This paper addresses the coverage problem for a collection of agents and fixed obstacles (e.g., the “gallery” and the “patrolling” problems). A collection of sufficient conditions over the positions of the agents are provided such that whenever these are verified there is no “blind” region in the feasible space. These conditions are expressed by making use of hyperplane arrangements which lead to a mixed-integer formulation. Practical applications regarding the coverage problem inside an augmented space with obstacles validate these concepts and provide an efficient implementation (in terms of computing power).