TABLE_TET_MESH
A Tet Mesh of Points in 3D

TABLE_TET_MESH is a FORTRAN90 program which computes the Delaunay tet mesh of a set of points in the 3D.

Specifically, TABLE_TET_MESH reads a data file containing the coordinates of a set of points in 3D, computes the Delaunay tet mesh, and writes out a file of sets of four node indices that form a mesh of tetrahedrons.

The input node coordinate data file and the output tetrahedron node index file are in the simple TABLE file format, one set of node coordinates or one set of four node indices, respectively, on each line.

A tet mesh of 3d points is the analog of the triangularization of points in 2d. In other words, it is a maximal organization of the points into nonintersecting tetrahedrons. Since it is a Delaunay tet mesh, it has the additional property that, of all maximal tet meshes, this one has the largest minimum angle.

Usage:

table_tet_mesh nodes.txt

reads the node coordinates in nodes.txt, computes the tetrahedron information, and writes it to the file nodes.tetras.txt.

Related Programs:

CVT_TET_MESH is an executable FORTRAN90 program which uses CVT methods to compute a tet mesh in a region.

GEOMPACK3 is a FORTRAN90 library, written by Barry Joe, from which some routines were extracted for computing the tet mesh.

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

MESH_BANDWIDTH is an interactive executable FORTRAN90 program which returns the geometric bandwidth associated with a mesh of elements of any order and in a space of arbitrary dimension.

TABLE is the format used for the input to this program.

TABLE_BARPLOT_PPMA is an executable FORTRAN90 program which reads a table file and creates a PPMA bargraph of the data.

TABLE_BORDER is an executable FORTRAN90 program which can be used to add a border (of zero values) to a table file.

TABLE_COLUMNS is an executable FORTRAN90 program which can extract specific columns of data from a table file.

TABLE_COLUMNS_PERMUTE is an executable FORTRAN90 program which permutes the columns of a table file.

TABLE_DELAUNAY is an executable FORTRAN90 program which computes the Delaunay triangulation of a set of points.

TABLE_DIAPHONY is an executable FORTRAN90 program which computes the diaphony of a set of points stored in a table file.

TABLE_HISTOGRAM is an executable FORTRAN90 program which can make a histogram of a set of points stored in a table file.

TABLE_IO is a FORTRAN90 library which supplies the routines used to read the TABLE file.

TABLE_LATINIZE is an executable FORTRAN90 program that reads a file of points and creates a "latinized" version by adjusting the data.

TABLE_MERGE is an executable FORTRAN90 program that reads a file of points, and removes duplicates, and points that are close to each other.

TABLE_ORTHONORMALIZE is an executable FORTRAN90 program that reads a file of points and orthonormalizes the columns.

TABLE_QUALITY is an executable FORTRAN90 program that reads a file of points and computes the quality of dispersion.

TABLE_READ is a MATLAB script that can read in a TABLE file.

TABLE_RECORD_MATCH is an executable FORTRAN90 program that can be used to find close records in a table file.

TABLE_SCALE is an executable FORTRAN90 program that can be used to multiply the entries of a table file by a scale vector.

TABLE_SHIFT is an executable FORTRAN90 program that can be used to shift the entries of a table file by a shift vector.

TABLE_STATS is an executable FORTRAN90 program that can read a table file and compute certain statistics.

TABLE_TOP is an executable FORTRAN90 program that can read a table file of M-dimensional data and make a table of plots of all pairs of coordinates.

TABLE_UNBORDER is an executable FORTRAN90 program that can be used to remove the border from a table file.

TABLE_UNIFORM_NOISE is an executable FORTRAN90 program that can be used to add a uniform noise term to the data in a table file.

TABLE_VORONOI is an executable FORTRAN90 program which can be used to compute information about the Voronoi diagram of the points.

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

TET_MESH_DISPLAY is a 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 a FORTRAN90 program which can read in the node and tetra files defining a 4-node tet mesh and write out files for a 10-node tet mesh by adding midside nodes.

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

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

TET_MESH_Q2L is an executable FORTRAN90 program which converts a quadratic to linear tet mesh.

TET_MESH_QUALITY is an executable FORTRAN90 program which computes the quality of a tet 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_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,
   QA377.E36,
   ISBN 0-521-79309-2.
2. Barry Joe,
   GEOMPACK - a software package for the generation of meshes using geometric algorithms,
   Advances in Engineering Software,
   Volume 13, pages 325-331, 1991.
3. Per-Olof Persson, Gilbert Strang,
   A Simple Mesh Generator in MATLAB,
   SIAM Review,
   Volume 46, Number 2, pages 329-345, June 2004.

Source Code:

• table_tet_mesh.f90, the source code.
• table_tet_mesh.csh, commands to compile, link and load the source code.

Examples and Tests:

CUBE is a simple dataset of 8 nodes:

• cube_nodes.txt, the coordinates of 8 nodes that form the vertices of a cube.
• cube_nodes_tetras.txt, the tetrahedron file.

P01_00050 is a dataset of 50 nodes in a 3x1x1 channel.

• p01_00050_nodes.txt, the coordinates of 50 nodes.
• p01_00050_tetras.txt, the tetrahedron file.
• p01_00050_output.txt, the output file.

P01_00400 is a dataset of 400 nodes in a 3x1x1 channel.

• p01_00400_nodes.txt, the coordinates of 400 nodes.
• p01_00400_tetras.txt, the tetrahedron file.
• p01_00400_output.txt, the output file.

P01_03200 is a dataset of 3200 nodes in a 3x1x1 channel.

• p01_03200_nodes.txt, the coordinates of 3200 nodes.
• p01_03200_tetras.txt, the tetrahedron file.
• p01_03200_output.txt, the output file.

List of routines:

• MAIN is the main program for TABLE_TET_MESH.
• AVAILF returns the index of the next available record in the FC array.
• BARYTH computes barycentric coordinates of a point in 3D.
• CCSPH finds the circumsphere through the vertices of a tetrahedron.
• 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.
• DHPSRT sorts a list of double precision points in KD.
• DLESS determines the lexicographically lesser of two double precision values.
• DSFTDW does one step of the heap sort algorithm for double precision data.
• DTABLE_DATA_PRINT_SOME prints some of a real table dataset.
• DTABLE_DATA_READ reads real table data from a file.
• DTABLE_HEADER_READ reads header data from a file.
• DTRIS3 constructs a Delaunay triangulation of vertices in 3D.
• 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.
• FRSTET shifts vertices so the first 4 vertices are in general position in 3D.
• GET_UNIT returns a free FORTRAN unit number.
• HTDEL deletes a record from the hash table.
• HTINS inserts a record into the hash table.
• HTSRC searches for a record in the hash table.
• I4_MODP returns the nonnegative remainder of integer division.
• I4_SWAP swaps two I4's.
• I4_WRAP forces an integer to lie between given limits by wrapping.
• I4MAT_TRANSPOSE_PRINT prints an I4MAT, transposed.
• I4MAT_TRANSPOSE_PRINT_SOME prints some of the transpose of an I4MAT.
• ITABLE_DATA_WRITE writes an integer table dataset to a file.
• ITABLE_HEADER_WRITE writes the table header data to a file.
• ITABLE_TETRA_WRITE writes an integer tet mesh table to a file.
• NWTHOU creates new tetrahedra outside the current convex hull.
• OPSIDE tests if points are on opposite sides of a triangular face.
• ORDER3 reorders 3 integers into ascending order.
• 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_R8 reads an R8 from a string.
• S_TO_R8VEC reads an R8VEC from a string.
• S_WORD_COUNT counts the number of "words" in a string.
• SWAPES swaps faces in a 3D triangulation.
• TETLST constructs a list of tetrahedra from the FC array.
• TIMESTAMP prints the current YMDHMS date as a time stamp.
• TIMESTRING writes the current YMDHMS date into a string.
• UPDATF updates a record in FC after a local transformation.
• VBFAC determines the boundary faces of a 3D triangulation.

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