Centroidal Voronoi Tessellations: Applications and Algorithms

From MaRDI portal
Publication:4699117

DOI10.1137/S0036144599352836zbMath0983.65021WikidataQ62111348 ScholiaQ62111348MaRDI QIDQ4699117

Vance Faber, Qiang Du, Max D. Gunzburger

Publication date: 23 November 1999

Published in: SIAM Review (Search for Journal in Brave)




Related Items

Optimum quantization and its applications, On the minimum of the mean-squared error in 2-means clustering, Numerical studies of MacQueen's \(k\)-means algorithm for computing the centroidal Voronoi tessellations, On approximation of linear functionals over convex functions: construction techniques and new directions, Adaptive mixed-hybrid and penalty discontinuous Galerkin method for two-phase flow in heterogeneous media, Stable and convergent approximation of two-dimensional vector fields on unstructured meshes, Kernel-based adaptive sampling for image reconstruction and meshing, Tetrahedral meshing via maximal Poisson-disk sampling, Extended finite element method on polygonal and quadtree meshes, Meshfree, probabilistic determination of point sets and support regions for meshless computing, Mesh sensitivity in peridynamic simulations, Construction of positive definite cubature formulae and approximation of functions via Voronoi tessellations, High-order virtual element method on polyhedral meshes, A new hybrid adaptive mesh algorithm based on Voronoi tessellations and equi-distribution principle: algorithms and numerical experiments, A geometric approach to non-parametric density estimation, High order accurate conservative remapping scheme on polygonal meshes using \textit{a posteriori} MOOD limiting, Least upper bound of the exact formula for optimal quantization of some uniform Cantor distributions, Generalized edge-weighted centroidal Voronoi tessellations for geometry processing, A local search approximation algorithm for \(k\)-means clustering, Approximating the pathway axis and the persistence diagrams for a collection of balls in 3-space, \texttt{PolyMesher}: a general-purpose mesh generator for polygonal elements written in Matlab, A modified NBI and NC method for the solution of \(N\)-multiobjective optimization problems, Microscale prediction of deformation in an austenitic stainless steel under uniaxial loading, Auto-balancing algorithm for parallel SPH simulation of materials in extremes, Sparsity enabled cluster reduced-order models for control, Effectiveness-based Voronoi partition: a new tool for solving a class of location optimization problems, A physics-motivated centroidal Voronoi particle domain decomposition method, GPU based detection of topological changes in Voronoi diagrams, Boundary feedback control of the Burgers equations by a reduced-order approach using centroidal Voronoi tessellations, On energy, discrepancy and group invariant measures on measurable subsets of Euclidean space, Hybrid feedback stabilization of systems with quantized signals, Error reduction of the adaptive conforming and nonconforming finite element methods with red-green refinement, High order compact schemes for gradient approximation, Constructing Voronoi diagrams from hollow spheres using conformal geometric algebra, A nominally second-order accurate finite volume cell-centered scheme for anisotropic diffusion on two-dimensional unstructured grids, Obtuse triangle suppression in anisotropic meshes, An effective 3D leapfrog scheme for electromagnetic modelling of arbitrary shaped dielectric objects using unstructured meshes, Centroidal Voronoi tessellation in universal covering space of manifold surfaces, On staggering techniques and the non-staggered Z-grid scheme, Constrained shrinking dimer dynamics for saddle point search with constraints, Decentralized swarm coordination: a combined coverage/connectivity approach, Self-triggered coordination of robotic networks for optimal deployment, Interior boundary-aligned unstructured grid generation and cell-centered versus vertex-centered CVD-MPFA performance, On vehicle placement to intercept moving targets, Deployment of an unreliable robotic sensor network for spatial estimation, Voronoi-based finite volume methods, optimal Voronoi meshes, and PDEs on the sphere., Efficient mesh optimization schemes based on optimal Delaunay triangulations, Differentiation and regularity of semi-discrete optimal transport with respect to the parameters of the discrete measure, An adaptive edge finite element method for electromagnetic cloaking simulation, Two-step hybrid conservative remapping for multimaterial arbitrary Lagrangian-Eulerian methods, Optimal grid drawings of complete multipartite graphs and an integer variant of the algebraic connectivity, Adaptive anisotropic meshing for steady convection-dominated problems, Anisotropic mesh generation methods based on ACVT and natural metric for anisotropic elliptic equation, Finite element approximation of the Cahn-Hilliard equation on surfaces, A versatile technique for the optimal approximation of random processes by functional quantization, High-quality 2D mesh generation without obtuse and small angles, Exploring high-order three dimensional virtual elements: bases and stabilizations, Fast centroidal Voronoi Delaunay triangulation for unstructured mesh generation, A new method for the generation of arbitrarily shaped 3D random polycrystalline domains, Higher order mobile coverage control with applications to clustering of discrete sets, Micro-scale analysis on shear characteristics of unsaturated soil by considering capillary suction and adsorption suction based on DDA, New cubature formulas and Hermite-Hadamard type inequalities using integrals over some hyperplanes in the \(d\)-dimensional hyper-rectangle, Unstructured Voronoi grids conforming to lower dimensional objects, Observer-based feedback boundary stabilization of the Navier-Stokes equations, A new multi-resolution parallel framework for SPH, An isotropic unstructured mesh generation method based on a fluid relaxation analogy, Constrained CVT meshes and a comparison of triangular mesh generators, Voronoi grids conforming to 3D structural features, Efficient estimation of cardiac conductivities via POD-DEIM model order reduction, Serendipity virtual elements for general elliptic equations in three dimensions, A new parallel algorithm for constructing Voronoi tessellations from distributed input data, A fast minimum spanning tree algorithm based on \(K\)-means, Generalised primal-dual grids for unstructured co-volume schemes, A unified approach to energy conservation and potential vorticity dynamics for arbitrarily-structured C-grids, ReALE: a Reconnection Arbitrary-Lagrangian-Eulerian method in cylindrical geometry, A fuzzy edge-weighted centroidal Voronoi tessellation model for image segmentation, Stabilized reduced order models for the advection-diffusion-reaction equation using operator splitting, Surface reconstruction by parallel and unified particle-based resampling from point clouds, A bivariate \(C^1\) subdivision scheme based on cubic half-box splines, Numerical simulations of the quantized vortices on a thin superconducting hollow sphere, Reale: a Reconnection-based Arbitrary-Lagrangian-Eulerian method, Subdivision connectivity remeshing via Teichmüller extremal map, Mollified finite element approximants of arbitrary order and smoothness, Adaptive higher-order phase-field modeling of anisotropic brittle fracture in 3D polycrystalline materials, A model to simplify 2D triangle meshes with irregular shapes, A feature-aware SPH for isotropic unstructured mesh generation, Viewpoint independent object recognition in cluttered scenes exploiting ray-triangle intersection and SIFT algorithms, A critical appraisal of design of experiments for uncertainty quantification, Adaptive reconnection-based arbitrary Lagrangian Eulerian method, Mesh adaptation on the sphere using optimal transport and the numerical solution of a Monge-Ampère type equation, Cell-based maximum-entropy approximants, An advancement in clustering via nonparametric density estimation, Optimal quantization for mixed distributions, Mesh free Galerkin method based on natural neighbors and conformal mapping, Adaptive computations using material forces and residual-based error estimators on quadtree meshes, Anisotropic mesh quality measures and adaptation for polygonal meshes, Bounds on the geometric complexity of optimal centroidal Voronoi tesselations in 3D, Adaptive sampling-based quadrature rules for efficient Bayesian prediction, Adaptive triangular mesh coarsening with centroidal Voronoi tessellations, Grid generation and optimization based on centroidal Voronoi tessellations, Surface reconstruction using simplex splines on feature-sensitive configurations, Sliver-suppressing tetrahedral mesh optimization with gradient-based shape matching energy, Longest minimal length partitions, The average-distance problem with an Euler elastica penalization, Multiscale methods for mechanical science of complex materials: Bridging from quantum to stochastic multiresolution continuum, Modelling pipeline for subject-specific arterial blood flow-A review, Tailoring unstructured meshes for use with a 3D time domain co-volume algorithm for computational electromagnetics, A method for generating moving, orthogonal, area preserving polygonal meshes, Local time stepping for the shallow water equations in MPAS, Quadratic serendipity element shape functions on general planar polygons, TCB-spline-based isogeometric analysis method with high-quality parameterizations, Stable honeycomb structures and temperature based trajectory optimization for wire-arc additive manufacturing, Canonical sequences of optimal quantization for condensation measures, Coverage boundary of unknown environment using mobile sensor networks, Congruent Voronoi tessellations from equiangular lines, Approximation by finitely supported measures, The optimal centroidal Voronoi tessellations and the Gersho's conjecture in the three-dimensional space, Virtual element method on polyhedral meshes for bi-harmonic eigenvalues problems, Multi-robots Gaussian estimation and coverage control: from client-server to peer-to-peer architectures, Benchmarking the geometrical robustness of a virtual element Poisson solver, A boundary-partition-based Voronoi diagram of \(d\)-dimensional balls: definition, properties, and applications, A finite element framework based on bivariate simplex splines on triangle configurations, A three-dimensional Hellinger-Reissner virtual element method for linear elasticity problems, CSIOR: circle-surface intersection ordered resampling, Robustly computing restricted Voronoi diagrams (RVD) on thin-plate models, Coordination of nonholonomic mobile robots for diffusive threat defense, Optimal One-Dimensional Coverage by Unreliable Sensors, Machine learning based refinement strategies for polyhedral grids with applications to virtual element and polyhedral discontinuous Galerkin methods, A new implementation of the geometric method for solving the Eady slice equations, Optimization of Subdivision Invariant Tetrahedra, Data science applications to string theory, Centroidal Voronoi tessellation based polycube construction for adaptive all-hexahedral mesh generation, Second-order convex maximum entropy approximants with applications to high-order PDE, Mesh improvement by minimizing a weighted sum of squared element volumes, A new particle shifting technique for SPH methods based on Voronoi diagram and volume compensation, Distributed stochastic multi-vehicle routing in the Euclidean plane with no communications, Optimal quantization for the Cantor distribution generated by infinite similutudes, A unified derivation of Voronoi, power, and finite-element Lagrangian computational fluid dynamics, A stabilized quasi and bending consistent meshfree Galerkin formulation for Reissner-Mindlin plates, Fast spherical centroidal Voronoi mesh generation: a Lloyd-preconditioned LBFGS method in parallel, Defects and frustration in the packing of soft balls, \(H^1, H(\text{curl})\) and \(H(\text{div})\) conforming elements on polygon-based prisms and cones, A mathematical framework for modeling axon guidance, Periodic three-dimensional mesh generation for particle reinforced composites with application to metal matrix composites, Contact pressure models for spiral phyllotaxis and their computer simulation, Smoothed Particle Hydrodynamics with Stress Points and Centroid Voronoi Tessellation (CVT) Topology Optimization, A \(C^1\) virtual element method on polyhedral meshes, Parallel solvers for virtual element discretizations of elliptic equations in mixed form, Comparative concepts, Conservative explicit local time-stepping schemes for the shallow water equations, Minimal degree $H(\mathrm {curl})$ and $H(\mathrm {div})$ conforming finite elements on polytopal meshes, Distributed coordination of multi-agent systems for neutralizing unknown threats based on a mixed coverage-tracking metric, Quadratic maximum-entropy serendipity shape functions for arbitrary planar polygons, Mesh generation for FEM based on centroidal Voronoi tessellations, POD and CVT-based reduced-order modeling of Navier-Stokes flows, Reduced-order modeling of time-dependent PDEs with multiple parameters in the boundary data, Fast methods for computing centroidal Laguerre tessellations for prescribed volume fractions with applications to microstructure generation of polycrystalline materials, Conservative numerical schemes with optimal dispersive wave relations: part I. Derivation and analysis, A virtual element method for the steady-state Poisson-Nernst-Planck equations on polygonal meshes, CGALmesh, Asymptotic optimality of the triangular lattice for a class of optimal location problems, A general SPH framework for transient seepage flows through unsaturated porous media considering anisotropic diffusion, Variational surface reconstruction based on Delaunay triangulation and graph cut, Adaptive surface mesh remeshing based on a sphere packing method and a node insertion/deletion method, Voronoi residual analysis of spatial point process models with applications to California earthquake forecasts, Centroidal Voronoi tessellation algorithms for image compression, segmentation, and multichannel restoration, A variational meshfree method for solving time-discrete diffusion equations, On a stochastic sensor selection algorithm with applications in sensor scheduling and sensor coverage, Recent progress in robust and quality Delaunay mesh generation, Quantization for uniform distributions on stretched Sierpiński triangles, Manifold Intrinsic Similarity, On the inter-comparison of two tracer transport schemes on icosahedral grids, Optimal transportation meshfree approximation schemes for fluid and plastic flows, Goal-oriented a posteriori error estimation for finite volume methods, Superconvergence analysis for the explicit polynomial recovery method, When do birds of a feather flock together? \(k\)-means, proximity, and conic programming, Efficient topology preserving triangular remeshing algorithm with adaptive vertices insertion, Geometric Self-Assembly of Rigid Shapes: A Simple Voronoi Approach, Mixed virtual element methods for general second order elliptic problems on polygonal meshes, Pointwise Convergence of the Lloyd I Algorithm in Higher Dimension, Optimal number and length of point-like and line-like facilities of grid and random patterns, A consistent parallel isotropic unstructured mesh generation method based on multi-phase SPH, High precision numerical computation of principal points for univariate distributions, Lowest order virtual element approximation of magnetostatic problems, A High Order Stable Conservative Method for Solving Hyperbolic Conservation Laws on Arbitrarily Distributed Point Clouds, An efficient iterative method for solving parameter-dependent and random convection-diffusion problems, Large-Scale Three-Dimensional Acoustic Horn Optimization, Semi-discrete optimal transport methods for the semi-geostrophic equations, Staggered DG method with small edges for Darcy flows in fractured porous media, An improved KF-RBF based estimation algorithm for coverage control with unknown density function, A multiscale analysis of multi-agent coverage control algorithms, Anisotropic mesh generation and adaptation for quads using the \(L_p\)-CVT method, Strategic information transmission despite conflict, Optimal quantization for some triadic uniform Cantor distributions with exact bounds, Human-swarm collaboration with coverage control under nonidentical and limited sensory ranges, Performance of a class of multi-robot deploy and search strategies based on centroidal voronoi configurations, Some virtual element methods for infinitesimal elasticity problems, On the compression of locational and environmental data in multi-vehicle missions: a control systems approach, Heterogeneous locational optimisation using a generalised Voronoi partition, Fast methods for computing centroidal Voronoi tessellations, Free-form deformation, mesh morphing and reduced-order methods: enablers for efficient aerodynamic shape optimisation, Combining CFD-EFD-FFD data via Gappy Proper Orthogonal Decomposition, A priori error estimates of a meshless method for optimal control problems of stochastic elliptic PDEs, Cluster-based reduced-order modelling of a mixing layer, An efficient trajectory sampling design method for elementary effect based global sensitivity analysis, Centroidal Power Diagrams, Lloyd's Algorithm, and Applications to Optimal Location Problems, Recursive marginal quantization of higher-order schemes, Linear finite element superconvergence on simplicial meshes, Two-Point Centroidal Voronoi Tessellations, A Conforming Quadratic Polygonal Element and Its Application to Stokes Equations, Quantization for a probability distribution generated by an infinite iterated function system, Survey of Multifidelity Methods in Uncertainty Propagation, Inference, and Optimization, Unnamed Item, Unnamed Item, Unnamed Item, Skew Jensen-Bregman Voronoi Diagrams, An optimal particle setup method with centroidal Voronoi particle dynamics, Parallel SPH modeling using dynamic domain decomposition and load balancing displacement of Voronoi subdomains, Spatial bootstrapped microeconometrics: Forecasting for out‐of‐sample geo‐locations in big data, Minimizing optimal transport for functions with fixed-size nodal sets, Initialization of metaheuristics: comprehensive review, critical analysis, and research directions, Stochastic collocation for optimal control problems with stochastic PDE constraints by meshless techniques, Kirchhoff-Love shell representation and analysis using triangle configuration B-splines, Cluster‐based gradient method for stochastic optimal control problems with elliptic partial differential equation constraint, Cellular topology optimization on differentiable Voronoi diagrams, Stability analysis for the virtual element method, Comparison of reduced basis construction methods for model order reduction, with application to non-linear low frequency electromagnetics, An extension to \textsc{Voro++} for multithreaded computation of Voronoi cells, Optimal quantizers for a nonuniform distribution on a Sierpiński carpet, A semi-meshless Lagrangian finite-volume framework based on Voronoi diagram for general elastoplastic Reissner-Mindlin shell, Sensitivity analysis and tailored design of minimization diagrams, A Multi-level Optimization Approach for the Planning of Heterogeneous Sensor Networks, Optimal Sensor Positioning; A Probability Perspective Study, Voronoi Polygonal Hybrid Finite Elements and Their Applications, A Measure-Theoretic Interpretation of Sample Based Numerical Integration with Applications to Inverse and Prediction Problems under Uncertainty, A general method for numerical identifiability and sensitivity analysis of failure criteria for continuous fibre-reinforced plastics, The projector algorithm: a simple parallel algorithm for computing Voronoi diagrams and Delaunay graphs, Accelerating surface remeshing through GPU-based computation of the restricted tangent face, On pointwise error estimates for Voronoï-based finite volume methods for the Poisson equation on the sphere, Optimal Transport Approximation of 2-Dimensional Measures, Improving exploration strategies in large dimensions and rate of convergence of global random search algorithms, A family of three-dimensional virtual elements for Hellinger-Reissner elasticity problems, A Measure Approximation for Distributionally Robust PDE-Constrained Optimization Problems, Mixed variational formulations of virtual elements for the polyharmonic operator \((-\Delta)^n\), Data-driven games in computational mechanics, Bayesian Quadrature, Energy Minimization, and Space-Filling Design, Dynamic distributed clustering in wireless sensor networks via Voronoi tessellation control, A Multilevel Monte Carlo Ensemble Scheme for Random Parabolic PDEs, Mathematical Challenges in Measuring Variability Patterns for Precipitation Analysis, Numerical methods for low‐order modeling of fluid flows based on POD, Quality-Diversity Optimization: A Novel Branch of Stochastic Optimization, Coverage tracking control for multiple cooperative agents, New family of tilings of three-dimensional Euclidean space by tetrahedra and octahedra, Impact of Local Grid Refinements of Spherical Centroidal Voronoi Tessellations for Global Atmospheric Models, Polygonal finite elements for topology optimization: A unifying paradigm, A Distributed Optimal Control Problem with Averaged Stochastic Gradient Descent, Localized Exponential Time DifferencingMethod for Shallow Water Equations: Algorithms and Numerical Study, Multi-outlet retail site location assessment, An Adaptive Coverage Control for Deployment of Nonholonomic Mobile Sensor Networks Over Time‐Varying Sensory Functions, Adaptive tetrahedral mesh generation by constrained centroidal voronoi‐delaunay tessellations for finite element methods, Shape regularity conditions for polygonal/polyhedral meshes, exemplified in a discontinuous Galerkin discretization, Weighted Triangulations for Geometry Processing, Introduction to vector quantization and its applications for numerics, Simple-closed-curve sculptures of knots and links, Centroidal Voronoi tessellation-based finite element superconvergence, On spatial thinning-replacement processes based on Voronoi cells, Quantization for uniform distributions of Cantor dusts on $\mathbb{R}^2$, A POINT-PLACEMENT STRATEGY FOR CONFORMING DELAUNAY TETRAHEDRALIZATION, Geometric Aspects of the Space of Triangulations, Stochastic finite element methods for partial differential equations with random input data, Stability and Fluctuations in a Simple Model of Phonetic Category Change, Anisotropic Error Estimates of the Linear Virtual Element Method on Polygonal Meshes, A Family of Three-Dimensional Virtual Elements with Applications to Magnetostatics, Spatially-distributed coverage optimization and control with limited-range interactions, On privacy vs. cooperation in multi-agent systems, Dense Glyph Sampling for Visualization, Constructing Centroidal Voronoi Tessellations on Surface Meshes, Unnamed Item, GEOMETRIC ALGORITHMS FOR THE CONSTRAINED 1-D K-MEANS CLUSTERING PROBLEMS AND IMRT APPLICATIONS, Human–Swarm Interactions via Coverage of Time-Varying Densities, Comparison of descriptive statistics for multidimensional point sets, Extended Multidimensional Integration Formulas on Polytope Meshes, A Simple Geometric Method for Navigating the Energy Landscape of Centroidal Voronoi Tessellations, A Convergent Discretization Method for Transition Path Theory for Diffusion Processes, Unnamed Item, Numerical approximations of the Ginzburg–Landau models for superconductivity, Sharp multidimensional numerical integration for strongly convex functions on convex polytopes, Hybridization of the virtual element method for linear elasticity problems, TetGen, a Delaunay-Based Quality Tetrahedral Mesh Generator, On The Characterization and Uniqueness of Centroidal Voronoi Tessellations


Uses Software