# Bounding the Distance between a Loop Subdivision Surface and Its Limit Mesh

• Zhangjin Huang
• Guoping Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4975)

## 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.

## Keywords

Loop subdivision surfaces Limit mesh Error bound Subdivision depth

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