Hyperbolic Delaunay Complexes and Voronoi Diagrams Made Practical - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2013

Hyperbolic Delaunay Complexes and Voronoi Diagrams Made Practical

Mikhail Bogdanov
  • Function : Author
  • PersonId : 933126
Olivier Devillers
Monique Teillaud


We study Delaunay complexes and Voronoi diagrams in the Poincaré ball, a conformal model of the hyperbolic space,in any dimension. We elaborate on our earlier work on the space of spheres [Devillers et al. CCCG92], giving a detailed description of algorithms. 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 integration into the CGAL library
Fichier principal
Vignette du fichier
hal-version.pdf (705.65 Ko) Télécharger le fichier
Vignette du fichier
vignette.jpg (35.13 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Format : Figure, Image

Dates and versions

hal-00833760 , version 1 (13-06-2013)



Mikhail Bogdanov, Olivier Devillers, Monique Teillaud. Hyperbolic Delaunay Complexes and Voronoi Diagrams Made Practical. Proceedings of the 29th Annual Symposium on Computational Geometry, Jun 2013, Rio, Brazil. pp.67-76, ⟨10.1145/2462356.2462365⟩. ⟨hal-00833760⟩
224 View
421 Download



Gmail Facebook X LinkedIn More