Poisson disk sampling : modern techniques

Abstract

Poisson disk sampling has proven to be very useful and versatile in a variety of computer graphics applications in the past 35 years, since it was first introduced to solve the ray tracing sampling problem. It can simply and mathematically be defined as a set of samples (points) in a certain distance space such that each sample is at least a certain distance away from others. Poisson disk sampling is far better than any other sampling methods in the sense that it achieves the combined objective of acquiring the highest quality in visual appearance and producing the least spectral artifacts in the spectral domain. Henceforth, it is favored for ray tracing, which desires the least artifacts when using a small number of ray samples, stippling which requires a uniform distribution of drawing metaphors to represent gray scale smoothly without any noticeable structure, surface remeshing for its random and uniform resultant vertex positions, and many other applications which ask for a uniform distribution of objects in any distance space. In this thesis, I present my three works on Poisson disk sampling, each of which addresses certain problems in a more specific context: Poisson disk sampling on surface by using dual Poisson disk tiling, the acceleration of capacity constrained Voronoi tessellation in 2D Euclidean space and anisotropic Poisson disk sampling in Riemannian distance space. Apart from the detailed description of my own work, prior work on the same topic is also discussed to serve as a background to current Poisson disk sampling research. I categorized the algorithms into 3 chapters based on their working domain: 2D Euclidean space, manifold surface and Riemannian space. Finally, I compare different Poisson disk sampling algorithms in terms of quality and performance in order to provide a reference by which the audience can grasp the usage of Poisson disk sampling in their own research problems.