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Published July 2003 | Supplemental Material
Book Section - Chapter Open

Globally smooth parameterizations with low distortion

Abstract

Good parameterizations are of central importance in many digital geometry processing tasks. Typically the behavior of such processing algorithms is related to the smoothness of the parameterization and how much distortion it contains. Since a parameterization maps a bounded region of the plane to the surface, a parameterization for a surface which is not homeomorphic to a disc must be made up of multiple pieces. We present a novel parameterization algorithm for arbitrary topology surface meshes which computes a globally smooth parameterization with low distortion. We optimize the patch layout subject to criteria such as shape quality and metric distortion, which are used to steer a mesh simplification approach for base complex construction. Global smoothness is achieved through simultaneous relaxation over all patches, with suitable transition functions between patches incorporated into the relaxation procedure. We demonstrate the quality of our parameterizations through numerical evaluation of distortion measures and the excellent rate distortion performance of semi-regular remeshes produced with these parameterizations. The numerical algorithms required to compute the parameterizations are robust and run on the order of minutes even for large meshes.

Additional Information

© 2003 ACM. This work was supported in part by NSF (DMS-0220905, DMS-0138458, ACI-0219979), the DOE (W-7405-ENG-48/B341492), nVidia, the Center for Integrated Multiscale Modeling and Simulation, Intel, Alias|Wavefront, Pixar, Microsoft, and the Packard Foundation. Special thanks to Ilja Friedel, Eitan Grinspun, Kai Hormann, Mark Meyer, Steven Schkolne, Zoë Wood, and to our reviewers for their helpful suggestions.

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