Let D be a connected region inside a simple polygon P. Authors define the angle hull, AH(D), of D to be the set of all points in P that can see two points of D at a right angle. They further prove that the perimeter AH(D) is at most twice the perimeter of the relative convex hull of D. In special case, when P is the full plane, this bound is given as {/pi}/2. Both bounds are tight.
The practical application of this topic is found in designing on-line competitive navigation strategies for autonomous robots in unknown environments.