Maximal Poisson-disk sampling by sampling radius optimization

Abstract

In the field of computer graphics, maximal Poisson-disk sampling (MPS) is a fundamental research topic. An ideal sampling set should satisfy unbiased sampling property, minimal distance property, and maximal sampling property. In general, MPS is obtained by Dart Throwing, as we all know, the drawback of this method is unable to precisely control the number of samples. In view of the above problem, this work proposes a novelty algorithm that can precisely control the number of samples of two-dimensional radius-equal MPS, and satisfy other properties simultaneously. Unlike existing methods, the proposed method controls the number of samples by adjusting sampling radius. Firstly, according to user-specified the number of samples and sampling domain (closed polygon), initial samples are randomly obtained, then Delaunay triangulation is conducted, and taking as current sampling radius the shortest edge length of the triangulation. Secondly, iteratively removing the endpoint of global shortest edge with larger neighborhood-averaged edge length, and then using Dart Throwing to randomly insert it into gap region that is calculated at current sampling radius. By iteratively adjusting the position of points, the sampling radius increases gradually, finally, MPS with fixed number of sampling point can be achieved. Experimental results show that this method generates point sets with high quality, at the same time, ensures the excellent blue-noise property for MPS.