摘要
本文推导了在分段矩阵表示下的三次均匀 B 样条曲线段的非均匀细分变换的通用公式,其结果发展了 J.M.Lane、R.F.Riesenfeld(1980)和施法中(1988)从不同角度提出的均匀 B 样条曲线段的对分原理,具有更广泛的通用性。依据公式,本文给出了三次均匀 B 样条曲线、曲面的细分算法,在计算机辅助几何设计和计算机图形中学具有广泛的实用价值。
This paper presents the general transforming matrix between new vertices and old vertices for splitting non-uniformly the B-Spline curve segment.The result obtained in this paper extends and improves the subdivision principle presented by Lane,J.M.and Riesenfeld,R.F.in 1980,and by Shi Fazhong in 1988 in different forms,and has a wide generality.Accordlng to the general formulae, this paper presents the two algorithms for splitting non-uniformly the uniform B-Spline curve segment and surface patch.They have a widespread practical vaiue in computer aided geometric design and computer graphics
关键词
CAD
计算机图形学
B样条
细分
computer aided geometric design
computer graphics
B-Spline
subdivision
algorithm
