Anisotropic Triangular Meshing of Parametric Surfaces via Close Packing of Ellipsoidal Bubbles

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 x 3 tensor eld that speciies a desired anisotropic node-spacing, this new approach rst packs ellipsoids closely in the domain by deening proximity-based interacting forces among the ellipsoids and nding a force-balancing connguration using dynamic simulation. The centers of the ellipsoids are then connected by anisotropic Delaunay triangulation for a complete mesh topology. Since a speciied tensor eld controls the directions and the lengths of the ellipsoids' principal axes, the method generates a high quality anisotropic mesh whose elements conform precisely to the given tensor eld.