tet_mesh, a FORTRAN90 code which constructs, describes, and modifies a mesh of tetrahedrons.

Linear and Quadratic Meshes

The simplest tet mesh, which we term an order 4 or linear mesh, uses four points to define each tetrahedron. A second type of mesh, known as an order 10 or quadratic mesh, uses ten points.

While an order 4 mesh can naturally be constructed directly from most sets of data points, a mesh of order 10 is not usually constructed directly from the data; at least in the simplest case, one wants the 6 extra nodes to be the midpoints of the sides determined by the 4 vertices.

Thus, an order 10 tet mesh is typically generated in two steps:

MATLAB has a command delaunay3 that can compute the tet mesh for a set of 3D points.


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


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

Related Programs:

CVT_TET_MESH, a FORTRAN90 code which uses CVT methods to compute a tet mesh in a region.

TABLE_TET_MESH, a FORTRAN90 code which computes the tet mesh for a given set of points.

TEST_TET_MESH, a FORTRAN90 code which defines a few test regions for the generation of a tet mesh.


TET_MESH_BOUNDARY, a FORTRAN90 code which returns the nodes and faces of the boundary of a tetrahedral mesh, which themselves form a 3D triangular mesh or "TRI_SURFACE".

TET_MESH_L2Q, a FORTRAN90 code which converts a linear to quadratic tet mesh.

TET_MESH_ORDER4, a data directory which contains a description and examples of a tet mesh using order 4 elements.

TET_MESH_ORDER10, a data directory which contains a description and examples of a tet mesh using order 10 elements.

TET_MESH_Q2L, a FORTRAN90 code which converts a quadratic to linear tet mesh.

TET_MESH_QUALITY, a FORTRAN90 code which computes the quality of a tet mesh.

TET_MESH_RCM, a FORTRAN90 code which takes a tet mesh and relabels the nodes to reduce the bandwidth of the corresponding adjacency matrix.

TET_MESH_REFINE, a FORTRAN90 code which refines a tet mesh.

TET_MESH_TET_NEIGHBORS, a FORTRAN90 code which computes the tetrahedral adjacency information.

TET_MESH_VOLUMES, a FORTRAN90 code which computes the volume of each tetrahedron in a tet mesh;


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Source code:

Last revised on 05 September 2020.