TET_MESH_L2Q
10-Node Tet Mesh
from
4-Node Tet Mesh

TET_MESH_L2Q is a FORTRAN90 program which converts a 4-node tetrahedral mesh ("tet mesh") into a 10-node tet mesh.

In particular, TET_MESH_L2Q reads information describing a set of 3D points, and a 4 node ("linear") tet mesh of those points. It creates a "quadratic" tet mesh, which has the same number of tetrahedrons, but in which each tetrahedron is defined by 10 nodes. In the process, it adds just enough nodes, at the midsides of the edges of the original mesh, to define the new mesh. The data defining the new mesh is written out to files for further use.

The refinement of a single tetrahedron is easy. Every pair of nodes generates a new node whose location is the average of the locations of the original two nodes. The problem is that many tetrahedrons may share the same edge. The new node needs to be generated exactly once, and assigned a unique index, which all the tetrahedrons will share. The tricky part of this calculation is thus figuring out whether it is time to generate a new node, or whether the node has already been generated, in which case the appropriate index must be retrieved.

Usage:

tet_mesh_l2q nodes.txt tetras.txt

This creates a new node file called nodes.l2q.txt and a new tetra file called tetras.l2q.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 nodes.txt contains the coordinate information for the 4-node tet mesh. Each data line contains the X and Y coordinates of a single node.

The input file tetras.txt contains the tetrahedron information for the 4-node tet mesh. Each data line contains the indices of four nodes that form a tetrahedron.

The output file nodes.l2q.txt contains the coordinate information for the 10-node tet mesh. The data lines begin with the node information from nodes.txt, followed by the coordinates of the new nodes.

The output file tetras.l2q.txt contains the tetrahedron information for the 10-node tet mesh. There are exactly as many tetrahedrons as before, but now each tetrahedron uses 10 nodes. Each line of the file contains the indices of 10 nodes that form the tetrahedron, listed in a particular order. The first four node indices are the same as for the linear tet mesh. The next six node indices may be thought of as being obtained as averages of pairs of the first four nodes. Symbolically, this may be thought of as:

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

Related Programs:

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

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 FORTRAN90 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 a C++ executable program which reads a tet mesh and displays the nodes and edges using OpenGL.

TET_MESH_L2Q is also available in a C++ version and a MATLAB version.

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 an executable FORTRAN90 program which takes a 10-node tet mesh and makes a 4-node tet mesh.

TET_MESH_QUALITY is an executable FORTRAN90 program which takes a 4-node tet mesh and computes the "quality" of the mesh.

TET_MESH_RCM is an executable FORTRAN90 program which takes a tet mesh and relabels the nodes to reduce the bandwidth of the corresponding adjacency matrix.

TET_MESH_REFINE is an executable FORTRAN90 program which can refine a tet mesh.

TET_MESH_TET_NEIGHBORS is an executable FORTRAN90 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, 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:

• tet_mesh_l2q.f90, the source code.
• tet_mesh_l2q.csh, commands to compile the source code.

Examples and Tests:

You may copy data defining an initial 4-node tet mesh:

• nodes_order4.txt, the nodes for the 4-node tet mesh.
• tetras_order4.txt, the tetras for the 4-node tet mesh.

You may copy data defining the resultant 10-node tet mesh:

• nodes_order4.l2q.txt, the nodes for the 10-node tet mesh.
• tetras_order4.l2q.txt, the tetras for the 10-node tet mesh.
• tet_mesh_l2q_output.txt, printed output from the program.

List of Routines:

• MAIN is the main program for TET_MESH_L2Q.
• 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.
• DTABLE_CLOSE_WRITE closes a file used to write a DTABLE.
• DTABLE_DATA_READ reads data from a DTABLE file.
• DTABLE_DATA_WRITE writes data to a DTABLE file.
• DTABLE_HEADER_READ reads the header from a DTABLE file.
• DTABLE_HEADER_WRITE writes the header to a DTABLE file.
• DTABLE_OPEN_WRITE opens a file to write a DTABLE.
• DTABLE_WRITE writes a table to a file.
• FILE_COLUMN_COUNT counts the number of columns in the first line of a file.
• FILE_NAME_EXT_GET determines the "extension" of a file name.
• FILE_NAME_EXT_SWAP replaces the current "extension" of a file name.
• FILE_ROW_COUNT counts the number of row records in a file.
• GET_UNIT returns a free FORTRAN unit number.
• I4_SWAP swaps two I4's.
• I4COL_COMPARE compares columns I and J of an I4COL.
• I4COL_SORT_A ascending sorts an I4COL.
• I4COL_SORT2_A ascending sorts the elements of each column of an I4COL.
• I4COL_SORTED_UNIQUE_COUNT counts unique elements in an I4COL.
• I4COL_SWAP swaps columns I and J of an I4COL.
• I4I4_SORT_A ascending sorts a pair of I4's.
• I4MAT_TRANSPOSE_PRINT_SOME prints some of the transpose of an I4MAT.
• ITABLE_CLOSE_WRITE closes a file used to write an ITABLE.
• ITABLE_DATA_READ reads data from an integer table file.
• ITABLE_DATA_WRITE writes data to an integer table file.
• ITABLE_HEADER_READ reads the header from an integer table file.
• ITABLE_HEADER_WRITE writes the header to an integer table file.
• ITABLE_OPEN_WRITE opens a file to write ITABLE data.
• ITABLE_WRITE writes an ITABLE file.
• R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
• S_BLANK_DELETE removes blanks from a string, left justifying the remainder.
• 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_TO_R8 reads an R8VEC from a string.
• S_TO_R8VEC reads an R8VEC from a string.
• S_WORD_COUNT counts the number of "words" in a string.
• SORT_HEAP_EXTERNAL externally sorts a list of items into ascending order.
• TET_MESH_ORDER4_TO_ORDER10_COMPUTE computes a quadratic tet mesh from a linear one.
• TET_MESH_ORDER4_TO_ORDER10_SIZE sizes a quadratic tet mesh from a linear one.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TIMESTRING writes the current YMDHMS date into a string.

You can go up one level to the FORTRAN90 source codes.