The art gallery problem is to determine the number of guards that are sufficient to cover or see every point in the interior of an art gallery. An art gallery can be viewed as a polygon P with or without holes with a total of n vertices and guards as points in P . Any point z ∈ P is said to be visible from a guard g if the line segment joining z and g does not intersect the exterior of P . Usua...

We consider guarding classes of simple polygons using mobile guards (polygon edges and diagonals) under the constraint that no two guards may see each other. In contrast to most other art gallery problems, existence is the primary question: does a specific type of polygon admit some guard set? Types include simple polygons and the subclasses of orthogonal, monotone, and starshaped polygons. Add...

We study the problem of guarding orthogonal art galleries with horizontal mobile guards (alternatively, vertical) and point guards, using “rectangular vision”. We prove a sharp bound on the minimum number of point guards required to cover the gallery in terms of the minimum number of vertical mobile guards and the minimum number of horizontal mobile guards required to cover the gallery. Further...

This paper focuses on a variation of the Art Gallery problem that considers open edge guards and open mobile guards. A mobile guard can be placed on edges and diagonals of a polygon, and the “open” prefix means that the endpoints of such edge or diagonal are not taken into account for visibility purposes. This paper studies the number of guards that are sufficient and sometimes necessary to gua...

One of the earliest and most well known problems in computational geometry is the socalled art gallery problem. The goal is to compute the minimum possible number guards placed on the vertices of a simple polygon in such a way that they cover the interior of the polygon. In this paper we consider the problem of guarding an art gallery which is modeled as a polygon with curvilinear walls. Our ma...

We consider guarding a city of k vertical buildings, each having a rectangular base, by placing guards only at vertices. The aim is to use the smallest number of guards. The problem is a 2.5D variant of the traditional art gallery problem, and finds applications in urban security. We give upper and lower bounds on the number of guards needed for a few versions of the problem. Specifically, we p...

In football, injuries from opponent contact occur commonly in the lower extremities. FIFA the world's governing body for football requires players to wear shin guards. The aim of this study was to compare the protective effectiveness of polypropylene based shin guards with custom-made carbon fiber ones. Three commercial polypropylene shin guards (Adidas Predator™, Adidas UCL™, and Nike Mercuria...