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10.1109/SMI.2005.32guideproceedingsArticle/Chapter ViewAbstractPublication PagesConference Proceedingsacm-pubtype
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Practical Spherical Embedding of Manifold Triangle Meshes

Published: 13 June 2005 Publication History

Abstract

Gotsman et al. (SIGGRAPH 2003) presented the first method to generate a provably bijective parameterization of a closed genus-0 manifold mesh to the unit sphere. This involves the solution of a large system of non-linear equations. However, they did not show how to solve these equations efficiently, so, while theoretically sound, the method has remained impractical till now. We show why simple iterative methods to solve the equations are bound to fail, and provide an efficient numerical scheme that succeeds. Our method uses a number of optimization methods combined with an algebraic multigrid technique. With these, we are able to spherically parameterize meshes containing up to a hundred thousand vertices in a matter of minutes.

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cover image Guide Proceedings
SMI '05: Proceedings of the International Conference on Shape Modeling and Applications 2005
June 2005
374 pages
ISBN:076952379X

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IEEE Computer Society

United States

Publication History

Published: 13 June 2005

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