A simple algorithm for determining the envelope of a set of lines
Information Processing Letters
Moldable and castable polygons
Computational Geometry: Theory and Applications
Overlaying simply connected planar subdivisions in linear time
Proceedings of the eleventh annual symposium on Computational geometry
Computational geometry: algorithms and applications
Computational geometry: algorithms and applications
Handbook of discrete and computational geometry
Handbook of discrete and computational geometry
Computational Geometry in C
Optimally computing a shortest weakly visible line segment inside a simple polygon
Computational Geometry: Theory and Applications
An Optimal Algorithm for Determining the Visibility of a Polygon from an Edge
IEEE Transactions on Computers
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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(n^2) time for simple polygons. We show that both algorithms are worst-case optimal by constructing a class of simple polygons with @W(n^2) 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 the cast is removed by rotations once the liquid has hardened.