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<html>
<head>
<title>
TET_MESH_BOUNDARY - Triangular Surface formed by Tet Mesh Boundary
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TET_MESH_BOUNDARY <br>
Triangular Surface Formed by Tet Mesh Boundary
</h1>
<hr>
<p>
<b>TET_MESH_BOUNDARY</b>
is a FORTRAN90 program which
reads information defining
a tetrahedral mesh of points in 3D, and determines the triangular
faces that form the boundary of the mesh; it writes out files containing
the nodes and elements defining this triangulated surface.
</p>
<p>
The tet mesh is defined by a <i>node file</i> containing
the coordinates of nodes, and an <i>element file</i> containing
sets of 4 or 10 node indices.
</p>
<p>
Each tetrahedron has 4 triangular faces. Most of these faces
will be shared by a neighbor tetrahedron, but some are not.
It is precisely those faces that are not shared by a neighbor
that constitute the boundary faces of the mesh.
</p>
<p>
The program identifies the triangular faces that form the boundary,
and writes two files, a "boundary_node" file that lists the coordinates
of the boundary nodes, and a "boundary_element" file that lists the
(renumbered) indices of the boundary nodes used to form the boundary
faces. This pair of files defines a triangulated 3D surface, or
"TRI_SURFACE", and can be plotted, for instance, by
<b>tri_surface_display</b> or <b>tri_surface_display_open_gl</b>.
</p>
<p>
The program also writes out a "boundary node mask" file, which
reports the value 1 for each boundary node, and 0 for interior nodes.
A boundary node is a node that occurs on a boundary face. This file
is of use to the <b>fem_to_mesh</b> program.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>tet_mesh_boundary</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>_boundary_node_mask.txt</b>, is 0 for each interior node,
1 for each boundary node;
</li>
<li>
<i>prefix</i><b>_boundary_nodes.txt</b>, the boundary node coordinates;
</li>
<li>
<i>prefix</i><b>_boundary_elements.txt</b>, the boundary 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_BOUNDARY</b> is available in
<a href = "../../cpp_src/tet_mesh_boundary/tet_mesh_boundary.html">a C++ version</a> and
<a href = "../../f_src/tet_mesh_boundary/tet_mesh_boundary.html">a FORTRAN90 version</a> and
<a href = "../../m_src/tet_mesh_boundary/tet_mesh_boundary.html">a MATLAB version</a>.
</p>
<h3 align = "center">
Related Programs:
</h3>
<p>
<a href = "../../f_src/tet_mesh/tet_mesh.html">
TET_MESH</a>,
a FORTRAN90 library which
is useful for work with tet meshes.
</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 = "../../data/tet_mesh_order4/tet_mesh_order4.html">
TET_MESH_ORDER4</a>,
a directory which
contains a description and
examples of a tet mesh using order 4 elements.
</p>
<p>
<a href = "../../data/tet_mesh_order10/tet_mesh_order10.html">
TET_MESH_ORDER10</a>,
a directory which
contains a description and
examples of a tet mesh using order 10 elements.
</p>
<p>
<a href = "../../data/tet_mesh_tet_neighbors/tet_mesh_tet_neighbors.html">
TET_MESH_TET_NEIGHBORS</a>,
a data directory which
contains a description
and examples of the format for storing information about neighboring
tetrahedrons in a tetrahedral mesh.
</p>
<p>
<a href = "../../data/tri_surface/tri_surface.html">
TRI_SURFACE</a>,
a data directory which
contains examples of TRI_SURFACE files,
a 3D surface described by a collection of triangles.
</p>
<p>
<a href = "../../m_src/tri_surface_display/tri_surface_display.html">
TRI_SURFACE_DISPLAY</a>,
a MATLAB program which
displays the 3D graphics information
in a TRI_SURFACE file;
</p>
<p>
<a href = "../../cpp_src/tri_surface_display_opengl/tri_surface_display_opengl.html">
TRI_SURFACE_DISPLAY_OPENGL</a>,
a C++ program which
displays the 3D graphics information in a TRI_SURFACE file using OpenGL.
</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>
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_boundary.f90">tet_mesh_boundary.f90</a>,
the source code.
</li>
<li>
<a href = "tet_mesh_boundary.sh">tet_mesh_boundary.sh</a>,
commands to compile, link and load the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests
</h3>
<p>
<b>CUBE</b> is a tetrahedral mesh of 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.png">cube.png</a>,
an image of the tetrahedral mesh.
</li>
<li>
<a href = "cube_boundary_node_mask.txt">cube_boundary_node_mask.txt</a>,
the boundary node mask file.
</li>
<li>
<a href = "cube_boundary_nodes.txt">cube_boundary_nodes.txt</a>,
the boundary node file.
</li>
<li>
<a href = "cube_boundary_elements.txt">cube_boundary_elements.txt</a>,
the boundary element file.
</li>
<li>
<a href = "cube_output.txt">cube_output.txt</a>,
the printed output from the program.
</li>
</ul>
</p>
<p>
<b>P04</b> is a tetrahedral mesh of a sphere.
<ul>
<li>
<a href = "p04_nodes.txt">p04_nodes.txt</a>,
the node file.
</li>
<li>
<a href = "p04_elements.txt">p04_elements.txt</a>,
the element file.
</li>
<li>
<a href = "p04.png">p04.png</a>,
an image of the tetrahedral mesh.
</li>
<li>
<a href = "p04_boundary_node_mask.txt">p04_boundary_node_mask.txt</a>,
the boundary node mask file.
</li>
<li>
<a href = "p04_boundary_nodes.txt">p04_boundary_nodes.txt</a>,
the boundary node file.
</li>
<li>
<a href = "p04_boundary_elements.txt">p04_boundary_elements.txt</a>,
the boundary element file.
</li>
<li>
<a href = "p04_output.txt">p04_output.txt</a>,
the printed output 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_BOUNDARY.
</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_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>I4COL_COMPARE</b> compares columns I and J of an I4COL.
</li>
<li>
<b>I4COL_SORT_A</b> ascending sorts an I4COL of columns.
</li>
<li>
<b>I4COL_SWAP</b> swaps columns J1 and J2 of a integer array of column data.
</li>
<li>
<b>I4I4I4_SORT_A</b> ascending sorts a triple of I4's.
</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>I4MAT_WRITE</b> writes an I4MAT file.
</li>
<li>
<b>I4VEC_CUM</b> computes the cumulutive sum of the entries of an I4VEC.
</li>
<li>
<b>MESH_BASE_ONE</b> ensures that the element definition is one-based.
</li>
<li>
<b>R8MAT_DATA_READ</b> reads data from an R8MAT file.
</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>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>SORT_HEAP_EXTERNAL</b> externally sorts a list of items into ascending order.
</li>
<li>
<b>TET_MESH_BOUNDARY_COUNT</b> counts boundary faces and nodes in a tet mesh.
</li>
<li>
<b>TET_MESH_BOUNDARY_SET</b> sets the boundary faces in a tet mesh.
</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 = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 22 December 2010.
</i>
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