On the covering radius of lattice zonotopes and its relation to view-obstructions and the lonely runner conjecture

The goal of this paper is twofold; first, we show the equivalence between certain problems in geometry, such as view-obstructions, billiard ball motions, and the estimation of covering radii of lattice zonotopes. Second, we utilize the latter interpretation and provide upper bounds of said radii by virtue of the Flatness Theorem. Our results allow us to specify how rational dependencies in the view-direction influence the obstruction parameter. These problems are similar in nature to the famous Lonely Runner Problem for which we draw analogous conclusions.