Algorithms for clustering data
Algorithms for clustering data
A Delaunay based numerical method for three dimensions: generation, formulation, and partition
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Tetrahedral mesh generation by Delaunay refinement
Proceedings of the fourteenth annual symposium on Computational geometry
Proceedings of the 28th annual conference on Computer graphics and interactive techniques
An Efficient k-Means Clustering Algorithm: Analysis and Implementation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Grid generation and optimization based on centroidal Voronoi tessellations
Applied Mathematics and Computation
Constrained Centroidal Voronoi Tessellations for Surfaces
SIAM Journal on Scientific Computing
Tiling space and slabs with acute tetrahedra
Computational Geometry: Theory and Applications
IEEE Transactions on Information Theory
On quantization with the Weaire-Phelan partition
IEEE Transactions on Information Theory
Asymptotically optimal block quantization
IEEE Transactions on Information Theory
Voronoi regions of lattices, second moments of polytopes, and quantization
IEEE Transactions on Information Theory
Least squares quantization in PCM
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
A Zador-like formula for quantizers based on periodic tilings
IEEE Transactions on Information Theory
Recent progress in robust and quality Delaunay mesh generation
Journal of Computational and Applied Mathematics - Special issue: The international symposium on computing and information (ISCI2004)
On centroidal voronoi tessellation—energy smoothness and fast computation
ACM Transactions on Graphics (TOG)
PolyMesher: a general-purpose mesh generator for polygonal elements written in Matlab
Structural and Multidisciplinary Optimization
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Optimal centroidal Voronoi tessellations have important applications in many different areas such as vector quantization, data and image processing, clustering analysis, and resource management. In the three-dimensional Euclidean space, they are also useful to the mesh generation and optimization. In this paper, we conduct extensive numerical simulations to investigate the asymptotic structures of optimal centroidal Voronoi tessellations for a given domain. Such a problem is intimately related to the famous Gersho's conjecture, for which a full proof is still not available. We provide abundant evidence to substantiate the claim of the conjecture: the body-centered-cubic lattice (or Par6) based centroidal Voronoi tessellation has the lowest cost (or energy) per unit volume and is the most likely congruent cell predicted by the three-dimensional Gersho conjecture. More importantly, we probe the various properties of this optimal configuration including its dual triangulations which bear significant consequences in applications to three-dimensional high quality meshing.