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J4  2009, Vol. 43 Issue (12): 2165-2170    DOI: 10.3785/j.issn.1008-973X.2009.12.007
自动化技术、计算机技术     
向量Padé逼近的改进及其在等距逼近上的应用
赵宏艳1,2,3,王国瑾1,2
(1.浙江大学 数学系,浙江 杭州 310027;2.浙江大学CAD&CG国家重点实验室,浙江 杭州 310027;3. 上海工程技术大学 基础教学学院, 上海 201620) 
Improved vector-valued Padé approximation and its application in offset approximation
ZHAO Hong-yan1,2,3, WANG Guo-jin1,2
(1.Department of Mathematics, Zhejiang University, Hangzhou 310027, China;
2.State Key Laboratory of CAD & CG, Zhejiang University, Hangzhou 310027, China;
3. College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai 201620, China)
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摘要:

为满足工业生产中CAD/CAM系统对等距曲线的表示和数据交换的特殊要求,提出一种可以产生任意次有理逼近的等距逼近新方法. 基于对传统的向量值Padé逼近方法的改进,提出向量类Padé逼近,可以实现以往各种有理等距逼近所不能执行、但为外形设计所迫切需要的低次逼近,因而应用价值显著.通过构造保端点插值的Padé逼近,综合运用曲线细分、中点展开构造等方法,可设计出任意次数的满足用户的特殊需要,达到预设精度的等距有理逼近. 大量实验表明,该算法简洁有效,适合于工程应用.

Abstract:

A new approximation method of offset curve was proposed in order to effectively meet the representation and data exchange requirements of CAD/CAM system in industry. Based on the improvement on the traditional vector-Padé approximation, the new method can generate low-order offset approximation, which is in urgent need for industry designing, but cannot be implemented by the existing methods. In this sense, the method has strong applicability. Endpoints interpolation was also considered together with curve subdivision and series expansion at midpoint, which helped to generate rational approximation under user-specified precision. Lots of experiments illustrated the feasibility and effectiveness of the proposed method.

出版日期: 2010-01-16
:  TP 391.41  
基金资助:

国家自然科学基金资助项目(60873111,60933007).

通讯作者: 王国瑾,男,教授,博导.     E-mail: wanggj@zju.edu.cn
作者简介: 赵宏艳(1981-),女,河南光山人,讲师,从事计算机辅助几何设计和计算机图形学研究.
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引用本文:

赵宏艳, 王国瑾. 向量Padé逼近的改进及其在等距逼近上的应用[J]. J4, 2009, 43(12): 2165-2170.

DIAO Hong-Yan, WANG Guo-Jin. Improved vector-valued Padé approximation and its application in offset approximation. J4, 2009, 43(12): 2165-2170.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2009.12.007        http://www.zjujournals.com/eng/CN/Y2009/V43/I12/2165


[1] HANSEN A, ARBAB F. An algorithm for generating NC tool paths for arbitrarily shaped pockets with islands
[J]. ACM Transactions on Graphics( TOG ), 1992, 11(2): 152-182.

[2] HELD M. On the computational geometry of pocket machining
[M]. Berlin: Springer-Verlag, 1991.

[3] CHEN Y J, RAVANI B. Offset surface generation and contouring in computer-aided design
[J]. ASME Journal of Mechanisms, Transmissions and Automation in Design, 1987, 109(3): 133-142.

[4] KURAGANO T. FRESDAM system for design of aesthetically pleasing freeform objects and generation of collision-free tool paths
[J]. Computer-Aided Design, 1992, 24(11): 573-581.

[5] PATRIKALAKIS N M, PRAKASH P V. Free-form plate modeling using offset surfaces
[J]. Journal of Offshore Mechanics and Arctic Engineering, 1988, 110(3): 287-294.

[6] FAROUKI R T, SAKKALIS T. Pythagorean hodographs
[J]. IBM Journal of Research and Development, 1990, 34(5): 736-752.

[7] LÜ Wei. Offset-rational parametric plane curves
[J]. Computer Aided Geometric Design, 1995, 12(6): 601-616.

[8] COBB E S. Design of sculptured surfaces using the B-spline representation
[D]. Salt Lake City: Department of Computer Science, University of Utah, 1984.

[9] TILLER W, HANSON E G. Offsets of two dimensional profiles
[J]. IEEE Computer Graphics and Application, 1984, 4(9): 36-46.

[10] KLASS R. An offset spline approximation for plane cubic splines
[J]. Computer-Aided design, 1983, 15(4): 297-299.

[11] PHAM B. Offset approximation of uniform B-splines
[J]. Computer-Aided design, 1988, 20(8): 471-474.

[12] HOSCHECK J. Spline approximation of offset curves
[J]. Computer Aided Geometric Design, 1988, 20(1): 33-40.

[13] SEDERBERG T W, BUEHLER D B. Offsets of polynomial Bezier curves: Hermite approximation with error bounds
[C] ∥LYCHE T, SCHUMAKER L L. Mathematical Methods in Computer Aided Geometric DesignⅡ. New York: Academic Press, 1992:549-558.

[14] PIEGL L A, TILLER W. Computing offsets of NURBS curves and surfaces
[J]. Computer-Aided Design, 1999, 31(2): 147-156.

[15] LI Y M, HSU V Y. Curve offsetting based on Legendre series
[J]. Computer Aided Geometric Design, 1998, 15(7): 711-720.

[16] LEE I K, KIM M S, ELBER G. Planar curve offset based on circle approximation
[J]. Computer-Aided Design, 1996, 28(8): 617-30.

[17] LEE I K, KIM M S, ELBER G. New approximation methods of planar offset and convolution curves
[C] ∥STRASSER W, KLEIN R, RAU R. Geometric Modeling: Theory and Practice. Berlin: Springer Verlag, 1997:83-101.

[18] LEE I K, KIM M S, ELBER G. Polynomial/ rational approximation of Minkowski sum boundary curves
[J]. Graphical Models and Image Processing, 1998, 60(2): 136-65.

[19] AHN Y J, KIM Y S, SHIN Y. Approximation of circular arcs and offset curves by Bezier curves of high degree
[J]. Journal of Computational and Applied Mathematics, 2004, 167(2): 405-416.

[20] CHENG M, WANG G J. Rational offset approximation of rational Bezier curves
[J]. Journal of Zhejiang University, 2006, 7(9): 1561-1565.

[21] BAKER G A, GRAVES-MORRIS P R. Padé approximants, partⅡ: Extension and Applications
[M]. London: Addison-wesley publishing company, 1981.

[22] 徐献瑜, 李家楷, 徐国良. Pade逼近概论
[M]. 上海: 上海科学技术出版社, 1990.

[23] GRAVES-MORRIS P R, JENKINS C D. Vector valued rational interpolants Ⅲ
[J]. Constructive Approximation., 1986, 2: 263-289.

[24] 王仁宏, 朱功勤. 有理函数逼近及其应用
[M]. 北京: 科学出版社, 2004.

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