@techreport{TR-IC-99-23,
  number = {IC-99-23},
  author = {Pedro J. Rezende and Rodrigo B. Westrupp},
  title = {An Optimal Algorithm to Construct All {Voronoi} Diagrams for $k$ Nearest Neighbor Search in {$T^2$}},
  month = {December},
  year = {1999}, 
  institution = {Institute of Computing, University of Campinas},
  note = {In English, 18 pages.
    \par\selectlanguage{english}\textbf{Abstract}
      In this paper, we generalize to the oriented projective plane
      $T^2$ 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 $T^2$ has an exact number of regions. Furthermore, we show
      that the order $k$ Voronoi diagram of a set of sites in $T^2$ is
      antipodal to its order $n-k$ Voronoi diagram, $\forall k: 1 \leq
      k < n$.
  }
}