ON THE NUMBER OF GUARD EDGES OF A POLYGON

Abstract

This paper establishes tight bounds on the number of edges of a polygon from which every point in the polygon is visible; we call them guard edges. For a nonstarshaped polygon, there can be at most three guard edges. For a polygon with holes, there may be at most six; three on the outer boundary and three on one of the holes. The results give new insights into the structure of visibility in polygons and shed light on developing an efficient algorithm for finding all guard edges of a polygon with or without holes.