Tetrahedralization of Isosurfaces with Guaranteed-Quality by Edge Rearrangement (TIGER)

We present a method for generating three-dimensional (3-D) unstructured tetrahedral meshes of solids whose boundary is a smooth surface. The method uses a background grid (bodycentered-cubic (BCC) lattice) from which to build the final conforming 3-D mesh. The algorithm is fast and robust and provides useful guaranteed dihedral angle bounds for the output tetrahedra. The dihedral angles are bounded between 8.5◦ and 164.2◦. If the lattice spacing is smaller than the “local feature size,” then the dihedral angles are between 11.4◦ and 157.6◦ (cf. Labelle and Shewchuk [SIGGRAPH ’07, ACM, New York, 2007]). The method is simple to implement and performs no extra refinement of the background grid. The most complicated mesh transformations are 4-4 edge flips. Moreover, the only parameter in the method is the BCC lattice spacing. If the surface has bounded curvature and if the background grid is sufficiently fine, then the boundary of the output mesh is guaranteed to be a geometrically and topologically accurate approximation of the solid surface. Applications of the method are in free boundary flows, modeling deformations, shape optimization, and anything that requires dynamic meshing, such as virtual surgery.