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Variational tetrahedral meshing

Alliez, Pierre and Cohen-Steiner, David and Yvinec, Mariette and Desbrun, Mathieu (2005) Variational tetrahedral meshing. ACM Transactions on Graphics, 24 (3). pp. 617-625. ISSN 0730-0301.

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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 L-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:Article
Related URLs:
URLURL TypeDescription
Desbrun, Mathieu0000-0003-3424-6079
Additional Information:Copyright © 2005 by the Association for Computing Machinery, Inc. The authors wish to thank Peter Schroder 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.
Subject Keywords:isotropic meshing; Delaunay mesh; sizing field; slivers
Issue or Number:3
Record Number:CaltechAUTHORS:ALLacmtog05
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:3839
Deposited By: Lindsay Cleary
Deposited On:25 Jul 2006
Last Modified:03 Mar 2020 13:01

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