Stochastic sampling in computer graphics
ACM Transactions on Graphics (TOG)
Generating antialiased images at low sampling densities
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Algorithms for solid noise synthesis
SIGGRAPH '89 Proceedings of the 16th annual conference on Computer graphics and interactive techniques
The design and analysis of spatial data structures
The design and analysis of spatial data structures
A simple method for box-sphere intersection testing
Graphics gems
Spectrally optimal sampling for distribution ray tracing
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Nonuniform random point sets via warping
Graphics Gems III
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Hierarchical Poisson disk sampling distributions
Proceedings of the conference on Graphics interface '92
A cellular texture basis function
SIGGRAPH '96 Proceedings of the 23rd annual conference on Computer graphics and interactive techniques
Realistic modeling and rendering of plant ecosystems
Proceedings of the 25th annual conference on Computer graphics and interactive techniques
Antialiasing through stochastic sampling
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Principles of Digital Image Synthesis
Principles of Digital Image Synthesis
Fast primitive distribution for illustration
EGRW '02 Proceedings of the 13th Eurographics workshop on 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
Journal of Computational Physics
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
An alternative for Wang tiles: colored edges versus colored corners
ACM Transactions on Graphics (TOG)
Advanced Global Illumination
ACM SIGGRAPH 2007 papers
Fast Poisson disk sampling in arbitrary dimensions
ACM SIGGRAPH 2007 sketches
IEEE Transactions on Visualization and Computer Graphics
Parallel Poisson disk sampling
ACM SIGGRAPH 2008 papers
Multidimensional adaptive sampling and reconstruction for ray tracing
ACM SIGGRAPH 2008 papers
A meshless hierarchical representation for light transport
ACM SIGGRAPH 2008 papers
Direct sampling on surfaces for high quality remeshing
Proceedings of the 2008 ACM symposium on Solid and physical modeling
Dual Poisson-Disk Tiling: An Efficient Method for Distributing Features on Arbitrary Surfaces
IEEE Transactions on Visualization and Computer Graphics
Poisson Disk Point Sets by Hierarchical Dart Throwing
RT '07 Proceedings of the 2007 IEEE Symposium on Interactive Ray Tracing
Blue-noise point sampling using kernel density model
ACM SIGGRAPH 2011 papers
Efficient maximal poisson-disk sampling
ACM SIGGRAPH 2011 papers
Farthest-point optimized point sets with maximized minimum distance
Proceedings of the ACM SIGGRAPH Symposium on High Performance Graphics
Customizing painterly rendering styles using stroke processes
Proceedings of the ACM SIGGRAPH/Eurographics Symposium on Non-Photorealistic Animation and Rendering
Efficient and good Delaunay meshes from random points
Computer-Aided Design
A Simple Algorithm for Maximal Poisson-Disk Sampling in High Dimensions
Computer Graphics Forum
Fast Generation of Approximate Blue Noise Point Sets
Computer Graphics Forum
Analysis and synthesis of point distributions based on pair correlation
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Blue noise through optimal transport
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Efficient computation of blue noise point sets through importance sampling
EGSR'11 Proceedings of the Twenty-second Eurographics conference on Rendering
Design and novel uses of higher-dimensional rasterization
EGGH-HPG'12 Proceedings of the Fourth ACM SIGGRAPH / Eurographics conference on High-Performance Graphics
Fourier analysis of stochastic sampling strategies for assessing bias and variance in integration
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 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)
k-d Darts: Sampling by k-dimensional flat searches
ACM Transactions on Graphics (TOG)
A parallel algorithm for improving the maximal property of Poisson disk sampling
Computer-Aided Design
Parallel structure-aware halftoning
Multimedia Tools and Applications
Fast adaptive blue noise on polygonal surfaces
Graphical Models
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We present an accurate and efficient method to generate samples based on a Poisson-disk distribution. This type of distribution, because of its blue noise spectral properties, is useful for image sampling. It is also useful for multidimensional Monte Carlo integration and as part of a procedural object placement function. Our method extends trivially from 2D to 3D or to any higher dimensional space. We demonstrate results for up to four dimensions, which are likely to be the most useful for computer graphics applications. The method is accurate because it generates distributions with the same statistical properties of those generated with the brute-force dart-throwing algorithm, the archetype against which all other Poisson-disk sampling methods are compared. The method is efficient because it employs a spatial subdivision data structure that signals the regions of space where the insertion of new samples is allowed. The method has O(N log N) time and space complexity relative to the total number of samples. The method generates maximal distributions in which no further samples can be inserted at the completion of the algorithm. The method is only limited in the number of samples it can generate and the number of dimensions over which it can work by the available physical memory.