Capturing Points with a Rotating Polygon (and a 3D Extension) - Alegría-Galicia, Carlos; Orden, David; Palios, Leonidas; Seara, Carlos; Urrutia, Jorge (Theory of computing systems, 2019)
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 segment or a line. 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.