Two-dimensional line space Voronoi Diagram

Given a set of points called sites, the Voronoi diagram is a partition of the plane into sets of points having the same closest site. Several generalizations of the Voronoi diagram have been studied, mainly Voronoi diagrams for different distances (other than the Euclidean one), and Voronoi diagrams for sites that are not necessarily points (line segments for example). In this paper we present a new generalization of the Voronoi diagram in the plane, in which we shift our interest from points to lines, that is, we compute the partition of the set of lines in the plane into sets of lines having the same closest site (where sites are points in the plane). We first define formally this diagram and give first properties. Then we use a duality relationship between points and lines to visualize this data structure and give more properties. We show that the size of this line space Voronoi diagram for n sites is in Θ(n2 ) and give an optimal algorithm for its explicit computation. We then...

• Type: Conference
• Year: 2007
• Where: ISVD
• Authors: Stéphane Rivière, Dominique Schmitt
• Keywords: Closest Site, ISVD 2007, Space Voronoi Diagram, Theoretical Computer Science, Voronoi Diagram