The Polygon Exploration Problem II: The Angle Hull
Frank Hoffmann, Christian Icking, Rolf Klein, Klaus Kriegel · 1998
Let D be a connected region inside a simple polygon, P . We define the angle hull of 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 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 di#erent from 90 # , and to settings where region D is surrounded by obstacles other than a simple polygon.