Anisotropic Delaunay Meshes of Surfaces - Inria - Institut national de recherche en sciences et technologies du numérique Accéder directement au contenu
Article Dans Une Revue ACM Transactions on Graphics Année : 2015

Anisotropic Delaunay Meshes of Surfaces

Kan-Le Shi
  • Fonction : Auteur
Jane Tournois
  • Fonction : Auteur
  • PersonId : 948729
Mariette Yvinec

Résumé

Anisotropic simplicial meshes are triangulations with elements elongated along prescribed directions. Anisotropic meshes have been shown to be well suited for interpolation of functions or solving PDEs. They can also significantly enhance the accuracy of a surface representation. Given a surface S endowed with a metric tensor field, we propose a new approach to generate an anisotropic mesh that approximates S with elements shaped according to the metric field. The algorithm relies on the well-established concepts of restricted Delaunay triangulation and Delaunay refinement and comes with theoretical guarantees. The star of each vertex in the output mesh is Delaunay for the metric attached to this vertex. Each facet has a good aspect ratio with respect to the metric specified at any of its vertices. The algorithm is easy to implement. It can mesh various types of surfaces like implicit surfaces, polyhedra or isosurfaces in 3D images. It can handle complicated geometries and topologies, and very anisotropic metric fields. Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies show this notice on the first page or initial screen of a display along with the full citation. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works requires prior specific permission and/or a fee. Permissions may be requested from Publications
Fichier principal
Vignette du fichier
acm-tog-free (1).pdf (6.89 Mo) Télécharger le fichier
Vignette du fichier
pickingregion3 (1).png (92.79 Ko) Télécharger le fichier
Vignette du fichier
pickingregion3 (1).jpg (46.94 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)
Format : Figure, Image
Origine : Fichiers produits par l'(les) auteur(s)
Format : Figure, Image
Origine : Fichiers produits par l'(les) auteur(s)
Loading...

Dates et versions

hal-01146307 , version 1 (28-04-2015)
hal-01146307 , version 2 (24-10-2016)
hal-01146307 , version 3 (02-11-2016)

Identifiants

Citer

Jean-Daniel Boissonnat, Kan-Le Shi, Jane Tournois, Mariette Yvinec. Anisotropic Delaunay Meshes of Surfaces. ACM Transactions on Graphics, 2015, 34 (2), pp.10. ⟨10.1145/2721895⟩. ⟨hal-01146307v3⟩
514 Consultations
631 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More