How to Subdivide Pyramids, Prisms, and Hexahedra into Tetrahedra

This paper discusses the problem of subdividing meshes containing tetrahedra, pyramids, prisms or hexahedra into a consistent set of tetrahedra. This problem occurs in computer graphics where meshes with pyramids, prisms or hexahedra must be subdivided into tetrahedra to use efficient algorithms for volume rendering, iso-contouring and particle advection. Another application is for the use of some tetrahedral finite element solvers on a non tetrahedral mesh, or even an hybrid mesh. Arbitrary splitting of quadrilateral faces into two triangles has two major drawbacks: it can lead to discontinuities across element faces, resulting in non conformal meshes, and the subdivision of some elements into tetrahedra may need to introduce new vertices. The algorithms presented in this paper split each quadrilateral face of pyramids, prisms and hexahedra in a consistent way that preserves the conformity of the mesh. Elements are subdivided into tetrahedra without introducing new vertices. The algorithms are fast, generic, robust, and local, i.e. they do not need any neighboring information.