一类有理Bézier曲线及其求积求导的多项式逼近  

Approximating a kind of rational Bézier curves and their integral computation and derivatives using polynomial curves

作　　者：王国瑾[1] 胡倩倩[1] 

机构地区：[1]浙江大学数学系浙江大学国家重点实验室,浙江杭州310027

出　　处：《高校应用数学学报（A辑）》2004年第1期89-96,共8页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(60173034);国家重点基础研究973项目基金(G1998030600)

摘　　要：用多项式曲线来逼近有理曲线在计算机辅助几何设计(CAGD)系统中可简化求积求导等繁琐的计算.然而,按现有的方法能检验一条已知的有理曲线是否具有收敛的多项式逼近曲线却不易选择适当的权因子来产生能用多项式曲线来加以逼近的有理曲线,即不易做到事先设计;同时,要减少求积、求导的逼近误差只能依靠提高多项式曲线的次数.文中给出一类有理Bézier曲线及其多项式逼近算法较好地克服了这两种缺陷,具有推广应用的价值.In the system of computer aided geometric design(CAGD),using polynomial curves to approximate rational Bézier curves can simplify the onerous calculation in their integral computation and derivatives.The existing solution only tests whether a known rational curve has its corresponding convergent polynomial approximate curve.However,it is not easy to select proper weights to generate the rational curve which can be approximated by a polynomial curve.That is,designing it beforehand is not simple.At the same time,only does it depend on elevating the degree of the polynomial curve to diminish the approximate error of its integral computation and derivatives.This paper gives a kind of rational Bézier curves and the algorithm of its approximation using polynomial curves.It can overcome the two disadvantages above and has the value of application.

关 键 词：有理BÉZIER曲线 多项式逼近 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]