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Volume 29, Issue 4
Fitting $C^1$ Surfaces to Scattered Data with $S^1_2(∆^{(2)}_{m,n})$

Kai Qu, Renhong Wang & Chungang Zhu

DOI: 10.4208/jcm.1101-m3203

J. Comp. Math., 29 (2011), pp. 396-414.

Published online: 2011-08

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  • 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.

  • Keywords

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

  • AMS Subject Headings

41A15, 65D07, 65D10.

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{JCM-29-396, author = {Kai Qu, Renhong Wang and Chungang Zhu}, title = {Fitting $C^1$ Surfaces to Scattered Data with $S^1_2(∆^{(2)}_{m,n})$}, journal = {Journal of Computational Mathematics}, year = {2011}, volume = {29}, number = {4}, pages = {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.

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.1101-m3203}, url = {http://global-sci.org/intro/article_detail/jcm/10385.html} }
TY - JOUR T1 - Fitting $C^1$ Surfaces to Scattered Data with $S^1_2(∆^{(2)}_{m,n})$ AU - Kai Qu, Renhong Wang & Chungang Zhu JO - Journal of Computational Mathematics VL - 4 SP - 396 EP - 414 PY - 2011 DA - 2011/08 SN - 29 DO - http://doi.org/10.4208/jcm.1101-m3203 UR - https://global-sci.org/intro/article_detail/jcm/10385.html KW - Bivariate spline, Scattered data, Surface fitting, Energy minimization, Type-2 triangulation, $C^1$-continuous. AB -

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.

Kai Qu, Renhong Wang and Chungang Zhu. (2011). Fitting $C^1$ Surfaces to Scattered Data with $S^1_2(∆^{(2)}_{m,n})$. Journal of Computational Mathematics. 29 (4). 396-414. doi:10.4208/jcm.1101-m3203
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