TET_MESH_QUALITY
Interactive Program for
Tet Mesh Quality

TET_MESH_QUALITY is a MATLAB program which computes and prints a variety of quality measures for a given tet mesh of a set of points in 3D.

The tet mesh is defined by a node file containing the coordinates of nodes, and a tetra file containing quadruples of node indices. For more information on this format, see order 4 Tet Mesh format.

The quality measures computed include:

• Measure 1, the minimum, over all tetrahedrons, of 3 times the radius of the insphere divided by the radius of the circumsphere.
• Measure 2, the minimum, over all tetrahedrons, of 2 times sqrt ( 6 ) times the radius of the insphere divided by the length of the longest side of the tetrahedron.
• Measure 3, the minimum, over all tetrahedrons, of 12 * ( 3 * volume )**(2/3) / (sum of squares of edge lengths);
• Measure 4, the minimum solid angle in any tetrahedron;
• Measure 5, a uniformity measure, the ratio of the maximum to minimum tetrahedron volume;

Each quality measure is defined as the minimum of its value over each tetrahedron. The maximum and best possible value is 1, and the minimum and worst value is 0.

Usage:

tet_mesh_quality 'prefix'

• 'prefix'_nodes.txt, the node coordinates;
• 'prefix'_elements.txt, the element definitions.

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

Related Programs:

CVT_TET_MESH, a FORTRAN90 library which uses CVT methods to compute a tet mesh in a region.

GEOMPACK3, a FORTRAN90 library which includes a routine DTRIS3 to compute the tet mesh of a set of points in 3D.

TABLE_QUALITY, a MATLAB program which computes quality measures for an arbitrary (untriangulated) pointset in any dimension.

TABLE_TET_MESH, a FORTRAN90 program which computes the tet mesh of a set of points in 3D.

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

TET_MESH, a MATLAB library which carries out computations involving a tet mesh.

TET_MESH_BOUNDARY, a MATLAB 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 reads a tet mesh and displays the nodes and edges using OpenGL.

TET_MESH_L2Q, a MATLAB program which converts a linear to quadratic tet mesh.

TET_MESH_NEIGHBORS, a MATLAB program which computes the tetrahedral adjacency information.

TET_MESH_Q2L, a MATLAB program which converts a quadratic to linear tet mesh.

TET_MESH_RCM, a MATLAB program which takes a tet mesh and relabels the nodes to reduce the bandwidth of the corresponding adjacency matrix.

TET_MESH_REFINE, a MATLAB program which can refine a tet mesh.

TET_MESH_VOLUMES, a MATLAB program which computes the volume of each tetrahedron in a tet mesh.

TRIANGULATION_QUALITY, a MATLAB program which computes triangle-based quality measures for a triangulation of a set of points in 2D.

Reference:

1. Herbert Edelsbrunner,
   Geometry and Topology for Mesh Generation,
   Cambridge, 2001,
   ISBN: 0-521-79309-2,
   LC: QA377.E36.
2. David Field,
   Qualitative Measures for Initial Meshes,
   International Journal of Numerical Methods in Engineering,
   Volume 47, 2000, pages 887-906.
3. Barry Joe,
   GEOMPACK - a software package for the generation of meshes using geometric algorithms,
   Advances in Engineering Software,
   Volume 13, 1991, pages 325-331.
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

• tet_mesh_quality.m the source code.

Tests and Examples

CUBE is a simple example of 8 nodes in a cube.

• cube_nodes.txt, the node file.
• cube_elements.txt, the element file.
• cube_quality.txt, the output file.

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