一种基于离散插值的多项式曲线逼近有理曲线的方法  

A method on polynomial curve approximation of rational curves based on the discrete interpolation

作　　者：李光耀 杨连喜[1] 徐晨东[1] 

机构地区：[1]宁波大学理学院,浙江宁波315211

出　　处：《浙江大学学报（理学版）》2017年第6期705-710,共6页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(11101230;11371209)

摘　　要：提出了一种用多项式曲线插值逼近有理曲线的方法.首先,构造一条含参数的多项式曲线,令其插值于有理曲线的一些固定点处,求解相应的方程得到待定参数的值,从而确定多项式插值曲线.然后,采用离散的Hausdorff距离计算插值曲线与有理曲线之间的误差,典型数值算例表明,本文方法具有较好的可行性.This paper presents a method for interpolating rational curves with polynomial curves.Firstly,we construct a polynomial curve with some undetermined parameters,and let this polynomial curve interpolate the given rational curve at some fixed points.By solving the corresponding equation of undetermined parameters,a suitable polynomial interpolation curve is formed.The error between the rational curve and the polynomial interpolation curve is estimated based on discrete Hausdorff distance.Some typical numerical examples illustrate the effectiveness of this method.

关 键 词：有理曲线 多项式曲线 插值 结式方法 HAUSDORFF距离 

分 类 号：O241.5[理学—计算数学] TP391[理学—数学]