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应用科学学报 ›› 2006, Vol. 24 ›› Issue (3): 278-282.

• 论文 • 上一篇    下一篇

等距曲线有理逼近的一种方法

郭清伟1,2   

  1. 1. 复旦大学数学所, 上海 200433;
    2. 合肥工业大学理学院, 安徽合肥 230009
  • 收稿日期:2004-10-29 修回日期:2005-05-30 出版日期:2006-05-31 发布日期:2006-05-31
  • 作者简介:郭清伟,副教授,博士,研究方向:数值逼近、计算机辅助几何设计,E-mail:qwguo-hffd@sohu.com
  • 基金资助:
    国家自然科学基金资助项目(60473114)

A Method for Rational Approximation of Offset Curves

GUO Qing-wei1,2   

  1. 1. Institute of Mathematics, Fudan University, Shanghai 200433, China;
    2. Department of Mathematics, Hefei University of Technology, Hefei 230009, China
  • Received:2004-10-29 Revised:2005-05-30 Online:2006-05-31 Published:2006-05-31

PDF

100

被引次数

7

摘要： 利用多项式逼近平面Bézier多项式曲线的参数速度模长,得到Bézier多项式曲线的等距曲线的有理逼近曲线,所得有理逼近曲线与等距曲线在端点处能够达到高阶插值.该方法与离散算法相结合,可得到等距曲线的高阶连续的有理样条逼近曲线,最后,通过数值实例与已有方法作了比较.

关键词: Bézier曲线, 等距曲线, 有理逼近, 离散

Abstract: The rational approximation of offset curve of Bézier curve is obtained when a polynomial is used to approximate the norm of parametric speed of Bézier curve.The obtained rational curve and the offset curve of Bézier curve have the same higher derivates at the endpoints.If the method is combined with the subdivision method of curve, the rational spline curve with higher-order continuity is presented which is the approximation of offset curve.Numerical examples are given to show effectiveness of the method.The results are compared with other methods, and conclusions are made based on the numerical examples.

Key words: Bézier curves, rational approximation, subdivision, offset curves

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