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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 MATLAB library which
constructs, describes, or 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>
<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 = "../../c_src/tet_mesh/tet_mesh.html">a C++ version</a> and
<a href = "../../cpp_src/tet_mesh/tet_mesh.html">a C++ version</a> and
<a href = "../../f77_src/tet_mesh/tet_mesh.html">a FORTRAN77 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 = "../../m_src/geometry/geometry.html">
GEOMETRY</a>,
a MATLAB library which
includes a number of routines for
making computations involving tetrahedrons.
</p>
<p>
<a href = "../../m_src/geompack/geompack.html">
GEOMPACK</a>,
a MATLAB 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 = "../../m_src/keast/keast.html">
KEAST</a>,
a MATLAB library which
defines a number of quadrature rules
for a tetrahedron.
</p>
<p>
<a href = "../../m_src/ncc_tetrahedron/ncc_tetrahedron.html">
NCC_TETRAHEDRON</a>,
a MATLAB library which
defines Newton-Cotes closed quadrature
rules on a tetrahedron.
</p>
<p>
<a href = "../../m_src/nco_tetrahedron/nco_tetrahedron.html">
NCO_TETRAHEDRON</a>,
a MATLAB library which
defines Newton-Cotes open quadrature
rules on a tetrahedron.
</p>
<p>
<a href = "../../datasets/quadrature_rules_tet/quadrature_rules_tet.html">
QUADRATURE_RULES_TET</a>,
a dataset directory which
contains triples of files defining various quadrature
rules on tetrahedrons.
</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_boundary/tet_mesh_boundary.html">
TET_MESH_BOUNDARY</a>,
a MATLAB 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 in the node and tetra files defining a tet mesh and displays 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
can read in the
node and tetra files defining a tet mesh and display a wireframe
image using OpenGL.
</p>
<p>
<a href = "../../m_src/tet_mesh_l2q/tet_mesh_l2q.html">
TET_MESH_L2Q</a>,
a MATLAB 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 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 = "../../m_src/tet_mesh_q2l/tet_mesh_q2l.html">
TET_MESH_Q2L</a>,
a MATLAB program which
converts a quadratic to linear tet mesh.
</p>
<p>
<a href = "../../m_src/tet_mesh_quad/tet_mesh_quad.html">
TET_MESH_QUAD</a>,
a MATLAB program which
estimates the integral of a function over a region defined by a tetrahedral mesh.
</p>
<p>
<a href = "../../m_src/tet_mesh_quality/tet_mesh_quality.html">
TET_MESH_QUALITY</a>,
a MATLAB program which
computes the quality of a tet mesh.
</p>
<p>
<a href = "../../m_src/tet_mesh_rcm/tet_mesh_rcm.html">
TET_MESH_RCM</a>,
a MATLAB program which
takes a tet mesh and
relabels the nodes to reduce the bandwidth of the
corresponding adjacency matrix.
</p>
<p>
<a href = "../../m_src/tet_mesh_refine/tet_mesh_refine.html">
TET_MESH_REFINE</a>,
a MATLAB program which
can refine a tet mesh.
</p>
<p>
<a href = "../../m_src/tet_mesh_tet_neighbors/tet_mesh_tet_neighbors.html">
TET_MESH_TET_NEIGHBORS</a>,
a MATLAB program which
computes the tetrahedral adjacency information.
</p>
<p>
<a href = "../../m_src/tet_mesh_volumes/tet_mesh_volumes.html">
TET_MESH_VOLUMES</a>,
a MATLAB program which
computes the volume of each tetrahedron in a tet mesh;
</p>
<p>
<a href = "../../m_src/tetrahedron_properties/tetrahedron_properties.html">
TETRAHEDRON_PROPERTIES</a>,
a MATLAB program which
computes properties of a given tetrahedron.
</p>
<p>
<a href = "../../datasets/tetrahedrons/tetrahedrons.html">
TETRAHEDRONS</a>,
a dataset directory which
contains examples of tetrahedrons;
</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 = "i4_swap.m">i4_swap.m</a>
swaps two I4's.
</li>
<li>
<a href = "i4_uniform.m">i4_uniform.m</a>
returns a pseudorandom I4.
</li>
<li>
<a href = "i4col_compare.m">i4col_compare.m</a>
compares columns I and J of an I4COL.
</li>
<li>
<a href = "i4col_sort_a.m">i4col_sort_a.m</a>
ascending sorts an I4COL.
</li>
<li>
<a href = "i4col_sort2_a.m">i4col_sort2_a.m</a>
ascending sorts the elements of each column of an I4COL.
</li>
<li>
<a href = "i4col_sorted_unique_count.m">i4col_sorted_unique_count.m</a>
counts unique elements in an I4COL.
</li>
<li>
<a href = "i4col_swap.m">i4col_swap.m</a>
swaps columns J1 and J2 of an I4COL.
</li>
<li>
<a href = "i4i4_sort_a.m">i4i4_sort_a.m</a>
ascending sorts a pair of I4's.
</li>
<li>
<a href = "i4i4i4_sort_a.m">i4i4i4_sort_a.m</a>
ascending sorts a triple of I4's.
</li>
<li>
<a href = "i4mat_transpose_print.m">i4mat_transpose_print.m</a>
prints the transpose of an I4MAT.
</li>
<li>
<a href = "i4mat_transpose_print_some.m">i4mat_transpose_print_some.m</a>
prints some of the transpose of an I4MAT.
</li>
<li>
<a href = "i4vec_print.m">i4vec_print.m</a>
prints an I4VEC.
</li>
<li>
<a href = "mesh_base_one.m">mesh_base_one.m</a>
detects and corrects 0-based indexing.
</li>
<li>
<a href = "r8_swap.m">r8_swap.m</a>
switches two R8's.
</li>
<li>
<a href = "r8_uniform_01.m">r8_uniform_01.m</a>
returns a unit pseudorandom R8.
</li>
<li>
<a href = "r8mat_det_4d.m">r8mat_det_4d.m</a>
computed the determiannt of a 4x4 R8MAT .
</li>
<li>
<a href = "r8mat_print.m">r8mat_print.m</a>
prints an R8MAT.
</li>
<li>
<a href = "r8mat_print_some.m">r8mat_print_some.m</a>
prints some of an R8MAT.
</li>
<li>
<a href = "r8mat_solve.m">r8mat_solve.m</a>
uses Gauss-Jordan elimination to solve an N by N linear system.
</li>
<li>
<a href = "r8mat_transpose_print.m">r8mat_transpose_print.m</a>
prints an R8MAT, transposed.
</li>
<li>
<a href = "r8mat_transpose_print_some.m">r8mat_transpose_print_some.m</a>
prints some of an R8MAT, transposed.
</li>
<li>
<a href = "r8mat_uniform_01.m">r8mat_uniform_01.m</a>
returns a unit pseudorandom R8MAT.
</li>
<li>
<a href = "r8vec_cross_3d.m">r8vec_cross_3d.m</a>
computes the cross product of two R8VEC's in 3D.
</li>
<li>
<a href = "r8vec_length.m">r8vec_length.m</a>
returns the Euclidean length of an R8VEC.
</li>
<li>
<a href = "r8vec_mean.m">r8vec_mean.m</a>
returns the mean of an R8VEC.
</li>
<li>
<a href = "r8vec_uniform_01.m">r8vec_uniform_01.m</a>
returns a unit pseudorandom R8VEC.
</li>
<li>
<a href = "r8vec_variance.m">r8vec_variance.m</a>
returns the variance of an R8VEC.
</li>
<li>
<a href = "s_len_trim.m">s_len_trim.m</a>
returns the length of a string to the last nonblank.
</li>
<li>
<a href = "sort_heap_external.m">sort_heap_external.m</a>
externally sorts a list of items into ascending order.
</li>
<li>
<a href = "tet_mesh_neighbor_tets.m">tet_mesh_neighbor_tets.m</a>
determines tetrahedron neighbors.
</li>
<li>
<a href = "tet_mesh_node_order.m">tet_mesh_node_order.m</a>
determine the order of nodes in a tet mesh.
</li>
<li>
<a href = "tet_mesh_order4_adj_count.m">
tet_mesh_order4_adj_count.m</a>
counts the number of nodal adjacencies for an order 4 tet mesh.
</li>
<li>
<a href = "tet_mesh_order4_adj_set.m">tet_mesh_order4_adj_set.m</a>
sets the nodal adjacency matrix for an order 4 tet mesh.
</li>
<li>
<a href = "tet_mesh_order4_boundary_face_count.m">
tet_mesh_order4_boundary_face_count.m</a>
counts the number of boundary faces for an order 4 tet mesh.
</li>
<li>
<a href = "tet_mesh_order4_edge_count.m">
tet_mesh_order4_edge_count.m</a>
counts the number of edges for an order 4 tet mesh.
</li>
<li>
<a href = "tet_mesh_order4_example_set.m">
tet_mesh_order4_example_set.m</a>
returns an example order 4 tet mesh for a cube.
</li>
<li>
<a href = "tet_mesh_order4_example_size.m">
tet_mesh_order4_example_size.m</a>
sizes an example order 4 tet mesh for a cube.
</li>
<li>
<a href = "tet_mesh_order4_refine_compute.m">tet_mesh_order4_refine_compute.m</a>
computes a refined order 4 tet mesh.
</li>
<li>
<a href = "tet_mesh_order4_refine_size.m">tet_mesh_order4_refine_size.m</a>
sizes a refined order 4 tet mesh
</li>
<li>
<a href = "tet_mesh_order4_to_order10_compute.m">tet_mesh_order4_to_order10_compute.m</a>
computes an order 10 tet mesh from an order 4 tet mesh.
</li>
<li>
<a href = "tet_mesh_order4_to_order10_size.m">tet_mesh_order4_to_order10_size.m</a>
sizes an order 10 tet mesh from an order 4 tet mesh.
</li>
<li>
<a href = "tet_mesh_order10_adj_count.m">
tet_mesh_order10_adj_count.m</a>
counts the number of nodal adjacencies for an order 10 tet mesh.
</li>
<li>
<a href = "tet_mesh_order10_adj_set.m">tet_mesh_order10_adj_set.m</a>
sets the nodal adjacency matrix for an order 10 tet mesh.
</li>
<li>
<a href = "tet_mesh_order10_example_set.m">
tet_mesh_order10_example_set.m</a>
returns an example order 10 tet mesh for a cube.
</li>
<li>
<a href = "tet_mesh_order10_example_size.m">
tet_mesh_order10_example_size.m</a>
sizes an example order 10 tet mesh for a cube.
</li>
<li>
<a href = "tet_mesh_order10_to_order4_compute.m">
tet_mesh_order10_to_order4_compute.m</a>
linearizes a quadratic tet mesh.
</li>
<li>
<a href = "tet_mesh_order10_to_order4_size.m">
tet_mesh_order10_to_order4_size.m</a>
sizes a linear mesh from a quadratic tet mesh.
</li>
<li>
<a href = "tet_mesh_quad.m">tet_mesh_quad.m</a>
approximates an integral over a tet mesh.
</li>
<li>
<a href = "tet_mesh_quality1.m">tet_mesh_quality1.m</a>
returns the quality of each tet in a mesh.
</li>
<li>
<a href = "tet_mesh_quality2.m">tet_mesh_quality2.m</a>
returns the quality of each tet in a mesh.
</li>
<li>
<a href = "tet_mesh_quality3.m">tet_mesh_quality3.m</a>
returns the quality of each tet in a mesh.
</li>
<li>
<a href = "tet_mesh_quality4.m">tet_mesh_quality4.m</a>
returns the quality of each tet in a mesh.
</li>
<li>
<a href = "tet_mesh_quality5.m">tet_mesh_quality5.m</a>
returns the quality of each tet in a mesh.
</li>
<li>
<a href = "tet_mesh_search_naive.m">tet_mesh_search_naive.m</a>
naively searches a tet mesh.
</li>
<li>
<a href = "tet_mesh_search_delaunay.m">tet_mesh_search_delaunay.m</a>
searches a Delaunay tet mesh.
</li>
<li>
<a href = "tetrahedron_barycentric.m">
tetrahedron_barycentric.m</a>
computes the barycentric coordinates of a point with respect to a tetrahedron.
</li>
<li>
<a href = "tetrahedron_circumsphere_3d.m">
tetrahedron_circumsphere_3d.m</a>
computes the circumsphere of a tetrahedron in 3D.
</li>
<li>
<a href = "tetrahedron_edge_length_3d.m">
tetrahedron_edge_length_3d.m</a>
returns edge lengths of a tetrahedron in 3D.
</li>
<li>
<a href = "tetrahedron_insphere_3d.m">tetrahedron_insphere_3d.m</a>
finds the insphere of a tetrahedron in 3D.
</li>
<li>
<a href = "tetrahedron_order4_physical_to_reference.m">
tetrahedron_order4_physical_to_reference.m</a>
converts physical points to reference points in a tetrahedron.
</li>
<li>
<a href = "tetrahedron_order4_reference_to_physical.m">
tetrahedron_order4_reference_to_physical.m</a>
converts reference points to physical points in a tetrahedron.
</li>
<li>
<a href = "tetrahedron_quality1_3d.m">tetrahedron_quality1_3d.m</a>
"quality" of a tetrahedron in 3D.
</li>
<li>
<a href = "tetrahedron_quality2_3d.m">tetrahedron_quality2_3d.m</a>
"quality" of a tetrahedron in 3D.
</li>
<li>
<a href = "tetrahedron_quality3_3d.m">tetrahedron_quality3_3d.m</a>
computes the mean ratio of a tetrahedron.
</li>
<li>
<a href = "tetrahedron_quality4_3d.m">tetrahedron_quality4_3d.m</a>
computes the minimum solid angle of a tetrahedron.
</li>
<li>
<a href = "tetrahedron_reference_sample.m">tetrahedron_reference_sample.m</a>
returns random points in the reference tetrahedron.
</li>
<li>
<a href = "tetrahedron_sample.m">tetrahedron_sample.m</a>
returns random points in a tetrahedron.
</li>
<li>
<a href = "tetrahedron_volume.m">tetrahedron_volume.m</a>
computes the volume of a tetrahedron.
</li>
<li>
<a href = "timestamp.m">timestamp.m</a>
prints the current YMDHMS date as a time stamp.
</li>
</ul>
</p>
<h3 align = "center">
Examples and Tests:
</h3>
<p>
<ul>
<li>
<a href = "tet_mesh_test.m">tet_mesh_test.m</a>,
a sample calling program.
</li>
<li>
<a href = "tet_mesh_test001.m">tet_mesh_test001.m</a>,
tests R8MAT_SOLVE.
</li>
<li>
<a href = "tet_mesh_test002.m">tet_mesh_test002.m</a>,
tests TETRAHEDRON_ORDER4_PHYSICAL_TO_REFERENCE and
TETRAHEDRON_ORDER4_REFERENCE_TO_PHYSICAL.
</li>
<li>
<a href = "tet_mesh_test003.m">tet_mesh_test003.m</a>,
tests TETRAHEDRON_ORDER10_TO_ORDER4.
</li>
<li>
<a href = "tet_mesh_test004.m">tet_mesh_test004.m</a>,
tests TET_MESH_NODE_ORDER.
</li>
<li>
<a href = "tet_mesh_test005.m">tet_mesh_test005.m</a>,
tests TETRAHEDRON_BARYCENTRIC.
</li>
<li>
<a href = "tet_mesh_test006.m">tet_mesh_test006.m</a>,
tests TET_MESH_NEIGHBOR_TETS.
</li>
<li>
<a href = "tet_mesh_test007.m">tet_mesh_test007.m</a>,
tests TET_MESH_SEARCH_NAIVE and TET_MESH_SEARCH_DELAUNAY.
</li>
<li>
<a href = "tet_mesh_test_output.txt">tet_mesh_test_output.txt</a>,
the output from a run of the sample program.
</li>
</ul>
</p>
<p>
You can go up one level to <a href = "../m_src.html">
the MATLAB source codes</a>.
</p>
<hr>
<i>
Last revised on 19 August 2009.
</i>
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