Anisotropic triangulation of parametric surfaces via close packing of ellipsoids

Abstract

This paper describes a new computational method of fully automated anisotropic triangulation of a trimmed parametric surface. Given as input: (1) a domain geometry and (2) a 3 × 3 tensor field that specifies a desired anisotropic node-spacing, this new approach first packs ellipsoids closely in the domain by defining proximity-based interacting forces among the ellipsoids and finding a force-balancing configuration using dynamic simulation. The centers of the ellipsoids are then connected by anisotropic Delaunay triangulation for a complete mesh topology. Since a specified tensor field controls the directions and the lengths of the ellipsoids' principal axes, the method generates a graded anisotropic mesh whose elements conform precisely to the given tensor field.