TET_MESH_VOLUMES
Compute Tetrahedral Volumes in a Tet Mesh

TET_MESH_VOLUMES is a C++ program which computes the volume of every tetrahedron in a tet mesh.

Usage:

tet_mesh_volume prefix

• prefix_nodes.txt, the node coordinates;
• prefix_elements.txt, the element definitions.
• prefix_volumes.txt, will contain the element volumes.

The element definition file will list node indices. In C++, it may be more natural to use 0-based indices. This program will accept an element definition file that is 0-based or 1-based, and will convert a 1-based input file so that it becomes 0-based internal to the program. The detection of 1-based data is determined by the absence of the use of a 0 index, and the use of an index equal to the number of nodes. This is an implicit and fallible, but reasonable, way to handle this problem.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Related Data and Programs:

TET_MESH is a C++ library which carries out various operations on tetrahedral meshes.

TET_MESH_DISPLAY is a MATLAB program which reads in the node and tetra files defining a tet mesh and displays a wireframe image.

TET_MESH_DISPLAY_OPEN_GL is a C++ program which reads a 3D tet mesh and displays the nodes and edges using OpenGL.

TET_MESH_L2Q is a C++ program which reads information about a 4-node (linear) tet mesh and creates data defining a corresponding 10-node (quadratic) tet mesh;

TET_MESH_ORDER4, a data directory which contains a description of a linear tet mesh of a set of 3D points, using a pair of files to list the node coordinates and the 4 nodes that make up each tetrahedron;

TET_MESH_ORDER4, a dataset directory which contains examples of order 4 tetrahedral meshes.

TET_MESH_ORDER10, a data directory which contains a description of a quadratic tet mesh of a set of 3D points, using a pair of files to list the node coordinates and the 10 nodes that make up each tetrahedron;

TET_MESH_ORDER10, a dataset directory which contains examples of order 10 tetrahedral meshes.

TET_MESH_Q2L is a C++ program which reads information about a 10-node (quadratic) tet mesh and creates data defining a corresponding 4-node (linear) tet mesh;

TET_MESH_QUALITY is a C++ program which computes quality measures of a tetrahedral mesh.

TET_MESH_RCM is a C++ program which computes the reverse Cuthill-McKee reordering for the nodes of a tet mesh that uses 4-node or 10-node tetrahedrons;

TET_MESH_REFINE is a C++ program which refines a tet mesh;

TET_MESH_TET_NEIGHBORS, a data directory which contains examples of TET_MESH_TET_NEIGHBOR files, description of a format for tetrahedron adjacency information in a tetrahedral mesh of 3D points;

TET_MESH_TET_NEIGHBORS is a C++ program which reads information about a tet mesh and writes out a list of the tetrahedrons that are adjacent to a given tetrahedron;

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

Source Code:

• tet_mesh_volumes.C, the source code.
• tet_mesh_volumes.csh, commands to compile the source code.

Examples and Tests:

CUBE is the 8 vertices of the unit cube [0,1]x[0,1]x[0,1], defining 6 elements of equal volume but not equal shape.

• cube_nodes.txt, the node coordinate file.
• cube_elements.txt, the element file.
• cube.png, a PNG image of the mesh.
• cube_volumes.txt, the volume file.

TWENTY is 20 random nodes, defining 70 elements.

• twenty_nodes.txt, the node coordinate file.
• twenty_elements.txt, the element file.
• twenty.png, a PNG image of the mesh.
• twenty_volumes.txt, the volume file.

List of Routines:

• MAIN is the main program for TET_MESH_QUALITY.
• 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_EXIST reports whether a file exists.
• 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.
• R8MAT_DATA_READ reads data from an R8MAT file.
• R8MAT_DET_4D computes the determinant of a 4 by 4 matrix.
• R8MAT_HEADER_READ reads the header from an R8MAT file.
• R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.
• R8MAT_WRITE writes an R8MAT file.
• R8VEC_PRINT prints an R8VEC.
• R8VEC_VARIANCE returns the variance of an R8VEC.
• S_TO_I4 reads an I4 from a string.
• S_TO_I4VEC reads an I4VEC from a string.
• 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.
• TETRAHEDRON_VOLUME_3D computes the volume of a tetrahedron in 3D.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

You can go up one level to the C++ source codes.