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diff --git a/src/qhull/html/qh-opto.htm b/src/qhull/html/qh-opto.htm new file mode 100644 index 000000000..e7b21745c --- /dev/null +++ b/src/qhull/html/qh-opto.htm @@ -0,0 +1,353 @@ +<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN"> +<html> + +<head> +<title>Qhull output options</title> +</head> + +<body> +<!-- Navigation links --> +<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></p> + +<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> Qhull output options</h1> + +<p>This section lists the output options for Qhull. These options +are indicated by lower case characters. See <a +href="qh-optf.htm#format">Formats</a>, <a +href="qh-optp.htm#print">Print</a>, and <a +href="qh-optg.htm#geomview">Geomview</a> for other output +options. </p> + +<p><b>Copyright © 1995-2015 C.B. Barber</b></p> + +<hr> + +<p><a href="index.htm#TOC">»</a> <a href="qh-quick.htm#programs">Programs</a> +<a name="output">•</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></p> + +<h2>Output options</h2> + +<p>Qhull prints its output to standard out. All output is printed +text. The default output is a summary (option '<a href="#s">s</a>'). +Other outputs may be specified as follows. </p> + +<dl compact> + <dt><a href="#f">f</a></dt> + <dd>print all fields of all facets</dd> + <dt><a href="#n">n</a></dt> + <dd>print hyperplane normals with offsets</dd> + <dt><a href="#m">m</a></dt> + <dd>print Mathematica output (2-d and 3-d)</dd> + <dt><a href="#o">o</a></dt> + <dd>print OFF file format (dim, points and facets)</dd> + <dt><a href="#s">s</a></dt> + <dd>print summary to stderr</dd> + <dt><a href="#p">p</a></dt> + <dd>print vertex and point coordinates</dd> + <dt><a href="#i">i</a></dt> + <dd>print vertices incident to each facet </dd> + <dt> </dt> + <dt> </dt> + <dd><b>Related options</b></dd> + <dt><a href="qh-optf.htm#format">F</a></dt> + <dd>additional input/output formats</dd> + <dt><a href="qh-optg.htm#geomview">G</a></dt> + <dd>Geomview output</dd> + <dt><a href="qh-optp.htm#print">P</a></dt> + <dd>Print options</dd> + <dt><a href="qh-optf.htm#Ft">Ft</a></dt> + <dd>print triangulation with added points</dd> + <dt> </dt> +</dl> + +<hr> + +<h3><a href="#output">»</a><a name="f">f - print all fields of +all facets </a></h3> + +<p>Print <a href=../src/libqhull.h#facetT>all fields</a> of all facets. +The facet is the primary <a href=index.htm#structure>data structure</a> for +Qhull. + +<p>Option 'f' is for +debugging. Most of the fields are available via the '<a +href="qh-optf.htm#format">F</a>' options. If you need specialized +information from Qhull, you can use the <a +href="qh-code.htm#library">Qhull library</a> or <a +href="qh-code.htm#cpp">C++ interface</a>.</p> + +<p>Use the '<a href="qh-optf.htm#FF">FF</a>' option to print the +facets but not the ridges. </p> + +<h3><a href="#output">»</a><a name="i">i - print vertices +incident to each facet </a></h3> + +<p>The first line is the number of facets. The remaining lines +list the vertices for each facet, one facet per line. The indices +are 0-relative indices of the corresponding input points. The +facets are oriented. Option '<a href="qh-optf.htm#Fv">Fv</a>' +displays an unoriented list of vertices with a vertex count per +line. Options '<a href="qh-opto.htm#o">o</a>' and '<a +href="qh-optf.htm#Ft">Ft</a>' displays coordinates for each +vertex prior to the vertices for each facet. </p> + +<p>Simplicial facets (e.g., triangles in 3-d) consist of <i>d</i> +vertices. Non-simplicial facets in 3-d consist of 4 or more +vertices. For example, a facet of a cube consists of 4 vertices. +Use option '<a href="qh-optq.htm#Qt">Qt</a>' to triangulate non-simplicial facets.</p> + +<p>For 4-d and higher convex hulls and 3-d and higher Delaunay +triangulations, <i>d</i> vertices are listed for all facets. A +non-simplicial facet is triangulated with its centrum and each +ridge. The index of the centrum is higher than any input point. +Use option '<a href="qh-optf.htm#Fv">Fv</a>' to list the vertices +of non-simplicial facets as is. Use option '<a +href="qh-optf.htm#Ft">Ft</a>' to print the coordinates of the +centrums as well as those of the input points. </p> + +<h3><a href="#output">»</a><a name="m">m - print Mathematica +output </a></h3> + +<p>Qhull writes a Mathematica file for 2-d and 3-d convex hulls, +2-d and 3-d halfspace intersections, +and 2-d Delaunay triangulations. Qhull produces a list of +objects that you can assign to a variable in Mathematica, for +example: "<tt>list= << <outputfilename> </tt>". +If the object is 2-d, it can be visualized by "<tt>Show[Graphics[list]] +</tt>". For 3-d objects the command is "<tt>Show[Graphics3D[list]] +</tt>". Now the object can be manipulated by commands of the +form <tt>"Show[%, <parametername> -> +<newvalue>]</tt>". </p> + +<p>For Delaunay triangulation orthogonal projection is better. +This can be specified, for example, by "<tt>BoxRatios: +Show[%, BoxRatios -> {1, 1, 1e-8}]</tt>". To see the +meaningful side of the 3-d object used to visualize 2-d Delaunay, +you need to change the viewpoint: "<tt>Show[%, ViewPoint +-> {0, 0, -1}]</tt>". By specifying different viewpoints +you can slowly rotate objects. </p> + +<p>For halfspace intersections, Qhull produces the dual +convex hull. + +<p>See <a href="qh-faq.htm#math">Is Qhull available for Mathematica?</a> +for URLs. + +<h3><a href="#output">»</a><a name="n">n - print hyperplane +normals with offsets </a></h3> + +<p>The first line is the dimension plus one. The second line is +the number of facets. The remaining lines are the normals for +each facet, one normal per line. The facet's offset follows its +normal coefficients.</p> + +<p>The normals point outward, i.e., the convex hull satisfies <i>Ax +<= -b </i>where <i>A</i> is the matrix of coefficients and <i>b</i> +is the vector of offsets.</p> + +<p>A point is <i>inside</i> or <i>below</i> a hyperplane if its distance +to the hyperplane is negative. A point is <i>outside</i> or <i>above</i> a hyperplane +if its distance to the hyperplane is positive. Otherwise a point is <i>on</i> or +<i>coplanar to</i> the hyperplane. + +<p>If cdd output is specified ('<a href="qh-optf.htm#FD">FD</a>'), +Qhull prints the command line, the keyword "begin", the +number of facets, the dimension (plus one), the keyword +"real", and the normals for each facet. The facet's +negative offset precedes its normal coefficients (i.e., if the +origin is an interior point, the offset is positive). Qhull ends +the output with the keyword "end". </p> + +<h3><a href="#output">»</a><a name="o">o - print OFF file format +</a></h3> + +<p>The output is: </p> + +<ul> + <li>The first line is the dimension </li> + <li>The second line is the number of points, the number of + facets, and the number of ridges. </li> + <li>All of the input points follow, one per line. </li> + <li>Then Qhull prints the vertices for each facet. Each facet + is on a separate line. The first number is the number of + vertices. The remainder is the indices of the + corresponding points. The vertices are oriented in 2-d, + 3-d, and in simplicial facets. </li> +</ul> + +<p>Option '<a href="qh-optf.htm#Ft">Ft</a>' prints the same +information with added points for non-simplicial facets.</p> + +<p>Option '<a href="qh-opto.htm#i">i</a>' displays vertices +without the point coordinates. Option '<a href="qh-opto.htm#p">p</a>' +displays the point coordinates without vertex and facet information.</p> + +<p>In 3-d, Geomview can load the file directly if you delete the +first line (e.g., by piping through '<tt>tail +2</tt>').</p> + +<p>For Voronoi diagrams (<a href=qvoronoi.htm>qvoronoi</a>), option +'o' prints Voronoi vertices and Voronoi regions instead of input +points and facets. The first vertex is the infinity vertex +[-10.101, -10.101, ...]. Then, option 'o' lists the vertices in +the Voronoi region for each input site. The regions appear in +site ID order. In 2-d, the vertices of a Voronoi region are +sorted by adjacency (non-oriented). In 3-d and higher, the +Voronoi vertices are sorted by index. See the '<a +href="qh-optf.htm#FN">FN</a>' option for listing Voronoi regions +without listing Voronoi vertices.</p> + +<p>If you are using the Qhull library, options 'v o' have the +side effect of reordering the neighbors for a vertex.</p> + +<h3><a href="#output">»</a><a name="p">p - print vertex and +point coordinates </a></h3> + +<p>The first line is the dimension. The second line is the number +of vertices. The remaining lines are the vertices, one vertex per +line. A vertex consists of its point coordinates</p> + +<p>With the '<a href="qh-optg.htm#Gc">Gc</a>' and '<a +href="qh-optg.htm#Gi">Gi</a>' options, option 'p' also prints +coplanar and interior points respectively.</p> + +<p>For <a href=qvoronoi.htm>qvoronoi</a>, it prints the +coordinates of each Voronoi vertex.</p> + +<p>For <a href=qdelaun.htm>qdelaunay</a>, it prints the +input sites as lifted to a paraboloid. For <a href=qhalf.htm>qhalf</a> +it prints the dual points. For both, option 'p' is the same as the first +section of option '<a href="qh-opto.htm#o">o</a>'.</p> + +<p>Use '<a href="qh-optf.htm#Fx">Fx</a>' to list the point ids of +the extreme points (i.e., vertices). </p> + +<p>If a subset of the facets is selected ('<a +href="qh-optp.htm#Pdk">Pdk</a>', '<a href="qh-optp.htm#PDk">PDk</a>', +'<a href="qh-optp.htm#Pg">Pg</a>' options), option 'p' only +prints vertices and points associated with those facets.</p> + +<p>If cdd-output format is selected ('<a href="qh-optf.htm#FD">FD</a>'), +the first line is "begin". The second line is the +number of vertices, the dimension plus one, and "real". +The vertices follow with a leading "1". Output ends +with "end". </p> + +<h3><a href="#output">»</a><a name="s">s - print summary to +stderr </a></h3> + +<p>The default output of Qhull is a summary to stderr. Options '<a +href="qh-optf.htm#FS">FS</a>' and '<a href="qh-optf.htm#Fs">Fs</a>' +produce the same information for programs. <b>Note</b>: Windows 95 and 98 +treats stderr the same as stdout. Use option '<a href="qh-optt.htm#TO">TO file</a>' to separate +stderr and stdout.</p> + +<p>The summary lists the number of input points, the dimension, +the number of vertices in the convex hull, and the number of +facets in the convex hull. It lists the number of selected +("good") facets for options '<a href="qh-optp.htm#Pg">Pg</a>', +'<a href="qh-optp.htm#Pdk">Pdk</a>', <a href=qdelaun.htm>qdelaunay</a>, +or <a href=qvoronoi.htm>qvoronoi</a> (Delaunay triangulations only +use the lower half of a convex hull). It lists the number of +coplanar points. For Delaunay triangulations without '<a +href="qh-optq.htm#Qc">Qc</a>', it lists the total number of +coplanar points. It lists the number of simplicial facets in +the output.</p> + +<p>The terminology depends on the output structure. </p> + +<p>The summary lists these statistics:</p> + +<ul> + <li>number of points processed by Qhull </li> + <li>number of hyperplanes created</li> + <li>number of distance tests (not counting statistics, + summary, and checking) </li> + <li>number of merged facets (if any)</li> + <li>number of distance tests for merging (if any)</li> + <li>CPU seconds to compute the hull</li> + <li>the maximum joggle for '<a href="qh-optq.htm#QJn">QJ</a>'<br> + or, the probability of precision errors for '<a + href="qh-optq.htm#QJn">QJ</a> <a href="qh-optt.htm#TRn">TRn</a>' + </li> + <li>total area and volume (if computed, see '<a + href="qh-optf.htm#FS">FS</a>' '<a href="qh-optf.htm#FA">FA</a>' + '<a href="qh-optf.htm#Fa">Fa</a>' '<a + href="qh-optp.htm#PAn">PAn</a>')</li> + <li>max. distance of a point above a facet (if non-zero)</li> + <li>max. distance of a vertex below a facet (if non-zero)</li> +</ul> + +<p>The statistics include intermediate hulls. For example 'rbox d +D4 | qhull' reports merged facets even though the final hull is +simplicial. </p> + +<p>Qhull starts counting CPU seconds after it has read and +projected the input points. It stops counting before producing +output. In the code, CPU seconds measures the execution time of +function qhull() in <tt>libqhull.c</tt>. If the number of CPU +seconds is clearly wrong, check qh_SECticks in <tt>user.h</tt>. </p> + +<p>The last two figures measure the maximum distance from a point +or vertex to a facet. They are not printed if less than roundoff +or if not merging. They account for roundoff error in computing +the distance (c.f., option '<a href="qh-optc.htm#Rn">Rn</a>'). +Use '<a href="qh-optf.htm#Fs">Fs</a>' to report the maximum outer +and inner plane. </p> + +<p>A number may appear in parentheses after the maximum distance +(e.g., 2.1x). It is the ratio between the maximum distance and +the worst-case distance due to merging two simplicial facets. It +should be small for 2-d, 3-d, and 4-d, and for higher dimensions +with '<a href="qh-optq.htm#Qx">Qx</a>'. It is not printed if less +than 0.05. </p> +<!-- 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></p> +<!-- 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> |