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Computational Science and Its Applications - ICCSA 2006

Volume 3984 of the series Lecture Notes in Computer Science pp 735-742

Hyperbolic Voronoi Diagram

  • Zahra NilforoushanAffiliated withCarnegie Mellon UniversityFaculty of Math. and Computer Sc., AmirKabir University of Tech.
  • , Ali MohadesAffiliated withCarnegie Mellon UniversityFaculty of Math. and Computer Sc., AmirKabir University of Tech.

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Abstract

Voronoi diagrams are among the most extensively studied objects in computational geometry with useful applications in different areas of science. To understand impacts of non-Euclidean geometry on computational geometry, this paper investigates the Voronoi diagram in hyperbolic space specially the one in the Poincaré hyperbolic disk, which is a 2-dimensional manifold with negative curvature. We first prove some lemma in Poincaré hyperbolic disk and then give an incremental algorithm to construct Voronoi diagram.