Deterministic Blue Noise Sampling by Solving Largest Empty Circle Problems

〈Summary〉 Sampling patterns with a blue noise distribution are widely used in many areas of computer graphics, yet their efficient generation remains a difficult problem. We propose a method to generate point sets with a blue noise distribution using a deterministic algorithm with no preprocessing. We insert each new sample at the center of the largest empty circle in the point set, which is obtained by calculating the Delaunay-triangulation of the set and finding the triangle with the largest circumcircle. Our method supports adaptive sampling according to a user-specified density function, as well as specifying the exact number of required samples. It can also be extended to perform sampling on a three-dimensional curved surface.