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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

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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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.

 : TP 391

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#### 引用本文:

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

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