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+<!DOCTYPE HTML PUBLIC "-//IETF//DTD HTML//EN">
+<html>
+
+<head>
+<title>Qhull trace options (T)</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>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <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 trace options (T)</h1>
+
+This section lists the trace options for Qhull. These options are
+indicated by 'T' followed by a letter.
+
+<p><b>Copyright &copy; 1995-2015 C.B. Barber</b></p>
+
+<hr>
+
+<p><a href="index.htm#TOC">&#187;</a> <a href="qh-quick.htm#programs">Programs</a>
+<a name="trace">&#149;</a> <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <a href="../src/libqhull_r/index.htm">Functions</a></p>
+
+<h2>Trace options</h2>
+
+<dl compact>
+ <dt>&nbsp;</dt>
+ <dd><b>General</b></dd>
+ <dt><a href="#Tz">Tz</a></dt>
+ <dd>output error information to stdout instead of stderr</dd>
+ <dt><a href="#TI">TI file</a></dt>
+ <dd>input data from a file</dd>
+ <dt><a href="#TO">TO file</a></dt>
+ <dd>output results to a file</dd>
+ <dt><a href="#Ts">Ts</a></dt>
+ <dd>print statistics</dd>
+ <dt><a href="#TFn">TFn</a></dt>
+ <dd>report progress whenever n or more facets created</dd>
+ <dt><a href="#TRn">TRn</a></dt>
+ <dd>rerun qhull n times</dd>
+ <dt><a href="#Tv">Tv</a></dt>
+ <dd>verify result: structure, convexity, and point inclusion</dd>
+
+ <dt>&nbsp;</dt>
+ <dt>&nbsp;</dt>
+ <dd><b>Debugging</b></dd>
+ <dt><a href="#Tc">Tc</a></dt>
+ <dd>check frequently during execution</dd>
+ <dt><a href="#TVn2">TVn</a></dt>
+ <dd>stop qhull after adding point n </dd>
+ <dt><a href="#TCn">TCn</a></dt>
+ <dd>stop qhull after building cone for point n</dd>
+ <dt><a href="#TVn">TV-n</a></dt>
+ <dd>stop qhull before adding point n</dd>
+ <dt><a href="#Tn">T4</a></dt>
+ <dd>trace at level n, 4=all, 5=mem/gauss, -1= events</dd>
+ <dt><a href="#TWn">TWn</a></dt>
+ <dd>trace merge facets when width &gt; n</dd>
+ <dt><a href="#TMn">TMn</a></dt>
+ <dd>turn on tracing at merge n</dd>
+ <dt><a href="#TPn">TPn</a></dt>
+ <dd>turn on tracing when point n added to hull</dd>
+</dl>
+
+<hr>
+
+<h3><a href="#trace">&#187;</a><a name="Tc">Tc - check frequently
+during execution </a></h3>
+
+<p>Qhull includes frequent checks of its data structures. Option
+'Tc' will catch most inconsistency errors. It is slow and should
+not be used for production runs. Option '<a href="#Tv">Tv</a>'
+performs the same checks after the hull is constructed.</p>
+
+<h3><a href="#trace">&#187;</a><a name="TCn">TCn - stop qhull after
+building cone for point n</a></h3>
+
+<p>Qhull builds a cone from the point to its horizon facets.
+Option 'TCn' stops Qhull just after building the cone. The output
+for '<a href="qh-opto.htm#f">f</a>' includes the cone and the old
+hull.'. </p>
+
+<h3><a href="#trace">&#187;</a><a name="TFn">TFn - report summary
+whenever n or more facets created </a></h3>
+
+<p>Option 'TFn' reports progress whenever more than n facets are
+created. The test occurs just before adding a new point to the
+hull. During post-merging, 'TFn' reports progress after more than
+<i>n/2</i> merges. </p>
+
+<h3><a href="#trace">&#187;</a><a name="TI">TI file - input data from file</a></h3>
+
+<p>Input data from 'file' instead of stdin. The filename may not
+contain spaces or use single quotes.
+You may use I/O redirection
+instead (e.g., 'rbox 10 | qdelaunay >results').</P>
+
+<h3><a href="#trace">&#187;</a><a name="TMn">TMn - turn on tracing at
+merge n </a></h3>
+
+<p>Turn on tracing at n'th merge. </p>
+
+<h3><a href="#trace">&#187;</a><a name="Tn">Tn - trace at level n</a></h3>
+
+<p>Qhull includes full execution tracing. 'T-1' traces events.
+'T1' traces the overall execution of the program. 'T2' and 'T3'
+trace overall execution and geometric and topological events.
+'T4' traces the algorithm. 'T5' includes information about memory
+allocation and Gaussian elimination. 'T1' is useful for logging
+progress of Qhull in high dimensions.</p>
+
+<p>Option 'Tn' can produce large amounts of output. Use options '<a
+href="#TPn">TPn</a>', '<a href="#TWn">TWn</a>', and '<a href="#TMn">TMn</a>' to selectively
+turn on tracing. Since all errors report the last processed
+point, option '<a href="#TPn">TPn</a>' is particularly useful.</p>
+
+<p>Different executions of the same program may produce different
+traces and different results. The reason is that Qhull uses hashing
+to match ridges of non-simplicial facets. For performance reasons,
+the hash computation uses
+memory addresses which may change across executions.
+
+<h3><a href="#trace">&#187;</a><a name="TO">TO file - output results to file</a></h3>
+
+<p>Redirect stdout to 'file'. The filename may be enclosed in
+single quotes. Unix and Windows NT users may use I/O redirection
+instead (e.g., 'rbox 10 | qdelaunay >results').</P>
+<p>
+Windows95 users should always use 'TO file'. If they use I/O redirection,
+error output is not sent to the console. Qhull uses single quotes instead
+of double quotes because a missing double quote can
+freeze Windows95 (e.g., do not run, rbox 10 | qhull TO &quot;x)</p>
+<p>
+
+<h3><a href="#trace">&#187;</a><a name="TPn">TPn - turn on tracing
+when point n added to hull </a></h3>
+
+<p>Option 'TPn' turns on tracing when point n is added to
+the hull. It also traces partitions of point n. This option
+reduces the output size when tracing. It is the normal
+method to determine the cause of a Qhull error. All Qhull errors
+report the last point added.
+
+<p>Use options 'TPn <a href="qh-optt.htm#TVn">TVn</a>' to
+trace the addition of point n to the convex hull and stop when done.</p>
+
+<p>If used with option '<a href="qh-optt.htm#TWn">TWn</a>',
+'TPn' turns off tracing after adding point n to the hull.
+Use options 'TPn TWn' to
+trace the addition of point n to the convex hull, partitions
+of point n, and wide merges.</p>
+
+<h3><a href="#trace">&#187;</a><a name="TRn">TRn - rerun qhull n times</a></h3>
+
+<p>Option 'TRn' reruns Qhull n times. It is usually used
+with '<a href="qh-optq.htm#QJn">QJn</a>' to determine the probability
+that a given joggle will fail. The summary
+('<a href="qh-opto.htm#s">s</a>') lists the failure
+rate and the precision errors that occurred.
+Option '<a href="#Ts">Ts</a>' will report statistics for
+all of the runs. Trace and output options only apply to the last
+run. An event trace, '<a href="#Tn">T-1</a>' reports events for all runs.
+
+<p>Tracing applies to the last run of Qhull. If an error
+is reported, the options list the run number as "_run".
+To trace this run, set 'TRn' to the same value.</p>
+
+<h3><a href="#trace">&#187;</a><a name="Ts">Ts - print statistics </a></h3>
+
+<p>Option 'Ts' collects statistics and prints them to stderr. For
+Delaunay triangulations, the angle statistics are restricted to
+the lower or upper envelope.</p>
+
+<h3><a href="#trace">&#187;</a><a name="Tv">Tv - verify result:
+structure, convexity, and point inclusion </a></h3>
+
+<p>Option 'Tv' checks the topological structure, convexity, and
+point inclusion. If precision problems occurred, facet convexity
+is tested whether or not 'Tv' is selected. Option 'Tv' does not
+check point inclusion if forcing output with '<a
+href="qh-optp.htm#Po">Po</a>', or if '<a href="qh-optq.htm#Q5">Q5</a>'
+is set. </p>
+
+<p>The convex hull of a set of points is the smallest polytope
+that includes the points. Option 'Tv' tests point inclusion.
+Qhull verifies that all points are below all outer planes
+(facet-&gt;maxoutside). Point inclusion is exhaustive if merging
+or if the facet-point product is small enough; otherwise Qhull
+verifies each point with a directed search (qh_findbest). To
+force an exhaustive test when using option '<a
+href="qh-optc.htm#C0">C-0</a>' (default), use 'C-1e-30' instead. </p>
+
+<p>Point inclusion testing occurs after producing output. It
+prints a message to stderr unless option '<a
+href="qh-optp.htm#Pp">Pp</a>' is used. This allows the user to
+interrupt Qhull without changing the output. </p>
+
+<p>With '<a href=qvoronoi.htm>qvoronoi</a> <a href="qh-optf.htm#Fi2">Fi</a>'
+and '<a href=qvoronoi.htm>qvoronoi</a> <a href="qh-optf.htm#Fo2">Fo</a>',
+option 'Tv' collects statistics that verify all Voronoi vertices lie
+on the separating hyperplane, and for bounded regions, all
+separating hyperplanes are perpendicular bisectors.
+
+<h3><a href="#trace">&#187;</a><a name="TVn">TV-n - stop qhull before
+adding point n</a></h3>
+
+<p>Qhull adds one point at a time to the convex hull. See <a
+href="qh-eg.htm#how">how Qhull adds a point</a>. Option 'TV-n'
+stops Qhull just before adding a new point. Output shows the hull
+at this time.</p>
+
+<h3><a href="#trace">&#187;</a><a name="TVn2">TVn - stop qhull after
+adding point n</a></h3>
+
+<p>Option 'TVn' stops Qhull after it has added point n. Output
+shows the hull at this time.</p>
+
+<h3><a href="#trace">&#187;</a><a name="TWn">TWn - trace merge facets
+when width &gt; n </a></h3>
+
+<p>Along with TMn, this option allows the user to determine the
+cause of a wide merge.</p>
+<h3><a href="#trace">&#187;</a><a name="Tz">Tz - send all output to
+stdout </a></h3>
+
+<p>Redirect stderr to stdout. </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>
+&#149; <a href="qh-quick.htm#options">Options</a>
+&#149; <a href="qh-opto.htm#output">Output</a>
+&#149; <a href="qh-optf.htm#format">Formats</a>
+&#149; <a href="qh-optg.htm#geomview">Geomview</a>
+&#149; <a href="qh-optp.htm#print">Print</a>
+&#149; <a href="qh-optq.htm#qhull">Qhull</a>
+&#149; <a href="qh-optc.htm#prec">Precision</a>
+&#149; <a href="qh-optt.htm#trace">Trace</a>
+&#149; <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>