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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Nilforoushan, Z., Mohades, A. (2006). Hyperbolic Voronoi Diagram. In: Gavrilova, M.L., et al. Computational Science and Its Applications - ICCSA 2006. ICCSA 2006. Lecture Notes in Computer Science, vol 3984. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11751649_81
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DOI: https://doi.org/10.1007/11751649_81
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34079-9
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