Abstract: In many graphics tasks, such as pixel antialiasing, a set of spatially "uniform" samples must be generated on a unit square. Some algorithms attempt to create sets of samples whose x and y coordinates are each themselves uniform, while making sure that the samples are also uniform in two dimensions. However, this is hard to do if the number of samples is not a perfect square. In this paper, we introduce a new sampling strategy which generates any number of uniform two-dimensional samples while maintaining uniformity in x and y as well.