Voronoi diagrams and arrangements
Discrete & Computational Geometry
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Algorithmic geometry
Exploring Large Graphs in 3D Hyperbolic Space
IEEE Computer Graphics and Applications
Optimal Möbius Transformations for Information Visualization and Meshing
WADS '01 Proceedings of the 7th International Workshop on Algorithms and Data Structures
IEEE Transactions on Visualization and Computer Graphics
Hyperbolic Voronoi Diagrams Made Easy
ICCSA '10 Proceedings of the 2010 International Conference on Computational Science and Its Applications
Resilient routing for sensor networks using hyperbolic embedding of universal covering space
INFOCOM'10 Proceedings of the 29th conference on Information communications
Hyperbolic centroidal Voronoi tessellation
Proceedings of the 14th ACM Symposium on Solid and Physical Modeling
Revisiting Hyperbolic Voronoi Diagrams from Theoretical, Applied and Generalized Viewpoints
ISVD '10 Proceedings of the 2010 International Symposium on Voronoi Diagrams in Science and Engineering
Perturbations for Delaunay and weighted Delaunay 3D triangulations
Computational Geometry: Theory and Applications
Delaunay triangulations of point sets in closed euclidean d-manifolds
Proceedings of the twenty-seventh annual symposium on Computational geometry
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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.