In a cellular network, the service coverage area is divided into cells, each of which is served by a base station. Although the cellular network provides great convenience for mobile users, the transmitter at the base station emits radio frequency (RF) radiation which can be harmful to humans nearby. To minimize human exposure to RF radiation, the base stations should be placed as far away from densely populated sites as possible in network planning. The problem to be solved in this paper, referred to as the minimal exposure problem, is abstracted as follows: given a set of sites and a planned cellular network that has a fixed cell size and network orientation but is movable, find a position to deploy the planned network such that the minimal distance between the sites and their corresponding base stations in the deployed network is maximized. To solve the problem, the paper proposes a new geometric diagram called the nearest-point umbrella diagram. The nearest-point umbrella diagram is comparable to the famous nearest-point Voronoi diagram. The Voronoi diagram uses the Euclidian distance between two points whereas the umbrella diagram uses the distance between a point and a cellular network. Based on the umbrella diagram, the minimal exposure problem can be solved in O(n^2logn) time if there are n sites to be considered.