TETGEN
A Quality Tetrahedral Mesh Generator and 3D Delaunay Triangulator

TETGEN is a C++ program which can create a 3D mesh of tetrahedrons, suitable for use in finite element or finite volume calculations, with the mesh satisfying the 3D Delaunay criterion. The program is by Hang Si.

For a 3D point set, the program generates the Delaunay tetrahedralization and the convex hull.

For a 3D domain, in which the user has defined boundaries, the program can generate additional internal points, which are then organized into a boundary-constrained conforming quality Delaunay mesh.

tetgen works with the following files:

.node, (input/output), a list of nodes;
.poly, (input), a piecewise linear complex;
.smesh, (input/output), a simple piecewise linear complex;
.ele, (input/output), a list of tetrahedral elements;
.face, (input/output), a list of triangular faces;
.edge, (output), a list of boundary edges;
.vol, (input), a list of maximum volumes;
.var, (input), a list of variant constraints for facets or segments;
.neighb (output), a list of neighbors;

tetgen can read and write the following common polyhedral file formats:

.mesh, (input/output), Medit's surface mesh file format;
.off, (input/output), the polyhedral file format for Geomview;
.ply, (input), a polyhedral file format;
.stl, (input), the stereolithography file format;

Licensing:

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

Related Data and Programs:

BAMG, examples which illustrate the use of BAMG, a program for generating 2D meshes that can be used to define the geometry for the the finite element package FREEFEM++.

DIST_PLOT, a MATLAB program which creates a color contour plot of the distance functions that are used by DISTMESH.

DISTMESH, a MATLAB library which creates meshes, for 2D or 3D data.

DISTMESH_3D, a MATLAB program which is a subset of the DISTMESH routines, exclusively for 3D problems.

GMSH, examples which illustrate the use of the gmsh program, a 3D mesh generator for the finite element method (FEM).

MESH, a data directory which contains examples of MESH files, which can be used to define the geometry of a finite element mesh in 2D or 3D, using triangles, quadrilaterals, tetrahedrons or hexahedrons. These files can be viewed by the medit graphics program.

MESH2D, a MATLAB library which can automatically create a triangular mesh for a given polygonal region, by Darren Engwirda.

OFF, a data directory which contains examples of Object File Format (OFF) files, a Geomview file format for 3D graphics;

PLY, a data directory which contains examples of PLY files, a format for objects defined as a collection of polygons, 3D graphics;

POLY_3D, a data directory which contains examples of 3D POLY files, a 3D format used by tetgen and tetview, for a Piecewise Linear Complex.

STLA, a data directory which contains examples of ASCII stereolithography (STL) files for 3D graphics;

TETVIEW, examples of the use of TETVIEW which can display the 3D meshes and tetrahedralizations created by TETGEN.

Author:

Hang Si

Reference:

G Miller, D Talmor, S-H Teng, N Walkington, H Wang,
Control volume meshes using sphere packing: generation, refinement and coarsening,
Proceedings of the Fifth International Meshing Roundtable,
pages 47-61, 1996.
Hang Si,
TetGen: A Quality Tetrahedral Mesh Generator and 3D Delaunay Trianulator,
Version 1.4 User Manual,
Weierstrass Institute for Applied Analysis and Stochastics (WIAS),
16 January 2006.
Hang Si,
TetGen, a Delaunay-based quality tetrahedral mesh generator,
ACM Transactions on Mathematical Software,
Volume 41, Number 2, January 2015, 36 pages.

Examples and Tests:

CUBE starts with a "poly" file that describes a cube.

cube.poly

Then we give the command "tetgen -pq cube"

cube.1.ele, the mesh elements.
cube.1.face, the mesh faces.
cube.1.node, the mesh nodes.

ELLELL starts with a "ply" file that describes a building with L-shaped base and profile.

ellell.ply

Then we give the quality mesh command "tetgen -pq ellell"

ellell.1.ele, the mesh elements.
ellell.1.face, the mesh faces.
ellell.1.node, the mesh nodes.
ellell.1.png, a mesh image from tetview.

Then we give the refinement command "tetgen -ra0.1 ellell.1"

ellell.2.ele, the mesh elements.
ellell.2.face, the mesh faces.
ellell.2.node, the mesh nodes.
ellell.2.png, a mesh image from tetview.

EXAMPLE starts with just a "poly" file that describes a compensated magic tee junction, with 54 nodes and 29 faces. The poly file describes a piecewise linear complex (PLC).

example.poly

The command tetgen -pg example reads the PLC, and writes its constrained Delaunay tetrahedralization to node, element and face files. The additional "g" switch creates a ".mesh" file which can be used by the MEDIT graphics program.

example.poly
example.1.mesh
example.1.png, a snapshot of the region taking while viewing the mesh file with Medit.
example.1.node
example.1.ele
example.1.face
example.1.output.txt, the output file.

The command tetgen -pgq example reads the PLC and creates a quality mesh, with a quality ratio (circumradius to shortest edge) bounded by 2.0 (the default). The additional "g" switch creates a ".mesh" file which can be used by the MEDIT graphics program.

example.poly
example.1.mesh
example.1.png, a snapshot of the region taking while viewing the mesh file with Medit.
example.1.node
example.1.ele
example.1.face
example.1.output.txt, the output file.

The command tetgen -pgq1.414V example forces the quality ratio to be bounded by 1.414. The additional "g" switch creates a ".mesh" file which can be used by the MEDIT graphics program.

example.poly
example.1.mesh
example.1.png, a snapshot of the region taking while viewing the mesh file with Medit.
example.1.node
example.1.ele
example.1.face
example.1.output.txt, the output file.

Creating a "node" file, the command tetgen example now simply computes the Delaunay tetrahedralization and the convex hull of the given nodes.

You can go up one level to the Examples directory.