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<html>
<head>
<title>
TET_MESH_VOLUMES - Compute Tetrahedral Volumes in a Tet Mesh
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TET_MESH_VOLUMES <br> Compute Tetrahedral Volumes in a Tet Mesh
</h1>
<hr>
<p>
<b>TET_MESH_VOLUMES</b>
is a C++ program which
computes the volume of every tetrahedron in a tet mesh.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>tet_mesh_volume</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>
<li>
<i>prefix</i><b>_volumes.txt</b>, will contain the element volumes.
</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_VOLUMES</b> is available in
<a href = "../../cpp_src/tet_mesh_volumes/tet_mesh_volumes.html">a C++ version</a> and
<a href = "../../f_src/tet_mesh_volumes/tet_mesh_volumes.html">a FORTRAN90 version</a> and
<a href = "../../m_src/tet_mesh_volumes/tet_mesh_volumes.html">a MATLAB version.</a>
</p>
<h3 align = "center">
Related Data and Programs:
</h3>
<p>
<a href = "../../cpp_src/tet_mesh/tet_mesh.html">
TET_MESH</a>,
a C++ library which
carries out various operations on tetrahedral meshes.
</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
reads in the node and tetra files defining a tet mesh and displays 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 3D 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
reads information about a 4-node (linear) tet mesh and
creates data defining a corresponding 10-node (quadratic)
tet mesh;
</p>
<p>
<a href = "../../data/tet_mesh_order4/tet_mesh_order4.html">
TET_MESH_ORDER4</a>,
a data directory which
contains a description of a linear tet mesh of a
set of 3D points, using a pair of files to list the node coordinates
and the 4 nodes that make up each tetrahedron;
</p>
<p>
<a href = "../../datasets/tet_mesh_order4/tet_mesh_order4.html">
TET_MESH_ORDER4</a>,
a dataset directory which
contains examples of order 4 tetrahedral meshes.
</p>
<p>
<a href = "../../data/tet_mesh_order10/tet_mesh_order10.html">
TET_MESH_ORDER10</a>,
a data directory which
contains a description of a quadratic tet mesh
of a set of 3D points, using a pair of files to list the node
coordinates and the 10 nodes that make up each tetrahedron;
</p>
<p>
<a href = "../../datasets/tet_mesh_order10/tet_mesh_order10.html">
TET_MESH_ORDER10</a>,
a dataset directory which
contains examples of order 10 tetrahedral meshes.
</p>
<p>
<a href = "../../cpp_src/tet_mesh_q2l/tet_mesh_q2l.html">
TET_MESH_Q2L</a>,
a C++ program which
reads information about a 10-node (quadratic) tet mesh and
creates data defining a corresponding 4-node (linear)
tet mesh;
</p>
<p>
<a href = "../../cpp_src/tet_mesh_quality/tet_mesh_quality.html">
TET_MESH_QUALITY</a>,
a C++ program which
computes quality measures of a tetrahedral mesh.
</p>
<p>
<a href = "../../cpp_src/tet_mesh_rcm/tet_mesh_rcm.html">
TET_MESH_RCM</a>,
a C++ program which
computes the reverse Cuthill-McKee reordering for the nodes
of a tet mesh that uses 4-node or 10-node tetrahedrons;
</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 = "../../data/tet_mesh_tet_neighbors/tet_mesh_tet_neighbors.html">
TET_MESH_TET_NEIGHBORS</a>,
a data directory which
contains examples of TET_MESH_TET_NEIGHBOR files,
description of a format for tetrahedron
adjacency information in a tetrahedral mesh of 3D points;
</p>
<p>
<a href = "../../cpp_src/tet_mesh_tet_neighbors/tet_mesh_tet_neighbors.html">
TET_MESH_TET_NEIGHBORS</a>,
a C++ program which
reads information about a tet mesh and writes out a list of the
tetrahedrons that are adjacent to a given tetrahedron;
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "tet_mesh_volumes.cpp">tet_mesh_volumes.cpp</a>, the source code.
</li>
<li>
<a href = "tet_mesh_volumes.sh">tet_mesh_volumes.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>CUBE</b> is the 8 vertices of the unit cube [0,1]x[0,1]x[0,1], defining 6
elements of equal volume but not equal shape.
<ul>
<li>
<a href = "../../datasets/tet_mesh_order4/cube_nodes.txt">cube_nodes.txt</a>,
the node coordinate file.
</li>
<li>
<a href = "../../datasets/tet_mesh_order4/cube_elements.txt">cube_elements.txt</a>,
the element file.
</li>
<li>
<a href = "../../datasets/tet_mesh_order4/cube.png">cube.png</a>,
a PNG image of the mesh.
</li>
<li>
<a href = "cube_volumes.txt">cube_volumes.txt</a>,
the volume file.
</li>
</ul>
</p>
<p>
<b>TWENTY</b> is 20 random nodes, defining 70 elements.
<ul>
<li>
<a href = "../../datasets/tet_mesh_order4/twenty_nodes.txt">twenty_nodes.txt</a>,
the node coordinate file.
</li>
<li>
<a href = "../../datasets/tet_mesh_order4/twenty_elements.txt">twenty_elements.txt</a>,
the element file.
</li>
<li>
<a href = "../../datasets/tet_mesh_order4/twenty.png">twenty.png</a>,
a PNG image of the mesh.
</li>
<li>
<a href = "twenty_volumes.txt">twenty_volumes.txt</a>,
the volume file.
</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 a case insensitive comparison of two characters for equality.
</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 number of columns in the first line of a file.
</li>
<li>
<b>FILE_EXIST</b> reports whether a file exists.
</li>
<li>
<b>FILE_ROW_COUNT</b> counts the number of row records in a file.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</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.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT_SOME</b> prints some of the transpose of an I4MAT.
</li>
<li>
<b>R8MAT_DATA_READ</b> reads data from an R8MAT file.
</li>
<li>
<b>R8MAT_DET_4D</b> computes the determinant of a 4 by 4 matrix.
</li>
<li>
<b>R8MAT_HEADER_READ</b> reads the header from an R8MAT file.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT_SOME</b> prints some of an R8MAT, transposed.
</li>
<li>
<b>R8MAT_WRITE</b> writes an R8MAT file.
</li>
<li>
<b>R8VEC_PRINT</b> prints an R8VEC.
</li>
<li>
<b>R8VEC_VARIANCE</b> returns the variance of an R8VEC.
</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>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 13 August 2009.
</i>
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