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.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Zahra Nilforoushan
    • 1
  • Ali Mohades
    • 1
  1. 1.Faculty of Math. and Computer Sc.AmirKabir University of Tech.TehranIran

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