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

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2 Author(s)
De Rezende, P.J. ; Inst. de Comput., Univ. Estadual de Campinas, Sao Paulo, Brazil ; Westrupp, R.B.

We generalize to the oriented projective plane T2 an algorithm for constructing all order k Voronoi diagrams 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 set of n sites in T2 is antipodal to its order n-k Voronoi diagram, ∀k: 1⩽k<n

Published in:

Computer Graphics and Image Processing, 1999. Proceedings. XII Brazilian Symposium on

Date of Conference:

1999