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

Shimada, Kenji, Atsushi Yamada and Takayuki Itoh

Proceedings, 6th International Meshing Roundtable, Sandia National Laboratories, pp.375-390, October 1997


Kenji Shimada
Carnegie Mellon University

Atsushi Yamada and Takayuki Itoh
IBM Research, Tokyo Research Laboratory

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 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 high quality anisotropic mesh whose elements conform precisely to the given tensor field.

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