An optimal algorithm for finding all visible edges in a simple polygon

By treating the floor plan of the building as a polygon, the authors study the problem of locating a camera for surveillance. A polygon P is point-visible if there exists a point x in P such that every other point in P is visible from x. If the polygon is point-visible then only one camera is needed. A visible edge corresponds to the wall on which the camera is to be mounted. While a given edge can be tested for visibility in time linear in the number of edges, there can be O(n) such edges. An O(n) time algorithm for finding all visible edges in a point-visible polygon is given. Specifically, it is shown that if the kernel of a simple polygon is nonempty, then all visible edges, whether completely, strongly, or weakly visible, can be found in O(n) time.<
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