tet_mesh


tet_mesh, an Octave 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 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

geometry, an Octave code which includes a number of routines for making computations involving tetrahedrons.

quadrature_rules_tet, a dataset directory which contains triples of files defining various quadrature rules on tetrahedrons.

tet_mesh_boundary, an Octave code 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, an Octave code which reads in the node and tetra files defining a tet mesh and displays a wireframe image.

tet_mesh_l2q, an Octave code 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, an Octave code which converts a quadratic to linear tet mesh.

tet_mesh_quad, an Octave code which estimates the integral of a function over a region defined by a tetrahedral mesh.

tet_mesh_quality, an Octave code which computes the quality of a tet mesh.

tet_mesh_rcm, an Octave code which takes a tet mesh and relabels the nodes to reduce the bandwidth of the corresponding adjacency matrix.

tet_mesh_refine, an Octave code which can refine a tet mesh.

tet_mesh_tet_neighbors, an Octave code which computes the tetrahedral adjacency information.

tet_mesh_volumes, an Octave code which computes the volume of each tetrahedron in a tet mesh;

tetrahedron, an Octave code which carries out geometric calculations involving a general tetrahedron, including solid and facial angles, face areas, point containment, distances to a point, circumsphere and insphere, measures of shape quality, centroid, barycentric coordinates, edges and edge lengths, random sampling, and volumes.

tetrahedron_keast_rule, an Octave code which defines a number of quadrature rules for a tetrahedron.

tetrahedron_ncc_rule, an Octave code which defines newton-cotes closed quadrature rules on a tetrahedron.

tetrahedron_nco_rule, an Octave code which defines newton-cotes open quadrature rules on a tetrahedron.

tetrahedron_properties, an Octave code 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.

Source code:


Last revised on 06 July 2023.