tet_mesh

tet_mesh, a Fortran77 code 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 MIT license

Languages:

tet_mesh is available in a C++ version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version.

Related Programs:

tet_mesh_test

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:

1. Adrian Bowyer, John Woodwark,
   A Programmer's Geometry,
   Butterworths, 1983,
   ISBN: 0408012420.
2. Paul Bratley, Bennett Fox, Linus Schrage,
   A Guide to Simulation,
   Second Edition,
   Springer, 1987,
   ISBN: 0387964673.
3. 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.
4. Herbert Edelsbrunner,
   Geometry and Topology for Mesh Generation,
   Cambridge, 2001,
   ISBN: 0-521-79309-2,
   LC: QA377.E36.
5. 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.
6. 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.
7. Albert Nijenhuis, Herbert Wilf,
   Combinatorial Algorithms for Computers and Calculators,
   Second Edition,
   Academic Press, 1978,
   ISBN: 0-12-519260-6,
   LC: QA164.N54.
8. Per-Olof Persson, Gilbert Strang,
   A Simple Mesh Generator in MATLAB,
   SIAM Review,
   Volume 46, Number 2, June 2004, pages 329-345.
9. Philip Schneider, David Eberly,
   Geometric Tools for Computer Graphics,
   Elsevier, 2002,
   ISBN: 1558605940.

Source code:

• tet_mesh.f, the source code.
• tet_mesh.sh, commands to compile the source code.