Bézier Approximation of PDE Surface.pdfVIP

ISSN 1000-9825, CODEN RUXUEW E-mail: jos@ Journal of Software, Vol.18, No.11, November 2007, pp .2914−2920 DOI: 10. 1360/jos1 82914 Tel/Fax : +86-10 © 2007 by Journal of Software. All rights reserved. ∗ PDE 曲面的Bézier逼近 + 徐 岗, 汪国昭 (浙江大学 数学系 计算机图像图形研究所,浙江 杭州 310027) Bézier Approximation of PDE Surface + XU Gang , WANG Guo-Zhao (Institute of Image Processing and Computer Graphics, Department of Mathematics, Zhejia ng University, Hangzhou 310027, China) + Corresponding author: E-mail: xugangzju@, /cagd/ Xu G, Wang GZ. Bézier approximation of PDE surface. Journal of Software, 2007,18(11):2914−2920. /1000-9825/18/2914.htm Abstract: In order to exchange data between PDE (partial differential equation) modeling technique and the conventional CAD (computer aided design) systems, this paper presents a novel algorithm for approximating PDE surface by tensor product Bézier surface based on constrained optimization. The algorithm is also improved by the subdivision property of tensor product Bézier surface. The computational examples and the results of error analysis demonstrate the validity of the algorithm. Key words: PDE (partial differential equation) surface; least squares method; constrained optimization; subdivision of Bézier surface; CAD (computer aided design) system 摘 要: 为了实现PDE(partial differential equation)曲面造型技术与传统CAD(computer aided design)造型系统的 数据交换,基于约束优化的思想,给出了PDE 曲面的Bézier 逼近算法,并利用张量积Bézier 曲面的细分性质对该算 法进行了优化.所给出的计算实例及误差比较结果说明了该算法的有效性. 关键词: PDE(partial differential equation) 曲面;最小二乘法;约束优化; Bézier 曲面的细分;CAD(computer aided design) 系统 中图法分类号: TP391 文献标识码: A