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Journal Articles Journal of Computational Geometry Year : 2014

Hyperbolic Delaunay Complexes and Voronoi Diagrams Made Practical

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Mikhail Bogdanov
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Olivier Devillers
Monique Teillaud

Abstract

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 [CCCG'92], 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.
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Dates and versions

hal-00961390 , version 1 (20-03-2014)

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Mikhail Bogdanov, Olivier Devillers, Monique Teillaud. Hyperbolic Delaunay Complexes and Voronoi Diagrams Made Practical. Journal of Computational Geometry, 2014, 5 (1), pp.56-85. ⟨10.20382/jocg.v5i1a4⟩. ⟨hal-00961390⟩

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