圆弧的五次PH曲线等弧长逼近  

Arc-Length-Preserving Approximation of Circular Arcs by Quintic PH Curves

作　　者：张伟红[1,2] 蔡亦青[1] 冯玉瑜[1] 

机构地区：[1]中国科学技术大学数学系,合肥230026 [2]合肥师范学院数学系,合肥230061

出　　处：《计算机辅助设计与图形学学报》2010年第7期1082-1086,共5页Journal of Computer-Aided Design & Computer Graphics

基　　金：国家自然科学基金(60533060;10671192);新世纪优秀人才支持计划(NCET-08-0514)

摘　　要：针对圆弧多项式逼近中弧长不相等的问题,对给定圆弧在逼近多项式插值圆弧端点和端点切向量的条件下,结合PH曲线弧长可用多项式精确表示的性质,提出等弧长多项式逼近方法,并给出了五次PH多项式逼近圆弧的精确表示.最后通过实例说明了该方法的有效性.Most of the existing polynomial approximation methods of circular arcs do not preserve the arc lengths. To solve this problem, a new polynomial approximation method of circular arcs is proposed, where the result curves have the same endpoint positions, tangent vectors, and lengths as the given arcs. Here the PH curves are involved since their arc lengths can be represented using polynomial form. The accurate representations of the results in quintic PH curves are provided. Numerical examples are given to show the effectiveness of the new method.

关 键 词：圆弧 PH曲线 多项式逼近 

分 类 号：O241.5[理学—计算数学]