论区间B样条曲线的升阶与割角的关系  

The Degree Elevation of Interval B-Spline Curves and Corner Cutting

作　　者：魏永伟[1,2] 汪国昭[1] 

机构地区：[1]浙江大学数学系计算机图象图形研究所,杭州310027 [2]上海海事大学应用数学系,上海201306

出　　处：《计算机辅助设计与图形学学报》2010年第2期306-311,共6页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(60773179);国家"九七三"重点基础研究发展计划项目(2004CB318000)

摘　　要：为了解决区间B样条曲线的升阶理论问题,提出区间控制多边形概念,利用双次B样条基函数证明了区间B样条曲线具有升阶性质;并阐明了区间B样条曲线的升阶就是对其控制多边形的割角过程.最后证明了当升阶次数趋于无穷时,区间B样条曲线的控制多边形收敛到该曲线.This paper investigates degree elevation of interval B-spline. Based on the concept of interval control polygon, we prove that interval B-spline curves hold the degree elevation property by using bi- degree B-spline basis functions. Further, we show that the degree elevation of interval B-spline curves is equivalent to corner cutting of control polygons. Finally, it＇s proved that the control polygon sequence by degree elevation will converge to the interval B-spline curve.

关 键 词：区间B样条曲线 区间控制多边形 双次B样条基函数 升阶 割角 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]