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2007 Conformal Spherical Parametrization for High Genus Surfaces
Wei Zeng, Xin Li, Shing-Tung Yau, Xianfeng Gu
Commun. Inf. Syst. 7(3): 273-286 (2007).

Abstract

Surface parameterization establishes bijective maps from a surface onto a topologically equivalent standard domain. It is well known that the spherical parameterization is limited to genus-zero surfaces. In this work, we design a new parameter domain, two-layered sphere, and present a framework for mapping high genus surfaces onto sphere. This setup allows us to trans- fer the existing applications based on general spherical parameterization to the field of high genus surfaces, such as remeshing, consistent parameterization, shape analysis, and so on. Our method is based on Riemann surface theory. We construct meromorphic functions on surfaces: for genus one surfaces, we apply Weierstrass $P$-functions; for high genus surfaces, we compute the quotient between two holomorphic one-forms. Our method of spherical parameterization is theoretically sound and practically efficient. It makes the subsequent applications on high genus surfaces very promising.

Citation

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Wei Zeng. Xin Li. Shing-Tung Yau. Xianfeng Gu. "Conformal Spherical Parametrization for High Genus Surfaces." Commun. Inf. Syst. 7 (3) 273 - 286, 2007.

Information

Published: 2007
First available in Project Euclid: 28 January 2008

zbMATH: 1171.30311
MathSciNet: MR2516244

Rights: Copyright © 2007 International Press of Boston

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Vol.7 • No. 3 • 2007
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