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
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
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 maximal poisson-disk sampling
ACM SIGGRAPH 2011 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
Parallel Blue-noise Sampling by Constrained Farthest Point Optimization
Computer Graphics Forum
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
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
FEM with Trefftz trial functions on polyhedral elements
Journal of Computational and Applied Mathematics
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We provide a simple algorithm and data structures for d-dimensional unbiased maximal Poisson-disk sampling. We use an order of magnitude less memory and time than the alternatives. Our results become more favorable as the dimension increases. This allows us to produce bigger samplings. Domains may be non-convex with holes. The generated point cloud is maximal up to round-off error. The serial algorithm is provably bias-free. For an output sampling of size n in fixed dimension d, we use a linear memory budget and empirical θ(n) runtime. No known methods scale well with dimension, due to the “curse of dimensionality.” The serial algorithm is practical in dimensions up to 5, and has been demonstrated in 6d. We have efficient GPU implementations in 2d and 3d. The algorithm proceeds through a finite sequence of uniform grids. The grids guide the dart throwing and track the remaining disk-free area. The top-level grid provides an efficient way to test if a candidate dart is disk-free. Our uniform grids are like quadtrees, except we delay splits and refine all leaves at once. Since the quadtree is flat it can be represented using very little memory: we just need the indices of the active leaves and a global level. Also it is very simple to sample from leaves with uniform probability. © 2012 Wiley Periodicals, Inc.