组合NURBS曲面转化Catmull-Clark曲面的多分辨率算法

Multi-resolution algorithm for the transformation from composite NURBS curved surface to Catmull-Clark curved surface

为了将多分辨率造型技术应用于NURBS形体,基于小波重构技术给出了组合NURBS曲面转化为Catmull-Clark曲面的多分辨率算法,可以实现NURBS形体的小波分解与重构等多分辨率操作。首先利用Catmull-Clark曲面求值公式计算出初始控制网格,通过计算拟合误差,利用局部插值算法计算小波系数,在此基础上,利用提升B样条小波重构公式构造出Catmull-Clark曲面,提出一种自适应算法,加快了曲面重构速度,运行实例验证了算法的有效性。

For the sake of letting the multi-resolution modeling technology be applied to the NURBS body, and based on wavelet reconstruction technique the multi-resolution algorithm for transforming the composite NURBS curved surface into the Catmull-Clark curved surface was given out. It may actualize the multi-resolution operation for the wavelet decomposition and reconstruction etc. of the NURBS body. Firstly work out the initial controlling grid by using the evaluation formula of Catmull-Clark curved surface; by means of computing the fitting errors and utilizing the partial interpolation algorithm to calculate the wavelet coefficient. Based on this foundation, utilizing upgrading the wavelet reconstruction formula of B spline to construct the Catmull-Clark curved surface and a kind of self-adapting algorithm was put forward, thus expedited the speed of curved surface reconstruction. The operational living example verified the effectiveness of this algorithm.