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An algorithm for the construction of intrinsic Delaunay triangulations with applications to digital geometry processing

Fisher, M. and Springborn, B. and Schröder, P. and Bobenko, A. I. (2007) An algorithm for the construction of intrinsic Delaunay triangulations with applications to digital geometry processing. Computing, 81 (2-3). pp. 199-213. ISSN 0010-485X. doi:10.1007/s00607-007-0249-8.

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The discrete Laplace–Beltrami operator plays a prominent role in many digital geometry processing applications ranging from denoising to parameterization, editing, and physical simulation. The standard discretization uses the cotangents of the angles in the immersed mesh which leads to a variety of numerical problems. We advocate the use of the intrinsic Laplace–Beltrami operator. It satisfies a local maximum principle, guaranteeing, e.g., that no flipped triangles can occur in parameterizations. It also leads to better conditioned linear systems. The intrinsic Laplace–Beltrami operator is based on an intrinsic Delaunay triangulation of the surface. We detail an incremental algorithm to construct such triangulations together with an overlay structure which captures the relationship between the extrinsic and intrinsic triangulations. Using a variety of example meshes we demonstrate the numerical benefits of the intrinsic Laplace–Beltrami operator.

Item Type:Article
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URLURL TypeDescription DOIArticle ReadCube access
Fisher, M.0000-0002-8908-3417
Schröder, P.0000-0002-0323-7674
Additional Information:© 2007 Springer-Verlag. Received 4 December 2006; Accepted 22 August 2007; Published online 6 November 2007. This work was supported in part by NSF (CCF-0528101), DFG Research Center Matheon “Mathematics for Key Technologies,” DFG research unit “Polyhedral Surfaces,” DOE (W-7405-ENG-48/B341492), the Alexander von Humboldt Stiftung, the Caltech Center for the Mathematics of Information, nVidia, Autodesk, and Pixar Animation Studios. Special thanks to Mathieu Desbrun, Yiying Tong, Liliya Kharevych, Herbert Edelsbrunner, and Cici Koenig.
Funding AgencyGrant Number
Deutsche Forschungsgemeinschaft (DFG)UNSPECIFIED
Department of Energy (DOE)W-7405-ENG-48/B341492
Center for the Mathematics of Information, CaltechUNSPECIFIED
Pixar Animation StudiosUNSPECIFIED
Issue or Number:2-3
Record Number:CaltechAUTHORS:20100820-152952201
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Official Citation:Fisher, M., Springborn, B., Schröder, P. et al. Computing (2007) 81: 199.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19569
Deposited By: Tony Diaz
Deposited On:23 Aug 2010 21:14
Last Modified:08 Nov 2021 23:53

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