Various industrial applications require point sets that cover arbitrarily shaped surfaces of 3D objects. The nature of the sampling required depends on the application; while common machining or inspection processes need regularly arranged points for smooth path generation, the application described in this paper requires a more subtle distribution to provide a high-quality result. We contrast two sampling algorithms developed to support a novel, contactless robotic painting system which creates images on surfaces by selectively exposing a photographic coating using a robot-mounted laser. We assume the object to be painted is represented as a triangular mesh. A straightforward layered approach to sample point generation is compared to framework that produces a density-controlled low-discrepancy distribution. We show that the distortions associated with laminar slicing are avoided if the more sophisticated distribution is used.