Hyperbolic Voronoi Diagram
- Cite this paper as:
- Nilforoushan Z., Mohades A. (2006) Hyperbolic Voronoi Diagram. In: Gavrilova M.L. et al. (eds) Computational Science and Its Applications - ICCSA 2006. ICCSA 2006. Lecture Notes in Computer Science, vol 3984. Springer, Berlin, Heidelberg
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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