Anisotropic triangulation of parametric surfaces via close packing of ellipsoids

This paper describes a new computational method of fully automated anisotro pic triangulation of a trimmed parametric surface. Given as input: (1) a do main geometry and (2) a 3 x 3 tensor field that specifies a desired anisotr opic 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 c enters of the ellipsoids are then connected by anisotropic Delaunay triangu lation for a complete mesh topology. Since a specified tensor field control s the directions and the lengths of the ellipsoids' principal axes, the met hod generates a graded anisotropic mesh whose elements conform precisely to the given tensor field.