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Globally smooth parameterizations with low distortion

Khodakovsky, Andrei and Litke, Nathan and Schröder, Peter (2003) Globally smooth parameterizations with low distortion. ACM Transactions on Graphics, 22 (3). pp. 350-357. ISSN 0730-0301. doi:10.1145/882262.882275.

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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.

Item Type:Article
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URLURL TypeDescription
Schröder, Peter0000-0002-0323-7674
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.
Funding AgencyGrant Number
Department of Energy (DOE)W-7405-ENG-48/B341492
Center for Integrated Multiscale Modeling and SimulationUNSPECIFIED
David and Lucile Packard FoundationUNSPECIFIED
Subject Keywords:Parameterization, compression, resampling, smoothness, rate distortion
Issue or Number:3
Classification Code:CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling Curve, surface, solid, and object representations
Record Number:CaltechAUTHORS:20161116-144000826
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Official Citation:Andrei Khodakovsky, Nathan Litke, and Peter Schröder. 2003. Globally smooth parameterizations with low distortion. ACM Trans. Graph. 22, 3 (July 2003), 350-357. DOI:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:72065
Deposited On:17 Nov 2016 00:58
Last Modified:11 Nov 2021 04:55

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