631 lines
26 KiB
HTML
631 lines
26 KiB
HTML
<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
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<html>
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<head>
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<title>qconvex -- convex hull</title>
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</head>
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<body>
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<!-- Navigation links -->
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<a name="TOP"><b>Up</b></a><b>:</b>
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<a href="http://www.qhull.org">Home page</a> for Qhull<br>
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<b>Up:</b> <a href="index.htm#TOC">Qhull manual</a> -- Table of Contents<br>
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<b>To:</b> <a href="qh-quick.htm#programs">Programs</a>
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• <a href="qh-quick.htm#options">Options</a>
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• <a href="qh-opto.htm#output">Output</a>
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• <a href="qh-optf.htm#format">Formats</a>
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• <a href="qh-optg.htm#geomview">Geomview</a>
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• <a href="qh-optp.htm#print">Print</a>
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• <a href="qh-optq.htm#qhull">Qhull</a>
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• <a href="qh-optc.htm#prec">Precision</a>
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• <a href="qh-optt.htm#trace">Trace</a>
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• <a href="../src/libqhull_r/index.htm">Functions</a><br>
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<b>To:</b> <a href="#synopsis">sy</a>nopsis
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• <a href="#input">in</a>put • <a href="#outputs">ou</a>tputs
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• <a href="#controls">co</a>ntrols • <a href="#graphics">gr</a>aphics
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• <a href="#notes">no</a>tes • <a href="#conventions">co</a>nventions
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• <a href="#options">op</a>tions
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<hr>
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<!-- Main text of document -->
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<h1><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="qh--cone.gif" alt="[cone]" align="middle" width="100"
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height="100"></a>qconvex -- convex hull</h1>
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<p>The convex hull of a set of points is the smallest convex set
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containing the points. See the detailed introduction by O'Rourke
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[<a href="index.htm#orou94">'94</a>]. See <a
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href="index.htm#description">Description of Qhull</a> and <a
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href="qh-eg.htm#how">How Qhull adds a point</a>.</p>
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<blockquote>
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<dl>
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<dt><b>Example:</b> rbox 10 D3 | qconvex <a
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href="qh-opto.htm#s">s</a> <a href="qh-opto.htm#o">o</a> <a
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href="qh-optt.htm#TO">TO result</a></dt>
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<dd>Compute the 3-d convex hull of 10 random points. Write a
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summary to the console and the points and facets to
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'result'.</dd>
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<dt> </dt>
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<dt><b>Example:</b> rbox c | qconvex <a
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href="qh-opto.htm#n">n</a></dt>
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<dd>Print the normals for each facet of a cube.</dd>
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<dt> </dt>
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<dt><b>Example:</b> rbox c | qconvex <a
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href="qh-opto.htm#i">i</a> <a href="qh-optq.htm#Qt">Qt</a></dt>
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<dd>Print the triangulated facets of a cube.</dd>
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<dt> </dt>
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<dt><b>Example:</b> rbox y 500 W0 | qconvex</dt>
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<dd>Compute the convex hull of a simplex with 500
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points on its surface.</dd>
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<dt> </dt>
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<dt><b>Example:</b> rbox x W1e-12 1000 | qconvex
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<a href="qh-optq.htm#QR">QR0</a></dt>
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<dd>Compute the convex hull of 1000 points near the
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surface of a randomly rotated simplex. Report
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the maximum thickness of a facet.</dd>
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<dt> </dt>
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<dt><b>Example:</b> rbox 1000 s | qconvex <a
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href="qh-opto.htm#s">s</a> <a
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href="qh-optf.htm#FA">FA</a> </dt>
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<dd>Compute the convex hull of 1000 cospherical
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points. Verify the results and print a summary
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with the total area and volume.</dd>
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<dt> </dt>
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<dt><b>Example:</b> rbox d D12 | qconvex <a
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href="qh-optq.htm#QRn">QR0</a> <a
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href="qh-optf.htm#FA">FA</a></dt>
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<dd>Compute the convex hull of a 12-d diamond.
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Randomly rotate the input. Note the large number
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of facets and the small volume.</dd>
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<dt> </dt>
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<dt><b>Example:</b> rbox c D7 | qconvex <a
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href="qh-optf.htm#FA">FA</a> <a
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href="qh-optt.htm#TFn">TF1000</a></dt>
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<dd>Compute the convex hull of the 7-d hypercube.
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Report on progress every 1000 facets. Computing
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the convex hull of the 9-d hypercube takes too
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much time and space. </dd>
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<dt> </dt>
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<dt><b>Example:</b> rbox c d D2 | qconvex <a
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href="qh-optq.htm#Qc">Qc</a> <a
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href="qh-opto.htm#s">s</a> <a
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href="qh-opto.htm#f">f</a> <a
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href="qh-optf.htm#Fx">Fx</a> | more</dt>
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<dd>Dump all fields of all facets for a square and a
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diamond. Also print a summary and a list of
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vertices. Note the coplanar points.</dd>
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<dt> </dt>
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</dl>
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</blockquote>
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<p>Except for rbox, all of the qhull programs compute a convex hull.
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<p>By default, Qhull merges coplanar facets. For example, the convex
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hull of a cube's vertices has six facets.
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<p>If you use '<a href="qh-optq.htm#Qt">Qt</a>' (triangulated output),
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all facets will be simplicial (e.g., triangles in 2-d). For the cube
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example, it will have 12 facets. Some facets may be
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degenerate and have zero area.
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<p>If you use '<a href="qh-optq.htm#QJn">QJ</a>' (joggled input),
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all facets will be simplicial. The corresponding vertices will be
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slightly perturbed and identical points will be joggled apart.
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Joggled input is less accurate that triangulated
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output.See <a
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href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p>
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<p>The output for 4-d convex hulls may be confusing if the convex
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hull contains non-simplicial facets (e.g., a hypercube). See
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<a href=qh-faq.htm#extra>Why
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are there extra points in a 4-d or higher convex hull?</a><br>
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</p>
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</p>
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<p>The 'qconvex' program is equivalent to
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'<a href=qhull.htm#outputs>qhull</a>' in 2-d to 4-d, and
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'<a href=qhull.htm#outputs>qhull</a> <a href=qh-optq.htm#Qx>Qx</a>'
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in 5-d and higher. It disables the following Qhull
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<a href=qh-quick.htm#options>options</a>: <i>d v H Qbb Qf Qg Qm
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Qr Qu Qv Qx Qz TR E V Fp Gt Q0,etc</i>.
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<p><b>Copyright © 1995-2015 C.B. Barber</b></p>
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<hr>
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<h3><a href="#TOP">»</a><a name="synopsis">qconvex synopsis</a></h3>
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<pre>
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qconvex- compute the convex hull.
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input (stdin): dimension, number of points, point coordinates
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comments start with a non-numeric character
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options (qconvex.htm):
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Qt - triangulated output
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QJ - joggle input instead of merging facets
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Tv - verify result: structure, convexity, and point inclusion
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. - concise list of all options
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- - one-line description of all options
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output options (subset):
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s - summary of results (default)
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i - vertices incident to each facet
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n - normals with offsets
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p - vertex coordinates (includes coplanar points if 'Qc')
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Fx - extreme points (convex hull vertices)
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FA - compute total area and volume
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o - OFF format (dim, n, points, facets)
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G - Geomview output (2-d, 3-d, and 4-d)
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m - Mathematica output (2-d and 3-d)
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QVn - print facets that include point n, -n if not
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TO file- output results to file, may be enclosed in single quotes
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examples:
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rbox c D2 | qconvex s n rbox c D2 | qconvex i
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rbox c D2 | qconvex o rbox 1000 s | qconvex s Tv FA
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rbox c d D2 | qconvex s Qc Fx rbox y 1000 W0 | qconvex s n
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rbox y 1000 W0 | qconvex s QJ rbox d G1 D12 | qconvex QR0 FA Pp
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rbox c D7 | qconvex FA TF1000
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</pre>
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<h3><a href="#TOP">»</a><a name="input">qconvex
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input</a></h3>
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<blockquote>
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<p>The input data on <tt>stdin</tt> consists of:</p>
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<ul>
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<li>dimension
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<li>number of points</li>
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<li>point coordinates</li>
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</ul>
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<p>Use I/O redirection (e.g., qconvex < data.txt), a pipe (e.g., rbox 10 | qconvex),
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or the '<a href=qh-optt.htm#TI>TI</a>' option (e.g., qconvex TI data.txt).
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<p>Comments start with a non-numeric character. Error reporting is
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simpler if there is one point per line. Dimension
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and number of points may be reversed.
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<p>Here is the input for computing the convex
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hull of the unit cube. The output is the normals, one
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per facet.</p>
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<blockquote>
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<p>rbox c > data </p>
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<pre>
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3 RBOX c
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8
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-0.5 -0.5 -0.5
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-0.5 -0.5 0.5
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-0.5 0.5 -0.5
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-0.5 0.5 0.5
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0.5 -0.5 -0.5
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0.5 -0.5 0.5
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0.5 0.5 -0.5
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0.5 0.5 0.5
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</pre>
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<p>qconvex s n < data</p>
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<pre>
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Convex hull of 8 points in 3-d:
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Number of vertices: 8
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Number of facets: 6
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Number of non-simplicial facets: 6
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Statistics for: RBOX c | QCONVEX s n
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Number of points processed: 8
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Number of hyperplanes created: 11
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Number of distance tests for qhull: 35
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Number of merged facets: 6
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Number of distance tests for merging: 84
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CPU seconds to compute hull (after input): 0.081
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4
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6
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0 0 -1 -0.5
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0 -1 0 -0.5
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1 0 0 -0.5
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-1 0 0 -0.5
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0 1 0 -0.5
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0 0 1 -0.5
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</pre>
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</blockquote>
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</blockquote>
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<h3><a href="#TOP">»</a><a name="outputs">qconvex outputs</a></h3>
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<blockquote>
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<p>These options control the output of qconvex. They may be used
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individually or together.</p>
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<blockquote>
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<dl compact>
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<dt> </dt>
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<dd><b>Vertices</b></dd>
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<dt><a href="qh-optf.htm#Fx">Fx</a></dt>
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<dd>list extreme points (i.e., vertices). The first line is the number of
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extreme points. Each point is listed, one per line. The cube example
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has eight vertices.</dd>
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<dt><a href="qh-optf.htm#Fv">Fv</a></dt>
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<dd>list vertices for each facet. The first line is the number of facets.
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Each remaining line starts with the number of vertices. For the cube example,
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each facet has four vertices.</dd>
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<dt><a href="qh-opto.htm#i">i</a></dt>
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<dd>list vertices for each facet. The first line is the number of facets. The
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remaining lines list the vertices for each facet. In 4-d and
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higher, triangulate non-simplicial facets by adding an extra point.</dd>
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<dt> </dt>
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<dt> </dt>
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<dd><b>Coordinates</b></dd>
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<dt><a href="qh-opto.htm#o">o</a></dt>
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<dd>print vertices and facets of the convex hull in OFF format. The
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first line is the dimension. The second line is the number of
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vertices, facets, and ridges. The vertex
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coordinates are next, followed by the facets. Each facet starts with
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the number of vertices. The cube example has four vertices per facet.</dd>
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<dt><a href="qh-optf.htm#Ft">Ft</a></dt>
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<dd>print a triangulation of the convex hull in OFF format. The first line
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is the dimension. The second line is the number of vertices and added points,
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followed by the number of facets and the number of ridges.
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The vertex coordinates are next, followed by the centrum coordinates. There is
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one centrum for each non-simplicial facet.
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The cube example has six centrums, one per square.
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Each facet starts with the number of vertices or centrums.
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In the cube example, each facet uses two vertices and one centrum.</dd>
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<dt><a href="qh-opto.htm#p">p</a></dt>
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<dd>print vertex coordinates. The first line is the dimension and the second
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line is the number of vertices. The following lines are the coordinates of each
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vertex. The cube example has eight vertices.</dd>
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<dt><a href="qh-optq.htm#Qc">Qc</a> <a href="qh-opto.htm#p">p</a></dt>
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<dd>print coordinates of vertices and coplanar points. The first line is the dimension.
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The second line is the number of vertices and coplanar points. The coordinates
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are next, one line per point. Use '<a href="qh-optq.htm#Qc">Qc</a> <a href="qh-optq.htm#Qi">Qi</a> p'
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to print the coordinates of all points.</dd>
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<dt> </dt>
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<dt> </dt>
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<dd><b>Facets</b></dd>
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<dt><a href="qh-optf.htm#Fn">Fn</a></dt>
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<dd>list neighboring facets for each facet. The first line is the
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number of facets. Each remaining line starts with the number of
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neighboring facets. The cube example has four neighbors per facet.</dd>
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<dt><a href="qh-optf.htm#FN">FN</a></dt>
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<dd>list neighboring facets for each point. The first line is the
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total number of points. Each remaining line starts with the number of
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neighboring facets. Each vertex of the cube example has three neighboring
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facets. Use '<a href="qh-optq.htm#Qc">Qc</a> <a href="qh-optq.htm#Qi">Qi</a> FN'
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to include coplanar and interior points. </dd>
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<dt><a href="qh-optf.htm#Fa">Fa</a></dt>
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<dd>print area for each facet. The first line is the number of facets.
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Facet area follows, one line per facet. For the cube example, each facet has area one.</dd>
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<dt><a href="qh-optf.htm#FI">FI</a></dt>
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<dd>list facet IDs. The first line is the number of
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facets. The IDs follow, one per line.</dd>
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<dt> </dt>
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<dt> </dt>
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<dd><b>Coplanar and interior points</b></dd>
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<dt><a href="qh-optf.htm#Fc">Fc</a></dt>
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<dd>list coplanar points for each facet. The first line is the number
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of facets. The remaining lines start with the number of coplanar points.
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A coplanar point is assigned to one facet.</dd>
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<dt><a href="qh-optq.htm#Qi">Qi</a> <a href="qh-optf.htm#Fc">Fc</a></dt>
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<dd>list interior points for each facet. The first line is the number
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of facets. The remaining lines start with the number of interior points.
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A coplanar point is assigned to one facet.</dd>
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<dt><a href="qh-optf.htm#FP">FP</a></dt>
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<dd>print distance to nearest vertex for coplanar points. The first line is the
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number of coplanar points. Each remaining line starts with the point ID of
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a vertex, followed by the point ID of a coplanar point, its facet, and distance.
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Use '<a href="qh-optq.htm#Qc">Qc</a> <a href="qh-optq.htm#Qi">Qi</a>
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<a href="qh-optf.htm#FP">FP</a>' for coplanar and interior points.</dd>
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<dt> </dt>
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<dt> </dt>
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<dd><b>Hyperplanes</b></dd>
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<dt><a href="qh-opto.htm#n">n</a></dt>
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<dd>print hyperplane for each facet. The first line is the dimension. The
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second line is the number of facets. Each remaining line is the hyperplane's
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coefficients followed by its offset.</dd>
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<dt><a href="qh-optf.htm#Fo">Fo</a></dt>
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<dd>print outer plane for each facet. The output plane is above all points.
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The first line is the dimension. The
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second line is the number of facets. Each remaining line is the outer plane's
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coefficients followed by its offset.</dd>
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<dt><a href="qh-optf.htm#Fi">Fi</a></dt>
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<dd>print inner plane for each facet. The inner plane of a facet is
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below its vertices.
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The first line is the dimension. The
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second line is the number of facets. Each remaining line is the inner plane's
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coefficients followed by its offset.</dd>
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<dt> </dt>
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<dt> </dt>
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<dd><b>General</b></dd>
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<dt><a href="qh-opto.htm#s">s</a></dt>
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<dd>print summary for the convex hull. Use '<a
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href="qh-optf.htm#Fs">Fs</a>' and '<a
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href="qh-optf.htm#FS">FS</a>' if you need numeric data.</dd>
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<dt><a href="qh-optf.htm#FA">FA</a></dt>
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<dd>compute total area and volume for '<a
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href="qh-opto.htm#s">s</a>' and '<a href="qh-optf.htm#FS">FS</a>'</dd>
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<dt><a href="qh-opto.htm#m">m</a></dt>
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<dd>Mathematica output for the convex hull in 2-d or 3-d.</dd>
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<dt><a href="qh-optf.htm#FM">FM</a></dt>
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<dd>Maple output for the convex hull in 2-d or 3-d.</dd>
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<dt><a href="qh-optg.htm#G">G</a></dt>
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<dd>Geomview output for the convex hull in 2-d, 3-d, or 4-d.</dd>
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<dt> </dt>
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<dt> </dt>
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<dd><b>Scaling and rotation</b></dd>
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<dt><a href="qh-optq.htm#Qbk">Qbk:n</a></dt>
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<dd>scale k'th coordinate to lower bound.</dd>
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<dt><a href="qh-optq.htm#QBk">QBk:n</a></dt>
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<dd>scale k'th coordinate to upper bound.</dd>
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<dt><a href="qh-optq.htm#QbB">QbB</a></dt>
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<dd>scale input to unit cube centered at the origin.</dd>
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<dt><a href="qh-optq.htm#QRn">QRn</a></dt>
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<dd>randomly rotate the input with a random seed of n. If n=0, the
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seed is the time. If n=-1, use time for the random seed, but do
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not rotate the input.</dd>
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<dt><a href="qh-optq.htm#Qb0">Qbk:0Bk:0</a></dt>
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<dd>remove k'th coordinate from input. This computes the
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convex hull in one lower dimension.</dd>
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</dl>
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</blockquote>
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</blockquote>
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<h3><a href="#TOP">»</a><a name="controls">qconvex controls</a></h3>
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<blockquote>
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<p>These options provide additional control:</p>
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<blockquote>
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<dl compact>
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<dt><a href="qh-optq.htm#Qt">Qt</a></dt>
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<dd>triangulated output. Qhull triangulates non-simplicial facets. It may produce
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degenerate facets of zero area.</dd>
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<dt><a href="qh-optq.htm#QJn">QJ</a></dt>
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<dd>joggle the input instead of merging facets. This guarantees simplicial facets
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|
(e.g., triangles in 3-d). It is less accurate than triangulated output ('Qt').</dd>
|
|
<dt><a href="qh-optq.htm#Qc">Qc</a></dt>
|
|
<dd>keep coplanar points</dd>
|
|
<dt><a href="qh-optq.htm#Qi">Qi</a></dt>
|
|
<dd>keep interior points</dd>
|
|
<dt><a href="qh-opto.htm#f">f </a></dt>
|
|
<dd>facet dump. Print the data structure for each facet.</dd>
|
|
<dt><a href="qh-optq.htm#QVn">QVn</a></dt>
|
|
<dd>select facets containing point <em>n</em> as a vertex,</dd>
|
|
<dt><a href="qh-optq.htm#QGn">QGn</a></dt>
|
|
<dd>select facets that are visible from point <em>n</em>
|
|
(marked 'good'). Use <em>-n</em> for the remainder.</dd>
|
|
<dt><a href="qh-optp.htm#PDk">PDk:0</a></dt>
|
|
<dd>select facets with a negative coordinate for dimension <i>k</i></dd>
|
|
<dt><a href="qh-optt.htm#TFn">TFn</a></dt>
|
|
<dd>report progress after constructing <em>n</em> facets</dd>
|
|
<dt><a href="qh-optt.htm#Tv">Tv</a></dt>
|
|
<dd>verify result</dd>
|
|
<dt><a href="qh-optt.htm#TO">TI file</a></dt>
|
|
<dd>input data from file. The filename may not use spaces or quotes.</dd>
|
|
<dt><a href="qh-optt.htm#TO">TO file</a></dt>
|
|
<dd>output results to file. Use single quotes if the filename
|
|
contains spaces (e.g., <tt>TO 'file with spaces.txt'</tt></dd>
|
|
<dt><a href="qh-optq.htm#Qs">Qs</a></dt>
|
|
<dd>search all points for the initial simplex. If Qhull can
|
|
not construct an initial simplex, it reports a
|
|
descriptive message. Usually, the point set is degenerate and one
|
|
or more dimensions should be removed ('<a href="qh-optq.htm#Qb0">Qbk:0Bk:0</a>').
|
|
If not, use option 'Qs'. It performs an exhaustive search for the
|
|
best initial simplex. This is expensive is high dimensions.</dd>
|
|
</dl>
|
|
</blockquote>
|
|
|
|
</blockquote>
|
|
<h3><a href="#TOP">»</a><a name="graphics">qconvex graphics</a></h3>
|
|
<blockquote>
|
|
|
|
<p>Display 2-d, 3-d, and 4-d convex hulls with Geomview ('<a
|
|
href="qh-optg.htm#G">G</a>').</p>
|
|
|
|
<p>Display 2-d and 3-d convex hulls with Mathematica ('<a
|
|
href="qh-opto.htm#m">m</a>').</p>
|
|
|
|
<p>To view 4-d convex hulls in 3-d, use '<a
|
|
href="qh-optp.htm#Pdk">Pd0d1d2d3</a>' to select the positive
|
|
octant and '<a href="qh-optg.htm#GDn">GrD2</a>' to drop dimension
|
|
2. </p>
|
|
|
|
</blockquote>
|
|
<h3><a href="#TOP">»</a><a name="notes">qconvex notes</a></h3>
|
|
<blockquote>
|
|
|
|
<p>Qhull always computes a convex hull. The
|
|
convex hull may be used for other geometric structures. The
|
|
general technique is to transform the structure into an
|
|
equivalent convex hull problem. For example, the Delaunay
|
|
triangulation is equivalent to the convex hull of the input sites
|
|
after lifting the points to a paraboloid.</p>
|
|
|
|
</blockquote>
|
|
<h3><a href="#TOP">»</a><a name="conventions">qconvex
|
|
conventions</a></h3>
|
|
<blockquote>
|
|
|
|
<p>The following terminology is used for convex hulls in Qhull.
|
|
See <a href="index.htm#structure">Qhull's data structures</a>.</p>
|
|
|
|
<ul>
|
|
<li><em>point</em> - <em>d</em> coordinates</li>
|
|
<li><em>vertex</em> - extreme point of the input set</li>
|
|
<li><em>ridge</em> - <i>d-1</i> vertices between two
|
|
neighboring facets</li>
|
|
<li><em>hyperplane</em> - halfspace defined by a unit normal
|
|
and offset</li>
|
|
<li><em>coplanar point</em> - a nearly incident point to a
|
|
hyperplane</li>
|
|
<li><em>centrum</em> - a point on the hyperplane for testing
|
|
convexity</li>
|
|
<li><em>facet</em> - a facet with vertices, ridges, coplanar
|
|
points, neighboring facets, and hyperplane</li>
|
|
<li><em>simplicial facet</em> - a facet with <em>d</em>
|
|
vertices, <em>d</em> ridges, and <em>d</em> neighbors</li>
|
|
<li><em>non-simplicial facet</em> - a facet with more than <em>d</em>
|
|
vertices</li>
|
|
<li><em>good facet</em> - a facet selected by '<a
|
|
href="qh-optq.htm#QVn">QVn</a>', etc.</li>
|
|
</ul>
|
|
</blockquote>
|
|
<h3><a href="#TOP">»</a><a name="options">qconvex options</a></h3>
|
|
|
|
<pre>
|
|
qconvex- compute the convex hull
|
|
http://www.qhull.org
|
|
|
|
input (stdin):
|
|
first lines: dimension and number of points (or vice-versa).
|
|
other lines: point coordinates, best if one point per line
|
|
comments: start with a non-numeric character
|
|
|
|
options:
|
|
Qt - triangulated output
|
|
QJ - joggle input instead of merging facets
|
|
Qc - keep coplanar points with nearest facet
|
|
Qi - keep interior points with nearest facet
|
|
|
|
Qhull control options:
|
|
Qbk:n - scale coord k so that low bound is n
|
|
QBk:n - scale coord k so that upper bound is n (QBk is 0.5)
|
|
QbB - scale input to unit cube centered at the origin
|
|
Qbk:0Bk:0 - remove k-th coordinate from input
|
|
QJn - randomly joggle input in range [-n,n]
|
|
QRn - random rotation (n=seed, n=0 time, n=-1 time/no rotate)
|
|
Qs - search all points for the initial simplex
|
|
QGn - good facet if visible from point n, -n for not visible
|
|
QVn - good facet if it includes point n, -n if not
|
|
|
|
Trace options:
|
|
T4 - trace at level n, 4=all, 5=mem/gauss, -1= events
|
|
Tc - check frequently during execution
|
|
Ts - print statistics
|
|
Tv - verify result: structure, convexity, and point inclusion
|
|
Tz - send all output to stdout
|
|
TFn - report summary when n or more facets created
|
|
TI file - input data from file, no spaces or single quotes
|
|
TO file - output results to file, may be enclosed in single quotes
|
|
TPn - turn on tracing when point n added to hull
|
|
TMn - turn on tracing at merge n
|
|
TWn - trace merge facets when width > n
|
|
TVn - stop qhull after adding point n, -n for before (see TCn)
|
|
TCn - stop qhull after building cone for point n (see TVn)
|
|
|
|
Precision options:
|
|
Cn - radius of centrum (roundoff added). Merge facets if non-convex
|
|
An - cosine of maximum angle. Merge facets if cosine > n or non-convex
|
|
C-0 roundoff, A-0.99/C-0.01 pre-merge, A0.99/C0.01 post-merge
|
|
Rn - randomly perturb computations by a factor of [1-n,1+n]
|
|
Un - max distance below plane for a new, coplanar point
|
|
Wn - min facet width for outside point (before roundoff)
|
|
|
|
Output formats (may be combined; if none, produces a summary to stdout):
|
|
f - facet dump
|
|
G - Geomview output (see below)
|
|
i - vertices incident to each facet
|
|
m - Mathematica output (2-d and 3-d)
|
|
n - normals with offsets
|
|
o - OFF file format (dim, points and facets; Voronoi regions)
|
|
p - point coordinates
|
|
s - summary (stderr)
|
|
|
|
More formats:
|
|
Fa - area for each facet
|
|
FA - compute total area and volume for option 's'
|
|
Fc - count plus coplanar points for each facet
|
|
use 'Qc' (default) for coplanar and 'Qi' for interior
|
|
FC - centrum for each facet
|
|
Fd - use cdd format for input (homogeneous with offset first)
|
|
FD - use cdd format for numeric output (offset first)
|
|
FF - facet dump without ridges
|
|
Fi - inner plane for each facet
|
|
FI - ID for each facet
|
|
Fm - merge count for each facet (511 max)
|
|
FM - Maple output (2-d and 3-d)
|
|
Fn - count plus neighboring facets for each facet
|
|
FN - count plus neighboring facets for each point
|
|
Fo - outer plane (or max_outside) for each facet
|
|
FO - options and precision constants
|
|
FP - nearest vertex for each coplanar point
|
|
FQ - command used for qconvex
|
|
Fs - summary: #int (8), dimension, #points, tot vertices, tot facets,
|
|
for output: #vertices, #facets,
|
|
#coplanar points, #non-simplicial facets
|
|
#real (2), max outer plane, min vertex
|
|
FS - sizes: #int (0)
|
|
#real(2) tot area, tot volume
|
|
Ft - triangulation with centrums for non-simplicial facets (OFF format)
|
|
Fv - count plus vertices for each facet
|
|
FV - average of vertices (a feasible point for 'H')
|
|
Fx - extreme points (in order for 2-d)
|
|
|
|
Geomview output (2-d, 3-d, and 4-d)
|
|
Ga - all points as dots
|
|
Gp - coplanar points and vertices as radii
|
|
Gv - vertices as spheres
|
|
Gi - inner planes only
|
|
Gn - no planes
|
|
Go - outer planes only
|
|
Gc - centrums
|
|
Gh - hyperplane intersections
|
|
Gr - ridges
|
|
GDn - drop dimension n in 3-d and 4-d output
|
|
|
|
Print options:
|
|
PAn - keep n largest facets by area
|
|
Pdk:n - drop facet if normal[k] <= n (default 0.0)
|
|
PDk:n - drop facet if normal[k] >= n
|
|
Pg - print good facets (needs 'QGn' or 'QVn')
|
|
PFn - keep facets whose area is at least n
|
|
PG - print neighbors of good facets
|
|
PMn - keep n facets with most merges
|
|
Po - force output. If error, output neighborhood of facet
|
|
Pp - do not report precision problems
|
|
|
|
. - list of all options
|
|
- - one line descriptions of all options
|
|
|
|
</pre>
|
|
|
|
<!-- Navigation links -->
|
|
<hr>
|
|
|
|
<p><b>Up:</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>
|
|
• <a href="../src/libqhull_r/index.htm">Functions</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
|
|
<!-- GC common information -->
|
|
<hr>
|
|
|
|
<p><a href="http://www.geom.uiuc.edu/"><img src="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: Sept. 25, 1995 --- <!-- hhmts start --> Last modified: see top <!-- hhmts end --> </p>
|
|
</body>
|
|
</html>
|