Capturing points with a rotating polygon (and a 3D extension)
Carlos Alegr\'ia-Galicia, David Orden, Leonidas Palios, Carlos Seara,, and Jorge Urrutia
TL;DR
This paper investigates optimal rotation strategies for polygons and polyhedra to maximize the inclusion of points from a given set, covering various geometric constraints and extending to three dimensions.
Contribution
It introduces new algorithms for rotating polygons and polyhedra to maximize point inclusion under different constraints, including a 3D extension.
Findings
Optimal rotation algorithms for polygons with fixed centers
Extension of methods to 3D polyhedra
Effective solutions for various geometric constraints
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.
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