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triangulation_quality.html
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<html>
<head>
<title>
TRIANGULATION_QUALITY - Triangulation Quality Measures
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TRIANGULATION_QUALITY <br>
Triangulation Quality Measures
</h1>
<hr>
<p>
<b>TRIANGULATION_QUALITY</b>
is a MATLAB program which
computes and prints a variety
of quality measures for a given triangulation of a set of points in 2D.
</p>
<p>
The triangulation is defined by a <i>node file</i> containing
the coordinates of nodes, and a <i>triangle file</i> containing
sets of 3 or 6 node indices.
</p>
<p>
The quality measures computed include:
<ul>
<li>
<b>Alpha</b>, the minimum angle divided by the maximum possible
minimum angle.
</li>
<li>
<b>Area</b>, the ratio of the minimum area to the maximum area;
</li>
<li>
<b>Q</b>, the triangle shape uniformity measure, twice the
radius of the inscribed circle divided by the radius of the
circumscribed circle;
</li>
</ul>
</p>
<p>
Each quality measure is defined as the minimum of its value
over all the triangles; the maximum and best possible value is
1, and the minimum and worst possible value is 0.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>triangulation_quality</b> ( <i>'prefix'</i> )
</blockquote>
where <i>'prefix'</i> is the common prefix for the node and triangle files
<ul>
<li>
<i>prefix</i><b>_nodes.txt</b>, the node coordinates;
</li>
<li>
<i>prefix</i><b>_elements.txt</b>, the triangulation.
</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_QUALITY</b> is available in
<a href = "../../cpp_src/triangulation_quality/triangulation_quality.html">a C++ version</a> and
<a href = "../../f_src/triangulation_quality/triangulation_quality.html">a FORTRAN90 version</a> and
<a href = "../../m_src/triangulation_quality/triangulation_quality.html">a MATLAB version.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../m_src/distmesh/distmesh.html">
DISTMESH</a>,
a MATLAB library which
carries out triangular or tetrahedral mesh generation,
by Per-Olof Persson and Gilbert Strang.
</p>
<p>
<a href = "../../m_src/mesh2d/mesh2d.html">
MESH2D</a>,
a MATLAB library which
can automatically create a triangular mesh for a given polygonal region,
by Darren Engwirda.
</p>
<p>
<a href = "../../m_src/tet_mesh_quality/tet_mesh_quality.html">
TET_MESH_QUALITY</a>,
a MATLAB program which
computes quality measures of a tetrahedral mesh.
</p>
<p>
<a href = "../../c_src/triangle/triangle.html">
TRIANGLE</a>,
a C program which
computes a triangulation of a geometric region.
</p>
<p>
<a href = "../../m_src/triangulation/triangulation.html">
TRIANGULATION</a>,
a MATLAB library which
carries out various operations on order 3 ("linear") or order 6
("quadratic") triangulations.
</p>
<p>
<a href = "../../data/triangulation_order3/triangulation_order3.html">
TRIANGULATION_ORDER3</a>,
a 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 directory which
contains a description and
examples of order 6 triangulations.
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "triangulation_quality.m">triangulation_quality.m</a>,
the program.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>ELL3</b> is a set of nodes in an L-shaped region, which have
been arranged into an order 3 triangulation.
<ul>
<li>
<a href = "../../data/triangulation_order3/ell3_nodes.txt">ell3_nodes.txt</a>,
the node file.
</li>
<li>
<a href = "../../data/triangulation_order3/ell3_elements.txt">ell3_elements.txt</a>,
the element file.
</li>
<li>
<a href = "ell3_quality.txt">ell3_quality.txt</a>,
the report from the program.
</li>
</ul>
</p>
<p>
<b>HEX_HOLES6</b> is a set of nodes in an square region, with
two hexagonal holes, which have
been arranged into an order 6 triangulation.
<ul>
<li>
<a href = "../../data/triangulation_order6/hex_holes6_nodes.txt">hex_holes6_nodes.txt</a>,
the node file.
</li>
<li>
<a href = "../../data/triangulation_order6/hex_holes6_elements.txt">hex_holes6_elements.txt</a>,
the element file.
</li>
<li>
<a href = "hex_holes6_quality.txt">hex_holes6_quality.txt</a>,
the report from the program.
</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 21 June 2009.
</i>
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</html>