On the Peeper's Voronoi diagram

In the peeper's Voronoi diagram for <i>n</i> sites, any point in the plane belongs to the region of the closest site visible from it. Visibility is constrained to a segment on a line avoiding the convex hull of the sites. We show that the peeper's Voronoi diagram attains a size of &Theta;(<i>n</i><sup>2</sup>) in the worst case, and that it can be computed in <i>O</i>(<i>n</i><sup>2</sup>)time and space.