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<html>
<head>
<title>
TABLE_TET_MESH - A Tet Mesh of Points in 3D
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TABLE_TET_MESH <br> A Tet Mesh of Points in 3D
</h1>
<hr>
<p>
<b>TABLE_TET_MESH</b>
is a FORTRAN90 program which
computes the
Delaunay tetrahedral mesh ("tet mesh") of a set of points in 3D.
</p>
<p>
Specifically, <b>TABLE_TET_MESH</b> reads a data file containing
the coordinates of a set of points in 3D, computes the Delaunay
tet mesh, and writes out a file of sets of
four node indices that form a mesh of tetrahedrons.
</p>
<p>
The input node coordinate data file and the output tetrahedron
node index file are in the simple
<a href = "../../data/table/table.html">
TABLE file format</a>, one set of node coordinates or one
set of four node indices, respectively, on each line.
</p>
<p>
A <i>tet mesh</i> of 3d points is the analog of the
triangularization of points in 2d. In other words, it is a maximal
organization of the points into nonintersecting tetrahedrons.
Since it is a Delaunay tet mesh, it has the additional
property that, of all maximal tet meshes, this one has the
largest minimum angle.
</p>
<h3 align = "center">
Usage:
</h3>
<p>
<dl>
<dt>
<b>table_tet_mesh</b> <i>nodes.txt</i>
</dt>
<dd>
reads the node coordinates in <i>nodes.txt</i>, computes
the tetrahedron information, and writes it to the file
<i>nodes</i>.<b>tetras</b>.<i>txt</i>.
</dd>
</dl>
</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">
Related Programs:
</h3>
<p>
<a href = "../../f_src/cvt_tet_mesh/cvt_tet_mesh.html">
CVT_TET_MESH</a>,
a FORTRAN90 program 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
computes Delaunay meshes and Voronoi diagrams in 3D, by Barry Joe.
</p>
<p>
<a href = "../../f_src/mesh_bandwidth/mesh_bandwidth.html">
MESH_BANDWIDTH</a>,
a FORTRAN90 program which
returns the geometric bandwidth associated with a mesh of
elements of any order and in a space of arbitrary dimension.
</p>
<p>
<a href = "../../f_src/table_barplot_ppma/table_barplot_ppma.html">
TABLE_BARPLOT_PPMA</a>,
a FORTRAN90 program which
reads a table file and creates a
PPMA bargraph of the data.
</p>
<p>
<a href = "../../f_src/table_border/table_border.html">
TABLE_BORDER</a>,
a FORTRAN90 program which
can be used to add a border
(of zero values) to a table file.
</p>
<p>
<a href = "../../f_src/table_columns/table_columns.html">
TABLE_COLUMNS</a>,
a FORTRAN90 program which
can extract specific columns of data
from a table file.
</p>
<p>
<a href = "../../f_src/table_columns_permute/table_columns_permute.html">
TABLE_COLUMNS_PERMUTE</a>,
a FORTRAN90 program which
permutes the columns of a
table file.
</p>
<p>
<a href = "../../f_src/table_delaunay/table_delaunay.html">
TABLE_DELAUNAY</a>,
a FORTRAN90 program which
computes the Delaunay triangulation of a set
of points.
</p>
<p>
<a href = "../../f_src/table_histogram/table_histogram.html">
TABLE_HISTOGRAM</a>,
a FORTRAN90 program which
can make a histogram of a set of points
stored in a table file.
</p>
<p>
<a href = "../../f_src/table_io/table_io.html">
TABLE_IO</a>,
a FORTRAN90 library which
supplies the routines used to read the TABLE file.
</p>
<p>
<a href = "../../f_src/table_latinize/table_latinize.html">
TABLE_LATINIZE</a>,
a FORTRAN90 program which
reads a file of
points and creates a "latinized" version by adjusting the data.
</p>
<p>
<a href = "../../f_src/table_merge/table_merge.html">
TABLE_MERGE</a>,
a FORTRAN90 program which
reads a file of
points, and removes duplicates, and points that are close to each other.
</p>
<p>
<a href = "../../f_src/table_orthonormalize/table_orthonormalize.html">
TABLE_ORTHONORMALIZE</a>,
a FORTRAN90 program which
reads a file of
points and orthonormalizes the columns.
</p>
<p>
<a href = "../../f_src/table_quality/table_quality.html">
TABLE_QUALITY</a>,
a FORTRAN90 program which
reads a file of
points and computes the quality of dispersion.
</p>
<p>
<a href = "../../f_src/table_record_match/table_record_match.html">
TABLE_RECORD_MATCH</a>,
a FORTRAN90 program which
can be used to find close records in a table file.
</p>
<p>
<a href = "../../f_src/table_scale/table_scale.html">
TABLE_SCALE</a>,
a FORTRAN90 program which
can be used to multiply the entries of a table file
by a scale vector.
</p>
<p>
<a href = "../../f_src/table_shift/table_shift.html">
TABLE_SHIFT</a>,
a FORTRAN90 program which
can be used to shift the entries of a table file
by a shift vector.
</p>
<p>
<a href = "../../f_src/table_stats/table_stats.html">
TABLE_STATS</a>,
a FORTRAN90 program which
can read a table file and compute certain statistics.
</p>
<p>
<a href = "../../f_src/table_top/table_top.html">
TABLE_TOP</a>,
a FORTRAN90 program which
can read a table file of M-dimensional data and
make a table of plots of all pairs of coordinates.
</p>
<p>
<a href = "../../f_src/table_unborder/table_unborder.html">
TABLE_UNBORDER</a>,
a FORTRAN90 program which
can be used to remove the border from a table file.
</p>
<p>
<a href = "../../f_src/table_uniform_noise/table_uniform_noise.html">
TABLE_UNIFORM_NOISE</a>,
a FORTRAN90 program which
can be used to add a uniform noise term to the data
in a table file.
</p>
<p>
<a href = "../../f_src/table_voronoi/table_voronoi.html">
TABLE_VORONOI</a>,
a FORTRAN90 program which
can be used to compute information about
the Voronoi diagram of the 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 = "../../m_src/tet_mesh_display_matlab/tet_mesh_display_matlab.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
can read in the
node and tetra files defining a 4-node tet mesh and write out
files for a 10-node tet mesh by adding midside nodes.
</p>
<p>
<a href = "../../data/tet_mesh_order4/tet_mesh_order4.html">
TET_MESH_ORDER4</a>,
a data 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 data 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
converts a quadratic to linear tet mesh.
</p>
<p>
<a href = "../../f_src/tet_mesh_quality/tet_mesh_quality.html">
TET_MESH_QUALITY</a>,
a FORTRAN90 program which
computes the quality of a tet 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>
<h3 align = "center">
Reference:
</h3>
<p>
<ol>
<li>
Herbert Edelsbrunner,<br>
Geometry and Topology for Mesh Generation,<br>
Cambridge, 2001,<br>
QA377.E36,<br>
ISBN 0-521-79309-2.
</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, pages 325-331, 1991.
</li>
<li>
Per-Olof Persson, Gilbert Strang,<br>
A Simple Mesh Generator in MATLAB,<br>
SIAM Review,<br>
Volume 46, Number 2, pages 329-345, June 2004.
</li>
</ol>
</p>
<h3 align = "center">
Source Code:
</h3>
<p>
<ul>
<li>
<a href = "table_tet_mesh.f90">table_tet_mesh.f90</a>, the source code.
</li>
<li>
<a href = "table_tet_mesh.sh">table_tet_mesh.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 simple dataset of 8 nodes:
<ul>
<li>
<a href = "cube_nodes.txt">cube_nodes.txt</a>,
the coordinates of 8 nodes that form the vertices of a cube.
</li>
<li>
<a href = "cube_nodes_tetras.txt">
cube_nodes_tetras.txt</a>,
the tetrahedron file.
</li>
</ul>
</p>
<p>
<b>P01_00050</b> is a dataset of 50 nodes in a 3x1x1 channel.
<ul>
<li>
<a href = "../cvt_tetra/p01_00050_nodes.txt">p01_00050_nodes.txt</a>,
the coordinates of 50 nodes.
</li>
<li>
<a href = "p01_00050_tetras.txt">
p01_00050_tetras.txt</a>,
the tetrahedron file.
</li>
<li>
<a href = "p01_00050_output.txt">
p01_00050_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
<b>P01_00400</b> is a dataset of 400 nodes in a 3x1x1 channel.
<ul>
<li>
<a href = "../cvt_tetra/p01_00400_nodes.txt">p01_00400_nodes.txt</a>,
the coordinates of 400 nodes.
</li>
<li>
<a href = "p01_00400_tetras.txt">
p01_00400_tetras.txt</a>,
the tetrahedron file.
</li>
<li>
<a href = "p01_00400_output.txt">
p01_00400_output.txt</a>,
the output file.
</li>
</ul>
</p>
<p>
<b>P01_03200</b> is a dataset of 3200 nodes in a 3x1x1 channel.
<ul>
<li>
<a href = "../cvt_tetra/p01_03200_nodes.txt">p01_03200_nodes.txt</a>,
the coordinates of 3200 nodes.
</li>
<li>
<a href = "p01_03200_tetras.txt">
p01_03200_tetras.txt</a>,
the tetrahedron file.
</li>
<li>
<a href = "p01_03200_output.txt">
p01_03200_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
List of routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for TABLE_TET_MESH.
</li>
<li>
<b>AVAILF</b> returns the index of the next available record in the FC array.
</li>
<li>
<b>BARYTH</b> computes barycentric coordinates of a point in 3D.
</li>
<li>
<b>CCSPH</b> finds the circumsphere through the vertices of a tetrahedron.
</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>DHPSRT</b> sorts a list of double precision points in KD.
</li>
<li>
<b>DLESS</b> determines the lexicographically lesser of two double precision values.
</li>
<li>
<b>DSFTDW</b> does one step of the heap sort algorithm for double precision data.
</li>
<li>
<b>DTRIS3</b> constructs a Delaunay triangulation of vertices in 3D.
</li>
<li>
<b>FILE_COLUMN_COUNT</b> counts the number of columns in the first line of a file.
</li>
<li>
<b>FILE_NAME_EXT_GET</b> determines the "extension" of a file name.
</li>
<li>
<b>FILE_NAME_EXT_SWAP</b> replaces the current "extension" of a file name.
</li>
<li>
<b>FILE_ROW_COUNT</b> counts the number of row records in a file.
</li>
<li>
<b>FRSTET</b> shifts vertices so the first 4 vertices are in general position in 3D.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>HTDEL</b> deletes a record from the hash table.
</li>
<li>
<b>HTINS</b> inserts a record into the hash table.
</li>
<li>
<b>HTSRC</b> searches for a record in the hash table.
</li>
<li>
<b>I4_MODP</b> returns the nonnegative remainder of integer division.
</li>
<li>
<b>I4_SWAP</b> swaps two I4's.
</li>
<li>
<b>I4_WRAP</b> forces an integer to lie between given limits by wrapping.
</li>
<li>
<b>I4MAT_TRANSPOSE_PRINT</b> prints an I4MAT, transposed.
</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>NWTHOU</b> creates new tetrahedra outside the current convex hull.
</li>
<li>
<b>OPSIDE</b> tests if points are on opposite sides of a triangular face.
</li>
<li>
<b>ORDER3</b> reorders 3 integers into ascending order.
</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>S_BLANK_DELETE</b> removes blanks from a string, left justifying the remainder.
</li>
<li>
<b>S_INDEX_LAST</b> finds the LAST occurrence of a given substring.
</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>SWAPES</b> swaps faces in a 3D triangulation.
</li>
<li>
<b>TETLST</b> constructs a list of tetrahedra from the FC array.
</li>
<li>
<b>TIMESTAMP</b> prints the current YMDHMS date as a time stamp.
</li>
<li>
<b>UPDATF</b> updates a record in FC after a local transformation.
</li>
<li>
<b>VBFAC</b> determines the boundary faces of a 3D triangulation.
</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 20 October 2009.
</i>
<!-- John Burkardt -->
</body>
</html>