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<html>
<head>
<title>
TRIANGULATION_HISTOGRAM - Per-Triangle Histogram for Triangulation
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TRIANGULATION_HISTOGRAM <br> Per-Triangle Histogram for Triangulation
</h1>
<hr>
<p>
<b>TRIANGULATION_HISTOGRAM</b>
is a MATLAB program which
computes the number of points from a dataset that are contained in
each triangle of a triangulation.
</p>
<p>
One application of this program is simply to determine whether the dataset
represents an approximately uniform sampling of the region covered by
the triangulation.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>triangulation_histogram</b> ( <i>'prefix'</i>, <i>'data_filename'</i> )
</blockquote>
where <i>'prefix'</i> is the common prefix for the node and element files
<ul>
<li>
<i>'prefix'</i><b>_nodes.txt</b>, the node coordinates;
</li>
<li>
<i>'prefix'</i><b>_elements.txt</b>, the element definitions.
</li>
</ul>
and
<ul>
<li>
<i>'data_filename'</i> is the name of the file containing the data points.
</li>
</ul>
</p>
<h3 align = "center">
Licensing:
</h3>
<p>
The computer code and data files described and made available on this web page
are distributed under
<a href = "../../txt/gnu_lgpl.txt">the GNU LGPL license.</a>
</p>
<h3 align = "center">
Languages:
</h3>
<p>
<b>TRIANGULATION_HISTOGRAM</b> is available in
<a href = "../../cpp_src/triangulation_histogram/triangulation_histogram.html">a C++ version</a> and
<a href = "../../f_src/triangulation_histogram/triangulation_histogram.html">a FORTRAN90 version</a> and
<a href = "../../m_src/triangulation_histogram/triangulation_histogram.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/random_data/random_data.html">
RANDOM_DATA</a>,
a MATLAB library which
generates sample points for
various probability distributions, spatial dimensions, and geometries;
</p>
<p>
<a href = "../../m_src/triangle_histogram/triangle_histogram.html">
TRIANGLE_HISTOGRAM</a>,
a MATLAB program which
computes histograms of data on the unit triangle.
</p>
<p>
<a href = "../../m_src/triangulation/triangulation.html">
TRIANGULATION</a>,
a MATLAB library which
performs various operations on order 3 ("linear") or order 6 ("quadratic") triangulations.
</p>
<p>
<a href = "../../m_src/triangulation_boundary_edges/triangulation_boundary_edges.html">
TRIANGULATION_BOUNDARY_EDGES</a>,
a MATLAB program which
reads data defining a triangulation, determines which edges
lie on the boundary, organizes them into connected components,
and writes this information to a file.
</p>
<p>
<a href = "../../m_src/triangulation_boundary_nodes/triangulation_boundary_nodes.html">
TRIANGULATION_BOUNDARY_NODES</a>,
a MATLAB program which
reads data defining a triangulation, determines which nodes
lie on the boundary, and writes their coordinates to a file.
</p>
<p>
<a href = "../../m_src/triangulation_corner/triangulation_corner.html">
TRIANGULATION_CORNER</a>,
a MATLAB program which
patches triangulations so that no triangle has two sides on the boundary.
</p>
<p>
<a href = "../../m_src/triangulation_delaunay_discrepancy/triangulation_delaunay_discrepancy.html">
TRIANGULATION_DELAUNAY_DISCREPANCY</a>,
a MATLAB program which
measures the amount by which a triangulation fails the local Delaunay test;
</p>
<p>
<a href = "../../cpp_src/triangulation_display_opengl/triangulation_display_opengl.html">
TRIANGULATION_DISPLAY_OPENGL</a>,
a C++ program which
reads files defining a triangulation and displays an image using Open GL.
</p>
<p>
<a href = "../../m_src/triangulation_l2q/triangulation_l2q.html">
TRIANGULATION_L2Q</a>,
a MATLAB program which
reads data defining a 3-node triangulation and generates
midside nodes and writes out the corresponding 6-node triangulation.
</p>
<p>
<a href = "../../m_src/triangulation_mask/triangulation_mask.html">
TRIANGULATION_MASK</a>,
a MATLAB program which
takes an existing triangulation and deletes triangles and
their corresponding nodes as requested by the user.
</p>
<p>
<a href = "../../data/triangulation_order3/triangulation_order3.html">
TRIANGULATION_ORDER3</a>,
a data directory which
contains a description and
examples of order 3 triangulations.
</p>
<p>
<a href = "../../data/triangulation_order6/triangulation_order6.html">
TRIANGULATION_ORDER6</a>,
a data directory which
contains a description and
examples of order 6 triangulations.
</p>
<p>
<a href = "../../m_src/triangulation_orient/triangulation_orient.html">
TRIANGULATION_ORIENT</a>,
a MATLAB program which
reads data defining a triangulation, makes sure that
every triangle has positive orientation, and if not, writes a
corrected triangle file.
</p>
<p>
<a href = "../../m_src/triangulation_plot/triangulation_plot.html">
TRIANGULATION_PLOT</a>,
a MATLAB program which
reads data defining a triangulation and creates a
PostScript image of the nodes and triangles.
</p>
<p>
<a href = "../../m_src/triangulation_q2l/triangulation_q2l.html">
TRIANGULATION_Q2L</a>,
a MATLAB program which
reads data defining a 6-node triangulation, and subdivides
each triangle into 4 3-node triangles, writing the resulting
triangulation to a file.
</p>
<p>
<a href = "../../m_src/triangulation_quad/triangulation_quad.html">
TRIANGULATION_QUAD</a>,
a MATLAB program which
estimates the integral of a function over a triangulated region.
</p>
<p>
<a href = "../../m_src/triangulation_quality/triangulation_quality.html">
TRIANGULATION_QUALITY</a>
is a MATLAB program which
reads data defining a triangulation and computes a number
of quality measures.
</p>
<p>
<a href = "../../m_src/triangulation_rcm/triangulation_rcm.html">
TRIANGULATION_RCM</a>
is a MATLAB program which
reads data defining a triangulation, determines an ordering
of the nodes that will reduce the bandwidth of the adjacency
matrix, and writes the new triangulation information to a file.
</p>
<p>
<a href = "../../m_src/triangulation_refine/triangulation_refine.html">
TRIANGULATION_REFINE</a>
is a MATLAB program which
reads data defining a triangulation, replaces each triangle
by four congruent smaller ones, and writes the new triangulation
information to a file.
</p>
<p>
<a href = "../../m_src/triangulation_triangle_neighbors/triangulation_triangle_neighbors.html">
TRIANGULATION_TRIANGLE_NEIGHBORS</a>
is a MATLAB program which
reads data defining a triangulation, determines the neighboring
triangles of each triangle, and writes that information to a file.
</p>
<p>
<a href = "../../m_src/uniform/uniform.html">
UNIFORM</a>
is a MATLAB library which
computes elements of a uniform pseudorandom sequence.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "triangulation_histogram.m">triangulation_histogram.m</a>, the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "house3_nodes.txt">house3_nodes.txt</a>,
the nodes for the HOUSE3 triangulation.
</li>
<li>
<a href = "house3_elements.txt">house3_elements.txt</a>,
the elements for the HOUSE3 triangulation.
</li>
<li>
<a href = "thousand_xy.txt">thousand_xy.txt</a>,
1000 points in the region [0,2]x[0,3].
</li>
<li>
<a href = "house3_output.txt">house3_output.txt</a>,
the output file from the command <b>triangulation_histogram ( 'house3', 'thousand_xy.txt' )</b>
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 26 September 2009.
</i>
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