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Constructing constant mean curvature surfaces with fixed-point half dynamic model

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Abstract

In this paper, we present a method to generate a constant mean curvature (CMC) surface with the given boundary. By assuming the velocity to zero in the dynamic model for every step, a fixed-point iteration is carried out. Either the variation of Dirichlet energy or area energy can be chosen to be the approximation of the mean curvature. Experiments and results show that our method can work for minimal surfaces or CMC surfaces with nonzero mean curvature and with fixed or free boundary. Meanwhile it is robust with poor quality initial mesh as well as non-uniformly distributed vertices.

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Acknowledgments

This work is supported by the National Natural Science Foundation of China (Grant No. 11371320), Zhejiang Natural Science Foundation (Grant No. LZ14A010002), Foundation of Science and Technology Department (Grant No. 2013C31084) of Zhejiang Province, and Scientific Research Fund of Zhejiang Provincial Education Department (Grant Nos. Y201431077 and Y201329420).

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Authors and Affiliations

  1. Department of Mathematics, Zhejiang University, Hangzhou, 310027, Zhejiang, People’s Republic of China

    Yang Yu & Qingbiao Wu

  2. Department of Mathematics, University of Hafr Al-Batin, Hafr Al-Batin, 31991, Saudi Arabia

    Yasir Khan

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  1. Yang Yu
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  2. Qingbiao Wu
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  3. Yasir Khan
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Correspondence to Yang Yu.

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Yu, Y., Wu, Q. & Khan, Y. Constructing constant mean curvature surfaces with fixed-point half dynamic model. Neural Comput & Applic 27, 2577–2586 (2016). https://doi.org/10.1007/s00521-015-2026-5

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  • DOI: https://doi.org/10.1007/s00521-015-2026-5

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