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tet_mesh_quality.html
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<html>
<head>
<title>
TET_MESH_QUALITY - Tet mesh Quality Measures
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TET_MESH_QUALITY <br>
Interactive Program for <br>
Tet Mesh Quality
</h1>
<hr>
<p>
<b>TET_MESH_QUALITY</b>
is a MATLAB program which
computes and prints a variety of quality measures for a given tet mesh of a set of
points in 3D.
</p>
<p>
The tet mesh is defined by a <i>node file</i> containing
the coordinates of nodes, and a <i>tetra file</i> containing
quadruples of node indices. For more information on this format,
see
<a href = "../../data/tet_mesh_order4/tet_mesh_order4.html">
order 4 Tet Mesh format</a>.
</p>
<p>
The quality measures computed include:
<ul>
<li>
<b>Measure 1</b>, the minimum, over all tetrahedrons, of 3 times
the radius of the insphere divided by the radius of the circumsphere.
</li>
<li>
<b>Measure 2</b>, the minimum, over all tetrahedrons, of 2 times
sqrt ( 6 ) times the radius of the insphere divided by the
length of the longest side of the tetrahedron.
</li>
<li>
<b>Measure 3</b>, the minimum, over all tetrahedrons, of
12 * ( 3 * volume )**(2/3) / (sum of squares of edge lengths);
</li>
<li>
<b>Measure 4</b>, the minimum solid angle in any tetrahedron;
</li>
<li>
<b>Measure 5</b>, a uniformity measure, the ratio of the
maximum to minimum tetrahedron volume;
</li>
</ul>
</p>
<p>
Each quality measure is defined as the minimum of its value
over each tetrahedron. The maximum and best possible value is 1, and
the minimum and worst value is 0.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>tet_mesh_quality</b> <i>'prefix'</i>
</blockquote>
where <i>'prefix'</i> is the common file prefix:
<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>
</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>TET_MESH_QUALITY</b> is available in
<a href = "../../cpp_src/tet_mesh_quality/tet_mesh_quality.html">a C++ version</a> and
<a href = "../../f_src/tet_mesh_quality/tet_mesh_quality.html">a FORTRAN90 version</a> and
<a href = "../../m_src/tet_mesh_quality/tet_mesh_quality.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Programs:
</h3>
<p>
<a href = "../../f_src/cvt_tet_mesh/cvt_tet_mesh.html">
CVT_TET_MESH</a>,
a FORTRAN90 library which
uses CVT methods to compute a tet mesh in a region.
</p>
<p>
<a href = "../../f_src/geompack3/geompack3.html">
GEOMPACK3</a>,
a FORTRAN90 library which
includes a routine <b>DTRIS3</b> to compute the tet mesh of a set
of points in 3D.
</p>
<p>
<a href = "../../m_src/table_quality/table_quality.html">
TABLE_QUALITY</a>,
a MATLAB program which
computes quality measures for
an arbitrary (untriangulated) pointset in any dimension.
</p>
<p>
<a href = "../../f_src/table_tet_mesh/table_tet_mesh.html">
TABLE_TET_MESH</a>,
a FORTRAN90 program which
computes the
tet mesh of a set of points in 3D.
</p>
<p>
<a href = "../../f_src/test_tet_mesh/test_tet_mesh.html">
TEST_TET_MESH</a>,
a FORTRAN90 library which
defines a few test regions for the
generation of a tet mesh.
</p>
<p>
<a href = "../../m_src/tet_mesh/tet_mesh.html">
TET_MESH</a>,
a MATLAB library which
carries out computations involving
a tet mesh.
</p>
<p>
<a href = "../../m_src/tet_mesh_boundary/tet_mesh_boundary.html">
TET_MESH_BOUNDARY</a>,
a MATLAB program which
returns the nodes and faces of the boundary of a tetrahedral mesh,
which themselves form a 3D triangular mesh or "TRI_SURFACE".
</p>
<p>
<a href = "../../m_src/tet_mesh_display/tet_mesh_display.html">
TET_MESH_DISPLAY</a>,
a MATLAB program which
can read in the
node and tetra files defining a tet mesh and display a wireframe
image.
</p>
<p>
<a href = "../../cpp_src/tet_mesh_display_opengl/tet_mesh_display_opengl.html">
TET_MESH_DISPLAY_OPENGL</a>,
a C++ program which
reads a tet mesh and displays the
nodes and edges using OpenGL.
</p>
<p>
<a href = "../../m_src/tet_mesh_l2q/tet_mesh_l2q.html">
TET_MESH_L2Q</a>,
a MATLAB program which
converts a linear to quadratic tet mesh.
</p>
<p>
<a href = "../../m_src/tet_mesh_tet_neighbors/tet_mesh_tet_neighbors.html">
TET_MESH_TET_NEIGHBORS</a>,
a MATLAB program which
computes the tetrahedral adjacency information.
</p>
<p>
<a href = "../../m_src/tet_mesh_q2l/tet_mesh_q2l.html">
TET_MESH_Q2L</a>,
a MATLAB program which
converts a quadratic to linear tet mesh.
</p>
<p>
<a href = "../../m_src/tet_mesh_rcm/tet_mesh_rcm.html">
TET_MESH_RCM</a>,
a MATLAB program which
takes a tet mesh and
relabels the nodes to reduce the bandwidth of the
corresponding adjacency matrix.
</p>
<p>
<a href = "../../m_src/tet_mesh_refine/tet_mesh_refine.html">
TET_MESH_REFINE</a>,
a MATLAB program which
can refine a tet mesh.
</p>
<p>
<a href = "../../m_src/tet_mesh_volumes/tet_mesh_volumes.html">
TET_MESH_VOLUMES</a>,
a MATLAB program which
computes the volume of each tetrahedron in a tet mesh.
</p>
<p>
<a href = "../../m_src/triangulation_quality/triangulation_quality.html">
TRIANGULATION_QUALITY</a>,
a MATLAB program which
computes triangle-based quality
measures for a triangulation of a set of points in 2D.
</p>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Herbert Edelsbrunner,<br>
Geometry and Topology for Mesh Generation,<br>
Cambridge, 2001,<br>
ISBN: 0-521-79309-2,<br>
LC: QA377.E36.
</li>
<li>
David Field,<br>
Qualitative Measures for Initial Meshes,<br>
International Journal of Numerical Methods in Engineering,<br>
Volume 47, 2000, pages 887-906.
</li>
<li>
Barry Joe,<br>
GEOMPACK - a software package for the generation of meshes
using geometric algorithms,<br>
Advances in Engineering Software,<br>
Volume 13, 1991, pages 325-331.
</li>
<li>
Per-Olof Persson, Gilbert Strang,<br>
A Simple Mesh Generator in MATLAB,<br>
SIAM Review,<br>
Volume 46, Number 2, June 2004, pages 329-345.
</li>
</ol>
</p>
<h3 align = "center">
Source code
</h3>
<p>
<ul>
<li>
<a href = "tet_mesh_quality.m">tet_mesh_quality.m</a>
the source code.
</li>
</ul>
</p>
<h3 align = "center">
Tests and Examples
</h3>
<p>
<b>CUBE</b> is a simple example of 8 nodes in a cube.
<ul>
<li>
<a href = "cube_nodes.txt">cube_nodes.txt</a>,
the node file.
</li>
<li>
<a href = "cube_elements.txt">cube_elements.txt</a>,
the element file.
</li>
<li>
<a href = "cube_quality.txt">cube_quality.txt</a>,
the output file.
</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 01 October 2009.
</i>
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