Stochastic sampling in computer graphics
ACM Transactions on Graphics (TOG)
Power diagrams: properties, algorithms and applications
SIAM Journal on Computing
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
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Spectrally optimal sampling for distribution ray tracing
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
Hierarchical Poisson disk sampling distributions
Proceedings of the conference on Graphics interface '92
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
A new Voronoi-based surface reconstruction algorithm
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
Regular triangulations of dynamic sets of points
Computer Aided Geometric Design
Fast hierarchical importance sampling with blue noise properties
ACM SIGGRAPH 2004 Papers
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
Fast Poisson disk sampling in arbitrary dimensions
ACM SIGGRAPH 2007 sketches
Generic Remeshing of 3D Triangular Meshes with Metric-Dependent Discrete Voronoi Diagrams
IEEE Transactions on Visualization and Computer Graphics
Parallel Poisson disk sampling
ACM SIGGRAPH 2008 papers
Direct sampling on surfaces for high quality remeshing
Proceedings of the 2008 ACM symposium on Solid and physical modeling
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)
Isotropic remeshing with fast and exact computation of Restricted Voronoi Diagram
SGP '09 Proceedings of the Symposium on Geometry Processing
Multi-class blue noise sampling
ACM SIGGRAPH 2010 papers
Parallel Poisson disk sampling with spectrum analysis on surfaces
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
Farthest-point optimized point sets with maximized minimum distance
Proceedings of the ACM SIGGRAPH Symposium on High Performance Graphics
Efficient and good Delaunay meshes from random points
Computer-Aided Design
ACM Transactions on Graphics (TOG) - SIGGRAPH 2012 Conference Proceedings
Applications of Geometry Processing: Blue noise sampling of surfaces
Computers and Graphics
Efficient and Flexible Sampling with Blue Noise Properties of Triangular Meshes
IEEE Transactions on Visualization and Computer Graphics
Least squares quantization in PCM
IEEE Transactions on Information Theory
A Simple Algorithm for Maximal Poisson-Disk Sampling in High Dimensions
Computer Graphics Forum
Variational Blue Noise Sampling
IEEE Transactions on Visualization and Computer Graphics
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
EGSR'09 Proceedings of the Twentieth Eurographics conference on Rendering
Efficient computation of clipped Voronoi diagram for mesh generation
Computer-Aided Design
ACM Transactions on Graphics (TOG)
A parallel algorithm for improving the maximal property of Poisson disk sampling
Computer-Aided Design
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In this article, we study the generation of maximal Poisson-disk sets with varying radii. First, we present a geometric analysis of gaps in such disk sets. This analysis is the basis for maximal and adaptive sampling in Euclidean space and on manifolds. Second, we propose efficient algorithms and data structures to detect gaps and update gaps when disks are inserted, deleted, moved, or when their radii are changed. We build on the concepts of regular triangulations and the power diagram. Third, we show how our analysis contributes to the state-of-the-art in surface remeshing.