Skip to Main content Skip to Navigation
Journal articles

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 \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.
Document type :
Journal articles
Complete list of metadata

Cited literature [27 references]  Display  Hide  Download
Contributor : Mariette Yvinec Connect in order to contact the contributor
Submitted on : Wednesday, January 30, 2008 - 4:19:29 PM
Last modification on : Friday, February 4, 2022 - 3:25:40 AM
Long-term archiving on: : Friday, April 30, 2010 - 8:00:16 PM


Files produced by the author(s)




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



Record views


Files downloads