tet_mesh_q2l

tet_mesh_q2l, a Fortran90 code 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 information on this web page is distributed under the MIT license.

Languages:

tet_mesh_q2l is available in a C++ version and a Fortran90 version and a MATLAB version and an Octave version.

Related Programs:

tet_mesh_q2l_test

cvt_tet_mesh, a Fortran90 code which uses CVT methods to compute a tet mesh in a region.

geompack, a Fortran90 code 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 code which can compute the tet mesh for a given set of points.

test_tet_mesh, a Fortran90 code which defines a few test regions for the generation of a tet mesh.

tet_mesh, a Fortran90 code which includes a variety of routines for working with tetrahedral meshes.

tet_mesh_display, a MATLAB code which reads the node and tetra files defining a tet mesh and displays a wireframe image.

tet_mesh_display_opengl, a C++ code which reads a tet mesh and displays the nodes and edges using OpenGL.

tet_mesh_l2q, a Fortran90 code which takes a 4-node tet mesh and makes a 10-node tet mesh, by inserting new nodes.

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 Fortran90 code which computes the quality of a mesh.

tet_mesh_rcm, a Fortran90 code 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 Fortran90 code which refines a tet mesh.

tet_mesh_tet_neighbors, a Fortran90 code which computes the tetrahedral adjacency information.

tet_mesh_volumes, a Fortran90 code which computes the volume of each tetrahedron in a tet mesh;

tetrahedron, a Fortran90 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, 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.f90, 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 elements for a 10-node tet mesh of the nodes.
• cube_output.txt, the printed output.
• cube_q2l_elements.txt, the elements for a 4-node tet mesh derived from the quadratic mesh.

List of Routines:

• MAIN is the main code for TET_MESH_Q2L.
• CH_CAP capitalizes a single character.
• CH_EQI is a case insensitive comparison of two characters for equality.
• CH_TO_DIGIT returns the integer value of a base 10 digit.
• FILE_COLUMN_COUNT counts the number of columns in the first line of a file.
• FILE_ROW_COUNT counts the number of row records in a file.
• GET_UNIT returns a free Fortran unit number.
• I4MAT_DATA_READ reads data from an I4MAT file.
• I4MAT_HEADER_READ reads the header from an I4MAT.
• I4MAT_TRANSPOSE_PRINT_SOME prints some of the transpose of an I4MAT.
• I4MAT_WRITE writes an I4MAT file.
• S_INDEX_LAST finds the LAST occurrence of a given substring.
• S_TO_I4 reads an I4 from a string.
• S_TO_I4VEC reads an I4VEC from a string.
• S_WORD_COUNT counts the number of "words" in a string.
• TET_MESH_ORDER10_TO_ORDER4_COMPUTE linearizes a quadratic tet mesh.
• TET_MESH_ORDER10_TO_ORDER4_SIZE sizes a linear tet mesh from a quadratic one.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the Fortran90 source codes.