Practical spherical embedding of manifold triangle meshes

Shadi Saba, Irad Yavneh, Craig Gotsman, Alla Sheffer

Research output: Chapter in Book/Report/Conference proceedingConference contribution

37 Scopus citations

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 methoa 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.

Original languageEnglish (US)
Title of host publicationProceedings - International Conference on Shape Modeling and Applications, SMI'05
Pages258-267
Number of pages10
DOIs
StatePublished - 2005
Externally publishedYes
EventInternational Conference on Shape Modeling and Applications, SMI'05 - Cambridge, MA, United States
Duration: Jun 13 2005Jun 17 2005

Publication series

NameProceedings - International Conference on Shape Modeling and Applications, SMI'05
Volume2005

Other

OtherInternational Conference on Shape Modeling and Applications, SMI'05
Country/TerritoryUnited States
CityCambridge, MA
Period6/13/056/17/05

All Science Journal Classification (ASJC) codes

  • Engineering(all)

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