The coverage control problem for mobile sensor networks in non-convex environments is addressed in this article. The sensing model of each node is assumed identical and radial either in the geodesic or the Euclidean sense. Depending on the selected metric, the partitioning of the non-convex domain can result either in the geodesic or the Euclidean Voronoi diagram. The coverage problem is examined from a two-fold aspect: based on a) proper selection of the sensing model, and b) the partitioning scheme, as directed by the application itself. Distributed collaborative control schemes are developed, further validated via extensive numerical studies.