The Polygon Exploration Problem II : The Angle Hull
Let D be a connected region inside a simple polygon, P. We define the angle hull of D, AH(D), to be the set of all points in P that can see two points of D at a right angle. We show that the perimeter of AH(D) cannot exceed in length the perimeter of D by more than a factor of 2. This upper bound is tight. Our result can be generalized to angles different from 90°, and to settings where region D is surrounded by obstacles other than a simple polygon.
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