Stochastic sampling in computer graphics
ACM Transactions on Graphics (TOG)
Digital halftoning
Generating antialiased images at low sampling densities
SIGGRAPH '87 Proceedings of the 14th annual conference on Computer graphics and interactive techniques
Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
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
The aliasing problem in computer-generated shaded images
Communications of the ACM
NPAR '02 Proceedings of the 2nd international symposium on Non-photorealistic animation and rendering
Wang Tiles for image and texture generation
ACM SIGGRAPH 2003 Papers
Fast hierarchical importance sampling with blue noise properties
ACM SIGGRAPH 2004 Papers
Voronoi treemaps for the visualization of software metrics
SoftVis '05 Proceedings of the 2005 ACM symposium on Software visualization
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)
ACM SIGGRAPH 2007 papers
Fast Poisson disk sampling in arbitrary dimensions
ACM SIGGRAPH 2007 sketches
Parallel Poisson disk sampling
ACM SIGGRAPH 2008 papers
Capacity-constrained point distributions: a variant of Lloyd's method
ACM SIGGRAPH 2009 papers
On centroidal voronoi tessellation—energy smoothness and fast computation
ACM Transactions on Graphics (TOG)
Accurate multidimensional Poisson-disk sampling
ACM Transactions on Graphics (TOG)
Capacity-Constrained Voronoi Diagrams in Continuous Spaces
ISVD '09 Proceedings of the 2009 Sixth International Symposium on Voronoi Diagrams
Fast capacity constrained Voronoi tessellation
Proceedings of the 2010 ACM SIGGRAPH symposium on Interactive 3D Graphics and Games
Multi-class blue noise sampling
ACM SIGGRAPH 2010 papers
Parallel Poisson disk sampling with spectrum analysis on surfaces
ACM SIGGRAPH Asia 2010 papers
Anisotropic blue noise sampling
ACM SIGGRAPH Asia 2010 papers
Blue-noise point sampling using kernel density model
ACM SIGGRAPH 2011 papers
Efficient maximal poisson-disk sampling
ACM SIGGRAPH 2011 papers
Differential domain analysis for non-uniform sampling
ACM SIGGRAPH 2011 papers
HOT: Hodge-optimized triangulations
ACM SIGGRAPH 2011 papers
SMI 2011: Full Paper: Capacity-Constrained Delaunay Triangulation for point distributions
Computers and Graphics
Farthest-point optimized point sets with maximized minimum distance
Proceedings of the ACM SIGGRAPH Symposium on High Performance Graphics
Displacement interpolation using Lagrangian mass transport
Proceedings of the 2011 SIGGRAPH Asia Conference
Algorithm 915, SuiteSparseQR: Multifrontal multithreaded rank-revealing sparse QR factorization
ACM Transactions on Mathematical Software (TOMS)
Parallel and accurate Poisson disk sampling on arbitrary surfaces
SIGGRAPH Asia 2011 Sketches
Point sampling with general noise spectrum
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Applications of Geometry Processing: Blue noise sampling of surfaces
Computers and Graphics
Least squares quantization in PCM
IEEE Transactions on Information Theory
Variational Blue Noise Sampling
IEEE Transactions on Visualization and Computer Graphics
Ardeco: automatic region detection and conversion
EGSR'06 Proceedings of the 17th Eurographics conference on Rendering Techniques
Computing self-supporting surfaces by regular triangulation
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
PixelPie: maximal Poisson-disk sampling with rasterization
Proceedings of the 5th High-Performance Graphics Conference
ACM Transactions on Graphics (TOG)
Gap processing for adaptive maximal poisson-disk sampling
ACM Transactions on Graphics (TOG)
Improving spatial coverage while preserving the blue noise of point sets
Computer-Aided Design
Fast adaptive blue noise on polygonal surfaces
Graphical Models
Approximating functions on a mesh with restricted Voronoï diagrams
SGP '13 Proceedings of the Eleventh Eurographics/ACMSIGGRAPH Symposium on Geometry Processing
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We present a fast, scalable algorithm to generate high-quality blue noise point distributions of arbitrary density functions. At its core is a novel formulation of the recently-introduced concept of capacity-constrained Voronoi tessellation as an optimal transport problem. This insight leads to a continuous formulation able to enforce the capacity constraints exactly, unlike previous work. We exploit the variational nature of this formulation to design an efficient optimization technique of point distributions via constrained minimization in the space of power diagrams. Our mathematical, algorithmic, and practical contributions lead to high-quality blue noise point sets with improved spectral and spatial properties.