Routines for a Tet Mesh

TET_MESH is a C 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:


The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.


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:

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

KEAST, a C++ library which defines a number of quadrature rules for a tetrahedron.

TEST_TET_MESH, a FORTRAN90 library which defines a few test regions for the generation of a tet mesh.


  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:

Examples and Tests:

List of Routines:

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

Last revised on 05 October 2014.