Abstract: We investigate choosing point samples on a model comprising parametric patches to meet a user specified budget. These samples may then be triangulated, rendered as points or ray-traced. The main idea is to pre-compute a set of samples on the surface and at the rendering time, use a subset that meets the total budget while reducing the screen-space error across the model. We have used this algorithm for interactive display of large spline models on low-end graphics workstations. This is done by distributing the points on the surface to minimize surface error. These points are then drawn as screen-space squares to fill the gaps between them. Our algorithm works well in practice and has a low memory footprint.