TET_MESH
Routines for a 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:

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 FORTRAN90 version and a MATLAB version.

Related Programs:

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.

tet_mesh_test

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:

  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 25 April 2020.