📄 qvoron_f.htm
字号:
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
<html>
<head>
<title>qvoronoi Qu -- furthest-site Voronoi diagram</title>
</head>
<body>
<!-- Navigation links -->
<a name="TOP"><b>Up</b></a><b>:</b>
<a href="http://www.qhull.org">Home page</a> for Qhull<br>
<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a>: Table of Contents<br>
<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>
<b>To:</b> <a href="#synopsis">sy</a>nopsis
• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
• <a href="#options">op</a>tions
<hr>
<!-- Main text of document -->
<h1><a
href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/delaunay.html"><img
src="qh--dt.gif" alt="[delaunay]" align="middle" width="100"
height="100"></a>qvoronoi Qu -- furthest-site Voronoi diagram</h1>
<p>The furthest-site Voronoi diagram is the furthest-neighbor map for a set of
points. Each region contains those points that are further
from one input site than any other input site. See the
survey article by Aurenhammer [<a href="index.htm#aure91">'91</a>]
and the brief introduction by O'Rourke [<a
href="index.htm#orou94">'94</a>]. The furthest-site Voronoi diagram is the dual of the <a
href="qdelau_f.htm">furthest-site Delaunay triangulation</a>.
</p>
<blockquote>
<dl>
<dt><b>Example:</b> rbox 10 D2 | qvoronoi <a
href="qh-optq.htm#Qu">Qu</a> <a href="qh-opto.htm#s">s</a>
<a href="qh-opto.htm#o">o</a> <a href="qh-optt.htm#TO">TO
result</a></dt>
<dd>Compute the 2-d, furthest-site Voronoi diagram of 10
random points. Write a summary to the console and the Voronoi
regions and vertices to 'result'. The first vertex of the
result indicates unbounded regions. Almost all regions
are unbounded.</dd>
</dl>
<dl>
<dt><b>Example:</b> rbox r y c G1 D2 | qvoronoi <a
href="qh-optq.htm#Qu">Qu</a>
<a href="qh-opto.htm#s">s</a>
<a href="qh-optf.htm#Fn">Fn</a> <a href="qh-optt.htm#TO">TO
result</a></dt>
<dd>Compute the 2-d furthest-site Voronoi diagram of a square
and a small triangle. Write a summary to the console and the Voronoi
vertices for each input site to 'result'.
The origin is the only furthest-site Voronoi vertex. The
negative indices indicate vertices-at-infinity.</dd>
</dl>
</blockquote>
<p>
Qhull computes the furthest-site Voronoi diagram via the <a href="qdelau_f.htm">
furthest-site Delaunay triangulation</a>.
Each furthest-site Voronoi vertex is the circumcenter of an upper
facet of the Delaunay triangulation. Each furthest-site Voronoi
region corresponds to a vertex of the Delaunay triangulation
(i.e., an input site).</p>
<p>See <a href="http://www.qhull.org/html/qh-faq.htm#TOC">Qhull FAQ</a> - Delaunay and
Voronoi diagram questions.</p>
<p>Options '<a href="qh-optq.htm#Qt">Qt</a>' (triangulated output)
and '<a href="qh-optq.htm#QJn">QJ</a>' (joggled input), may produce
unexpected results. Cocircular and cospherical input sites will
produce duplicate or nearly duplicate furthest-site Voronoi vertices. See also <a
href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p>
<p>The 'qvonoroi' program is equivalent to
'<a href=qhull.htm#outputs>qhull v</a> <a href=qh-optq.htm#Qbb>Qbb</a>' in 2-d to 3-d, and
'<a href=qhull.htm#outputs>qhull v</a> <a href=qh-optq.htm#Qbb>Qbb</a> <a href=qh-optq.htm#Qx>Qx</a>'
in 4-d and higher. It disables the following Qhull
<a href=qh-quick.htm#options>options</a>: <i>d n m v H U Qb
QB Qc Qf Qg Qi Qm Qr QR Qv Qx TR E V Fa FA FC Fp FS Ft FV Gt Q0,etc</i>.
<p><b>Copyright © 1995-2003 The Geometry Center, Minneapolis MN</b></p>
<hr>
<h3><a href="#TOP">⌨️ 快捷键说明
复制代码
Ctrl + C
搜索代码
Ctrl + F
全屏模式
F11
切换主题
Ctrl + Shift + D
显示快捷键
?
增大字号
Ctrl + =
减小字号
Ctrl + -