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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 C++ 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">
the order4 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>_nodes.txt contains the node coordinates;
</li>
<li>
<i>prefix</i>_elements.txt or<br> the node indices forming each element.
</li>
</ul>
</p>
<p>
The element definition file will list node indices. In C++, it may be
more natural to use 0-based indices. This program will accept an element
definition file that is 0-based or 1-based, and will convert a 1-based
input file so that it becomes 0-based internal to the program. The detection
of 1-based data is determined by the absence of the use of a 0 index, and
the use of an index equal to the number of nodes. This is an implicit
and fallible, but reasonable, way to handle this problem.
</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 = "../../cpp_src/geompack/geompack.html">
GEOMPACK</a>,
a C++ library which
includes a routine <b>DTRIS3</b> to compute the tet mesh of a set
of points in 3D.
</p>
<p>
<a href = "../../f_src/table_quality/table_quality.html">
TABLE_QUALITY</a>,
a FORTRAN90 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 = "../../cpp_src/tet_mesh/tet_mesh.html">
TET_MESH</a>,
a C++ library which
carries out computations with
a tet mesh.
</p>
<p>
<a href = "../../cpp_src/tet_mesh_boundary/tet_mesh_boundary.html">
TET_MESH_BOUNDARY</a>,
a C++ 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 = "../../cpp_src/tet_mesh_l2q/tet_mesh_l2q.html">
TET_MESH_L2Q</a>,
a C++ program which
converts a linear to quadratic tet mesh.
</p>
<p>
<a href = "../../cpp_src/tet_mesh_q2l/tet_mesh_q2l.html">
TET_MESH_Q2L</a>,
a C++ program which
converts a quadratic to linear tet mesh.
</p>
<p>
<a href = "../../cpp_src/tet_mesh_rcm/tet_mesh_rcm.html">
TET_MESH_RCM</a>,
a C++ program which
takes a tet mesh and
relabels the nodes to reduce the bandwidth of the
corresponding adjacency matrix.
</p>
<p>
<a href = "../../cpp_src/tet_mesh_refine/tet_mesh_refine.html">
TET_MESH_REFINE</a>,
a C++ program which
refines a tet mesh.
</p>
<p>
<a href = "../../cpp_src/tet_mesh_tet_neighbors/tet_mesh_tet_neighbors.html">
TET_MESH_TET_NEIGHBORS</a>,
a C++ program which
computes the tetrahedral adjacency information.
</p>
<p>
<a href = "../../cpp_src/tet_mesh_volumes/tet_mesh_volumes.html">
TET_MESH_VOLUMES</a>,
a C++ program which
computes the volume of each tetrahedron in a tet mesh.
</p>
<p>
<a href = "../../cpp_src/triangulation_quality/triangulation_quality.html">
TRIANGULATION_QUALITY</a>,
a C++ 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.cpp">tet_mesh_quality.cpp</a>,
the source code.
</li>
<li>
<a href = "tet_mesh_quality.sh">tet_mesh_quality.sh</a>,
commands to compile, link and load 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.
Test files you may copy include:
<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 tetrahedron file.
</li>
<li>
<a href = "cube_quality.txt">cube_quality.txt</a>,
the report from the program.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for TET_MESH_QUALITY.
</li>
<li>
<b>CH_CAP</b> capitalizes a single character.
</li>
<li>
<b>CH_EQI</b> is true if two characters are equal, disregarding case.
</li>
<li>
<b>CH_TO_DIGIT</b> returns the integer value of a base 10 digit.
</li>
<li>
<b>FILE_COLUMN_COUNT</b> counts the columns in the first line of a file.
</li>
<li>
<b>FILE_ROW_COUNT</b> counts the number of row records in a file.
</li>
<li>
<b>I4MAT_DATA_READ</b> reads data from an I4MAT file.
</li>
<li>
<b>I4MAT_HEADER_READ</b> reads the header from an I4MAT file.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT</b> prints an I4MAT, transposed.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT_SOME</b> prints some of an I4MAT, transposed.
</li>
<li>
<b>I4_MAX</b> returns the maximum of two I4's.
</li>
<li>
<b>I4_MIN</b> returns the smaller of two I4's.
</li>
<li>
<b>I4VEC_HISTOGRAM</b> computes a histogram of the elements of an I4VEC.
</li>
<li>
<b>I4VEC_MAX</b> returns the value of the maximum element in an I4VEC.
</li>
<li>
<b>I4VEC_PRINT</b> prints an I4VEC.
</li>
<li>
<b>I4VEC_ZERO</b> zeroes an I4VEC.
</li>
<li>
<b>R8_HUGE</b> returns a "huge" double precision value.
</li>
<li>
<b>R8_MAX</b> returns the maximum of two R8's.
</li>
<li>
<b>R8_MIN</b> returns the minimum of two R8's.
</li>
<li>
<b>R8_SWAP</b> switches two R8's.
</li>
<li>
<b>R8MAT_DATA_READ</b> reads the data from an R8MAT file.
</li>
<li>
<b>R8MAT_DET_4D</b> computes the determinant of a 4 by 4 R8MAT.
</li>
<li>
<b>R8MAT_HEADER_READ</b> reads the header from an R8MAT file.
</li>
<li>
<b>R8MAT_SOLVE</b> uses Gauss-Jordan elimination to solve an N by N linear system.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT</b> prints an R8MAT, transposed.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT_SOME</b> prints some of an R8MAT, transposed.
</li>
<li>
<b>R8VEC_CROSS_3D</b> computes the cross product of two R8VEC's in 3D.
</li>
<li>
<b>R8VEC_LENGTH</b> returns the Euclidean length of a vector.
</li>
<li>
<b>R8VEC_MAX</b> returns the maximum element in an R8VEC.
</li>
<li>
<b>R8VEC_MEAN</b> returns the mean of an R8VEC.
</li>
<li>
<b>R8VEC_MIN</b> returns the minimum element in an R8VEC.
</li>
<li>
<b>R8VEC_VARIANCE</b> returns the variance of an R8VEC.
</li>
<li>
<b>R8VEC_ZERO</b> zeroes an R8VEC.
</li>
<li>
<b>S_LEN_TRIM</b> returns the length of a string to the last nonblank.
</li>
<li>
<b>S_TO_I4</b> reads an I4 from a string.
</li>
<li>
<b>S_TO_I4VEC</b> reads an I4VEC from a string.
</li>
<li>
<b>S_TO_R8</b> reads an R8 from a string.
</li>
<li>
<b>S_TO_R8VEC</b> reads an R8VEC from a string.
</li>
<li>
<b>S_WORD_COUNT</b> counts the number of "words" in a string.
</li>
<li>
<b>TET_MESH_NODE_ORDER:</b> determines the order of nodes.
</li>
<li>
<b>TET_MESH_QUALITY1</b> returns a tet mesh quality factor.
</li>
<li>
<b>TET_MESH_QUALITY2</b> returns a tet mesh quality factor.
</li>
<li>
<b>TET_MESH_QUALITY3</b> returns a tet mesh quality factor.
</li>
<li>
<b>TET_MESH_QUALITY4</b> returns a tet mesh quality factor.
</li>
<li>
<b>TET_MESH_QUALITY5</b> returns a tet mesh quality factor.
</li>
<li>
<b>TETRAHEDRON_CIRCUMSPHERE_3D</b> computes the circumsphere of a tetrahedron in 3D.
</li>
<li>
<b>TETRAHEDRON_EDGE_LENGTH_3D</b> returns edge lengths of a tetrahedron in 3D.
</li>
<li>
<b>TETRAHEDRON_INSPHERE_3D</b> finds the insphere of a tetrahedron in 3D.
</li>
<li>
<b>TETRAHEDRON_QUALITY1_3D:</b> "quality" of a tetrahedron in 3D.
</li>
<li>
<b>TETRAHEDRON_QUALITY2_3D:</b> "quality" of a tetrahedron in 3D.
</li>
<li>
<b>TETRAHEDRON_QUALITY3_3D</b> computes the mean ratio of a tetrahedron.
</li>
<li>
<b>TETRAHEDRON_QUALITY4_3D</b> computes the minimum solid angle of a tetrahedron.
</li>
<li>
<b>TETRAHEDRON_VOLUME_3D</b> computes the volume of a tetrahedron in 3D.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../cpp_src.html">
the C++ source codes</a>.
</p>
<hr>
<i>
Last revised on 12 August 2009.
</i>
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