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
Generating random points in triangles
Graphics gems
Incremental topological flipping works for regular triangulations
SCG '92 Proceedings of the eighth annual symposium on Computational geometry
Antialiasing through stochastic sampling
SIGGRAPH '85 Proceedings of the 12th annual conference on Computer graphics and interactive techniques
Wang Tiles for image and texture generation
ACM SIGGRAPH 2003 Papers
Physically Based Rendering: From Theory to Implementation
Physically Based Rendering: From Theory to Implementation
A Linear Bound on the Complexity of the Delaunay Triangulation of Points on Polyhedral Surfaces
Discrete & Computational Geometry
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
ACM SIGGRAPH 2007 papers
Fast Poisson disk sampling in arbitrary dimensions
ACM SIGGRAPH 2007 sketches
Scan primitives for GPU computing
Proceedings of the 22nd ACM SIGGRAPH/EUROGRAPHICS symposium on Graphics hardware
Parallel white noise generation on a GPU via cryptographic hash
Proceedings of the 2008 symposium on Interactive 3D graphics and games
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
Accurate multidimensional Poisson-disk sampling
ACM Transactions on Graphics (TOG)
Parallel Poisson disk sampling with spectrum analysis on surfaces
ACM SIGGRAPH Asia 2010 papers
Efficient and good Delaunay meshes from random points
Computer-Aided Design
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
A Low-Memory, Straightforward and Fast Bilateral Filter Through Subsampling in Spatial Domain
Computer Graphics Forum
A Simple Algorithm for Maximal Poisson-Disk Sampling in High Dimensions
Computer Graphics Forum
Parameterization-Aware MIP-Mapping
Computer Graphics Forum
Fast Generation of Approximate Blue Noise Point Sets
Computer Graphics Forum
Parallel Blue-noise Sampling by Constrained Farthest Point Optimization
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
Design and novel uses of higher-dimensional rasterization
EGGH-HPG'12 Proceedings of the Fourth ACM SIGGRAPH / Eurographics conference on High-Performance Graphics
Adaptive maximal Poisson-disk sampling on surfaces
SIGGRAPH Asia 2012 Technical Briefs
Line segment sampling with blue-noise properties
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)
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
Improving spatial coverage while preserving the blue noise of point sets
Computer-Aided Design
Parallel structure-aware halftoning
Multimedia Tools and Applications
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We solve the problem of generating a uniform Poisson-disk sampling that is both maximal and unbiased over bounded non-convex domains. To our knowledge this is the first provably correct algorithm with time and space dependent only on the number of points produced. Our method has two phases, both based on classical dart-throwing. The first phase uses a background grid of square cells to rapidly create an unbiased, near-maximal covering of the domain. The second phase completes the maximal covering by calculating the connected components of the remaining uncovered voids, and by using their geometry to efficiently place unbiased samples that cover them. The second phase converges quickly, overcoming a common difficulty in dart-throwing methods. The deterministic memory is O(n) and the expected running time is O(n log n), where n is the output size, the number of points in the final sample. Our serial implementation verifies that the log n dependence is minor, and nearly O(n) performance for both time and memory is achieved in practice. We also present a parallel implementation on GPUs to demonstrate the parallel-friendly nature of our method, which achieves 2.4x the performance of our serial version.