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<html>
<head>
<title>
TEST_TET_MESH - Mesh Generation Test Regions
</title>
</head>
<body bgcolor="#EEEEEE" link="#CC0000" alink="#FF3300" vlink="#000055">
<h1 align = "center">
TEST_TET_MESH <br> Mesh Generation Test Regions
</h1>
<hr>
<p>
<b>TEST_TET_MESH</b>
is a FORTRAN90 library which
sets up a number
of test problems for mesh generation ("tetrahedralization")
in 3D.
</p>
<p>
As far as possible, a uniform and abstract approach has been used.
For each test region, a number of routines are provided, via which
it is possible for the user to determine many things about the region.
Often, just one or two routines would be needed for a particular
purpose. The names of the routines, and their purposes are:
<ul>
<li>
<b>BOUNDARY_NEAREST:</b> returns the nearest point on the boundary
of the region to a given point or set of points;
</li>
<li>
<b>BOUNDARY_PROJECT:</b> projects exterior points onto the boundary.
</li>
<li>
<b>BOUNDARY_SEGMENT:</b> returns a sequence of roughly equally spaced
points that lie on one particular boundary segment;
</li>
<li>
<b>BOUNDARY_SEGMENT_LENGTH:</b> returns the "length" (number of
nodes) of a particular boundary segment. This simply counts
the number of points needed to trace or approximate the
boundary segment;
</li>
<li>
<b>BOUNDARY_SEGMENT_NUM:</b> returns the number of boundary segments.
Simple regions have one boundary segment. A region with one hole
has two, and so on;
</li>
<li>
<b>BOX:</b> returns a bounding box for the region. All points in
the region are within this box;
</li>
<li>
<b>DENSITY:</b> the value of the mesh density function at any
point in the region. If this is not constant, then high values
correspond to places where many more mesh points should be placed;
</li>
<li>
<b>ELEMENT_SIZE:</b> returns a requested typical element size. This
refers to the average size of the triangles formed by a triangulation
of the points;
</li>
<li>
<b>FIXED_NUM:</b> returns the number of points which must be
included as nodes of the mesh (which may be zero);
</li>
<li>
<b>FIXED_POINTS:</b> returns the coordinates of the points which
must be included as nodes of the mesh;
</li>
<li>
<b>HEADER:</b> prints a brief description of the problem;
</li>
<li>
<b>HOLE_NUM:</b> returns the number of "holes" in the region;
</li>
<li>
<b>HOLE_POINT:</b> returns the coordinates of one point in a hole
(useful when TRIANGLE is to be invoked);
</li>
<li>
<b>INSIDE:</b> reports which of a given set of points are
inside the region.
</li>
<li>
<b>SAMPLE:</b> returns a set of sample points from the region,
chosen with uniform probability;
</li>
<li>
<b>SDIST:</b> returns the signed distance to the boundary of
the region for each of a set of input points.
(a positive distance means the point is outside the region,
a negative distance means it is inside);
<i>(Not ready for problems 4, 5, 6, 7, 8, 9 )</i>
</li>
<li>
<b>TITLE:</b> a title for the problem;
</li>
</ul>
</p>
<p>
The test problems include:
<ol>
<li>
The 3x1x1 channel;
</li>
<li>
The vertical cylinder, R = 1, H = 4;
</li>
<li>
The unit cube;
</li>
<li>
The unit sphere;
</li>
</ol>
</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">
Related Data and 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/geompack/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/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/tet_mesh/tet_mesh.html">
TET_MESH</a>,
a FORTRAN90 library which
is useful for tet mesh calculations.
</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
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>
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 = "test_tet_mesh.f90">test_tet_mesh.f90</a>,
the source code.
</li>
<li>
<a href = "test_tet_mesh.sh">test_tet_mesh.sh</a>,
commands to compile the source code.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
TEST_TET_MESH_PRB carries out some simple tasks with the
sample problems.
<ul>
<li>
<a href = "test_tet_mesh_prb.f90">test_tet_mesh_prb.f90</a>,
a sample calling program.
</li>
<li>
<a href = "test_tet_mesh_prb.sh">test_tet_mesh_prb.sh</a>,
commands to compile and run the sample program.
</li>
<li>
<a href = "test_tet_mesh_prb_output.txt">test_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>ARC_COSINE</b> computes the arc cosine function, with argument truncation.
</li>
<li>
<b>BALL_UNIT_SAMPLE_3D</b> picks a random point in the unit ball in 3D.
</li>
<li>
<b>CYLINDER_POINT_DIST_3D</b> determines the distance from a cylinder to a point in 3D.
</li>
<li>
<b>CYLINDER_POINT_DIST_SIGNED_3D:</b> signed distance from cylinder to point in 3D.
</li>
<li>
<b>CYLINDER_POINT_INSIDE_3D</b> determines if a cylinder contains a point in 3D.
</li>
<li>
<b>CYLINDER_POINT_NEAR_3D</b> determines the nearest point on a cylinder to a point in 3D.
</li>
<li>
<b>DISK_POINT_DIST_3D</b> determines the distance from a disk to a point in 3D.
</li>
<li>
<b>P00_BOUNDARY_EDGE_NUM</b> counts the boundary edges in a problem.
</li>
<li>
<b>P00_BOUNDARY_EDGES</b> returns the boundary edges for any problem.
</li>
<li>
<b>P00_BOUNDARY_FACE_NUM</b> counts the boundary faces in a problem.
</li>
<li>
<b>P00_BOUNDARY_FACES</b> returns the boundary faces in any problem.
</li>
<li>
<b>P00_BOUNDARY_NODE_NUM</b> counts the boundary nodes in a problem.
</li>
<li>
<b>P00_BOUNDARY_NODES</b> returns the boundary nodes in problem 01.
</li>
<li>
<b>P00_BOUNDARY_PROJECT</b> projects exterior points to the boundary.
</li>
<li>
<b>P00_BOX</b> returns a bounding box for a problem.
</li>
<li>
<b>P00_FIXED_NUM</b> returns the number of fixed points in a problem.
</li>
<li>
<b>P00_FIXED_POINTS</b> returns the fixed points in a problem.
</li>
<li>
<b>P00_HEADER</b> prints some information about a problem.
</li>
<li>
<b>P00_INSIDE</b> reports if a point is inside the region in a problem.
</li>
<li>
<b>P00_SAMPLE</b> samples points from the region in a problem.
</li>
<li>
<b>P00_SAMPLE_H1</b> samples points from the enlarged region in a problem.
</li>
<li>
<b>P00_SDIST</b> returns the signed distance to the region in a problem.
</li>
<li>
<b>P00_TEST_NUM</b> returns the number of available tests.
</li>
<li>
<b>P00_TITLE</b> returns a title for a problem.
</li>
<li>
<b>P01_BOUNDARY_EDGE_NUM</b> counts the boundary edges in problem 01.
</li>
<li>
<b>P01_BOUNDARY_EDGES</b> returns the boundary edges in problem 01.
</li>
<li>
<b>P01_BOUNDARY_FACE_NUM</b> counts the boundary faces in problem 01.
</li>
<li>
<b>P01_BOUNDARY_FACES</b> returns the boundary faces in problem 01.
</li>
<li>
<b>P01_BOUNDARY_NODE_NUM</b> counts the boundary nodes in problem 01.
</li>
<li>
<b>P01_BOUNDARY_NODES</b> returns the boundary nodes in problem 01.
</li>
<li>
<b>P01_BOUNDARY_PROJECT</b> projects exterior points to the boundary in problem 01.
</li>
<li>
<b>P01_BOX</b> returns a bounding box for problem 01.
</li>
<li>
<b>P01_FIXED_NUM</b> returns the number of fixed points in problem 01.
</li>
<li>
<b>P01_FIXED_POINTS</b> returns the fixed points in problem 01.
</li>
<li>
<b>P01_HEADER</b> prints some information about problem 01.
</li>
<li>
<b>P01_INSIDE</b> reports if a point is inside the region in problem 01.
</li>
<li>
<b>P01_SAMPLE</b> samples points from the region in problem 01.
</li>
<li>
<b>P01_SAMPLE_H1</b> samples points from the enlarged region in problem 01.
</li>
<li>
<b>P01_SDIST</b> returns the signed distance to the region in problem 01.
</li>
<li>
<b>P01_TITLE</b> returns a title for problem 01.
</li>
<li>
<b>P02_BOUNDARY_EDGE_NUM</b> counts the boundary edges in problem 02.
</li>
<li>
<b>P02_BOUNDARY_EDGES</b> returns the boundary edges in problem 02.
</li>
<li>
<b>P02_BOUNDARY_FACE_NUM</b> counts the boundary faces in problem 02.
</li>
<li>
<b>P02_BOUNDARY_FACES</b> returns the boundary faces in problem 02.
</li>
<li>
<b>P02_BOUNDARY_NODE_NUM</b> counts the boundary nodes in problem 02.
</li>
<li>
<b>P02_BOUNDARY_NODES</b> returns the boundary nodes in problem 02.
</li>
<li>
<b>P02_BOUNDARY_PROJECT</b> projects exterior points to the boundary in problem 02.
</li>
<li>
<b>P02_BOX</b> returns a bounding box for problem 02.
</li>
<li>
<b>P02_FIXED_NUM</b> returns the number of fixed points in problem 02.
</li>
<li>
<b>P02_FIXED_POINTS</b> returns the fixed points in problem 02.
</li>
<li>
<b>P02_HEADER</b> prints some information about problem 02.
</li>
<li>
<b>P02_INSIDE</b> reports if a point is inside the region in problem 02.
</li>
<li>
<b>P02_SAMPLE</b> samples points from the region in problem 02.
</li>
<li>
<b>P02_SAMPLE_H1</b> samples points from the enlarged region in problem 02.
</li>
<li>
<b>P02_SDIST</b> returns the signed distance to the region in problem 02.
</li>
<li>
<b>P02_TITLE</b> returns a title for problem 02.
</li>
<li>
<b>P03_BOUNDARY_EDGE_NUM</b> counts the boundary edges in problem 03.
</li>
<li>
<b>P03_BOUNDARY_EDGES</b> returns the boundary edges in problem 03.
</li>
<li>
<b>P03_BOUNDARY_FACE_NUM</b> counts the boundary faces in problem 03.
</li>
<li>
<b>P03_BOUNDARY_FACES</b> returns the boundary faces in problem 03.
</li>
<li>
<b>P03_BOUNDARY_NODE_NUM</b> counts the boundary nodes in problem 03.
</li>
<li>
<b>P03_BOUNDARY_NODES</b> returns the boundary nodes in problem 03.
</li>
<li>
<b>P03_BOUNDARY_PROJECT</b> projects exterior points to the boundary in problem 03.
</li>
<li>
<b>P03_BOX</b> returns a bounding box for problem 03.
</li>
<li>
<b>P03_FIXED_NUM</b> returns the number of fixed points in problem 03.
</li>
<li>
<b>P03_FIXED_POINTS</b> returns the fixed points in problem 03.
</li>
<li>
<b>P03_HEADER</b> prints some information about problem 03.
</li>
<li>
<b>P03_INSIDE</b> reports if a point is inside the region in problem 03.
</li>
<li>
<b>P03_SAMPLE</b> samples points from the region in problem 03.
</li>
<li>
<b>P03_SAMPLE_H1</b> samples points from the enlarged region in problem 03.
</li>
<li>
<b>P03_SDIST</b> returns the signed distance to the region in problem 03.
</li>
<li>
<b>P03_TITLE</b> returns a title for problem 03.
</li>
<li>
<b>P04_BOUNDARY_EDGE_NUM</b> counts the boundary edges in problem 04.
</li>
<li>
<b>P04_BOUNDARY_EDGES</b> returns the boundary edges in problem 04.
</li>
<li>
<b>P04_BOUNDARY_FACE_NUM</b> counts the boundary faces in problem 04.
</li>
<li>
<b>P04_BOUNDARY_FACES</b> returns the boundary faces in problem 04.
</li>
<li>
<b>P04_BOUNDARY_NODE_NUM</b> counts the boundary nodes in problem 04.
</li>
<li>
<b>P04_BOUNDARY_NODES</b> returns the boundary nodes in problem 04.
</li>
<li>
<b>P04_BOUNDARY_PROJECT</b> projects exterior points to the boundary in problem 04.
</li>
<li>
<b>P04_BOX</b> returns a bounding box for problem 04.
</li>
<li>
<b>P04_FIXED_NUM</b> returns the number of fixed points in problem 04.
</li>
<li>
<b>P04_FIXED_POINTS</b> returns the fixed points in problem 04.
</li>
<li>
<b>P04_HEADER</b> prints some information about problem 04.
</li>
<li>
<b>P04_INSIDE</b> reports if a point is inside the region in problem 04.
</li>
<li>
<b>P04_SAMPLE</b> samples points from the region in problem 04.
</li>
<li>
<b>P04_SAMPLE_H1</b> samples points from the enlarged region in problem 04.
</li>
<li>
<b>P04_SDIST</b> returns the signed distance to the region in problem 04.
</li>
<li>
<b>P04_TITLE</b> returns a title for problem 04.
</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>R8VEC_ANY_NORMAL</b> returns some normal vector to V1.
</li>
<li>
<b>R8VEC_LENGTH</b> returns the Euclidean length of a vector.
</li>
<li>
<b>R8VEC_UNIFORM_01</b> returns a unit pseudorandom R8VEC.
</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 27 October 2005.
</i>
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