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Fitting $C^1$ Surfaces to Scattered Data with $S^1_2(∆^{(2)}_{m,n})$

Fitting $C^1$ Surfaces to Scattered Data with $S^1_2(∆^{(2)}_{m,n})$

Year:    2011

Journal of Computational Mathematics, Vol. 29 (2011), Iss. 4 : pp. 396–414

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 $S^1_2(∆^{(2)}_{m,n})$ 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.1101-m3203

Journal of Computational Mathematics, Vol. 29 (2011), Iss. 4 : pp. 396–414

Published online:    2011-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Bivariate spline Scattered data Surface fitting Energy minimization Type-2 triangulation $C^1$-continuous.