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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 doublecones of directions. (A doublecone 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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 Spring '08
 Mitchell,J

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