TET_MESH_Q2L
10-Node Tet Mesh
to
4-Node Tet Mesh

TET_MESH_Q2L is a MATLAB program which reads information describing a tet mesh of a set of points using 10-node ("quadratic") triangles, and creates a 4-node ("linear") tet mesh.

The same nodes are used, but each 10-node tetrahedron is broken up into 8 smaller 4-node tetrahedrons.

Usage:

tet_mesh_q2l 'prefix'

• 'prefix'_nodes.txt, the node coordinates (not needed by this program);
• 'prefix'_elements.txt, the element definitions.
• 'prefix'_q2l_elements.txt, the linear element definitions created by this program, and based on the same set of nodes.

The input and output files use the simple TABLE format; comment lines begin with a "#" character. Otherwise, each line of the file contains one set of information, either the coordinates of a node (for a node file), or the indices of nodes that make up a tetrahedron, (for a tetrahedron file).

The input file tetras.txt contains the tetrahedron information for the 10-node tet mesh. Each line contains the indices of 10 nodes that form a tetrahedron, in a particular order. The first 4 indices are the vertices. Subsequent nodes can be described by the pair of vertices they lie between, as follows:

        1  2  3  4  (1+2)  (1+3)  (1+4)  (2+3)  (2+4)  (3+4)
      

The output file tetras.l2q.txt contains the tetrahedron information for the 4-node tet mesh.

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_Q2L 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.

GEOMPACK, a MATLAB library which contains a routine DTRIS3 that can compute the tet mesh for a set of 3D points, as well as the adjacency information.

TABLE_TET_MESH, a FORTRAN90 program which can compute the tet mesh for a given set of points.

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 includes a variety of routines for working with tetrahedral meshes.

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_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_QUALITY, a MATLAB program which computes the "quality" of a mesh.

TET_MESH_RCM, a MATLAB program which takes a 4-node or 10-node 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_TET_NEIGHBORS, a MATLAB program which computes the tetrahedral adjacency information.

TET_MESH_VOLUMES, a MATLAB 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, 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:

• tet_mesh_q2l.m, the source code.

Examples and Tests:

You may copy data for an example problem:

• cube_nodes.txt, a set of nodes.
• cube_elements.txt, the tetrahedrons for a 10-node tet mesh of the nodes.
• cube_output.txt, the printed output from the program.
• cube_q2l_elements.txt, the tetrahedrons for a 4-node tet mesh derived from the quadratic mesh.

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