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		<doi>10.1109/SIBGRA.1999.805592</doi>
		<citationkey>RezendeWest:1999:OpAlCo</citationkey>
		<title>An optimal algorithm to construct all voronoi diagrams for k nearest neighbor search in T2</title>
		<year>1999</year>
		<numberoffiles>3</numberoffiles>
		<size>220 KiB</size>
		<author>Rezende, Pedro J. de,</author>
		<author>Westrupp, Rodrigo B.,</author>
		<editor>Stolfi, Jorge,</editor>
		<editor>Tozzi, Clésio Luis,</editor>
		<conferencename>Brazilian Symposium on Computer Graphics and Image Processing, 12 (SIBGRAPI)</conferencename>
		<conferencelocation>Campinas, SP, Brazil</conferencelocation>
		<date>17-20 Oct. 1999</date>
		<publisher>IEEE Computer Society</publisher>
		<publisheraddress>Los Alamitos</publisheraddress>
		<pages>7-15</pages>
		<booktitle>Proceedings</booktitle>
		<tertiarytype>Full Paper</tertiarytype>
		<organization>SBC - Brazilian Computer Society and UNICAMP - University of Campinas</organization>
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		<keywords>t2, voronoi, euclidean, k.</keywords>
		<abstract>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.</abstract>
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		<notes>The conference was held in Campinas, SP, Brazil, from October 17 to 20.</notes>
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		<url>http://sibgrapi.sid.inpe.br/rep-/dpi.inpe.br/vagner/1999/11.26.17.01</url>
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