 
Summary: On the Peeper's Voronoi Diagram
F. Aurenhammer and G. Stockl
Institutes for Information Processing, Graz Technical University
Schiesstattgasse 4a, A{8010 Graz, Austria
Abstract
In the peeper's Voronoi diagram for n 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 (n 2 ) in the worst case, and that it can be computed in O(n 2 ) time and space.
1 Introduction
Let S be a set of n points (called sites) in the plane. The Voronoi diagram of S is a
partition of the plane which assignes each point x to the site in S that is closest to
x. Voronoi diagrams in the original and in generalized settings have proved useful
in solving a variety of problems in computational geometry. See, e.g., the survey
paper by Aurenhammer (1988).
Recently, Voronoi diagrams involving visibility constraints have received atten
tion. Each point x of the plane is assigned to the closest among those sites in S
that are visible from x. The case where visibility is constrained by (noncrossing)
line segments joining sites has been investigated by Chew (1989), Wang & Schubert
(1987), and Seidel (1988). Constraining visibility in this way does not change the
