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<html>
<head>
<title>
CVT_TET_MESH - Centroidal Voronoi Tessellation for 3D Regions
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
CVT_TET_MESH <br> Centroidal Voronoi Tessellation <br>
for 3D Regions
</h1>
<hr>
<p>
<b>CVT_TET_MESH</b>
is a FORTRAN90 program which
applies CVT methods to produce a tet mesh
of various test regions in 3D.
</p>
<p>
Note that, when using this program, we begin with a <i>region</i>,
which is to be filled up with a number of (unspecified) points
and then organized into tetrahedrons.
</p>
<p>
Other programs, such as <b>TABLE_TET_MESH</b>, are available for
the case where the points are already given, and only the tetrahedrons
need to be determined.
</p>
<p>
The CVT points are written to files in the
<a href = "../../data/table/table.html">
TABLE format</a>.
</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_triangulation/cvt_triangulation.html">
CVT_TRIANGULATION</a>,
a FORTRAN90 library which
applies CVT methods to produce a triangle mesh
of various test regions in 2D.
</p>
<p>
<a href = "../../f_srcgeompack/geompack.html">
GEOMPACK</a>,
a FORTRAN90 library which
contains a routine
<b>DTRIS3</b> that can compute the tet mesh for a set of 3D points,
as well as the adjacency information.
</p>
<p>
<a href = "../../f_src/keast/keast.html">
KEAST</a>,
a FORTRAN90 library which
defines a number of quadrature rules
for a tetrahedron.
</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_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 = "../../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
converts a linear to 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 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>
Franz Aurenhammer,<br>
Voronoi diagrams -
a study of a fundamental geometric data structure,<br>
ACM Computing Surveys,<br>
Volume 23, Number 3, pages 345-405, September 1991.
</li>
<li>
Qiang Du, Vance Faber, Max Gunzburger,<br>
Centroidal Voronoi Tessellations: Applications and Algorithms,<br>
SIAM Review, Volume 41, 1999, pages 637-676.
</li>
<li>
Lili Ju, Qiang Du, Max Gunzburger,<br>
Probabilistic methods for centroidal Voronoi tessellations
and their parallel implementations,<br>
Parallel Computing,<br>
Volume 28, 2002, pages 1477-1500.
</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 = "cvt_tet_mesh.f90">cvt_tet_mesh.f90</a>,
the source code.
</li>
<li>
<a href = "cvt_tet_mesh.sh">cvt_tet_mesh.sh</a>,
commands to compile, link and run the source code.
</li>
<li>
<a href = "cvt_tet_mesh_output.txt">cvt_tet_mesh_output.txt</a>,
the output file.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<b>P01</b> is the 3x1x1 channel. Test files you may copy include:
<ul>
<li>
<a href = "cvt_p01_test01.txt">cvt_p01_test01.txt</a>,
the dataset of 400 points created by test #1 on test region #1:
a standard CVT dataset.
</li>
<li>
<a href = "cvt_p01_test02.txt">cvt_p01_test02.txt</a>,
the dataset of 400 points created by test #2 on test region #1:
a CVT dataset modified so that some points are forced
to lie on the boundary.
</li>
<li>
<a href = "cvt_p01_test03.txt">cvt_p01_test03.txt</a>,
the dataset of 400 points created by test #3 on test region #1:
a CVT dataset modified so that some points are forced
to lie on the boundary, and some points are specified
by the user.
</li>
<li>
<a href = "cvt_p01_test03.png">cvt_p01_test03.png</a>,
a PNG image of the dataset, created by MATLAB.
</li>
</ul>
</p>
<p>
We also ran problem P01 with several sizes, using the
test #3 code (some points are forced to lie on the boundary,
and some points are specified by the user.) These three
sets of points where then used in other calculations,
the first of which is
<a href = "../table_tetra/table_tetra.html">TABLE_TETRA</a>,
which computes a "tetrahedronalization" of the points.
<ul>
<li>
<a href = "p01_00050_nodes.txt">p01_00050_nodes.txt</a>,
the dataset of 50 points created by test #3 on test region #1.
</li>
<li>
<a href = "p01_00400_nodes.txt">p01_00400_nodes.txt</a>,
the dataset of 400 points created by test #3 on test region #1.
</li>
<li>
<a href = "p01_03200_nodes.txt">p01_03200_nodes.txt</a>,
the dataset of 3200 points created by test #3 on test region #1.
</li>
</ul>
</p>
<p>
<b>P02</b> is the vertical cylinder. Test files you may copy include:
<ul>
<li>
<a href = "cvt_p02_test03.txt">cvt_p02_test03.txt</a>,
the dataset of 400 points created by test #3 on test region #2:
a CVT dataset modified so that some points are forced
to lie on the boundary.
</li>
<li>
<a href = "cvt_p02_test03.png">cvt_p02_test03.png</a>,
a PNG image of the dataset, created by MATLAB.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>MAIN</b> is the main program for CVT_TET_MESH.
</li>
<li>
<b>TEST01</b> uses CVT techniques on a given test problem.
</li>
<li>
<b>TEST02</b> uses CVT techniques on a given test problem.
</li>
<li>
<b>TEST03</b> uses CVT techniques on a given test problem.
</li>
<li>
<b>CVT_WRITE</b> writes a CVT dataset to a file.
</li>
<li>
<b>FIND_CLOSEST</b> finds the closest point to each sample.
</li>
<li>
<b>GET_UNIT</b> returns a free FORTRAN unit number.
</li>
<li>
<b>TIMESTRING</b> writes the current YMDHMS date into a string.
</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 17 July 2006.
</i>
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