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<html>
<head>
<title>
TET_MESH_REFINE - Simple Refinement of a Tet Mesh
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TET_MESH_REFINE <br> Simple Refinement of a Tet Mesh
</h1>
<hr>
<p>
<b>TET_MESH_REFINE</b>
is a FORTRAN90 program which
refines every tetrahedron
in a tet mesh, replacing each tetrahedron by 8 subtetrahedrons.
</p>
<p>
In particular, <b>TET_MESH_REFINE</b> reads two files,
one listing the coordinates of nodes, the other the indices
of nodes forming tetrahedrons. From this information, it
determines a refinement of the mesh, and writes out new
node and tetrahedron files corresponding to this refinement.
</p>
<p>
The refinement of a single tetrahedron is easy. Every pair
of nodes generates a new node whose location is the average of
the locations of the original two nodes. The problem is that
many tetrahedrons may share the same edge. The new node needs
to be generated exactly once, and assigned a unique index, which
all the tetrahedrons will share. The tricky part of this calculation
is thus figuring out whether it is time to generate a new node, or
whether the node has already been generated, in which case the
appropriate index must be retrieved.
</p>
<p>
The current version of the code can only refine a tet mesh
of order 4. There's no real reason why it could not also
handle meshes of order 10, except that the programming is
a bit more complex. For the moment, a mesh of order 10
could be handled by using the sequence of programs:
<pre><b>
TET_MESH_Q2L --> TET_MESH_REFINE --> TET_MESH_L2Q
</b></pre>
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<blockquote>
<b>tet_mesh_refine</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>_ref_nodes.txt</b>, the refined node coordinates;
</li>
<li>
<i>prefix</i><b>_ref_elements.txt</b>, the refined element definitions.
</li>
</ul>
</p>
<p>
The input and output files use the simple
<a href = "../../data/table/table.html">TABLE format</a>;
comment lines begin with a "#" character. Otherwise, each line
of the file contains one set of information, either the coordinates
of a node (for a node file), or the indices of nodes that make up
a tetrahedron, (for a tetrahedron file).
</p>
<p>
The input file <i>nodes.txt</i> contains the coordinate information
for the tet mesh. Each data line contains the X and
Y coordinates of a single node.
</p>
<p>
The input file <i>tetras.txt</i> contains the tetrahedron information
for the tet mesh. Each data line contains the indices
of the nodes that form a tetrahedron.
</p>
<p>
The output files have the same format.
</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_REFINE</b> is available in
<a href = "../../cpp_src/tet_mesh_refine/tet_mesh_refine.html">a C++ version</a> and
<a href = "../../f_src/tet_mesh_refine/tet_mesh_refine.html">a FORTRAN90 version</a> and
<a href = "../../m_src/tet_mesh_refine/tet_mesh_refine.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/table_tet_mesh/table_tet_mesh.html">
TABLE_TET_MESH</a>,
a FORTRAN90 program which
can compute the tet mesh
for a given set of points.
</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 = "../../f_src/tet_mesh/tet_mesh.html">
TET_MESH</a>,
a FORTRAN90 library which
includes a variety of routines for working
with tetrahedral 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 = "../../f_src/tet_mesh_l2q/tet_mesh_l2q.html">
TET_MESH_L2Q</a>,
a FORTRAN90 program which
takes a 4-node tet mesh
and makes a 10-node tet mesh by adding nodes.
</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 = "../../f_src/tet_mesh_q2l/tet_mesh_q2l.html">
TET_MESH_Q2L</a>,
a FORTRAN90 program which
takes a 10-node tet mesh and makes a 4-node tet mesh.
</p>
<p>
<a href = "../../f_src/tet_mesh_quality/tet_mesh_quality.html">
TET_MESH_QUALITY</a>,
a FORTRAN90 program which
takes a 4-node tet mesh and computes
the "quality" of the mesh.
</p>
<p>
<a href = "../../f_src/tet_mesh_rcm/tet_mesh_rcm.html">
TET_MESH_RCM</a>,
a FORTRAN90 program which
takes a tet mesh and
relabels the nodes to reduce the bandwidth of the
corresponding adjacency matrix.
</p>
<p>
<a href = "../../f_src/tet_mesh_tet_neighbors/tet_mesh_tet_neighbors.html">
TET_MESH_TET_NEIGHBORS</a>,
a FORTRAN90 program which
computes the tetrahedral adjacency information.
</p>
<p>
<a href = "../../f_src/tet_mesh_volumes/tet_mesh_volumes.html">
TET_MESH_VOLUMES</a>,
a FORTRAN90 program which
computes the volume of each tetrahedron in a tet mesh;
</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, Number 5, 1991, pages 325-331.
</li>
<li>
Anwei Liu, Barry Joe,<br>
Quality Local Refinement of Tetrahedral Meshes Based
on 8-Subtetrahedron Subdivision,<br>
Mathematics of Computation,<br>
Volume 65, Number 215, July 1996, pages 1183-1200.
</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_refine.f90">tet_mesh_refine.f90</a>,
the source code.
</li>
<li>
<a href = "tet_mesh_refine.sh">tet_mesh_refine.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>CUBE</b> defines an order 4 test mesh on a cube:
<ul>
<li>
<a href = "cube_nodes.txt">cube_nodes.txt</a>,
the nodes for the 4-node tet mesh.
</li>
<li>
<a href = "cube_elements.txt">cube_elements.txt</a>,
the elements for the 4-node tet mesh.
</li>
<li>
<a href = "cube_ref_nodes.txt">cube_ref_nodes.txt</a>,
the nodes for the refined tet mesh.
</li>
<li>
<a href = "cube_ref_elements.txt">cube_ref_elements.txt</a>,
the elements for the refined tet mesh.
</li>
<li>
<a href = "cube_output.txt">cube_output.txt</a>,
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_REFINE.
</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>I4_SWAP</b> swaps two I4's.
</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.
</li>
<li>
<b>I4COL_SORT2_A</b> ascending sorts the elements of each column of an I4COL.
</li>
<li>
<b>I4COL_SORTED_UNIQUE_COUNT</b> counts unique elements in an I4COL.
</li>
<li>
<b>I4COL_SWAP</b> swaps columns I and J of an I4COL.
</li>
<li>
<b>I4I4_SORT_A</b> ascending sorts a pair 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>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_INDEX_LAST</b> finds the LAST occurrence of a given substring.
</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 R8VEC 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_ORDER4_REFINE_COMPUTE</b> computes a refined order 4 tet mesh.
</li>
<li>
<b>TET_MESH_ORDER4_REFINE_SIZE</b> sizes a refined order 4 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 30 September 2009.
</i>
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