Poisson disk sampling is an important problem in computer graphics and has a wide variety of applications in imaging, geometry, rendering, etc. In this paper, we propose a novel Poisson disk sampling algorithm based on disk packing. The key idea uses the observation that a relatively dense disk packing layout naturally satisfies the Poisson disk distribution property that each point is no closer to the others than a specified minimum distance, i.e., the Poisson disk radius. We use this property to propose a relaxation algorithm that achieves a good balance between the random and uniform properties needed for Poisson disk distributions. Our algorithm is easily adapted to image stippling by extending identical disk packing to unequal disks. Experimental results demonstrate the efficacy of our approaches.