Voronoi Diagram in Simply Connected Complete Manifold

Kensuke ONISHI  Jin-ichi ITOH  

IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E85-A   No.5   pp.944-948
Publication Date: 2002/05/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
Voronoi diagram,  Hadamard manifold,  simply connected complete manifold,  

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In this paper we deal with Voronoi diagram in simply connected complete manifold with non positive curvature, called Hadamard manifold. We prove that a part of the Voronoi diagram can be characterized by hyperbolic Voronoi diagram. Voronoi diagram in simply connected complete manifold is also characterized for a given set of points satisfying a distance condition.