Catmull-Clark细分曲面的误差分析

Abstract

运用引入相邻点的方法和计算控制点的一阶差分的新的技术,研究Catmull Clark曲面细分过程的误差估计问题.证明了Catmull Clark曲面的控制网格按指数速率收敛于极限曲面;并给出关于Catmull Clark曲面误差估计的一个计算公式.本文的技术亦可适用于Doo Sabin曲面等细分曲面.

This paper studies error estimate of Catmull-Clark subdivision surfaces. The authors prove that the control polyhedron of Catmull-Clark surface converge to its limit surface in an exponential rate, and give a computing formula for error estimate of Catmull-Clark surfaces by using new methods of neighbor points of control points and first order difference of control points. The technique of this paper can be generalized to Doo-Sabin surfaces and other free form surfaces.