Capturing points with a rotating polygon (and a 3D extension)
arXiv:1805.02570 · doi:10.1007/s00224-018-9885-y
Abstract
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.
25 pages, 12 figures, submitted to journal in February 2017