TET_MESH\
Routines for a Tet Mesh {#tet_mesh-routines-for-a-tet-mesh align=”center”}
=======================
TET_MESH is a C++ library which constructs, describes, or modifies
a mesh of tetrahedrons.
Linear and Quadratic Meshes {#linear-and-quadratic-meshes align=”center”}
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.
Licensing: {#licensing align=”center”}
The computer code and data files described and made available on this
web page are distributed under the GNU LGPL
license.
Languages: {#languages align=”center”}
TET_MESH is available in a C++
version and a C++
version and a FORTRAN77
version and a FORTRAN90
version and a MATLAB
version.
CVT_TET_MESH, a
FORTRAN90 library which uses CVT methods to compute a tet mesh in a
region.
GEOMETRY, a C++ library which
includes a number of routines for making computations involving
tetrahedrons.
GEOMPACK, a C++ library which
contains a routine DTRIS3 that can compute the tet mesh for a set of
3D points, as well as the adjacency information.
KEAST, a C++ library which defines a
number of quadrature rules for a tetrahedron.
NCC_TETRAHEDRON,
a C++ library which defines Newton-Cotes closed quadrature rules on a
tetrahedron.
NCO_TETRAHEDRON,
a C++ library which defines Newton-Cotes open quadrature rules on a
tetrahedron.
QUADRATURE_RULES_TET,
a dataset directory which contains triples of files defining various
quadrature rules on tetrahedrons.
TABLE_TET_MESH, a
FORTRAN90 program which can compute the tet mesh for a given set of
points.
TEST_TET_MESH, a
FORTRAN90 library which defines a few test regions for the generation of
a tet mesh.
TET_MESH_BOUNDARY,
a C++ program which returns the nodes and faces of the boundary of a
tetrahedral mesh, which themselves form a 3D triangular mesh or
“TRI_SURFACE”.
TET_MESH_DISPLAY,
a MATLAB program which can read in the node and tetra files defining a
tet mesh and display a wireframe image.
TET_MESH_DISPLAY_OPENGL,
a C++ program which can read in the node and tetra files defining a tet
mesh and display a wireframe image.
TET_MESH_L2Q, a C++
program which converts a linear to quadratic tet mesh.
TET_MESH_ORDER4, a
directory which contains a description and examples of a tet mesh using
order 4 elements.
TET_MESH_ORDER10,
a directory which contains a description and examples of a tet mesh
using order 10 elements.
TET_MESH_Q2L, a C++
program which converts a quadratic to linear tet mesh.
TET_MESH_QUAD, a C++
program which estimates the integral of a function over a region defined
by a tetrahedral mesh.
TET_MESH_QUALITY,
a C++ program which computes the quality of a tet mesh.
TET_MESH_RCM, a C++
program which takes a tet mesh and relabels the nodes to reduce the
bandwidth of the corresponding adjacency matrix.
TET_MESH_REFINE,
a C++ program which can refine a tet mesh.
TET_MESH_TET_NEIGHBORS,
a C++ program which computes the tetrahedral adjacency information.
TET_MESH_VOLUMES,
a C++ program which computes the volume of each tetrahedron in a tet
mesh;
Reference: {#reference align=”center”}
- 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.
- Per-Olof Persson, Gilbert Strang,\
A Simple Mesh Generator in MATLAB,\
SIAM Review,\
Volume 46, Number 2, June 2004, pages 329-345.
Source Code: {#source-code align=”center”}
Examples and Tests: {#examples-and-tests align=”center”}
List of Routines: {#list-of-routines align=”center”}
- I4_MAX returns the maximum of two I4’s.
- I4_MIN returns the minimum of two I4’s.
- I4_SWAP switches two I4’s.
- I4_UNIFORM returns a scaled pseudorandom I4.
- I4COL_COMPARE compares columns I and J of an I4COL.
- I4COL_SORT_A ascending sorts the columns of 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 two columns 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 an I4MAT,
transposed.
- I4VEC_PRINT prints an I4VEC.
- I4VEC_SUM sums the entries of an I4VEC.
- I4VEC_ZERO zeroes an I4VEC.
- R4_ABS returns the absolute value of an R4.
- R4_NINT returns the nearest integer to an R4.
- R8_HUGE returns a “huge” R8.
- R8_MAX returns the maximum of two R8’s.
- R8_MIN returns the minimum of two R8’s.
- R8_SWAP switches two R8’s.
- R8_UNIFORM_01 returns a unit pseudorandom R8.
- R8MAT_DET_4D computes the determinant of a 4 by 4 R8MAT.
- R8MAT_MV multiplies a matrix times a vector.
- R8MAT_PRINT prints an R8MAT, with an optional title.
- 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 a double precision array with unit
pseudorandom values.
- R8VEC_CROSS_3D computes the cross product of two vectors in
3D.
- R8VEC_IS_NONNEGATIVE is true if all entries in an R8VEC are
nonnegative.
- R8VEC_IS_ZERO is true if the entries in an R8VEC are all zero.
- R8VEC_LENGTH returns the Euclidean length of a R8VEC
- R8VEC_MAX returns the maximum element in an R8VEC.
- R8VEC_MEAN returns the mean of a R8VEC.
- R8VEC_MIN returns the minimum element in an R8VEC.
- R8VEC_PRINT prints an R8VEC.
- R8VEC_SUM returns the sum of an R8VEC.
- R8VEC_UNIFORM_01 returns a unit pseudorandom R8VEC.
- R8VEC_VARIANCE returns the variance of a double vector.
- R8VEC_ZERO zeroes a real vector.
- S_LEN_TRIM returns the length of a string to the last
nonblank.
- SORT_HEAP_EXTERNAL externally sorts a list of items into
ascending order.
- TET_MESH_NEIGHBOR_TETS determines tetrahedron neighbors.
- TET_MESH_NODE_ORDER: determines the order of nodes.
- TET_MESH_ORDER4_ADJ_COUNT counts the number of nodal
adjacencies.
- 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 order 4
tet mesh
- TET_MESH_ORDER4_REFINE_SIZE sizes a refined order 4 tet
mesh.
- TET_MESH_ORDER4_TO_ORDER10_COMPUTE computes a 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_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 a tet mesh quality factor.
- TET_MESH_QUALITY2 returns a tet mesh quality factor.
- TET_MESH_QUALITY3 returns a tet mesh quality factor.
- TET_MESH_QUALITY4 returns a tet mesh quality factor.
- TET_MESH_QUALITY5 returns a tet mesh quality factor.
- TET_MESH_SEARCH_DELAUNAY searches a Delaunay tet mesh for a
point.
- TET_MESH_SEARCH_NAIVE naively searches a tet mesh.
- TETRAHEDRON_BARYCENTRIC returns the 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 maps physical
points to reference points.
- TETRAHEDRON_ORDER4_REFERENCE_TO_PHYSICAL maps reference
points to physical points.
- TETRAHEDRON_QUALITY1_3D: “quality” of a tetrahedron in 3D.
- TETRAHEDRON_QUALITY2_3D: “quality” of a tetrahedron in 3D.
- TETRAHEDRON_QUALITY3_3D computes the mean ratio of a
tetrahedron.
- TETRAHEDRON_QUALITY4_3D computes the minimum solid angle of a
tetrahedron.
- TETRAHEDRON_REFERENCE_SAMPLE samples points in the reference
tetrahedron.
- TETRAHEDRON_SAMPLE returns random points in a tetrahedron.
- TETRAHEDRON_VOLUME_3D computes the volume of a tetrahedron in
3D.
- TIMESTAMP prints the current YMDHMS date as a time stamp.
You can go up one level to the C++ source codes.
Last revised on 20 August 2009.