Digital geometry is about deriving geometric information from digital pictures. The field
emerged from its mathematical roots some forty-years ago through work in computer-based …

Two points in a polygon are called if the straight line between them lies entirely inside the
polygon. The art gallery problem for a polygon P is to find a minimum set of points G in P …

Abstract In 1973, Victor Klee posed the following question: How many guards are necessary,
and how many are sufficient to patrol the paintings and works of art in an art gallery with n …

Handbook of DISCRETE AND COMPUTATIONAL GEOMETRY Page 1 i “K25063” — 2017/9/15
— 18:58 — page 875 — i i i 33 VISIBILITY Joseph O’Rourke INTRODUCTION In a …

This is a review of various problems and results on the illumination of convex bodies in the
spirit of combinatorial geometry. The topics under review are: history of the Gohberg-Markus …

Given three angles summing to 2π, given n points in the plane and a tripartition k1+ k2+ k3=
n, we can tripartition the plane into three wedges of the given angles so that the i-th wedge …

Illumination problems of several kinds have been studied intensely in recent years [6]. One
of the first results in this area is that of Chvatal [2] which states that any simple polygon with n …

It is shown that a set of n disjoint line segments in the plane can always be illuminated by
⌊(n+1)/2⌋ light sources, improving an earlier bound of ⌊2n/3⌋ due to Czyzowicz et al. It is …

This thesis addressed the three-dimensional Art Gallery Problem (3D-AGP), a version of the
art gallery problem, which aims to determine the number of guards required to cover the …

In any surveillance or remote monitoring system, the location and configuration/orientation of
directed optical sensors is critical for efficient resource utilization as well as correct system …