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Journal Articles ACM Transactions on Graphics Year : 2005

Variational Tetrahedral Meshing

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Pierre Alliez
Mariette Yvinec
Mathieu Desbrun

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 \italic{and} connectivity. As this energy is known to be the ${\cal L}^1$ 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.
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Dates and versions

inria-00226418 , version 1 (30-01-2008)

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Pierre Alliez, David Cohen-Steiner, Mariette Yvinec, Mathieu Desbrun. Variational Tetrahedral Meshing. ACM Transactions on Graphics, 2005, ⟨10.1145/1186822.1073238⟩. ⟨inria-00226418⟩
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