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Conformal Equivalence of Triangle Meshes

Springborn, Boris and Schröder, Peter and Pinkall, Ulrich (2008) Conformal Equivalence of Triangle Meshes. ACM Transactions on Graphics, 27 (3). Art. No. 77. ISSN 0730-0301. doi:10.1145/1360612.1360676. https://resolver.caltech.edu/CaltechAUTHORS:20100722-120116172

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Abstract

We present a new algorithm for conformal mesh parameterization. It is based on a precise notion of discrete conformal equivalence for triangle meshes which mimics the notion of conformal equivalence for smooth surfaces. The problem of finding a flat mesh that is discretely conformally equivalent to a given mesh can be solved efficiently by minimizing a convex energy function, whose Hessian turns out to be the well known cot-Laplace operator. This method can also be used to map a surface mesh to a parameter domain which is flat except for isolated cone singularities, and we show how these can be placed automatically in order to reduce the distortion of the parameterization. We present the salient features of the theory and elaborate the algorithms with a number of examples.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://doi.acm.org/10.1145/1360612.1360676DOIUNSPECIFIED
http://portal.acm.org/citation.cfm?doid=1360612.1360676PublisherUNSPECIFIED
ORCID:
AuthorORCID
Schröder, Peter0000-0002-0323-7674
Additional Information:© 2008 ACM, Inc. Year of Publication: 2008 This work was supported in part by NSF (CCF-0528101 and CCF- 0635112), DOE (W-7405-ENG-48/B341492), the Caltech Center for Mathematics of Information, DFG Research Center Matheon, the Alexander von Humboldt Stiftung, and Autodesk. The authors are gratefully indebted to Alexander Bobenko for inspiring discussions. Special thanks to Cici Koenig, Andreas Fabri, Pierre Alliez, and Mathieu Desbrun.
Funders:
Funding AgencyGrant Number
NSFCCF-0528101
NSFCCF-0635112
DOEW-7405-ENG-48/B341492
Caltech Center for Mathematics of InformationUNSPECIFIED
DFG (Deutsche Forschungsgemeinschaft) Research Center MatheonUNSPECIFIED
Alexander von Humboldt StiftungUNSPECIFIED
AutodeskUNSPECIFIED
Subject Keywords:Discrete Differential Geometry; conformal parameterization; conformal equivalence; discrete Riemannian metric; cone singularities; texture mapping
Series Name:Proceedings of ACM SIGGRAPH 2008
Issue or Number:3
DOI:10.1145/1360612.1360676
Record Number:CaltechAUTHORS:20100722-120116172
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20100722-120116172
Official Citation:Springborn, B., Schröder, P., Pinkall, U. 2008. Conformal Equivalence of Triangle Meshes. ACM Trans. Graph. 27, 3, Article 77 (August 2008), 11 pages. DOI = 10.1145/1360612.1360676 http://doi.acm. org/10.1145/1360612.1360676.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19164
Collection:CaltechAUTHORS
Deposited By: Jason Perez
Deposited On:30 Jul 2010 17:08
Last Modified:08 Nov 2021 23:50

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