A parallel algorithm for improving the maximal property of Poisson disk sampling

• A simple algorithm for improving the maximal property of Poisson disk sampling.
• The algorithm is fully parallel and can be implemented on the GPU.
• It works for 2D and 3D, and can also be extended to surface in an intrinsic manner.

This paper presents a simple yet effective algorithm to improve an arbitrary Poisson disk sampling to reach the maximal property, i.e., no more Poisson disk can be inserted. Taking a non-maximal Poisson disk sampling as input, our algorithm efficiently detects the regions allowing additional samples and then generates Poisson disks in these regions. The key idea is to convert the complicated plane or space searching problem into a simple searching on circles or spheres, which is one dimensional lower than the original sampling domain. Our algorithm is memory efficient and flexible, which generates maximal Poisson disk sampling in an arbitrary 2D polygon or 3D polyhedron. Moreover, our parallel algorithm can be extended from the Euclidean space to curved surfaces in an intrinsic manner. Thanks to its parallel structure, our method can be implemented easily on modern graphics hardware. We have observed significance performance improvement compared to the existing techniques.