圆弧的低次多项式曲线等弧长逼近

doi:10.3969/j.issn.0253-2778.2011.05.003

中国科学技术大学学报 ›› 2011, Vol. 41 ›› Issue (5): 392-398.DOI: 10.3969/j.issn.0253-2778.2011.05.003

圆弧的低次多项式曲线等弧长逼近

王旭辉

1.合肥工业大学数学学院，安徽合肥 230009；2.中国科学技术大学数学科学学院，安徽合肥 230026

收稿日期:2010-02-05 修回日期:2010-04-30 出版日期:2011-05-31 发布日期:2011-05-31
通讯作者: 邓建松
作者简介:王旭辉，男，1980年生，博士生. 研究方向：计算机辅助几何设计. E-mail: wangxh05@mail.ustc.edu.cn
基金资助:
新世纪优秀人才支持计划（NCET-08-0514），高等学校学科创新引智计划（b07033），中央高校基本科研业务费专项资金（2010HGXJ0202）资助.

Arc-length preserving approximation of circular arcs by polynomial curves with lower degrees

WANG Xuhui

1.School of Mathematics, Hefei University of Technology, Hefei 230009, China; 2.School of Mathematics Science, University of Science and Technology of China, Hefei 230026,China

Received:2010-02-05 Revised:2010-04-30 Online:2011-05-31 Published:2011-05-31

摘要/Abstract

摘要： 主要研究了三次和四次多项式曲线等弧长逼近圆弧的求解算法.对于三次Bézier曲线，讨论了曲线弧长与相邻控制顶点之间距离的关系，从而得到稳定的数值方法求解曲线控制顶点.对于四次PH曲线，给出了等弧长逼近圆弧的精确解.实例表明，在保证弧长相等的条件下，低次多项式曲线能够较好地逼近圆弧.

关键词: 圆弧, 多项式逼近, Bézier曲线, PH曲线, 等弧长

Abstract: Arc-length-preserving approximation of circular arcs by cubic Bézier and quartic PH curves was discussed. For cubic Bézier curves, the relation between the length of the curve and the distance of adjacent control points was explored. Hence, a robust numerical method was derived to determine the control points of the curve. Accurate solutions were also provided for quartic PH curves to approximate circular arcs. The results show that polynomial curves with lower degrees can approximate circular arcs with high precision with the requirement of preserving arc-length.

Key words: circular arc, polynomial curve approximation, Bézier curve, PH curve, arc-length preserving

王旭辉，邓建松. 圆弧的低次多项式曲线等弧长逼近[J]. 中国科学技术大学学报, 2011, 41(5): 392-398.

WANG Xuhui, DENG Jiansong. Arc-length preserving approximation of circular arcs by polynomial curves with lower degrees[J]. Journal of University of Science and Technology of China, 2011, 41(5): 392-398.

圆弧的低次多项式曲线等弧长逼近

Arc-length preserving approximation of circular arcs by polynomial curves with lower degrees

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