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diff --git a/src/qhull/html/qconvex.htm b/src/qhull/html/qconvex.htm new file mode 100644 index 000000000..38a363b08 --- /dev/null +++ b/src/qhull/html/qconvex.htm @@ -0,0 +1,630 @@ +<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN"> +<html> + +<head> +<title>qconvex -- convex hull</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> +• <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 +<hr> +<!-- Main text of document --> +<h1><a +href="http://www.geom.uiuc.edu/graphics/pix/Special_Topics/Computational_Geometry/cone.html"><img +src="qh--cone.gif" alt="[cone]" align="middle" width="100" +height="100"></a>qconvex -- convex hull</h1> + +<p>The convex hull of a set of points is the smallest convex set +containing the points. See the detailed introduction by O'Rourke +[<a href="index.htm#orou94">'94</a>]. See <a +href="index.htm#description">Description of Qhull</a> and <a +href="qh-eg.htm#how">How Qhull adds a point</a>.</p> + +<blockquote> +<dl> + <dt><b>Example:</b> rbox 10 D3 | qconvex <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 3-d convex hull of 10 random points. Write a + summary to the console and the points and facets to + 'result'.</dd> + + <dt> </dt> + <dt><b>Example:</b> rbox c | qconvex <a + href="qh-opto.htm#n">n</a></dt> + <dd>Print the normals for each facet of a cube.</dd> + <dt> </dt> + <dt><b>Example:</b> rbox c | qconvex <a + href="qh-opto.htm#i">i</a> <a href="qh-optq.htm#Qt">Qt</a></dt> + <dd>Print the triangulated facets of a cube.</dd> + <dt> </dt> + <dt><b>Example:</b> rbox y 500 W0 | qconvex</dt> + <dd>Compute the convex hull of a simplex with 500 + points on its surface.</dd> + <dt> </dt> + <dt><b>Example:</b> rbox x W1e-12 1000 | qconvex + <a href="qh-optq.htm#QR">QR0</a></dt> + <dd>Compute the convex hull of 1000 points near the + surface of a randomly rotated simplex. Report + the maximum thickness of a facet.</dd> + <dt> </dt> + <dt><b>Example:</b> rbox 1000 s | qconvex <a + href="qh-opto.htm#s">s</a> <a + href="qh-optf.htm#FA">FA</a> </dt> + <dd>Compute the convex hull of 1000 cospherical + points. Verify the results and print a summary + with the total area and volume.</dd> + <dt> </dt> + <dt><b>Example:</b> rbox d D12 | qconvex <a + href="qh-optq.htm#QRn">QR0</a> <a + href="qh-optf.htm#FA">FA</a></dt> + <dd>Compute the convex hull of a 12-d diamond. + Randomly rotate the input. Note the large number + of facets and the small volume.</dd> + <dt> </dt> + <dt><b>Example:</b> rbox c D7 | qconvex <a + href="qh-optf.htm#FA">FA</a> <a + href="qh-optt.htm#TFn">TF1000</a></dt> + <dd>Compute the convex hull of the 7-d hypercube. + Report on progress every 1000 facets. Computing + the convex hull of the 9-d hypercube takes too + much time and space. </dd> + <dt> </dt> + <dt><b>Example:</b> rbox c d D2 | qconvex <a + href="qh-optq.htm#Qc">Qc</a> <a + href="qh-opto.htm#s">s</a> <a + href="qh-opto.htm#f">f</a> <a + href="qh-optf.htm#Fx">Fx</a> | more</dt> + <dd>Dump all fields of all facets for a square and a + diamond. Also print a summary and a list of + vertices. Note the coplanar points.</dd> + <dt> </dt> +</dl> +</blockquote> + +<p>Except for rbox, all of the qhull programs compute a convex hull. + +<p>By default, Qhull merges coplanar facets. For example, the convex +hull of a cube's vertices has six facets. + +<p>If you use '<a href="qh-optq.htm#Qt">Qt</a>' (triangulated output), +all facets will be simplicial (e.g., triangles in 2-d). For the cube +example, it will have 12 facets. Some facets may be +degenerate and have zero area. + +<p>If you use '<a href="qh-optq.htm#QJn">QJ</a>' (joggled input), +all facets will be simplicial. The corresponding vertices will be +slightly perturbed and identical points will be joggled apart. +Joggled input is less accurate that triangulated +output.See <a +href="qh-impre.htm#joggle">Merged facets or joggled input</a>. </p> + +<p>The output for 4-d convex hulls may be confusing if the convex +hull contains non-simplicial facets (e.g., a hypercube). See +<a href=qh-faq.htm#extra>Why +are there extra points in a 4-d or higher convex hull?</a><br> +</p> +</p> + +<p>The 'qconvex' program is equivalent to +'<a href=qhull.htm#outputs>qhull</a>' in 2-d to 4-d, and +'<a href=qhull.htm#outputs>qhull</a> <a href=qh-optq.htm#Qx>Qx</a>' +in 5-d and higher. It disables the following Qhull +<a href=qh-quick.htm#options>options</a>: <i>d v H Qbb Qf Qg Qm +Qr Qu Qv Qx Qz TR E V Fp Gt Q0,etc</i>. + +<p><b>Copyright © 1995-2015 C.B. Barber</b></p> + +<hr> + +<h3><a href="#TOP">»</a><a name="synopsis">qconvex synopsis</a></h3> +<pre> +qconvex- compute the convex hull. + input (stdin): dimension, number of points, point coordinates + comments start with a non-numeric character + +options (qconvex.htm): + Qt - triangulated output + QJ - joggle input instead of merging facets + Tv - verify result: structure, convexity, and point inclusion + . - concise list of all options + - - one-line description of all options + +output options (subset): + s - summary of results (default) + i - vertices incident to each facet + n - normals with offsets + p - vertex coordinates (includes coplanar points if 'Qc') + Fx - extreme points (convex hull vertices) + FA - compute total area and volume + o - OFF format (dim, n, points, facets) + G - Geomview output (2-d, 3-d, and 4-d) + m - Mathematica output (2-d and 3-d) + QVn - print facets that include point n, -n if not + TO file- output results to file, may be enclosed in single quotes + +examples: + rbox c D2 | qconvex s n rbox c D2 | qconvex i + rbox c D2 | qconvex o rbox 1000 s | qconvex s Tv FA + rbox c d D2 | qconvex s Qc Fx rbox y 1000 W0 | qconvex s n + rbox y 1000 W0 | qconvex s QJ rbox d G1 D12 | qconvex QR0 FA Pp + rbox c D7 | qconvex FA TF1000 +</pre> + +<h3><a href="#TOP">»</a><a name="input">qconvex +input</a></h3> +<blockquote> + +<p>The input data on <tt>stdin</tt> consists of:</p> +<ul> + <li>dimension + <li>number of points</li> + <li>point coordinates</li> +</ul> + +<p>Use I/O redirection (e.g., qconvex < data.txt), a pipe (e.g., rbox 10 | qconvex), +or the '<a href=qh-optt.htm#TI>TI</a>' option (e.g., qconvex TI data.txt). + +<p>Comments start with a non-numeric character. Error reporting is +simpler if there is one point per line. Dimension +and number of points may be reversed. + +<p>Here is the input for computing the convex +hull of the unit cube. The output is the normals, one +per facet.</p> + +<blockquote> + <p>rbox c > data </p> + <pre> +3 RBOX c +8 + -0.5 -0.5 -0.5 + -0.5 -0.5 0.5 + -0.5 0.5 -0.5 + -0.5 0.5 0.5 + 0.5 -0.5 -0.5 + 0.5 -0.5 0.5 + 0.5 0.5 -0.5 + 0.5 0.5 0.5 +</pre> + <p>qconvex s n < data</p> + <pre> + +Convex hull of 8 points in 3-d: + + Number of vertices: 8 + Number of facets: 6 + Number of non-simplicial facets: 6 + +Statistics for: RBOX c | QCONVEX s n + + Number of points processed: 8 + Number of hyperplanes created: 11 + Number of distance tests for qhull: 35 + Number of merged facets: 6 + Number of distance tests for merging: 84 + CPU seconds to compute hull (after input): 0.081 + +4 +6 + 0 0 -1 -0.5 + 0 -1 0 -0.5 + 1 0 0 -0.5 + -1 0 0 -0.5 + 0 1 0 -0.5 + 0 0 1 -0.5 +</pre> +</blockquote> + +</blockquote> +<h3><a href="#TOP">»</a><a name="outputs">qconvex outputs</a></h3> +<blockquote> + +<p>These options control the output of qconvex. They may be used +individually or together.</p> +<blockquote> +<dl compact> + <dt> </dt> + <dd><b>Vertices</b></dd> + <dt><a href="qh-optf.htm#Fx">Fx</a></dt> + <dd>list extreme points (i.e., vertices). The first line is the number of + extreme points. Each point is listed, one per line. The cube example + has eight vertices.</dd> + <dt><a href="qh-optf.htm#Fv">Fv</a></dt> + <dd>list vertices for each facet. The first line is the number of facets. + Each remaining line starts with the number of vertices. For the cube example, + each facet has four vertices.</dd> + <dt><a href="qh-opto.htm#i">i</a></dt> + <dd>list vertices for each facet. The first line is the number of facets. The + remaining lines list the vertices for each facet. In 4-d and + higher, triangulate non-simplicial facets by adding an extra point.</dd> + <dt> </dt> + <dt> </dt> + <dd><b>Coordinates</b></dd> + <dt><a href="qh-opto.htm#o">o</a></dt> + <dd>print vertices and facets of the convex hull in OFF format. The + first line is the dimension. The second line is the number of + vertices, facets, and ridges. The vertex + coordinates are next, followed by the facets. Each facet starts with + the number of vertices. The cube example has four vertices per facet.</dd> + <dt><a href="qh-optf.htm#Ft">Ft</a></dt> + <dd>print a triangulation of the convex hull in OFF format. The first line + is the dimension. The second line is the number of vertices and added points, + followed by the number of facets and the number of ridges. + The vertex coordinates are next, followed by the centrum coordinates. There is + one centrum for each non-simplicial facet. + The cube example has six centrums, one per square. + Each facet starts with the number of vertices or centrums. + In the cube example, each facet uses two vertices and one centrum.</dd> + <dt><a href="qh-opto.htm#p">p</a></dt> + <dd>print vertex coordinates. The first line is the dimension and the second + line is the number of vertices. The following lines are the coordinates of each + vertex. The cube example has eight vertices.</dd> + <dt><a href="qh-optq.htm#Qc">Qc</a> <a href="qh-opto.htm#p">p</a></dt> + <dd>print coordinates of vertices and coplanar points. The first line is the dimension. + The second line is the number of vertices and coplanar points. The coordinates + are next, one line per point. Use '<a href="qh-optq.htm#Qc">Qc</a> <a href="qh-optq.htm#Qi">Qi</a> p' + to print the coordinates of all points.</dd> + <dt> </dt> + <dt> </dt> + <dd><b>Facets</b></dd> + <dt><a href="qh-optf.htm#Fn">Fn</a></dt> + <dd>list neighboring facets for each facet. The first line is the + number of facets. Each remaining line starts with the number of + neighboring facets. The cube example has four neighbors per facet.</dd> + <dt><a href="qh-optf.htm#FN">FN</a></dt> + <dd>list neighboring facets for each point. The first line is the + total number of points. Each remaining line starts with the number of + neighboring facets. Each vertex of the cube example has three neighboring + facets. Use '<a href="qh-optq.htm#Qc">Qc</a> <a href="qh-optq.htm#Qi">Qi</a> FN' + to include coplanar and interior points. </dd> + <dt><a href="qh-optf.htm#Fa">Fa</a></dt> + <dd>print area for each facet. The first line is the number of facets. + Facet area follows, one line per facet. For the cube example, each facet has area one.</dd> + <dt><a href="qh-optf.htm#FI">FI</a></dt> + <dd>list facet IDs. The first line is the number of + facets. The IDs follow, one per line.</dd> + + <dt> </dt> + <dt> </dt> + <dd><b>Coplanar and interior points</b></dd> + <dt><a href="qh-optf.htm#Fc">Fc</a></dt> + <dd>list coplanar points for each facet. The first line is the number + of facets. The remaining lines start with the number of coplanar points. + A coplanar point is assigned to one facet.</dd> + <dt><a href="qh-optq.htm#Qi">Qi</a> <a href="qh-optf.htm#Fc">Fc</a></dt> + <dd>list interior points for each facet. The first line is the number + of facets. The remaining lines start with the number of interior points. + A coplanar point is assigned to one facet.</dd> + <dt><a href="qh-optf.htm#FP">FP</a></dt> + <dd>print distance to nearest vertex for coplanar points. The first line is the + number of coplanar points. Each remaining line starts with the point ID of + a vertex, followed by the point ID of a coplanar point, its facet, and distance. + Use '<a href="qh-optq.htm#Qc">Qc</a> <a href="qh-optq.htm#Qi">Qi</a> + <a href="qh-optf.htm#FP">FP</a>' for coplanar and interior points.</dd> + + <dt> </dt> + <dt> </dt> + <dd><b>Hyperplanes</b></dd> + <dt><a href="qh-opto.htm#n">n</a></dt> + <dd>print hyperplane for each facet. The first line is the dimension. The + second line is the number of facets. Each remaining line is the hyperplane's + coefficients followed by its offset.</dd> + <dt><a href="qh-optf.htm#Fo">Fo</a></dt> + <dd>print outer plane for each facet. The output plane is above all points. + The first line is the dimension. The + second line is the number of facets. Each remaining line is the outer plane's + coefficients followed by its offset.</dd> + <dt><a href="qh-optf.htm#Fi">Fi</a></dt> + <dd>print inner plane for each facet. The inner plane of a facet is + below its vertices. + The first line is the dimension. The + second line is the number of facets. Each remaining line is the inner plane's + coefficients followed by its offset.</dd> + + <dt> </dt> + <dt> </dt> + <dd><b>General</b></dd> + <dt><a href="qh-opto.htm#s">s</a></dt> + <dd>print summary for the convex hull. Use '<a + href="qh-optf.htm#Fs">Fs</a>' and '<a + href="qh-optf.htm#FS">FS</a>' if you need numeric data.</dd> + <dt><a href="qh-optf.htm#FA">FA</a></dt> + <dd>compute total area and volume for '<a + href="qh-opto.htm#s">s</a>' and '<a href="qh-optf.htm#FS">FS</a>'</dd> + <dt><a href="qh-opto.htm#m">m</a></dt> + <dd>Mathematica output for the convex hull in 2-d or 3-d.</dd> + <dt><a href="qh-optf.htm#FM">FM</a></dt> + <dd>Maple output for the convex hull in 2-d or 3-d.</dd> + <dt><a href="qh-optg.htm#G">G</a></dt> + <dd>Geomview output for the convex hull in 2-d, 3-d, or 4-d.</dd> + + <dt> </dt> + <dt> </dt> + <dd><b>Scaling and rotation</b></dd> + <dt><a href="qh-optq.htm#Qbk">Qbk:n</a></dt> + <dd>scale k'th coordinate to lower bound.</dd> + <dt><a href="qh-optq.htm#QBk">QBk:n</a></dt> + <dd>scale k'th coordinate to upper bound.</dd> + <dt><a href="qh-optq.htm#QbB">QbB</a></dt> + <dd>scale input to unit cube centered at the origin.</dd> + <dt><a href="qh-optq.htm#QRn">QRn</a></dt> + <dd>randomly rotate the input with a random seed of n. If n=0, the + seed is the time. If n=-1, use time for the random seed, but do + not rotate the input.</dd> + <dt><a href="qh-optq.htm#Qb0">Qbk:0Bk:0</a></dt> + <dd>remove k'th coordinate from input. This computes the + convex hull in one lower dimension.</dd> +</dl> +</blockquote> + +</blockquote> +<h3><a href="#TOP">»</a><a name="controls">qconvex controls</a></h3> +<blockquote> + +<p>These options provide additional control:</p> + +<blockquote> +<dl compact> + <dt><a href="qh-optq.htm#Qt">Qt</a></dt> + <dd>triangulated output. Qhull triangulates non-simplicial facets. It may produce + degenerate facets of zero area.</dd> + <dt><a href="qh-optq.htm#QJn">QJ</a></dt> + <dd>joggle the input instead of merging facets. This guarantees simplicial facets + (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> |