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Indexed by:期刊论文

Date of Publication:2018-01-01

Journal:JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

Included Journals:SCIE、EI

Volume:327

Page Number:175-187

ISSN No.:0377-0427

Key Words:Progressive iterative approximation; Bivariate B-spline surface; Regularized least square; Surface fitting; Successive over-relaxation iteration

Abstract:Recently, the use of progressive iterative approximation (PIA) to fit data points has received a deal of attention benefitting from its simplicity, flexibility, and generality. In this paper, we present a novel progressive iterative approximation for regularized least square bivariate B-spline surface fitting (RLSPIA). RLSPIA extends the PIA property of univariate NTP (normalized totally positive) bases to linear dependent non-tensor product bivariate B-spline bases, which leads to a lower order fitting result than common tensor product B-spline surface. During each iteration, the weights for generating fairing updating surface are obtained by solving an energy minimization problem with box constraints iteratively. Furthermore, an accelerating term is introduced to speed up the convergence rate of RLSPIA, which is comparable favourably with the theoretical optimal one. Several examples are provided to illustrate the efficiency and effectiveness of the proposed method. (C) 2017 Elsevier B.V. All rights reserved.