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

TET_MESH_Q2L is an executable MATLAB program, using double precision arithmetic, 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 ( 'tetras.txt' )

The program creates a new tetra file called tetras.q2l.txt.

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.

Related Programs:

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

GEOMPACK is 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.

MATLAB has a command delaunay3 that can compute the tet mesh for a set of 3D points.

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

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

TET_MESH is a MATLAB library which includes a variety of routines for working with tetrahedral meshes.

TET_MESH_DISPLAY is an executable MATLAB program which can read in the node and tetra files defining a tet mesh and display a wireframe image.

TET_MESH_DISPLAY_OPEN_GL is an executable C++ program which reads a tet mesh and displays the nodes and edges using OpenGL.

TET_MESH_L2Q is an executable MATLAB program which converts a linear to quadratic tet mesh.

TET_MESH_ORDER4 is a directory which contains a description and examples of a tet mesh using order 4 elements.

TET_MESH_ORDER10 is a directory which contains a description and examples of a tet mesh using order 10 elements.

TET_MESH_Q2L is also available in a FORTRAN90 version and a C++ version.

TET_MESH_QUALITY is an executable MATLAB program which computes the "quality" of a mesh.

TET_MESH_RCM is an executable 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 is an executable MATLAB program which can refine a tet mesh.

TET_MESH_TET_NEIGHBORS is an executable MATLAB program which computes the tetrahedral adjacency information.

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.

Tar File:

A GZIP'ed TAR file of the contents of this directory is available. This is only done as a convenience for users who want ALL the files, and don't want to download them individually. This is not a convenience for me, so don't be surprised if the tar file is somewhat out of date.

• tet_mesh_q2l_m_src.tar.csh the commands used to create the GZIP'ed TAR file.
• tet_mesh_q2l_m_src.tar.gz the GZIP'ed TAR file.

Source code:

• tet_mesh_q2l.m, the main program for TET_MESH_Q2L.
• ch_cap.m, capitalizes a single character.
• ch_eqi.m, is a case insensitive comparison of two characters for equality.
• ch_to_digit.m, returns the integer value of a base 10 digit.
• file_column_count.m, counts the number of columns in the first line of a file.
• file_name_ext_get.m, determines the "extension" of a file name.
• file_name_ext_swap.m, replaces the current "extension" of a file name.
• file_row_count.m, counts the number of row records in a file.
• i4mat_transpose_print_some.m, prints some of the transpose of an I4MAT.
• itable_data_read.m, reads data from an integer table file.
• itable_data_write.m, writes data to an integer table file.
• itable_header_read.m, reads the header from an integer table file.
• itable_header_write.m, writes the header to an integer table file.
• itable_write.m, writes an integer table file.
• s_blank_delete.m, removes blanks from a string, left justifying the remainder.
• s_index_last_c.m, finds the LAST occurrence of a given character.
• s_len_trim.m, returns the length of a string to the last nonblank.
• s_word_count.m, counts the number of "words" in a string.
• tet_mesh_order10_to_order4_compute.m, linearizes a quadratic tet mesh.
• tet_mesh_order10_to_order4_size.m, sizes a linear tet mesh from a quadratic one.
• timestamp.m, prints the current YMDHMS date as a time stamp.
• timestring.m, writes the current YMDHMS date into a string.

Examples and Tests:

You may copy data for an example problem:

• cube_nodes.txt, a set of nodes.
• cube_tetras.txt, the tetrahedrons for a 10-node tet mesh of the nodes.
• cube.out, the printed output from the program.
• cube_tetras.q2l.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.