Hyperbolic Delaunay Complexes and Voronoi Diagrams Made Practical

Mikhail Bogdanov 1 Olivier Devillers 1 Monique Teillaud 1
1 GEOMETRICA - Geometric computing
CRISAM - Inria Sophia Antipolis - Méditerranée , Inria Saclay - Ile de France
Abstract : We study Delaunay complexes and Voronoi diagrams in the Poincar ́e ball, a conformal model of the hyperbolic space, in any dimension. We elaborate on our earlier work on the space of spheres [CCCG92], giving a detailed description of al- gorithms. We also study algebraic and arithmetic issues, observing that only rational computations are needed. All proofs are based on geometric reasoning, they do not resort to any use of the analytic formula of the hyperbolic distance. This allows for an exact and efficient implementation in 2D. All degenerate cases are handled. The implementation will be submitted to the CGAL editorial board for future inte- gration into the CGAL library.
Type de document :
Communication dans un congrès
29th Annual Symposium on Computational Geometry, 2013, Rio, Brazil. ACM, pp.67-76, 2013, 〈10.1145/2462356.2462365〉
Liste complète des métadonnées

Littérature citée [39 références]  Voir  Masquer  Télécharger


https://hal.inria.fr/hal-00833760
Contributeur : Olivier Devillers <>
Soumis le : jeudi 13 juin 2013 - 14:39:54
Dernière modification le : samedi 27 janvier 2018 - 01:30:56
Document(s) archivé(s) le : samedi 14 septembre 2013 - 04:13:57

Fichiers

hal-version.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Mikhail Bogdanov, Olivier Devillers, Monique Teillaud. Hyperbolic Delaunay Complexes and Voronoi Diagrams Made Practical. 29th Annual Symposium on Computational Geometry, 2013, Rio, Brazil. ACM, pp.67-76, 2013, 〈10.1145/2462356.2462365〉. 〈hal-00833760〉

Partager

Métriques

Consultations de la notice

356

Téléchargements de fichiers

392