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tet_mesh.html
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tet_mesh.html
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<html>
<head>
<title>
TET_MESH - Routines for a Tet Mesh
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TET_MESH <br> Routines for a Tet Mesh
</h1>
<hr>
<p>
<b>TET_MESH</b>
is a FORTRAN90 library which
constructs, describes, and modifies a mesh of tetrahedrons.
</p>
<h3 align = "center">
Linear and Quadratic Meshes
</h3>
<p>
The simplest tet mesh, which we term an <i>order 4</i>
or <i>linear</i> mesh, uses four points to define each tetrahedron.
A second type of mesh, known as an <i>order 10</i> or <i>quadratic</i>
mesh, uses ten points.
</p>
<p>
While an order 4 mesh can naturally be constructed directly from
most sets of data points, a mesh of order 10 is not usually
constructed directly from the data; at least in the simplest case,
one wants the 6 extra nodes to be the midpoints of the sides
determined by the 4 vertices.
</p>
<p>
Thus, an order 10 tet mesh is typically generated in two steps:
<ul>
<li>
generate an order 4 mesh, in which every tetrahedral vertex
comes from a user data point;
</li>
<li>
generate an order 10 mesh from the order 4 mesh, in which
the new midside points are not user data points, but rather
<i>averages</i> of pairs of tetrahedral vertices.
</li>
</ul>
</p>
<p>
MATLAB has a command
<b>delaunay3</b> that can compute the tet mesh for a set of 3D points.
</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</b> is available in
<a href = "../../cpp_src/tet_mesh/tet_mesh.html">a C++ version</a> and
<a href = "../../f_src/tet_mesh/tet_mesh.html">a FORTRAN90 version</a> and
<a href = "../../m_src/tet_mesh/tet_mesh.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
computes 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_boundary/tet_mesh_boundary.html">
TET_MESH_BOUNDARY</a>,
a FORTRAN90 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 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 the node and tetra files defining a tet mesh and display a wireframe
image.
</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_refine/tet_mesh_refine.html">
TET_MESH_REFINE</a>,
a FORTRAN90 program which
refines a tet mesh.
</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>
Adrian Bowyer, John Woodwark,<br>
A Programmer's Geometry,<br>
Butterworths, 1983,<br>
ISBN: 0408012420.
</li>
<li>
Paul Bratley, Bennett Fox, Linus Schrage,<br>
A Guide to Simulation,<br>
Second Edition,<br>
Springer, 1987,<br>
ISBN: 0387964673.
</li>
<li>
Qiang Du, Desheng Wang,<br>
The Optimal Centroidal Voronoi Tesselations and the Gersho's
Conjecture in the Three-Dimensional Space,<br>
Computers and Mathematics with Applications,<br>
Volume 49, 2005, pages 1355-1373.
</li>
<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>
Albert Nijenhuis, Herbert Wilf,<br>
Combinatorial Algorithms for Computers and Calculators,<br>
Second Edition,<br>
Academic Press, 1978,<br>
ISBN: 0-12-519260-6,<br>
LC: QA164.N54.
</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>
<li>
Philip Schneider, David Eberly,<br>
Geometric Tools for Computer Graphics,<br>
Elsevier, 2002,<br>
ISBN: 1558605940.
</li>
</ol>
</p>
<h3 align = "center">
Source code:
</h3>
<p>
<ul>
<li>
<a href = "tet_mesh.f90">tet_mesh.f90</a>, the source code.
</li>
<li>
<a href = "tet_mesh.sh">tet_mesh.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "tet_mesh_prb.f90">tet_mesh_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "tet_mesh_prb.sh">tet_mesh_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "tet_mesh_prb_output.txt">tet_mesh_prb_output.txt</a>,
the output from a run of the sample program.
</li>
</ul>
</p>
<h3 align = "center">
List of Routines:
</h3>
<p>
<ul>
<li>
<b>I4_UNIFORM</b> returns a scaled pseudorandom I4.
</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 J1 and J2 of an I4COL.
</li>
<li>
<b>I4I4_SORT_A</b> ascending sorts a pair of I4's.
</li>
<li>
<b>I4I4I4_SORT_A</b> ascending sorts a triple of I4's.
</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>I4VEC_PRINT</b> prints an I4VEC.
</li>
<li>
<b>R8_UNIFORM_01</b> returns a unit pseudorandom R8.
</li>
<li>
<b>R8MAT_DET_4D</b> computes the determinant of a 4 by 4 R8MAT.
</li>
<li>
<b>R8MAT_PRINT</b> prints an R8MAT.
</li>
<li>
<b>R8MAT_PRINT_SOME</b> prints some of an R8MAT.
</li>
<li>
<b>R8MAT_SOLVE</b> uses Gauss-Jordan elimination to solve an N by N linear system.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT</b> prints an R8MAT, transposed.
</li>
<li>
<b>R8MAT_TRANSPOSE_PRINT_SOME</b> prints some of an R8MAT, transposed.
</li>
<li>
<b>R8MAT_UNIFORM_01</b> fills an R8MAT with unit pseudorandom numbers.
</li>
<li>
<b>R8VEC_CROSS_3D</b> computes the cross product of two R8VEC's in 3D.
</li>
<li>
<b>R8VEC_LENGTH</b> returns the Euclidean length of an R8VEC.
</li>
<li>
<b>R8VEC_MEAN</b> returns the mean of an R8VEC.
</li>
<li>
<b>R8VEC_PRINT</b> prints an R8VEC.
</li>
<li>
<b>R8VEC_UNIFORM_01</b> returns a unit pseudorandom R8VEC.
</li>
<li>
<b>R8VEC_VARIANCE</b> returns the variance of an R8VEC.
</li>
<li>
<b>SORT_HEAP_EXTERNAL</b> externally sorts a list of items into ascending order.
</li>
<li>
<b>TET_MESH_NEIGHBOR_TETS</b> determines tetrahedron neighbors.
</li>
<li>
<b>TET_MESH_NODE_ORDER:</b> determine the order of nodes in a tet mesh.
</li>
<li>
<b>TET_MESH_ORDER4_ADJ_COUNT</b> counts the number of nodal adjacencies.
</li>
<li>
<b>TET_MESH_ORDER4_ADJ_SET</b> sets the nodal adjacency matrix.
</li>
<li>
<b>TET_MESH_ORDER4_BOUNDARY_FACE_COUNT</b> counts the number of boundary faces.
</li>
<li>
<b>TET_MESH_ORDER4_EDGE_COUNT</b> counts the number of edges.
</li>
<li>
<b>TET_MESH_ORDER4_EXAMPLE_SET</b> sets an example linear tet mesh.
</li>
<li>
<b>TET_MESH_ORDER4_EXAMPLE_SIZE</b> sizes an example linear tet mesh.
</li>
<li>
<b>TET_MESH_ORDER4_REFINE_COMPUTE</b> computes a refined order4 tet mesh.
</li>
<li>
<b>TET_MESH_ORDER4_REFINE_SIZE</b> sizes a refined order 4 tet mesh.
</li>
<li>
<b>TET_MESH_ORDER4_TO_ORDER10_COMPUTE:</b> quadratic tet mesh from a linear one.
</li>
<li>
<b>TET_MESH_ORDER4_TO_ORDER10_SIZE</b> sizes a quadratic tet mesh from a linear one.
</li>
<li>
<b>TET_MESH_ORDER10_EXAMPLE_SET</b> sets an example quadratic tet mesh.
</li>
<li>
<b>TET_MESH_ORDER10_EXAMPLE_SIZE</b> sizes an example quadratic tet mesh.
</li>
<li>
<b>TET_MESH_ORDER10_TO_ORDER4_COMPUTE</b> linearizes a quadratic tet mesh.
</li>
<li>
<b>TET_MESH_ORDER10_TO_ORDER4_SIZE</b> sizes a linear tet mesh from a quadratic one.
</li>
<li>
<b>TET_MESH_QUAD</b> approximates an integral over a tet mesh.
</li>
<li>
<b>TET_MESH_QUALITY1</b> returns the quality of each tet in a mesh.
</li>
<li>
<b>TET_MESH_QUALITY2</b> returns the quality of each tet in a mesh.
</li>
<li>
<b>TET_MESH_QUALITY3</b> returns the quality of each tet in a mesh.
</li>
<li>
<b>TET_MESH_QUALITY4</b> returns the quality of each tet in a mesh.
</li>
<li>
<b>TET_MESH_QUALITY5</b> returns the quality of each tet in a mesh.
</li>
<li>
<b>TET_MESH_SEARCH_DELAUNAY</b> searches a Delaunay tet mesh for a point.
</li>
<li>
<b>TET_MESH_SEARCH_NAIVE</b> naively searches a tet mesh.
</li>
<li>
<b>TETRAHEDRON_BARYCENTRIC:</b> barycentric coordinates of a point.
</li>
<li>
<b>TETRAHEDRON_CIRCUMSPHERE_3D</b> computes the circumsphere of a tetrahedron in 3D.
</li>
<li>
<b>TETRAHEDRON_EDGE_LENGTH_3D</b> returns edge lengths of a tetrahedron in 3D.
</li>
<li>
<b>TETRAHEDRON_INSPHERE_3D</b> finds the insphere of a tetrahedron in 3D.
</li>
<li>
<b>TETRAHEDRON_ORDER4_PHYSICAL_TO_REFERENCE:</b> physical to reference points.
</li>
<li>
<b>TETRAHEDRON_ORDER4_REFERENCE_TO_PHYSICAL:</b> T4 reference to physical points.
</li>
<li>
<b>TETRAHEDRON_QUALITY1_3D:</b> "quality" of a tetrahedron in 3D.
</li>
<li>
<b>TETRAHEDRON_QUALITY2_3D:</b> "quality" of a tetrahedron in 3D.
</li>
<li>
<b>TETRAHEDRON_QUALITY3_3D</b> computes the mean ratio of a tetrahedron.
</li>
<li>
<b>TETRAHEDRON_QUALITY4_3D</b> computes the minimum solid angle of a tetrahedron.
</li>
<li>
<b>TETRAHEDRON_REFERENCE_SAMPLE</b> samples points in the reference tetrahedron.
</li>
<li>
<b>TETRAHEDRON_SAMPLE</b> returns random points in a tetrahedron.
</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 = "../f_src.html">
the FORTRAN90 source codes</a>.
</p>
<hr>
<i>
Last revised on 21 December 2010.
</i>
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