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.
作者
田玉峰
陈发来
TIAN Yufeng;CHEN Falai(School of Mathematical Science, University of Science and Technology of China, Hefei 23002)
出处
《系统科学与数学》
CSCD
北大核心
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