TET_MESH
Routines for a Tet Mesh
TET_MESH
is a FORTRAN77 library which
constructs, describes, and modifies a mesh of tetrahedrons.
Linear and Quadratic Meshes
The simplest tet mesh, which we term an order 4
or linear mesh, uses four points to define each tetrahedron.
A second type of mesh, known as an order 10 or quadratic
mesh, uses ten points.
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.
Thus, an order 10 tet mesh is typically generated in two steps:
-
generate an order 4 mesh, in which every tetrahedral vertex
comes from a user data point;
-
generate an order 10 mesh from the order 4 mesh, in which
the new midside points are not user data points, but rather
averages of pairs of tetrahedral vertices.
MATLAB has a command
delaunay3 that can compute the tet mesh for a set of 3D points.
Licensing:
The computer code and data files described and made available on this web page
are distributed under
the GNU LGPL license.
Languages:
TET_MESH is available in
a C++ version and
a C++ version and
a FORTRAN77 version and
a FORTRAN90 version and
a MATLAB version.
Related Programs:
>
TET_MESH_ORDER4,
a data directory which
contains a description and
examples of a tet mesh using order 4 elements.
TET_MESH_ORDER10,
a data directory which
contains a description and
examples of a tet mesh using order 10 elements.
Reference:
-
Adrian Bowyer, John Woodwark,
A Programmer's Geometry,
Butterworths, 1983,
ISBN: 0408012420.
-
Paul Bratley, Bennett Fox, Linus Schrage,
A Guide to Simulation,
Second Edition,
Springer, 1987,
ISBN: 0387964673.
-
Qiang Du, Desheng Wang,
The Optimal Centroidal Voronoi Tesselations and the Gersho's
Conjecture in the Three-Dimensional Space,
Computers and Mathematics with Applications,
Volume 49, 2005, pages 1355-1373.
-
Herbert Edelsbrunner,
Geometry and Topology for Mesh Generation,
Cambridge, 2001,
ISBN: 0-521-79309-2,
LC: QA377.E36.
-
Barry Joe,
GEOMPACK - a software package for the generation of meshes
using geometric algorithms,
Advances in Engineering Software,
Volume 13, Number 5, 1991, pages 325-331.
-
Anwei Liu, Barry Joe,
Quality Local Refinement of Tetrahedral Meshes Based
on 8-Subtetrahedron Subdivision,
Mathematics of Computation,
Volume 65, Number 215, July 1996, pages 1183-1200.
-
Albert Nijenhuis, Herbert Wilf,
Combinatorial Algorithms for Computers and Calculators,
Second Edition,
Academic Press, 1978,
ISBN: 0-12-519260-6,
LC: QA164.N54.
-
Per-Olof Persson, Gilbert Strang,
A Simple Mesh Generator in MATLAB,
SIAM Review,
Volume 46, Number 2, June 2004, pages 329-345.
-
Philip Schneider, David Eberly,
Geometric Tools for Computer Graphics,
Elsevier, 2002,
ISBN: 1558605940.
Source code:
Examples and Tests:
List of Routines:
-
I4_UNIFORM returns a scaled pseudorandom I4.
-
I4COL_COMPARE compares columns I and J of an I4COL.
-
I4COL_SORT_A ascending sorts an I4COL.
-
I4COL_SORT2_A ascending sorts the elements of each column of an I4COL.
-
I4COL_SORTED_UNIQUE_COUNT counts unique elements in an I4COL.
-
I4COL_SWAP swaps columns J1 and J2 of an I4COL.
-
I4I4_SORT_A ascending sorts a pair of I4's.
-
I4I4I4_SORT_A ascending sorts a triple of I4's.
-
I4MAT_TRANSPOSE_PRINT prints an I4MAT, transposed.
-
I4MAT_TRANSPOSE_PRINT_SOME prints some of the transpose of an I4MAT.
-
I4VEC_PRINT prints an I4VEC.
-
MESH_BASE_ONE ensures that the element definition is one-based.
-
R8_UNIFORM_01 returns a unit pseudorandom R8.
-
R8MAT_DET_4D computes the determinant of a 4 by 4 R8MAT.
-
R8MAT_PRINT prints an R8MAT.
-
R8MAT_PRINT_SOME prints some of an R8MAT.
-
R8MAT_SOLVE uses Gauss-Jordan elimination to solve an N by N linear system.
-
R8MAT_TRANSPOSE_PRINT prints an R8MAT, transposed.
-
R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
-
R8MAT_UNIFORM_01 fills an R8MAT with unit pseudorandom numbers.
-
R8VEC_CROSS_3D computes the cross product of two R8VEC's in 3D.
-
R8VEC_LENGTH returns the Euclidean length of an R8VEC.
-
R8VEC_MEAN returns the mean of an R8VEC.
-
R8VEC_PRINT prints an R8VEC.
-
R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
-
R8VEC_VARIANCE returns the variance of an R8VEC.
-
SORT_HEAP_EXTERNAL externally sorts a list of items into ascending order.
-
TET_MESH_NEIGHBOR_TETS determines tetrahedron neighbors.
-
TET_MESH_NODE_ORDER: determine the order of nodes in a tet mesh.
-
TET_MESH_ORDER4_ADJ_COUNT counts the number of nodal adjacencies.
-
TET_MESH_ORDER4_ADJ_SET sets the nodal adjacency matrix.
-
TET_MESH_ORDER4_BOUNDARY_FACE_COUNT counts the number of boundary faces.
-
TET_MESH_ORDER4_EDGE_COUNT counts the number of edges.
-
TET_MESH_ORDER4_EXAMPLE_SET sets an example linear tet mesh.
-
TET_MESH_ORDER4_EXAMPLE_SIZE sizes an example linear tet mesh.
-
TET_MESH_ORDER4_REFINE_COMPUTE computes a refined order4 tet mesh.
-
TET_MESH_ORDER4_REFINE_SIZE sizes a refined order 4 tet mesh.
-
TET_MESH_ORDER4_TO_ORDER10_COMPUTE: quadratic tet mesh from a linear one.
-
TET_MESH_ORDER4_TO_ORDER10_SIZE sizes a quadratic tet mesh from a linear one.
-
TET_MESH_ORDER10_ADJ_COUNT counts the number of nodal adjacencies.
-
TET_MESH_ORDER10_ADJ_SET sets the nodal adjacency matrix.
-
TET_MESH_ORDER10_EXAMPLE_SET sets an example quadratic tet mesh.
-
TET_MESH_ORDER10_EXAMPLE_SIZE sizes an example quadratic tet mesh.
-
TET_MESH_ORDER10_TO_ORDER4_COMPUTE linearizes a quadratic tet mesh.
-
TET_MESH_ORDER10_TO_ORDER4_SIZE sizes a linear tet mesh from a quadratic one.
-
TET_MESH_QUAD approximates an integral over a tet mesh.
-
TET_MESH_QUALITY1 returns the quality of each tet in a mesh.
-
TET_MESH_QUALITY2 returns the quality of each tet in a mesh.
-
TET_MESH_QUALITY3 returns the quality of each tet in a mesh.
-
TET_MESH_QUALITY4 returns the quality of each tet in a mesh.
-
TET_MESH_QUALITY5 returns the quality of each tet in a mesh.
-
TET_MESH_SEARCH_DELAUNAY searches a Delaunay tet mesh for a point.
-
TET_MESH_SEARCH_NAIVE naively searches a tet mesh.
-
TETRAHEDRON_BARYCENTRIC: barycentric coordinates of a point.
-
TETRAHEDRON_CIRCUMSPHERE_3D computes the circumsphere of a tetrahedron in 3D.
-
TETRAHEDRON_EDGE_LENGTH_3D returns edge lengths of a tetrahedron in 3D.
-
TETRAHEDRON_INSPHERE_3D finds the insphere of a tetrahedron in 3D.
-
TETRAHEDRON_ORDER4_PHYSICAL_TO_REFERENCE: physical to reference points.
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TETRAHEDRON_ORDER4_REFERENCE_TO_PHYSICAL: T4 reference to physical points.
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TETRAHEDRON_QUALITY1_3D: "quality" of a tetrahedron in 3D.
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TETRAHEDRON_QUALITY2_3D: "quality" of a tetrahedron in 3D.
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TETRAHEDRON_QUALITY3_3D computes the mean ratio of a tetrahedron.
-
TETRAHEDRON_QUALITY4_3D computes the minimum solid angle of a tetrahedron.
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TETRAHEDRON_REFERENCE_SAMPLE samples points in the reference tetrahedron.
-
TETRAHEDRON_SAMPLE returns random points in a tetrahedron.
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TETRAHEDRON_VOLUME computes the volume of a tetrahedron in 3D.
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TIMESTAMP prints the current YMDHMS date as a time stamp.
You can go up one level to
the FORTRAN77 source codes.
Last revised on 07 October 2014