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浙江大学学报(工学版)
J4  2009, Vol. 43 Issue (6): 999-1004    DOI: 10.3785/j.issn.1008-973X.2009.
计算机技术、自动化技术     
对数螺线段的多项式逼近与C-Bézier逼近
蔡华辉,王国瑾
(浙江大学 数学系计算机图像图形研究所,  CAD&CG国家重点实验室,浙江 杭州 310027)
Approximating logarithmic spiral segments by polynomial and C-Bézier
 CA Hua-Hui, WANG Guo-Jin
(State Key Laboratory of CAD&CG, Institute of Computer Images and Graphics, Zhejiang University,  Hangzhou 310027, China)
 全文: PDF(653 KB)  
摘要：

为了适合当前计算机辅助设计(CAD)系统中的曲线形式和工业设计中的美学需要, 提出了对数螺线段的两种逼近方法：（1）利用s-Power级数, 推导出s-Power系数的计算公式, 给出了对数螺线段的快速多项式逼近算法、对数螺线的等距曲线的具体表达式及其s-Power逼近算法；（2）首先推导出两端点C-Bézier形式的G2Hermite插值公式, 然后提出了对数螺线段的C-Bézie表示的G2Hermite插值逼近算法. 实例运算结果表明, 两种逼近方法是正确与有效的, 完全适合CAD系统使用．
关键词： 计算机辅助设计;  对数螺线;  逼近;  s-Power级数;  Hermite插值;  C-Bé;  zier    
Abstract:

To fit the curve forms  in  current computer aided design (CAD) systems and aesthetic needs in industrial designs, two approximation algorithms for logarithmic spiral segments were proposed. In the first method, the calculation formula for s-Power series was derived and a fast polynomial approximation algorithm was presented, and then the calculation formula for the offset curves of the logarithmic spiral and the corresponding approximation algorithm by s-Power series were presented. In the second method, the G2 Hermite interpolation  formula of  two end points by  C-Bézier form was firstly derived, and then  a G2 Hermite interpolation approximation algorithm by  C-Bézier form was presented. The computing results of examples show that these two approximation methods are correct and effective, suitable for the use of CAD systems．
Key words: computer aided design（CAD）    logarithmic spiral    approximation    s-Power series    Hermite interpolation    C-Bézier
出版日期: 2009-07-01
:  TP391  
基金资助:

国家自然科学基金资助项目(60873111)； 国家“973“重点基础研究发展规划资助项目(2004CB719400).
通讯作者: 王国瑾，男，教授, 博导.     E-mail: wanggj@zju.edu.cn
作者简介: 蔡华辉(1975－)，男，陕西安康人，博士生，主要从事计算机辅助几何设计与计算机图形学的研究.
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引用本文:

蔡华辉, 王国瑾. 对数螺线段的多项式逼近与C-Bézier逼近[J]. J4, 2009, 43(6): 999-1004.

CA Hua-Hui, WANG Guo-Jin. Approximating logarithmic spiral segments by polynomial and C-Bézier. J4, 2009, 43(6): 999-1004.

链接本文:

http://www.zjujournals.com/xueshu/eng/CN/10.3785/j.issn.1008-973X.2009.    或    http://www.zjujournals.com/xueshu/eng/CN/Y2009/V43/I6/999

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