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2004 Optimal Global Conformal Surface Parameterization for Visualization
Xianfeng Gu, Miao Jin, Yalin Wang, Shin-Tung Yau
Commun. Inf. Syst. 4(2): 117-134 (2004).

Abstract

All orientable metric surfaces are Riemann surfaces and admit global conformal parameterizations. Riemann surface structure is a fundamental structure and governs many natural physical phenomena, such as heat diffusion, electric-magnetic fields on the surface. Good parameterization is crucial for simulation and visualization. This paper gives an explicit method for finding optimal global conformal parameterizations of arbitrary surfaces. It relies on certain holomorphic differential forms and conformal mappings from differential geometry and Riemann surface theories. Algorithms are developed to modify topology, locate zero points, and determine cohomology types of differential forms. The implementation is based on finite dimensional optimization method. The optimal parameterization is intrinsic to the geometry, preserving angular structure, and can play an important role in various applications including texture mapping, remeshing, morphing and simulation. The method is demonstrated by visualizing the Riemann surface structure of real surfaces represented as triangle meshes.

Citation

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Xianfeng Gu. Miao Jin. Yalin Wang. Shin-Tung Yau. "Optimal Global Conformal Surface Parameterization for Visualization." Commun. Inf. Syst. 4 (2) 117 - 134, 2004.

Information

Published: 2004
First available in Project Euclid: 24 June 2005

zbMATH: 1092.14515
MathSciNet: MR2165683

Rights: Copyright © 2004 International Press of Boston

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Vol.4 • No. 2 • 2004
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