Hyperbolic voronoi diagram

Authors:
Zahra Nilforoushan;Ali Mohades
Affiliations:
Faculty of Math. and Computer Sc., AmirKabir University of Tech., Tehran, Iran;Faculty of Math. and Computer Sc., AmirKabir University of Tech., Tehran, Iran
Venue:
ICCSA'06 Proceedings of the 2006 international conference on Computational Science and Its Applications - Volume Part V
Year:
2006

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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.