Parallel and accurate Poisson disk sampling on arbitrary surfaces

• Authors: Ying Xiang;Shi-Qing Xin;Qian Sun;Ying He
• Venue: SIGGRAPH Asia 2011 Sketches
• Year: 2011

Sampling plays an important role in a variety of graphics applications. Among existing sampling methods, Poisson disk sampling is popular thanks to its useful statistical property in distribution and the absence of aliasing artifacts. Although many promising algorithms have been proposed for multi-dimensional sampling in Euclidean space, very few research studies have been reported with regard to the problem of generating Poisson disks on surfaces due to the complicated nature of the surface. This still remains a challenge due to the following reasons: first, a surface is a two-dimensional manifold that has arbitrary topology and complicated geometry, and is embedded in R3 or even higher dimensional space. Second, the exact geodesic distance should be used to enforce the minimum distance constraint between any pair of samples. Third, the algorithm should be parallelized such that it can make full use of all available threads. Last but not least, the generated samples should be randomly and uniformly distributed on surfaces, and exhibit the blue noise pattern without bias. Wei [2008] pioneered a parallel Poisson disk sampling algorithm by subdividing the sample domain into grid cells and drawing samples concurrently from multiple cells that are sufficiently far apart to avoid conflicts. Bowers et al. [2010] extended Wei's algorithm to 3D surfaces. Their method is highly efficient, allowing sampling on large-scale models at interactive speed. However, the generated distribution is not fully random since the sequence of processing the phase groups follows a predefined order. Moreover, the approximate geodesic computation in their approach results in large errors in models with rich features and thus compromises the sampling quality.