有理曲线的多项式逼近  

POLYNOMIAL APPROXIMATION OF RATIONAL CURVES

作　　者：陈效群[1,2] 陈发来[1,2] 陈长松[1,2] 

机构地区：[1]中国科学技术大学数学系 [2]合肥市中国科技大学数学系

出　　处：《高校应用数学学报（A辑）》1998年第B06期23-29,共7页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金;教委博士点基金;教委与科学院留学回国人员科研启动基金

摘　　要：利用曲线摄动的思想给出了用多项式曲线逼近有理曲线的一种新方法．其基本步骤是对有理曲线的控制顶点进行摄动，使之产生一多项式曲线，并使摄动误差在某种范数意义之下达到最小．同时，通过适当控制摄动曲线的顶点，使逼近多项式曲线与有理曲线在两端点保持一定的连续性．这一结果可以与细分（ｓｕｂｄｉｖｉｓｉｏｎ）技术结合给出有理曲线的整体光滑的分片多项式逼近．实例表明，在某些情况下本文中的方法要优于传统的Ｈｅｒｍｉｔｅ插值方法及Ｔ．Ｗ．Ｓｅｄｅｒｂｅｒｇ和Ｍ．Ｋａｋｉｍｏｔｏ（１９９１）提出的杂交曲线逼近算法．This paper presents a new approach to approximate rational curves with polynomial curves by perturbation method.The coeffcients of a rational curve under Bernstein bases is disturbed so as to get a polynomial curve,and such that the perturbation is minimized in L 2 norm.By constraining the perturbation it is possible to make the perturbed curve have certain order of contact with the rational curve at the two end points.This results can be combined with subdivision method to obtain a continuous piecewise polynomial approximation for a rational curve.Examples confirm that the approximation method presented in this paper is generally better than that of Hermite interpolation and hybrid curve approximation.

关 键 词：有理曲线 多项式曲线 杂交曲线 逼近 细分 HERMITE插值 

分 类 号：TP391.72[自动化与计算机技术—计算机应用技术]