Capturing points with a rotating polygon (and a 3D extension)

05/07/2018

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by   Carlos Alegría-Galicia, et al.

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We study the problem of rotating a simple polygon to contain the maximum number of elements from a given point set in the plane. We consider variations of this problem where the rotation center is a given point or lies on a line segment, a line, or a polygonal chain. We also solve an extension to 3D where we rotate a polyhedron around a given point to contain the maximum number of elements from a set of points in the space.