基于双阶样条的代数双曲B样条升阶及割角算法  

Degree Elevation of Algebraic Hyperbolic B-spline Curves and Corner Cutting Based on Bi-order Spline

作　　者：张波[1] 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

出　　处：《计算机学报》2008年第6期1056-1062,共7页Chinese Journal of Computers

基　　金：国家自然科学基金(10371110;60473130);国家"九七三"重点基础研究发展规划项目基金(2004CB318000)资助~~

摘　　要：考虑代数双曲B样条曲线的升阶问题,从理论上证明了曲线的升阶可以理解为控制顶点的割角过程.为了实现代数双曲B样条曲线的升阶,文中构造了一组基函数——双阶代数双曲B样条基函数,这组基函数并不具有统一的阶数,而具有"双阶"性质.代数双曲B样条基函数与双阶样条基函数之间的变换公式可以导出曲线升阶的割角算法.The authors consider the degree elevation of algebraic hyperbolic （AH） B-spline curves and prove that the degree elevation of AH B-spline curves can be interpreted as corner cutting process in theory. A new class of basis functions, to be called bi order algebraic hyperbolic B-spline basis functions, is constructed and discussed by the integral definition of spline. This class of basis functions has bi-order property and the transforming formulae between AH B-spline and bi-order AH B-spline lead to the corner cutting for degree elevation of AH B-spline curves.

关 键 词：双阶样条 代数双曲B样条曲线 升阶 割角算法 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]