Determining Sector Visibility of a Polygon

this paper we focus on weak external visibility of a polygon. This topic is as yet quite unexplored compared to its internal counterpart. Toussaint and Avis [TA] considered the problem of determining if a polygon is weakly externally visible. (Since we will restrict ourselves hereafter to notions of visibility that are both weak and external we will drop these adjectives for the sake of less cumbersome terminology). A polygon P is edge-visible if for each point x Î P there exists a ray that supports P at x. This is equivalent to saying that P is visible from a circle at infinity (or, in fact, any circle that properly encloses P). Toussaint and Avis [TA], using related results of [AT], show that edge-visibility of polygons can be recognized in O(n) time. This result is proved by showing that the edge-visibility problem is equivalent to the somewhat less constrained vertex-visibility problem: determine, for each vertex v Î P, if there exists a ray that supports P at v