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, show the equivalence between certain problems in geometry, such as view-obstruction and billiard ball motions, with the estimation of covering radii of lattice zonotopes. Second, we will estimate upper bounds of said radii by virtue of the Flatness Theorem. These problems are similar in nature with the famous lonely runner conjecture.