TETRAHEDRONS
Examples of Tetrahedrons

TETRAHEDRONS is a dataset directory which contains definitions of some example tetrahedrons.

Licensing:

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

Related Data and Programs:

FELIPPA, a C++ library which defines quadrature rules for lines, triangles, quadrilaterals, pyramids, wedges, tetrahedrons and hexahedrons.

GEOMETRY, a C++ library which performs geometric calculations in 2, 3 and N dimensional space.

GM_RULE, a C++ library which defines Grundmann-Moeller rules for quadrature over a triangle, tetrahedron, or general M-dimensional simplex.

KEAST, a C++ library which defines a number of quadrature rules for a tetrahedron.

NCC_TETRAHEDRON, a C++ library which defines Newton-Cotes Closed quadrature rules on a tetrahedron.

NCO_TETRAHEDRON, a C++ library which defines Newton-Cotes Open quadrature rules on a tetrahedron.

QUADRATURE_RULES_TET, a dataset directory which contains quadrature rules for tetrahedrons, stored as a file of abscissas, a file of weights, and a file of vertices.

TETRAHEDRON_PROPERTIES, a FORTRAN90 program which computes properties of a given tetrahedron.

Reference:

1. Marshall Bern, Paul Chew, David Eppstein, Jim Ruppert,
   Dihedral Bounds for Mesh Generation in High Dimensions,
   Proceedings of the Sixth Annual ACM-SIAM Symposium on Discrete Algorithms (SODA),
   SIAM, 1995,
   ISBN13: 978-0898713497,
   LC: QA76.9.A43.A34a.
2. Anwei Liu, Barry Joe,
   Quality Local Refinement of Tetrahedral Meshes Based on 8-Subtetrahedron Subdivision,
   Mathematics of Computation,
   Volume 65, Number 215, July 1996, pages 1183-1200.

Data Files:

TET_CAP is an example of a "cap" tetrahedron. A cap has one wide solid angle. This example has a volume of 1.

• tet_cap.txt, the node coordinates.

TET_EQUILATERAL is an example of an "equilateral" tetrahedron. This example has a volume of 8/3.

• tet_equilateral.txt, the node coordinates.

TET_EXAMPLE1 is tetrahedron example 1. This example has a volume of 8/3.

• tet_example1.txt, the node coordinates.
• tet_example1.png, a PNG image.

TET_EXAMPLE2 is tetrahedron example 2. It is a rhombic tetrahedron. This example has a volume of 2/3.

• tet_example2.txt, the node coordinates.
• tet_example2.png, a PNG image.

TET_EXAMPLE3 is tetrahedron example 3. This example has a volume of 1.

• tet_example3.txt, the node coordinates.

TET_NEEDLE is an example of a "needle" tetrahedron. A needle has good dihedral angles, and one small solid angle. This example has a volume of 1.

• tet_needle.txt, the node coordinates.

TET_REFERENCE is the reference tetrahedron. This example has a volume of 1/6.

• tet_reference.txt, the node coordinates.

TET_RIGHT is an example of a right tetrahedron. This example has a volume of 1.

• tet_right.txt, the node coordinates.

TET_SLIVER is an example of a "sliver" tetrahedron. A sliver is one of the hardest degenerate tetrahedrons to detect and remove from a mesh. It has a mixture of small and large dihedral angles. This example has a volume of 1.

• tet_sliver.txt, the node coordinates.

TET_SPINDLE is an example of a "spindle" tetrahedron. The spindle has two small solid angles and large dihedral angles. This example has a volume of 1.

• tet_spindle.txt, the node coordinates.

TET_WEDGE is an example of a "wedge" tetrahedron. The wedge has small dihedral angles and small solid angles. This example has a volume of 1.

• tet_wedge.txt, the node coordinates.

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