带参数的Catmull-Clark细分曲面  

Catmull-Clark Subdivision Surfaces with Parameters

作　　者：田玉峰 陈发来[1] TIAN Yufeng;CHEN Falai(School of Mathematical Science, University of Science and Technology of China, Hefei 23002)

机构地区：[1]中国科学技术大学数学科学学院,合肥230026

出　　处：《系统科学与数学》2017年第10期2070-2084,共15页Journal of Systems Science and Mathematical Sciences

基　　金：国家自然科学基金(11571338)资助课题

摘　　要：在均匀B样条曲线的Lane-Riesenfeld细分算法中,每一步细分可看成是对原控制多边形的"切角"操作.文章通过引入一个参数来控制切角的程度,提出加权的Lane-Riesenfeld算法,并从均匀三次B样条曲线出发,得到光滑性为C^1的单参数曲线细分格式.进一步将该算法推广到任意拓扑的四边形网格上,得到除奇异点外处处C^1的细分曲面(称之为带参数的Catmull-Clark(C-C)细分曲面).格式中的参数在一定范围内调整时,可以使细分曲线/曲面不同程度地逼近控制多边形/控制网格,具有较好的灵活性.In Lane-Riesenfeld algorithm for uniform B-spline curves, each subdivision step can be regarded geometrically as the corner-cutting process of the control polygon. In this paper, we control the corner cutting＇s degree by introducing a parameter to derive a weighted Lane-Riesenfeld algorithm, and from which a C^1-continuous subdivision scheme is obtained. We further generalize the subdivision scheme to arbitrary topological quad-meshes which produces a family of C^1 continuous surfaces except at the extraordinary points（i.e., Catmull-Clark subdivision surfaces with parameters）. By adjusting the values of the parameter, we obtain different subdivision surfaces which approximate the control meshes with different degree.

关 键 词：Lane-Riesenfeld算法 样条曲线 细分曲线/曲面 CATMULL-CLARK细分曲面 

分 类 号：TP391.7[自动化与计算机技术—计算机应用技术]