Efficient subdivision of finite-element datasets into consistent tetrahedra

This paper discusses the problem of subdividing unstructured mesh topologies containing hexahedra, prisms, pyramids and tetrahedra into a consistent set of only tetrahedra, while preserving the overall mesh topology. Efficient algorithms for volume rendering, iso-contouring and particle advection exist for mesh topologies comprised solely of tetrahedra. General finite-element simulations however, consist mainly of hexahedra, and possibly prisms, pyramids and tetrahedra. Arbitrary subdivision of these mesh topologies into tetrahedra can lead to discontinuous behavior across element faces. This will show up as visible artifacts in the iso-contouring and volume rendering algorithms, and lead to impossible face adjacency graphs for many algorithms. We present here, various properties of tetrahedral subdivisions, and an algorithm for determining a consistent subdivision containing a minimal set of tetrahedra.