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Published July 2005 | public
Journal Article Open

Variational tetrahedral meshing

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 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.

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.

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August 22, 2023
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October 16, 2023