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.


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:


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


  1. Herbert Edelsbrunner,
    Geometry and Topology for Mesh Generation,
    Cambridge, 2001,
    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:

You can go up one level to the DATA page.

Last revised on 17 January 2007.