354 lines
15 KiB
HTML
354 lines
15 KiB
HTML
<!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>
|