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J4  2010, Vol. 44 Issue (5): 887-892    DOI: 10.3785/j.issn.1008-973X.2010.05.009
自动化技术、计算机技术     
基于广义逆矩阵的张量积Bézier曲面合并逼近
朱平1,2, 汪国昭1
1.浙江大学 计算机图像图形研究所,浙江 杭州 310027; 2.东南大学 数学系,江苏 南京 211189
Approximate merging of tensor product Bézier surfaces based on
generalized inverse matrix
ZHU Ping1,2, WANG Guo-zhao1
1. Institute of Computer Graphics and Image Processing, Zhejiang University, Hangzhou 310027, China;
2. Department of Mathematics, Southeast University, Nanjing 211189, China
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摘要:

为了对CAD系统中的几何数据进行压缩,研究2张相邻张量积Bézier曲面合并逼近的问题.为了更好地进行曲面合并逼近,利用张量积Bézier曲面细分后的矩阵表示给出相邻张量积曲面可精确合并的充要条件,在此基础上通过广义逆矩阵的方法求解出在L2范数下合并逼近后的张量积Bézier曲面,得到其控制顶点的显示表达式.同时给出带角点插值条件的曲面合并逼近的结果.利用广义逆矩阵可以方便地求得最小二乘解,得到能够显示表示、算法执行时间最短且逼近效果好的合并逼近算法.数值实例显示了算法的有效性.

Abstract:

Approximate merging of two adjacent tensor product Bézier surfaces was investigated to guarantee the compression of geometric data in CAD system. The sufficient and necessary condition for precise merging of adjacent tensor product surfaces was obtained by using the matrix representation of subdivided Bézier surface. Then the  merged tensor product Bézier surface was solved by the generalized inverse matrix in L2 norm based on precise merging condition, and the explicit representation of the merged surface’s control points was also obtained. Meanwhile, the results of approximate merging with corner interpolation were shown. Since the minimal least squares solution can be directly obtained by the generalized inverse matrix, the algorithm possesses explicit formula, less time consumption and good approximation results. Numerical results demonstrated the effectiveness of the algorithm.

出版日期: 2012-03-19
:  TP 391  
基金资助:

国家自然科学基金资助项目(60773179,60970079);国家“973”重点基础研究发展规划资助项目(2004CB318000);国家自然科学基金青年基金资助项目(60904070).

通讯作者: 汪国昭,男,教授.     E-mail: wanggz@zju.edu.cn
作者简介: 朱平(1982—),男,浙江杭州人,博士生,从事计算机辅助几何设计与图形学的研究.E-mail: gumpforrest1982@yahoo.com.cn
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引用本文:

朱平, 汪国昭. 基于广义逆矩阵的张量积Bézier曲面合并逼近[J]. J4, 2010, 44(5): 887-892.

SHU Beng, HONG Guo-Zhao. Approximate merging of tensor product Bézier surfaces based on
generalized inverse matrix. J4, 2010, 44(5): 887-892.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2010.05.009        http://www.zjujournals.com/eng/CN/Y2010/V44/I5/887

[1] HOSCHEK J. Approximate conversion of spline curves[J]. Computer Aided Geometric Design, 1987, 4(1): 5966.[2] HU Qianqian, WANG Guojin. Optimal multidegree reduction of triangular Bézier surfaces with corners continuity in the norm L2[J]. Journal of Computational and Applied Mathematics, 2008, 215: 114126.
[3] CHEN Falai, WU Yang. Degree reduction of disk Bézier curves [J]. Computer Aided Geometric Design, 2004,21(2): 263280.
[4] LU Lizheng, WANG Guozhao. Multidegree reduction of triangular Bézier surfaces with boundary constraints[J]. Computer Aided Design, 2006,38(12): 12151223.
[5] HU Qianqian,WANG Guojin. A novel algorithm for explicit optimal multidegree reduction of triangular surfaces[J]. Science in China Series FInformation Science, 2008,51(1): 1324.
[6] 王国瑾,喻春明.Bézier曲线约束降多阶算法的分析与比较[J].浙江大学学报:工学版,2007,11(41): 18051809.
WANG Guojin,YU Chunming. Analysis and comparison of algorithms for multidegree reduction with constrained Béziercurves[J]. Journal of Zhejiang University: Engineering Science, 2007,11(41):18051809.
[7] HU Shimin, TONG Ruofeng, JU Tao, et al. Approximate merging of a pair of Bézier curves[J]. Computer Aided Design, 2001,33(2): 125136.
[8] TAI Chiewlan, HU Shimin, HUANG Qixing. Approximate merging of Bspline curves via knot adjustment and constrained optimization[J]. Computer Aided Design, 2003, 35: 893899.
[9] WU Yang, CHEN Falai. Merging a pair of disk Bézier curves [C]∥ Proceedings of the 2nd International Conference on Computer graphics and Interactive Techniques in Australasia and South East Asia. Singapore: ACM, 2002: 6570.
[10] 檀敬东,黄有度.两条连续的有理Bézier曲线的逼近合并[J].大学数学,2003,19(6):9497.
TAN Jingdong, HUANG Youdu. Approximate merging of a pair of rational Bézier curves by a rational Bézier curve[J]. College Mathematics, 2003, 19(6): 9497.
[11] 王国瑾,汪国昭,郑建民.计算机辅助几何设计[M].北京:高等教育出版社,海德堡施普林格出版社,2001: 8485.

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