TET_MESH_BOUNDARY

TET_MESH_BOUNDARY, a Fortran90 code which reads information defining a tetrahedral mesh of points in 3D, and determines the triangular faces that form the boundary of the mesh; it writes out files containing the nodes and elements defining this triangulated surface.

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.

Each tetrahedron has 4 triangular faces. Most of these faces will be shared by a neighbor tetrahedron, but some are not. It is precisely those faces that are not shared by a neighbor that constitute the boundary faces of the mesh.

The program identifies the triangular faces that form the boundary, and writes two files, a "boundary_node" file that lists the coordinates of the boundary nodes, and a "boundary_element" file that lists the (renumbered) indices of the boundary nodes used to form the boundary faces. This pair of files defines a triangulated 3D surface, or "TRI_SURFACE", and can be plotted, for instance, by tri_surface_display or tri_surface_display_open_gl.

The program also writes out a "boundary node mask" file, which reports the value 1 for each boundary node, and 0 for interior nodes. A boundary node is a node that occurs on a boundary face. This file is of use to the fem_to_mesh program.

Usage:

tet_mesh_boundary prefix

• prefix_nodes.txt, the node coordinates;
• prefix_elements.txt, the element definitions;
• prefix_boundary_node_mask.txt, is 0 for each interior node, 1 for each boundary node;
• prefix_boundary_nodes.txt, the boundary node coordinates;
• prefix_boundary_elements.txt, the boundary element definitions;

Licensing:

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

Languages:

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

Related Programs:

tet_mesh, a Fortran90 library which is useful for work with tet meshes.

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

tri_surface, a data directory which contains examples of TRI_SURFACE files, a 3D surface described by a collection of triangles.

tri_surface_display, a MATLAB program which displays the 3D graphics information in a TRI_SURFACE file;

tri_surface_display_opengl, a C++ program which displays the 3D graphics information in a TRI_SURFACE file using OpenGL.

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_boundary.f90, the source code.

Examples and Tests

CUBE is a tetrahedral mesh of a cube.

• cube_nodes.txt, the node file.
• cube_elements.txt, the element file.
• cube.png, an image of the tetrahedral mesh.
• cube_boundary_node_mask.txt, the boundary node mask file.
• cube_boundary_nodes.txt, the boundary node file.
• cube_boundary_elements.txt, the boundary element file.
• cube_output.txt, the printed output from the program.

P04 is a tetrahedral mesh of a sphere.

• p04_nodes.txt, the node file.
• p04_elements.txt, the element file.
• p04.png, an image of the tetrahedral mesh.
• p04_boundary_node_mask.txt, the boundary node mask file.
• p04_boundary_nodes.txt, the boundary node file.
• p04_boundary_elements.txt, the boundary element file.
• p04_output.txt, the printed output from the program.

List of Routines

• MAIN is the main program for TET_MESH_BOUNDARY.
• 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_SOME prints some of the transpose of an I4MAT.
• I4MAT_WRITE writes an I4MAT file.
• I4VEC_CUM computes the cumulutive sum of the entries of an I4VEC.
• MESH_BASE_ONE ensures that the element definition is one-based.
• R8MAT_DATA_READ reads data from an R8MAT file.
• 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.
• 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.
• SORT_HEAP_EXTERNAL externally sorts a list of items into ascending order.
• TET_MESH_BOUNDARY_COUNT counts boundary faces and nodes in a tet mesh.
• TET_MESH_BOUNDARY_SET sets the boundary faces in a tet mesh.
• TIMESTAMP prints the current YMDHMS date as a time stamp.

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