Bounding the distance between a loop subdivision surface and its limit mesh

Authors:
Zhangjin Huang;Guoping Wang
Affiliations:
School of Electronic Engineering and Computer Science, Peking University, Beijing, China;School of Electronic Engineering and Computer Science, Peking University, Beijing, China
Venue:
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Year:
2008

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Abstract

Given a control mesh of a Loop subdivision surface, by pushing the control vertices to their limit positions, a limit mesh of the Loop surface is obtained. Compared with the control mesh, the limit mesh is a tighter linear approximation in general, which inscribes the limit surface. We derive an upper bound on the distance between a Loop subdivision surface patch and its limit triangle in terms of the maximum norm of the mixed second differences of the initial control vertices and a constant that depends only on the valence of the patch's extraordinary vertex. A subdivision depth estimation formula for the limit mesh approximation is also proposed.