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CCCG
2006

Rotationally Monotone Polygons

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Rotationally Monotone Polygons
We introduce a generalization of monotonicity. An n-vertex polygon P is rotationally monotone with respect to a point r if there exists a partitioning of the boundary of P into exactly two polygonal chains, such that one chain can be rotated clockwise around r and the other chain can be rotated counterclockwise around r with neither chain intersecting the interior of the polygon. We present the following two results: (1) Given P and a center of rotation r in the plane, we determine in O(n) time whether P is rotationally monotone with respect to r. (2) We can find all the points in the plane from which P is rotationally monotone in O(n) time for convex polygons and in O(n2 ) time for simple polygons. We show that both algorithms are worst-case optimal by constructing a class of simple polygons with (n2 ) distinct valid centers of rotation. A direct application of rotational monotonicity is the popular manufacturing technique of clamshell casting, where liquid is poured into a cast and ...
Prosenjit Bose, Pat Morin, Michiel H. M. Smid, Ste
Added 30 Oct 2010
Updated 30 Oct 2010
Type Conference
Year 2006
Where CCCG
Authors Prosenjit Bose, Pat Morin, Michiel H. M. Smid, Stefanie Wuhrer
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