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Variational tetrahedral meshing

Alliez, Pierre and Cohen-Steiner, David and Yvinec, Mariette and Desbrun, Mathieu (2005) Variational tetrahedral meshing. In: ACM SIGGRAPH 2005 Papers. ACM , New York, NY, pp. 617-625. https://resolver.caltech.edu/CaltechAUTHORS:20160415-095336759

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Abstract

In this paper, a novel Delaunay-based variational approach to isotropic tetrahedral meshing is presented. To achieve both robustness and efficiency, we minimize a simple mesh-dependent energy through global updates of both vertex positions and connectivity. As this energy is known to be the ∠1 distance between an isotropic quadratic function and its linear interpolation on the mesh, our minimization procedure generates well-shaped tetrahedra. Mesh design is controlled through a gradation smoothness parameter and selection of the desired number of vertices. We provide the foundations of our approach by explaining both the underlying variational principle and its geometric interpretation. We demonstrate the quality of the resulting meshes through a series of examples.


Item Type:Book Section
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1145/1186822.1073238DOIPaper
http://dl.acm.org/citation.cfm?doid=1073204.1073238PublisherPaper
ORCID:
AuthorORCID
Desbrun, Mathieu0000-0003-3424-6079
Additional Information:© 2005 ACM. The authors wish to thank Peter Schröder as one of the instigators of this project. Many thanks to Alexandre Olivier-Mangon and George Drettakis for providing us with the torso model. Our gratitude also goes to Joe Warren, Sean Mauch, Peter Krysl, Fehmi Cirak and Tamer, Barbara Cutler, Steve Oudot, Sylvain Pion, and Andreas Fabri for precious help along the way. Sponsors include NSF (CARGO DMS-0221669 and DMS-0221666, CAREER CCR-0133983, and ITR DMS-0453145), DOE (DE-FG02-04ER25657), the EU Network of Excellence AIM@SHAPE (IST NoE No 506766), and Pixar.
Funders:
Funding AgencyGrant Number
NSFDMS-0221669
NSFDMS-0221666
NSFCCR-0133983
NSFDMS-0453145
Department of Energy (DOE)DE-FG02-04ER25657
EU Network of ExcellenceIST NoE No 506766
PixarUNSPECIFIED
Subject Keywords:Isotropic meshing, Delaunay mesh, sizing field, slivers
Record Number:CaltechAUTHORS:20160415-095336759
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20160415-095336759
Official Citation:Pierre Alliez, David Cohen-Steiner, Mariette Yvinec, and Mathieu Desbrun. 2005. Variational tetrahedral meshing. In ACM SIGGRAPH 2005 Papers (SIGGRAPH '05), Markus Gross (Ed.). ACM, New York, NY, USA, 617-625. DOI=http://dx.doi.org/10.1145/1186822.1073238
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:66216
Collection:CaltechAUTHORS
Deposited By: Kristin Buxton
Deposited On:15 Apr 2016 17:24
Last Modified:03 Mar 2020 13:01

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