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J. Comp. Math., 29 (2011), pp. 396-414. |
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Fitting C^1 Sufaces to Scattered Data with S^1_2(Δ^{(2)}_{m,n}) Kai Qu 1, Renhong Wang 2, Chungang Zhu 2 1 School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China1 Department of Mathematics, Dalian Maritime University, Dalian 116026, China 2 School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China Received 2009-9-7 Accepted 2010-12-22 Available online 2011-6-27 doi:10.4208/jcm.1101-m3203 Abstract This paper presents a fast algorithm (BS2 Algorithm) for fitting C^1 surfaces to scattered data points. By using energy minimization, the bivariate spline space S^{1}_{2}(Δ_{m,n}^{(2)}) is introduced to construct a C^1-continuous piecewise quadratic surface through a set of irregularly 3D points. Moreover, a multilevel method is also presented. Some experimental results show that the accuracy is satisfactory. Furthermore, the BS2 Algorithm is more suitable for fitting surfaces if the given data points have some measurement errors. Key words: Bivariate spline, Scattered data, Surface fitting, Energy AMS subject classifications: 41A15, 65D07, 65D10. Email: qukai8@dlmu.edu.cn, renhong@dlut.edu.cn, cgzhu@dlut.edu.cn |