TET_MESH Routines for a Tet Mesh

TET_MESH is a MATLAB library which constructs, describes, or 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.

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:

CVT_TET_MESH, a FORTRAN90 library which uses CVT methods to compute a tet mesh in a region.

GEOMETRY, a MATLAB library which includes a number of routines for making computations involving tetrahedrons.

GEOMPACK, a MATLAB 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 MATLAB library which defines a number of quadrature rules for a tetrahedron.

NCC_TETRAHEDRON, a MATLAB library which defines Newton-Cotes closed quadrature rules on a tetrahedron.

NCO_TETRAHEDRON, a MATLAB 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 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".

TET_MESH_DISPLAY, a MATLAB program which reads in the node and tetra files defining a tet mesh and displays 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 using OpenGL.

TET_MESH_L2Q, a MATLAB 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 MATLAB program which converts a quadratic to linear tet mesh.

TET_MESH_QUAD, a MATLAB program which estimates the integral of a function over a region defined by a tetrahedral mesh.

TET_MESH_QUALITY, a MATLAB program which computes the quality of a tet mesh.

TET_MESH_RCM, a MATLAB program which takes a tet mesh and relabels the nodes to reduce the bandwidth of the corresponding adjacency matrix.

TET_MESH_REFINE, a MATLAB program which can refine a tet mesh.

TET_MESH_TET_NEIGHBORS, a MATLAB program which computes the tetrahedral adjacency information.

TET_MESH_VOLUMES, a MATLAB program which computes the volume of each tetrahedron in a tet mesh;

TETRAHEDRON_PROPERTIES, a MATLAB program which computes properties of a given tetrahedron.

TETRAHEDRONS, a dataset directory which contains examples of tetrahedrons;

Reference:

1. Herbert Edelsbrunner,
Geometry and Topology for Mesh Generation,
Cambridge, 2001,
ISBN: 0-521-79309-2,
LC: QA377.E36.
2. 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.
3. 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.
4. Per-Olof Persson, Gilbert Strang,
A Simple Mesh Generator in MATLAB,
SIAM Review,
Volume 46, Number 2, June 2004, pages 329-345.

Examples and Tests:

You can go up one level to the MATLAB source codes.

Last revised on 19 August 2009.