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Spherical parametrization of genus-zero meshes by minimizing discrete harmonic energy

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Abstract

The problem of spherical parametrization is that of mapping a genus-zero mesh onto a spherical surface. For a given mesh, different parametrizations can be obtained by different methods. And for a certain application, some parametrization results might behave better than others. In this paper, we will propose a method to parametrize a genus-zero mesh so that a surface fitting algorithm with PHT-splines can generate good result. Here the parametrization results are obtained by minimizing discrete harmonic energy subject to spherical constraints. Then some applications are given to illustrate the advantages of our results. Based on PHT-splines, parametric surfaces can be constructed efficiently and adaptively to fit genus-zero meshes after their spherical parametrization has been obtained.

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Authors and Affiliations

  1. Department of Mathematics, University of Science and Technology of China, Hefei, 230026, China

    Li Ying, Yang Zhou-wang & Deng Jian-song

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  1. Li Ying
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  2. Yang Zhou-wang
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  3. Deng Jian-song
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Additional information

Project supported by the Outstanding Youth Grant of Natural Science Foundation of China (No. 60225002), the National Basic Research Program (973) of China (No. 2004CB318000), the National Natural Science Foundation of China (Nos. 60533060 and 60473132)

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Li, Y., Yang, Zw. & Deng, Js. Spherical parametrization of genus-zero meshes by minimizing discrete harmonic energy. J. Zhejiang Univ. - Sci. A 7, 1589–1595 (2006). https://doi.org/10.1631/jzus.2006.A1589

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  • DOI: https://doi.org/10.1631/jzus.2006.A1589

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