带矩阵权值的Catmull-Clark细分曲面渐进插值算法  

Progressive Interpolation Method of Catmull-Clark Subdivision Surface with Matrix Weight

作　　者：张莉[1] 佘祥荣 葛先玉 檀结庆[1,2] Zhang Li;She Xiangrong;Ge Xianyu;Tan Jieqing(School of Mathematics,Hefei University of Technology,Hefei 230009;School of Computer and Information,Hefei University of Technology,Hefei 230009)

机构地区：[1]合肥工业大学数学学院,合肥230009 [2]合肥工业大学计算机学院,合肥230009

出　　处：《计算机辅助设计与图形学学报》2019年第8期1312-1319,共8页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(61472466,61100126)

摘　　要：提出一种带矩阵权值的Catmull-Clark细分曲面渐进插值算法,旨在进一步解决渐进插值算法不能插值细分曲面法向量的局限.首先为渐进插值算法赋一个3′3的矩阵类型的权值,称之为矩阵权值,通过选取不同的矩阵权值来控制渐进插值算法的收敛速度和极限曲面的形状,并插值细分曲面法向量来实现细分曲面的光顺;其次,算法中矩阵权值可分解为2个矩阵之和,分别控制收敛速度和曲面形状及光顺;再次,文中还给出了2种矩阵权值的选取方法,即采用对角矩阵实现对x,y,z各分量收敛速度的控制;最后,采用旋转矩阵调整顶点位置实现极限曲面的光顺.文末给出大量的数值实例,展示了矩阵权值的作用.One progressive interpolation method of Catmull-Clark subdivision surface with matrix weight is presented in this paper.It aims to interpolate the normal vector of subdivision surface which normal progressive interpolation algorithm can’t make.First,a 3×3 weight matrix is presented as the weight of the given progressive interpolation method.Different matrix weights have been given in order to not only control convergence speeds and shapes but also interpolate the normal vector so as to smooth the limit surface.Second,the weight matrix can be decomposed into the sum of two matrices,one controls the convergence rate,the other controls the surface shape and smoothness.This paper also presents two different ways to determine the weight matrix.One is designing the diagonal matrix in order to control the convergence speed of x,y,z components.The other is designing the rotation matrix in order to iteratively adjust the vertex position and smooth the limit surface.At the end of this paper,a large number of numerical examples are given to demonstrate the effects of matrix weights.

关 键 词：细分曲面 渐进插值 任意拓扑网格 矩阵权值 

分 类 号：TP391.41[自动化与计算机技术—计算机应用技术]