Hyperbolic Delaunay complexes and Voronoi diagrams made practical
type: Dataset
description: We study Delaunay complexes and Voronoi diagrams in the Poincaré ball, a confomal 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, and presenting a static and a dynamic variants. 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.
identifier: Report N°: RR-8146
issued: 2026-06-02T04:54:42.658382
language: en
modified: 2026-06-02T04:54:42.658392
contact point: Organization
  fn: CCSD
keyword: infoeu-reposemanticsreport
keyword: infoinfo-cgcomputer-science-cscomputational-geometry-cscg
keyword: reports
landing page: https://inria.hal.science/hal-00756522

Hyperbolic Delaunay complexes and Voronoi diagrams made practical
type: Distribution
format: HTML
issued: 2026-06-02T04:54:42.709312
modified: 2026-06-02T04:54:42.628821
access URL: https://inria.hal.science/hal-00756522

test_moissonnage_selune
type: Agent