Stochastic sampling in computer graphics
ACM Transactions on Graphics (TOG)
Digital halftoning
Hierarchical Poisson disk sampling distributions
Proceedings of the conference on Graphics interface '92
The aliasing problem in computer-generated shaded images
Communications of the ACM
Anisotropic Centroidal Voronoi Tessellations and Their Applications
SIAM Journal on Scientific Computing
Variational tetrahedral meshing
ACM SIGGRAPH 2005 Papers
Centroidal Voronoi diagrams for isotropic surface remeshing
Graphical Models - Special issue on SMI 2003
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)
Fast capacity constrained Voronoi tessellation
Proceedings of the 2010 ACM SIGGRAPH symposium on Interactive 3D Graphics and Games
Anisotropic blue noise sampling
ACM SIGGRAPH Asia 2010 papers
Least squares quantization in PCM
IEEE Transactions on Information Theory
Applications of Geometry Processing: Blue noise sampling of surfaces
Computers and Graphics
Parallel Blue-noise Sampling by Constrained Farthest Point Optimization
Computer Graphics Forum
Special Section on CANS: Irregular pit placement for dithering images by self-occlusion
Computers and Graphics
Blue noise through optimal transport
ACM Transactions on Graphics (TOG) - Proceedings of ACM SIGGRAPH Asia 2012
Fast adaptive blue noise on polygonal surfaces
Graphical Models
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Sample point distributions possessing blue noise spectral characteristics play a central role in computer graphics, but are notoriously difficult to generate. We describe an algorithm to very efficiently generate these distributions. The core idea behind our method is to compute a Capacity-Constrained Delaunay Triangulation (CCDT), namely, given a simple polygon P in the plane, and the desired number of points n, compute a Delaunay triangulation of the interior of P with n Steiner points, whose triangles have areas which are as uniform as possible. This is computed iteratively by alternating update of the point geometry and triangulation connectivity. The vertex set of the CCDT is shown to have good blue noise characteristics, comparable in quality to those of state-of-the-art methods, achieved at a fraction of the runtime. Our CCDT method may be applied also to an arbitrary density function to produce non-uniform point distributions. These may be used to half-tone grayscale images.