Approximating Poisson Disk Distributions by Means of a Stochastic Dither Array

Abstract

Achieving blue noise point set distributions has been a common goal of two largely separate research communities: computer graphics and digital halftoning. Computer graphics research has focused largely on geometric solutions in continuous spaces. Digital halftoning research has focused on signal processing solutions in discrete imagebased space. Usage of Poisson Disk point sets in computer graphics has grown beyond sampling, including object distribution and texturing, among others. The image-based field of digital halftoning can provide additional tools for graphics researchers and practitioners. It is of interest to explore the suitability of digital halftoning technology to two classic problems in computer graphics: (1) approximating Poisson Disk point distributions of constant density and (2) importance sampling of an underlying importance function. Exemplary methods from each field are implemented and, by applying well-established measures of the radially averaged power spectrum and anisotropy plots, are shown to be quite similar, although the approaches are mathematically not equivalent. Additionally, we compare the relative radius of the point sets. Further, the ability of dither array construction techniques to shape spectral characteristics of dot patterns is shown with several variations of design parameters.