TET_MESH_TET_NEIGHBORS
Adjacency information in a tetrahedral mesh

TET_MESH_TET_NEIGHBORS is a data directory which contains examples of a format for recording tetrahedral adjacency in a tetrahedral mesh of 3D points.

The tetrahedral mesh is presumed to be constructed in such a way that the only possible adjacency occurs if two tetrahedrons share a face. A tetrahedron has four faces, and hence may have anywhere from 0 to 4 neighbors. The faces and neighbors are conveniently associated with the index of the single tetrahedron vertex that is not part of the shared face. Thus neighbor 1 is presumed to share the face constructed from local nodes 2, 3 and 4. If there is no neighbor sharing a particular face, the index of that neighbor is recorded as -1.

This adjacency information is derived from the more fundamental data structures that define the tetrahedral mesh. For more information, see order 4 tet mesh format or order 10 tet mesh format.

The neighbor information may be stored as an array with 4 rows and TETRA_NUM columns, or it may be written to a file of TETRA_NUM lines, each containing the indices of the four neighbors of the corresponding tetrahedron.

Example TET_MESH_TET_NEIGHBORS File:

For a tetrahedral mesh with 6 tetrahedrons, here is what a file might look like that contained the adjacency information:

       -1  2 -1  3
       -1  1 -1  5
       -1  1  4 -1
       -1  6  3 -1
       -1  2  6 -1
       -1  4  5 -1
      

TET_MESH_TET_NEIGHBORS File Characteristics:

• ASCII

Licensing:

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

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 and Gilbert Strang,
   A Simple Mesh Generator in MATLAB,
   SIAM Review,
   Volume 46, Number 2, pages 329-345, June 2004.

Sample Files:

CUBE is a tetrahedral mesh that dissects a cube. The files include:

• cube_nodes.txt, the node file for a linear tet mesh of a cube;
• cube_elements.txt, the tetra file for a linear tet mesh of a cube;
• cube_element_neighbors.txt, the neighbor file for a linear tet mesh of a cube;

You can go up one level to the DATA page.