Unbiased sampling techniques for image synthesis
Proceedings of the 18th annual conference on Computer graphics and interactive techniques
SIGGRAPH '92 Proceedings of the 19th annual conference on Computer graphics and interactive techniques
A Delaunay refinement algorithm for quality 2-dimensional mesh generation
SODA '93 Selected papers from the fourth annual ACM SIAM symposium on Discrete algorithms
Optimally combining sampling techniques for Monte Carlo rendering
SIGGRAPH '95 Proceedings of the 22nd annual conference on Computer graphics and interactive techniques
Guaranteed-quality Delaunay meshing in 3D (short version)
SCG '97 Proceedings of the thirteenth annual symposium on Computational geometry
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
On the Radius-Edge Condition in the Control Volume Method
SIAM Journal on Numerical Analysis
Smoothing and cleaning up slivers
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Mesh generation for domains with small angles
Proceedings of the sixteenth annual symposium on Computational geometry
Quality meshing for polyhedra with small angles
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
A Linear Bound on the Complexity of the Delaunay Triangulation of Points on Polyhedral Surfaces
Discrete & Computational Geometry
A time-optimal delaunay refinement algorithm in two dimensions
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
A spatial data structure for fast Poisson-disk sample generation
ACM SIGGRAPH 2006 Papers
Parallel Poisson disk sampling
ACM SIGGRAPH 2008 papers
Computational Geometry: Theory and Applications
Poisson Disk Point Sets by Hierarchical Dart Throwing
RT '07 Proceedings of the 2007 IEEE Symposium on Interactive Ray Tracing
Direct sampling on surfaces for high quality remeshing
Computer Aided Geometric Design
On centroidal voronoi tessellation—energy smoothness and fast computation
ACM Transactions on Graphics (TOG)
Accurate multidimensional Poisson-disk sampling
ACM Transactions on Graphics (TOG)
Delaunay Triangulations in O(sort(n)) Time and More
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Efficient maximal poisson-disk sampling
ACM SIGGRAPH 2011 papers
Least squares quantization in PCM
IEEE Transactions on Information Theory
Delaunay refinement algorithms for triangular mesh generation
Computational Geometry: Theory and Applications
A Simple Algorithm for Maximal Poisson-Disk Sampling in High Dimensions
Computer Graphics Forum
Adaptive maximal Poisson-disk sampling on surfaces
SIGGRAPH Asia 2012 Technical Briefs
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
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We present a Conforming Delaunay Triangulation (CDT) algorithm based on maximal Poisson disk sampling. Points are unbiased, meaning the probability of introducing a vertex in a disk-free subregion is proportional to its area, except in a neighborhood of the domain boundary. In contrast, Delaunay refinement CDT algorithms place points dependent on the geometry of empty circles in intermediate triangulations, usually near the circle centers. Unconstrained angles in our mesh are between 30^o and 120^o, matching some biased CDT methods. Points are placed on the boundary using a one-dimensional maximal Poisson disk sampling. Any triangulation method producing angles bounded away from 0^o and 180^o must have some bias near the domain boundary to avoid placing vertices infinitesimally close to the boundary. Random meshes are preferred for some simulations, such as fracture simulations where cracks must follow mesh edges, because deterministic meshes may introduce non-physical phenomena. An ensemble of random meshes aids simulation validation. Poisson-disk triangulations also avoid some graphics rendering artifacts, and have the blue-noise property. We mesh two-dimensional domains that may be non-convex with holes, required points, and multiple regions in contact. Our algorithm is also fast and uses little memory. We have recently developed a method for generating a maximal Poisson distribution of n output points, where n=@Q(Area/r^2) and r is the sampling radius. It takes O(n) memory and O(nlogn) expected time; in practice the time is nearly linear. This, or a similar subroutine, generates our random points. Except for this subroutine, we provably use O(n) time and space. The subroutine gives the location of points in a square background mesh. Given this, the neighborhood of each point can be meshed independently in constant time. These features facilitate parallel and GPU implementations. Our implementation works well in practice as illustrated by several examples and comparison to Triangle.