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Optimal multi-degree reduction of C-Bézier surfaces with constraints

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Abstract

We propose an optimal approach to solve the problem of multi-degree reduction of C-Bézier surfaces in the norm L2 with prescribed constraints. The control points of the degree-reduced C-Bézier surfaces can be explicitly obtained by using a matrix operation that is based on the transfer matrix of the C-Bézier basis. With prescribed boundary constraints, this method can be applied to piecewise continuous patches or to a single patch with the combination of surface subdivision. The resulting piecewise approximating patches are globally G1 continuous. Finally, numerical examples are presented to show the effectiveness of the method.

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Authors and Affiliations

  1. Department of Mathematics, Shanghai Maritime University, Shanghai, 201306, China

    Lian Zhou

  2. Zhejiang Institute of Economics and Trade, Hangzhou, 310018, China

    Xin-hui Lin

  3. College of Fundamental Studies, Shanghai University of Engineering Science, Shanghai, 201620, China

    Hong-yan Zhao

  4. Faculty of Science, Ningbo University of Technology, Ningbo, 315211, China

    Jun Chen

Authors
  1. Lian Zhou
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  2. Xin-hui Lin
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  3. Hong-yan Zhao
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  4. Jun Chen
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Corresponding author

Correspondence to Lian Zhou.

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11401373, 61402281, and 11601322) and the Zhejiang Provincial Natural Science Foundation, China (No. LY16F020020)

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Zhou, L., Lin, Xh., Zhao, Hy. et al. Optimal multi-degree reduction of C-Bézier surfaces with constraints. Frontiers Inf Technol Electronic Eng 18, 2009–2016 (2017). https://doi.org/10.1631/FITEE.1700458

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  • DOI: https://doi.org/10.1631/FITEE.1700458

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