Smooth Subdivision of Tetrahedral Meshes

Abstract

We describe a new subdivision scheme for unstructured tetrahedral meshes. Previous tetrahedral schemes based on generalizations of box splines have encoded arbitrary directional preferences in their associated subdivision rules that were not reflected in tetrahedral base mesh. Our method avoids this choice of preferred directions resulting a scheme that is simple to implement via repeated smoothing. In an extended appendix, we analyze this tetrahedral scheme and prove that the scheme generates C2 deformations everywhere except along edges of the tetrahedral base mesh. Along edges shared by four or more tetrahedra in the base mesh, we present strong evidence that the scheme generates C1 deformations.