# tet_mesh

tet_mesh, a C code 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 MIT license

### Languages:

tet_mesh is available in a C++ version and a C++ version and a FORTRAN90 version and a MATLAB version.

### Related Programs:

GEOMETRY, a C code which includes a number of routines for making computations involving 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.

### Source Code:

Last revised on 15 August 2019.