TET_MESH_TET_NEIGHBORS
Interactive Program for
Tet Mesh Neighbors

TET_MESH_TET_NEIGHBORS is a FORTRAN90 program which reads information defining a tet mesh of points in 3D, and determines, for each face of each tetrahedron, the index of the neighboring tetrahedron that shares that face.

The tet mesh is defined by a node file containing the coordinates of nodes, and an element file containing sets of 4 or 10 node indices. For this calculation, though, only the element file is needed.

If a tetrahedron is on the boundary, then one or more of its faces will not be shared by any tetrahedron. Such cases will be indicated by specifying the corresponding neighbor value as -1.

Usage:

tet_mesh_tet_neighbors prefix

• prefix_nodes.txt, the node coordinates (not needed by this program);
• prefix_elements.txt, the element definitions.
• prefix_element_neighbors.txt, the element neighbors.

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

Related Programs:

GEOMPACK, a FORTRAN90 library which contains a routine DTRIS3 that can compute the tet mesh for a set of 3D points, as well as the adjacency information.

NEIGHBORS_TO_METIS_GRAPH, a FORTRAN90 program which reads a tet mesh neighbor file created by TET_MESH_TET_NEIGHBORS and writes a modified version of the same data suitable for input to the mesh partitioning program METIS.

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 FORTRAN90 library which is useful for work with tet meshes.

TET_MESH_BOUNDARY, a FORTRAN90 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 FORTRAN90 program which can convert a linear (4-node) tet mesh to a quadratic (10-node) 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_Q2L, a FORTRAN90 program which can convert a quadratic (10-node) tet mesh to a linear (4-node) tet mesh.

TET_MESH_QUALITY, a FORTRAN90 program which can compute the quality of a tet mesh.

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

TET_MESH_REFINE, a FORTRAN90 program which can refine a tet mesh.

TET_MESH_TET_NEIGHBORS, a data directory which contains a description and examples of the format for storing information about neighboring tetrahedrons in a tetrahedral mesh.

TET_MESH_VOLUMES, a FORTRAN90 program which computes the volume of each tetrahedron in a tet mesh;

TETRAHEDRON_PROPERTIES, a FORTRAN90 program 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. 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_tet_neighbors.f90, the source code.

Examples and Tests

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

• cube_nodes.txt, the node file.
• cube_elements.txt, the element file.
• cube_element_neighbors.txt, the neighbor information computed by the program.
• cube_output.txt, the printed output from the program.

List of Routines

• MAIN is the main program for TET_MESH_TET_NEIGHBORS.
• 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.
• I4COL_COMPARE compares columns I and J of an I4COL.
• I4COL_SORT_A ascending sorts an I4COL of columns.
• I4COL_SWAP swaps columns J1 and J2 of a integer array of column data.
• I4I4I4_SORT_A ascending sorts a triple of I4's.
• I4MAT_DATA_READ reads data from an I4MAT file.
• I4MAT_HEADER_READ reads the header from an I4MAT.
• I4MAT_TRANSPOSE_PRINT prints an I4MAT, transposed.
• I4MAT_TRANSPOSE_PRINT_SOME prints some of the transpose of an I4MAT.
• I4MAT_WRITE writes an I4MAT file.
• MESH_BASE_ONE ensures that the element definition is one-based.
• S_INDEX_LAST_C finds the LAST occurrence of a given character.
• 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.
• SORT_HEAP_EXTERNAL externally sorts a list of items into ascending order.
• TET_MESH_NEIGHBOR_TETS determines tetrahedron neighbors.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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