An Optimal Algorithm for Determining the Visibility of a Polygon from an Edge

In many computer applications areas such as graphics, automated cartography, image processing, and robotics the notion of visibility among objects modeled as polygons is a recurring theme. This paper is concerned with the visibility of a simple polygon from one of its edges. Three natural definitions of the visibility of a polygon from an edge are presented. The following computational problem is considered. Given an n-sided simple polygon, is the polygon visible from a specified edge? An O(n), and thus optimal, algorithm is exhibited for determining edge visibility under any of the three definitions. The paper closes with an interesting characterization of visibility and some open problems in this area.