TET_MESH_BOUNDARY
Triangular Surface Formed by Tet Mesh Boundary

TET_MESH_BOUNDARY is a MATLAB program 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 "TRI_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. (The present version of the program will only handle the 4 node case.)

Each tetrahedron has 4 triangular faces. Most of these faces will be shared by a neighbor tetrahedron, but those faces that are not shared by a neighbor constitute the boundary 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 nodes, and a "boundary_element" file that lists the indices of the nodes used to form the faces. This pair of files defines a triangulated 3D surface, or "TRI_SURFACE".

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 GNU LGPL license.

Languages:

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

Related Programs:

TET_MESH, a MATLAB 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.m, 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.

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.

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