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An optimal algorithm to construct all voronoi diagrams for k nearest neighbor search in T2

Pedro J. de RezendeRodrigo B. Westrupp

In this paper, we generalize to the oriented projective plane T2 an algorithm for constructing all order k Voronoi diagram in the Euclidean plane. We also show that, for fixed K and for a finite set of sites, an order K Voronoi diagram in T2 has an exact number of regions. Furthermore, we show that the order K Voronoi diagram of a se of n sites in T2 is antipodal to its order n - K Voronoi diagram, VK: 1 <= K < n.

http://sibgrapi.sid.inpe.br/rep-/dpi.inpe.br/vagner/1999/11.26.17.01

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