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Unformatted text preview: AMS 345/CSE 355 (Fall, 2010) Joe Mitchell COMPUTATIONAL GEOMETRY Homework Set # 3 Solution Notes (1). Give an example of a monotone simple polygon for which the set of directions d with respect to which it is monotone consists of at least two distinct double-cones of directions. (A double-cone of directions consists of an interval of angles, and the interval of their opposites; e.g., a double- cone may consist of angles (in degrees) in the intervals (10,45) and (190, 225), or of angles in the intervals (-10,10) and (170,190).) Show the set of directions with respect to which your polygon is monotone (e.g., highlight arcs on a circle to show the set of directions/angles). There are many possible examples. One class of examples is based on taking a convex polygon and denting inward each of its sides. See the example below. Another example comes from a cross or plus sign, +, for which the set of directions with respect to which the (rectilinear) polygon is monotone consists of just 0 (=180) degrees and 90 (=270) degrees (two point intervals).polygon is monotone consists of just 0 (=180) degrees and 90 (=270) degrees (two point intervals)....
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