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Conformal equivalence of triangle meshes

Springborn, Boris and Schröder, Peter and Pinkall, Ulrich (2008) Conformal equivalence of triangle meshes. In: SIGGRAPH '08 ACM SIGGRAPH 2008 papers. ACM , New York, NY, Art. No. 77. ISBN 978-1-4503-0112-1.

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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:Book Section
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URLURL TypeDescription
Schröder, Peter0000-0002-0323-7674
Additional Information:© 2008 ACM. 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.
Funding AgencyGrant Number
Department of Energy (DOE)W-7405-ENG-48/B341492
Caltech Center for Mathematics of InformationUNSPECIFIED
Deutsche Forschungsgemeinschaft (DFG)UNSPECIFIED
Alexander von Humboldt StiftungUNSPECIFIED
Subject Keywords:Discrete Differential Geometry; conformal parameterization; conformal equivalence; discrete Riemannian metric; cone singularities; texture mapping
Record Number:CaltechAUTHORS:20161220-135710541
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Official Citation:Boris Springborn, Peter Schröder, and Ulrich Pinkall. 2008. Conformal equivalence of triangle meshes. In ACM SIGGRAPH 2008 papers (SIGGRAPH '08). ACM, New York, NY, USA, , Article 77 , 11 pages. DOI=
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:72998
Deposited On:20 Dec 2016 23:29
Last Modified:11 Nov 2021 05:09

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