i_</a> +assign 'ridge' and 'ridge_i' to each ridge in +ridges set </li> +<li><a href="libqhull.h#FOREACHvertex_i_">FOREACHvertex_i_</a> +assign 'vertex' and 'vertex_i' to each vertex in +vertices set </li> +<li><a href="poly.h#FOREACHvertexreverse12_">FOREACHvertexreverse12_</a> +assign 'vertex' to each vertex in vertex set; +reverse the order of first two vertices </li> +</ul> +<h3><a href="qh-poly.htm#TOC">»</a><a name="pmacro">Other macros for polyhedrons</a></h3> +<ul> +<li><a href="libqhull.h#getid_">getid_</a> return ID for +a facet, ridge, or vertex </li> +<li><a href="libqhull.h#otherfacet_">otherfacet_</a> +return neighboring facet for a ridge in a facet </li> +</ul> +<h3><a href="qh-poly.htm#TOC">»</a><a name="plist">Facetlist +functions</a></h3> +<ul> +<li><a href="poly.c#appendfacet">qh_appendfacet</a> +appends facet to end of qh.facet_list</li> +<li><a href="poly.c#attachnewfacets">qh_attachnewfacets</a> +attach new facets in qh.newfacet_list to the +horizon </li> +<li><a href="poly2.c#findgood">qh_findgood</a> +identify good facets for qh.PRINTgood </li> +<li><a href="poly2.c#findgood_all">qh_findgood_all</a> +identify more good facets for qh.PRINTgood </li> +<li><a href="poly2.c#furthestnext">qh_furthestnext</a> +move facet with furthest of furthest points to +facet_next </li> +<li><a href="poly2.c#initialhull">qh_initialhull</a> +construct the initial hull as a simplex of +vertices </li> +<li><a href="poly2.c#nearcoplanar">qh_nearcoplanar</a> + remove near-inside points from coplanar sets</li> +<li><a href="poly2.c#prependfacet">qh_prependfacet</a> +prepends facet to start of facetlist </li> +<li><a href="user.c#printfacetlist">qh_printfacetlist</a> +print facets in a facetlist</li> +<li><a href="poly2.c#printlists">qh_printlists</a> +print out facet list for debugging </li> +<li><a href="poly.c#removefacet">qh_removefacet</a> +unlinks facet from qh.facet_list</li> +<li><a href="poly2.c#resetlists">qh_resetlists</a> +reset qh.newvertex_list, qh.newfacet_list, and +qh.visible_list </li> +</ul> +<h3><a href="qh-poly.htm#TOC">»</a><a name="pfacet">Facet +functions</a></h3> +<ul> +<li><a href="poly2.c#createsimplex">qh_createsimplex</a> +create a simplex of facets from a set of vertices +</li> +<li><a href="poly2.c#findbestlower">qh_findbestlower</a> find best +non-upper, non-flipped facet for point at upperfacet</li> +<li><a href="poly2.c#furthestout">qh_furthestout</a> +make furthest outside point the last point of a +facet's outside set </li> +<li><a href="poly.c#makenew_nonsimplicial">qh_makenew_nonsimplicial</a> +make new facets from ridges of visible facets </li> +<li><a href="poly.c#makenew_simplicial">qh_makenew_simplicial</a> +make new facets for horizon neighbors </li> +<li><a href="poly.c#makenewfacet">qh_makenewfacet</a> +create a facet from vertices and apex </li> +<li><a href="poly2.c#makenewfacets">qh_makenewfacets</a> +make new facets from vertex, horizon facets, and +visible facets </li> +<li><a href="poly.c#makenewplanes">qh_makenewplanes</a> +make new hyperplanes for facets </li> +<li><a href="poly2.c#outcoplanar">qh_outcoplanar</a> +move points from outside set to coplanar set </li> +<li><a href="poly2.c#setvoronoi_all">qh_setvoronoi_all</a> +compute Voronoi centers for all facets </li> +<li><a href="poly2.c#triangulate">qh_triangulate</a> +triangulate non-simplicial facets</li> +<li><a href="poly2.c#triangulate_facet">qh_triangulate_facet</a> +triangulate a non-simplicial facet</li> +<li><a href="poly2.c#triangulate_link">qh_triangulate_link</a> +link facets together from qh_triangulate</li> +<li><a href="poly2.c#triangulate_mirror">qh_triangulate_mirror</a> +delete mirrored facets from qh_triangulate</li> +<li><a href="poly2.c#triangulate_null">qh_triangulate_null</a> +delete null facet from qh_triangulate</li> +</ul> +<h3><a href="qh-poly.htm#TOC">»</a><a name="pvertex">Vertex, +ridge, and point functions</a></h3> +<ul> +<li><a href="poly.c#appendvertex">qh_appendvertex</a> +append vertex to end of qh.vertex_list, </li> +<li><a href="io.c#detvridge">qh_detvridge</a> determine Voronoi +ridge for an input site +<li><a href="io.c#detvridge3">qh_detvridge3</a> determine 3-d Voronoi +ridge for an input site +<li><a href="poly2.c#facet3vertex">qh_facet3vertex</a> +return an oriented vertex set for a 3-d facet </li> +<li><a href="poly.c#facetintersect">qh_facetintersect</a> +return intersection of simplicial facets </li> +<li><a href="poly2.c#initialvertices">qh_initialvertices</a> +return non-singular set of initial vertices </li> +<li><a href="poly2.c#isvertex">qh_isvertex</a> true +if point is in a vertex set </li> +<li><a href="poly2.c#nearvertex">qh_nearvertex</a> +return nearest vertex to point </li> +<li><a href="poly2.c#nextridge3d">qh_nextridge3d</a> +iterate over each ridge and vertex for a 3-d +facet </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 temporary set of vertices indexed by point +ID </li> +<li><a href="poly.c#removevertex">qh_removevertex</a> +unlink vertex from qh.vertex_list, </li> +<li><a href="poly.c#updatevertices">qh_updatevertices</a> +update vertex neighbors and delete interior +vertices </li> +<li><a href="poly2.c#vertexintersect">qh_vertexintersect</a> +intersect two vertex sets </li> +<li><a href="poly2.c#vertexintersect_new">qh_vertexintersect_new</a> +return intersection of two vertex sets </li> +<li><a href="poly2.c#vertexneighbors">qh_vertexneighbors</a> +for each vertex in hull, determine facet +neighbors </li> +<li><a href="poly2.c#vertexsubset">qh_vertexsubset</a> +returns True if vertexsetA is a subset of +vertexsetB </li> +</ul> +<h3><a href="qh-poly.htm#TOC">»</a><a name="phash">Hashtable functions</a></h3> +<ul> +<li><a href="poly2.c#addhash">qh_addhash</a> add hash +element to linear hash table</li> +<li><a href="poly.c#gethash">qh_gethash</a> return +hash value for a set</li> +<li><a href="poly2.c#matchduplicates">qh_matchduplicates</a> +match duplicate ridges in hash table </li> +<li><a href="poly.c#matchneighbor">qh_matchneighbor</a> +try to match subridge of new facet with a +neighbor </li> +<li><a href="poly.c#matchnewfacets">qh_matchnewfacets</a> +match new facets with their new facet neighbors </li> +<li><a href="poly.c#matchvertices">qh_matchvertices</a> +tests whether a facet and hash entry match at a +ridge </li> +<li><a href="poly2.c#newhashtable">qh_newhashtable</a> +allocate a new qh.hash_table </li> +<li><a href="poly2.c#printhashtable">qh_printhashtable</a> +print hash table </li> +</ul> +<h3><a href="qh-poly.htm#TOC">»</a><a name="pnew">Allocation and +deallocation functions</a></h3> +<ul> +<li><a href="poly2.c#clearcenters">qh_clearcenters</a> +clear old data from facet->center </li> +<li><a href="poly.c#deletevisible">qh_deletevisible</a> +delete visible facets and vertices </li> +<li><a href="poly.c#delfacet">qh_delfacet</a> free up +the memory occupied by a facet </li> +<li><a href="poly2.c#delridge">qh_delridge</a> delete +ridge</li> +<li><a href="poly2.c#delvertex">qh_delvertex</a> +delete vertex </li> +<li><a href="poly.c#newfacet">qh_newfacet</a> create +and allocate space for a facet </li> +<li><a href="poly.c#newridge">qh_newridge</a> create +and allocate space for a ridge </li> +<li><a href="poly2.c#newvertex">qh_newvertex</a> +create and allocate space for a vertex </li> +</ul> +<h3><a href="qh-poly.htm#TOC">»</a><a name="pcheck">Check +functions</a></h3> +<ul> +<li><a href="poly2.c#check_bestdist">qh_check_bestdist</a> +check that points are not outside of facets </li> +<li><a href="poly2.c#check_dupridge">qh_check_dupridge</a> +check duplicate ridge between facet1 and facet2 for wide merge </li> +<li><a href="poly2.c#check_maxout">qh_check_maxout</a> +updates qh.max_outside and checks all points +against bestfacet </li> +<li><a href="poly2.c#check_output">qh_check_output</a> +check topological and geometric output</li> +<li><a href="poly2.c#check_point">qh_check_point</a> +check that point is not outside of facet </li> +<li><a href="poly2.c#check_points">qh_check_points</a> +check that all points are inside all facets </li> +<li><a href="poly2.c#checkconvex">qh_checkconvex</a> +check that each ridge in facetlist is convex </li> +<li><a href="poly2.c#checkfacet">qh_checkfacet</a> +check for consistency errors in facet </li> +<li><a href="poly.c#checkflipped">qh_checkflipped</a> +check facet orientation to the interior point </li> +<li><a href="poly2.c#checkflipped_all">qh_checkflipped_all</a> +check facet orientation for a facet list </li> +<li><a href="poly2.c#checkpolygon">qh_checkpolygon</a> +check topological structure </li> +<li><a href="poly2.c#checkvertex">qh_checkvertex</a> +check vertex for consistency </li> +<li><a href="poly2.c#infiniteloop">qh_infiniteloop</a> +report error for a loop of facets </li> +<li><a href="poly2.c#printlists">qh_printlists</a> +print out facet list for debugging </li> +</ul> + + +<p><!-- Navigation links --> </p> +<hr> +<p><b>Up:</b> +<a href="http://www.qhull.org">Home page for +Qhull</a> <br> +<b>Up:</b> <a href="../../html/index.htm#TOC">Qhull manual: Table of Contents</a> <br> +<b>Up:</b> <a href="../../html/qh-quick.htm#programs">Programs</a> +• <a href="../../html/qh-quick.htm#options">Options</a> +• <a href="../../html/qh-opto.htm#output">Output</a> +• <a href="../../html/qh-optf.htm#format">Formats</a> +• <a href="../../html/qh-optg.htm#geomview">Geomview</a> +• <a href="../../html/qh-optp.htm#print">Print</a> +• <a href="../../html/qh-optq.htm#qhull">Qhull</a> +• <a href="../../html/qh-optc.htm#prec">Precision</a> +• <a href="../../html/qh-optt.htm#trace">Trace</a> +• <a href="index.htm">Functions</a><br> +<b>Up:</b> <a href="../../html/qh-code.htm#TOC">Qhull code: Table of Contents</a> <br> +<b>To:</b> <a href="index.htm">Qhull functions</a>, macros, and data structures<br> +<b>To:</b> <a href="qh-geom.htm">Geom</a> • +<a href="qh-globa.htm">Global</a> • <a href="qh-io.htm">Io</a> +• <a href="qh-mem.htm">Mem</a> • <a href="qh-merge.htm">Merge</a> +• <a href="qh-poly.htm">Poly</a> • <a href="qh-qhull.htm#TOC">Qhull</a> +• <a href="qh-set.htm">Set</a> • <a href="qh-stat.htm">Stat</a> +• <a href="qh-user.htm">User</a><br> +</p> +<p><!-- GC common information --> </p> +<hr> +<p><a href="http://www.geom.uiuc.edu/"><img +src="../../html/qh--geom.gif" align="middle" width="40" height="40"></a><i>The +Geometry Center Home Page </i></p> +<p>Comments to: <a href=mailto:qhull@qhull.org>qhull@qhull.org</a> +</a><br> +Created: May 2, 1997 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p> +</body> +</html> |