For many applications, including robotic planning, obstacle avoidance, and mapping it has been observed with laser range-scanners and depth sensors that their sampling densities, i.e., the number of range measurements per unit length of the scanned contour, can vary greatly even within a single scan measurement. In this paper, an on-line placement algorithm is proposed that computes where the robot must next move so as to sample its environment uniformly and densely. The algorithm guarantees the minimum number of measurements per unit length of the observed space, obtaining a high and uniform spatial measurement density. It provides a Next-Best-View relative to a robot's current position while satisfying a locally-defined constraint function based on the sampling density of points. Three variants of this algorithm, suitable for different practical applications are demonstrated with experiments on real robots in interesting scenarios.