test_tet_mesh

test_tet_mesh, a FORTRAN90 code which sets test problems for mesh generation ("tetrahedralization") in 3D.

As far as possible, a uniform and abstract approach has been used. For each test region, a number of routines are provided, via which it is possible for the user to determine many things about the region. Often, just one or two routines would be needed for a particular purpose. The names of the routines, and their purposes are:

• BOUNDARY_NEAREST: returns the nearest point on the boundary of the region to a given point or set of points;
• BOUNDARY_PROJECT: projects exterior points onto the boundary.
• BOUNDARY_SEGMENT: returns a sequence of roughly equally spaced points that lie on one particular boundary segment;
• BOUNDARY_SEGMENT_LENGTH: returns the "length" (number of nodes) of a particular boundary segment. This simply counts the number of points needed to trace or approximate the boundary segment;
• BOUNDARY_SEGMENT_NUM: returns the number of boundary segments. Simple regions have one boundary segment. A region with one hole has two, and so on;
• BOX: returns a bounding box for the region. All points in the region are within this box;
• DENSITY: the value of the mesh density function at any point in the region. If this is not constant, then high values correspond to places where many more mesh points should be placed;
• ELEMENT_SIZE: returns a requested typical element size. This refers to the average size of the triangles formed by a triangulation of the points;
• FIXED_NUM: returns the number of points which must be included as nodes of the mesh (which may be zero);
• FIXED_POINTS: returns the coordinates of the points which must be included as nodes of the mesh;
• HEADER: prints a brief description of the problem;
• HOLE_NUM: returns the number of "holes" in the region;
• HOLE_POINT: returns the coordinates of one point in a hole (useful when TRIANGLE is to be invoked);
• INSIDE: reports which of a given set of points are inside the region.
• SAMPLE: returns a set of sample points from the region, chosen with uniform probability;
• SDIST: returns the signed distance to the boundary of the region for each of a set of input points. (a positive distance means the point is outside the region, a negative distance means it is inside); (Not ready for problems 4, 5, 6, 7, 8, 9 )
• TITLE: a title for the problem;

The test problems include:

1. The 3x1x1 channel;
2. The vertical cylinder, R = 1, H = 4;
3. The unit cube;
4. The unit sphere;

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

Licensing:

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

Languages:

test_tet_mesh is available in a FORTRAN90 version.

Related Data and Programs:

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

GEOMPACK, a FORTRAN90 code which contains a routine DTRIS3 that can compute the tet mesh for a set of 3D points, as well as the adjacency information.

KEAST, a FORTRAN90 code which defines a number of quadrature rules for a tetrahedron.

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

test_tet_mesh_test

TET_MESH, a FORTRAN90 code which is useful for tet mesh calculations.

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

Reference:

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

Source Code:

• test_tet_mesh.f90, the source code.
• test_tet_mesh.sh, compiles the source code.