Stochastic sampling in computer graphics
ACM Transactions on Graphics (TOG)
Digital halftoning
Nonuniform random point sets via warping
Graphics Gems III
Hierarchical Poisson disk sampling distributions
Proceedings of the conference on Graphics interface '92
Antialiasing through stochastic sampling
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
NPAR '02 Proceedings of the 2nd international symposium on Non-photorealistic animation and rendering
VMV '01 Proceedings of the Vision Modeling and Visualization Conference 2001
Wang Tiles for image and texture generation
ACM SIGGRAPH 2003 Papers
Fast hierarchical importance sampling with blue noise properties
ACM SIGGRAPH 2004 Papers
A procedural object distribution function
ACM Transactions on Graphics (TOG)
A spatial data structure for fast Poisson-disk sample generation
ACM SIGGRAPH 2006 Papers
Recursive Wang tiles for real-time blue noise
ACM SIGGRAPH 2006 Papers
Parallel Poisson disk sampling
ACM SIGGRAPH 2008 papers
Poisson Disk Point Sets by Hierarchical Dart Throwing
RT '07 Proceedings of the 2007 IEEE Symposium on Interactive Ray Tracing
Capacity-constrained point distributions: a variant of Lloyd's method
ACM SIGGRAPH 2009 papers
Accurate multidimensional Poisson-disk sampling
ACM Transactions on Graphics (TOG)
Anisotropic blue noise sampling
ACM SIGGRAPH Asia 2010 papers
Least squares quantization in PCM
IEEE Transactions on Information Theory
Point sampling with general noise spectrum
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
PixelPie: maximal Poisson-disk sampling with rasterization
Proceedings of the 5th High-Performance Graphics Conference
Gap processing for adaptive maximal poisson-disk sampling
ACM Transactions on Graphics (TOG)
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Dart-throwing can generate ideal Poisson-disk distributions with excellent blue noise properties, but is very computationally expensive if a maximal point set is desired. In this paper, we observe that the Poisson-disk sampling problem can be posed in terms of importance sampling by representing the available space to be sampled as a probability density function (pdf). This allows us to develop an efficient algorithm for the generation of maximal Poisson-disk distributions with quality similar to naïve dart-throwing but without rejection of samples. In our algorithm, we first position samples in one dimension based on its marginal cumulative distribution function (cdf). We then throw samples in the other dimension only in the regions which are available for sampling. After each 2D sample is placed, we update the cdf and data structures to keep track of the available regions. In addition to uniform sampling, our method is able to perform variable-density sampling with small modifications. Finally, we also propose a new min-conflict metric for variable-density sampling which results in better adaptation of samples to the underlying importance field.