一种基于离散插值的多项式曲线逼近有理曲线的方法

doi:10.3785/j.issn.1008-9497.2017.06.009

摘要
图/表
参考文献
相关文章 (5)

全文: PDF (2121 KB) HTML( )
输出: BibTeX | EndNote (RIS)

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.

	服务

	把本文推荐给朋友
	加入我的书架
	加入引用管理器
	E-mail Alert
	RSS
	作者相关文章
	李光耀
	杨连喜
	徐晨东

关键词 ：有理曲线, 多项式曲线, 插值, 结式方法, Hausdorff距离

Abstract：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.

Key words： rational curve polynomial curve interpolation resultant method Hausdorff distance

收稿日期: 2016-05-25

ZTFLH:	O241.5
	TP391

基金资助:国家自然科学基金资助项目（11101230，11371209）.

通讯作者: 徐晨东,ORCID:http://orcid.org/0000-0002-2759-4123,E-mail:xuchendong@nbu.edu.cn. E-mail: xuchendong@nbu.edu.cn

作者简介: 李光耀(1991-),ORCID:http://orcid.org/0000-0001-6205-4803,男,硕士研究生,主要从事计算几何研究.

引用本文:

李光耀, 杨连喜, 徐晨东. 一种基于离散插值的多项式曲线逼近有理曲线的方法[J]. 浙江大学学报（理学版）, 2017, 44(6): 705-710.
LI Guangyao, YANG Lianxi, XU Chendong. A method on polynomial curve approximation of rational curves based on the discrete interpolation. Journal of ZheJIang University(Science Edition), 2017, 44(6): 705-710.

链接本文:

http://www.zjujournals.com/sci/CN/10.3785/j.issn.1008-9497.2017.06.009 或 http://www.zjujournals.com/sci/CN/Y2017/V44/I6/705

[1] DEBOOR C,HÖLLIG K,SABIN M.High accuracy geometric Hermite interpolation[J].Computer Aided Geometric Design,1987,4(4):169-178.
[2] YANG X N.High accuracy approximation of helices by quintic curves[J].Computer Aided Geometric Design,2003,20:303-317.
[3] FLOATER M S.High order approximation of rational curves by polynomial curves[J].Computer Aided Geometric Design,2006,23(8):621-628.
[4] HUANG Y D,SU H M,LIN H W.A simple method for approximating rational Bézier curve using Bézier curves[J].Computer Aided Geometric Design,2008,25(8):697-699.
[5] FARIN G.Curves and Surfaces for Computer Aided Geometric Design,A Practical Guide[M].5th ed. San Diego:Academic Press,2002.
[6] CHEN J,WANG G J.A new type of the generalized Bézier curves[J].Applied Mathematics:A Journal of Chinese Universities (Ser B),2011(1):47-56.
[7] 陈发来.曲面隐式化新发展[J].中国科学技术大学学报,2014,44(5):345-361. CHEN F L.Recent advances on surface implicitization[J].Journal of University of Science and Technology of China,2014,44(5):345-361.
[8] 陈发来.有理曲线的近似隐式化表示[J].计算机学报,1998,21(9):855-859. CHEN F L.The implicitization of ration curves[J].Chinese Journal of Computers,1998,21(9):855-819.
[9] 李彩云,朱春钢,王仁宏.参数曲线的分段近似隐式化[J].高校应用数学学报:A辑,2010,25(2):202-210. LI C Y, ZHU C G, WANG R H. Piecewise approximate implicitization of parametric curves[J]. Applied Mathematics:A Journal of Chinese Universities,2010,25(2):202-210.
[10] FLOATER M S.High order approximation of rational curves by polynomial curves[J].Computer Aided Geometric Design,2006,23(8):621-628.
[11] 杨连喜,徐晨东.一种用多项式曲线逼近有理曲线的新方法[J].浙江大学学报:理学版,2015,42(1):21-27. YANG L X,XU C D.New method of parametric polynomial curves approximation rational curves[J].Journal of Zhejiang University:Science Edition,2015,42(1):21-27