Voronoi Applications

Accuracy of parameters

• Voronoi Diagram Based Cumulative Approximation for Engineering Optimization (PDF)
• The accuracy of parameters determined with the core-sampling method: Application to Voronoi tessellations Astronomy and Astrophysics Supplement Series
• Finding galaxy clusters using Voronoi tessellations Astronomy and Astrophysics Supplement Series
• The accuracy of analysis of Voronoi-tessellations Astronomy and Astrophysics Supplement Series

• Hub96b-Improving accuracy in a robust algorithm for three-dimensional voronoi diagrams

[edit]

Active learning

• CIS 610-Advaced Geometric Methods in Computer Science Course Information
• Meshing and Triangulation
• Course on Metaheuristics for Combinatorial Optimization Problems in Operations Research
• Lecture Notes-35.679 Computational Geometry S96
• Comp.Graphics.Algorithms FAQ
• Comp.Graphics.Algorithms FAQ, Section 6 - Geometric Structures and Mathematics
• Course on Metaheuristics for Combinatorial Optimization Problems in Operations Research
• Final Programming Project-Voronoi Diagram Application (PDF)
• Sergei Zuyev - Download

[edit]

Applets

• Packing Pennies in the Plane
• Voronoi diagram/Delaunay triangulation
• Voronoi Sweepline Algorithm
• Texture Garden links page

[edit]

Arrange objects

• Voronoi分割とDelaunay三角形網
• Nonparametric Maximum Likelihood Estimation of Features in Spatial Point Processes Using Voronoï Tessellation
• Voronoï Diagram (Dunlaing & Yap, 82) (PDF, page 9)
• MERL - V-Clip Collision Detection Library

[edit]

Biology

• Weighted Voronoi Diagrams in Biology
• Common Medial Model Generation Step 2. Determination of common model topology (PPT)
• Bioinformatics Exercises-Multipe Sequence Alignments: The Voronoi Weighting Scheme

[edit]

Chemistry

• Elastic moduli of model random three-dimensional closed-cell cellular solids - Voronoi tessellations
• Atom partitioning of integration grid (VORONOI)
• Voronoi-Dirichlet Polyhedra for Uranium(VI) Atoms in Oxygen-Containing Compounds
• Voronoi-Dirichlet Polyhedra of Uranium (ll-V) Atoms in Oxygen-Containing Compounds
• Locating Binding Sites in Protein Structures
• Modelling of Apple Tissue Using the Voronoi Tessellation Approach
• Mesoscopic Dyanmics of Voronoi Fluid Particles (PDF)
• Theoretical and numerical methods for mesoscale modelling of fluids:
• Dinamica determinista del modelo de particulas fluidas de Voronoi
• Softening of nanocrystalline metals at very small grain sizes
• GameDev.net - Practical Collision Detection
• Abstract-Non-atomic solvent driven Voronoi tessellation of proteins: an open tool to analyze protein folds
• Molecular Volume and Protein Packing
• Dynamics Simulations of Transport and Separation of Supercritical Fluid Mixtures through Nanoporous Membranes
• Analysis of Lanthanide pi Complexes in Terms of Voronoi–DirichletPolyhedra
• On a Voronoi Aggregative Process Related to a Bivariate Poisson Process
• Statistical Geometry of Water Structure
• Irregular Sampling-A First Guided Tour on the Irregular Sampling Problem
• Irregular Cellular Automata Page
• Voronoi Polyhedra and Delaunay Simplexes in the Structural Analysis of Molecular-Dynamics-Simulated Materials
• Voronoi polyhedra as tool for dealing with spatial structures of amorphous solids, liquids and dense gases

[edit]

Code

• Jun: Class sra.jun.voronoi.twoD.diagram.JunVoronoi2dDot
• Jun: Class sra.jun.voronoi.twoD.diagram.JunVoronoi2dPoint
• Jun: Class sra.jun.voronoi.twoD.diagram.JunVoronoi2dSide
• Jun: Package sra.jun.voronoi.twoD.diagram
• Uses the depth buffer to intersect cones drawn at each point selected by the user
• mmskiz - Skeleton of Influence Zone - also know as Generalized Voronoi Diagram
• Systems Biophysics - Research - Self-Organizing Networks - DemoGNG Code
• On the Voronoi Neighbor Ratio for Binary Linear Block Codes
• Tripack Lib
• Extensible HTML version 1.0 Strict DTD
• voronoi.h

[edit]

Computational mechanics

• Abstract: Machine Part Family Formation Utilizing the Hausdorff-Voronoi Neural Network (HAVNET) (DOC)
• Presentation: Machine Part Family Formation Utilizing the Hausdorff-Voronoi Neural Network (HAVNET) (PPT)
• Frequently Asked Questions about Qhull
• A Sequence of Generalized Coordinate Systems Based on Voronoi Diagrams and its Application to Interpolation
• A List-Processing Approach to Compute Voronoi Diagrams and the Euclidean Distance Transform
• Neural Network Design Using Voronoi Diagrams
• Computational Geometry
• The Open Problems Project
• Competitive Facility Location: The Voronoi Game (PDF)
• 1 Voronoi Diagrams
• Book-EDM/2 - The Codesmith's Library - Computational Geometry in C, 2nd Edition
• Directory of Computational Geometry Software
• Computing the Delaunay complex and the Voronoi diagram. What does it mean and how to do it with available software?
• Skew Voronoi Diagram
• Geometria Computacional - IME-USP
• Computer Assisted Sphere Packing in Higher Dimensions (PDF)
• Common Properties and Notational Conventions
• XYZ GeoBench for experimental geometric computation
• Computational Geometry
• Discovery of Influence Sets in Frequently Updated Databases (PDF)
• Meshless Finite Element Ideas (PDF)
• Computational Geometry

[edit]

General applications

• Dot Pattern Processing Using Voronoi Neighborhoods
• Voronoi Diagrams: Applications from Archaology to Zoology

[edit]

Geography

• Voronoi diagrams
• Watershed Delineation in the TRIM Watershed Atlas
• Catalog of Prebuilt Hipparchus Voronoi Index Structures Navigation Toolbar
• Catalog of Prebuilt Hipparchus Voronoi Index Structures
• Spatially-balanced Sampling of Natural Resources in the Presence of Frame Imperfections (PDF)
• Case Studies: Predicting Climate Change Effects on Forest Processes: Weather Station Measurements to Spatial Coverage
• Snow's investigation
• Modelling Retail Trade Areas with the use of Voronoi Diagrams (doc)
• Abstract: Voronoi Polyhedra
• RUM Description

[edit]

Geology

• Voronoi Diagrams: Applications from Archaology to Zoology
• Voronoi Percolation in Rd (PDF)
• Abstract: The critical probability for Voronoi percolation.

[edit]

Geophysics

• Geodyssey's Hipparchus Open GIS C/C Multi-thread Re-entrantGeographic and Spatial Mapping Components plus Galileo GIS Developer'sWorkbench and Georama Digital GPS-ready World Atlases and Gazetteers
• RSES Natural Neighbours homepage-Geophysical applications of Natural Neighbours

[edit]

Geoscientific modelling

• 3nd International Workshop on COMPUTATIONAL GEOMETRY AND APPLICATIONS (CGA'03)
• The svLis geometric modeller
• Abstract (Applying Voronoi Diagram in the Automatic Grouping of Polyphony)
• [1]
• HighRoad 6.0 User Manual - Chapter 24
• Geodesic Voronoi Diagrams in the Presence of Rectilinear Barriers
• A Brief Tour of Nonlinear Magnification
• CVonline: Object, World and Scene Representations
• Low dimensional Voronoi diagram, Delaunay triangulation
• Medial axis and constrained Delaunay triangulation
• RR-4585 : Approximate decomposition of some modulated-Poisson Voronoi tessellations
• Fraunhofer ITWM: Examples of models for microstructures
• Three-dimensional alpha shapes
• Constrained Centroidal Voronoi Tessellations on General Surfaces
• Centroidal Voronoi Tessellation (CVTs) and their applications to Numerical PDEs
• On zone-reduction in Voronoi-cells of lattices of the first kind
• Applications of 3D Delaunay triangulation algorithms in geoscientific modelling.
• Cihan H. Dagli's Research
• Abstract: SKEW VORONOI DIAGRAMS
• A Tight Bound for the Complexity of Voronoi Diagrams under Polyhedral Convex Distance Functions in 3D (PDF)

[edit]

Hydrodynamics

• Dynamic Segmentation and Thiessen Polygons: A Solution to the RiverMile Problem

[edit]

Imagery

• Viper Segmentation page
• Constructing Approximate Voronoi Diagrams from Digital Images of Generalized Polygons and Circular Objects (PDF)
• Voronoi Tiling via Raster Techniques
• Proximity Graphs
• Vector Set-Partitioning with Successive Refinement Voronoi Lattice VQ for Embedded Wavelet Image Coding (PDF)
• Image Segmentation using Voronoi Polygons and MCMC, with Application to Muscle Fibre Images (PDF)
• VoronoImage
• Wallpaper Groups: history
• Graphics Page
• My face on a Voronoi Diagram
• Multiresoultion Representation and Reconstruction of Adaptively Sampled Images
• Pseudo-Random Halftone Screening for Color and Black & White Printing (PDF)
• Janet Hansen Fine Art - Vivid Abstractions, Geometric Paintings
• Stylized Depiction: Non-Photorealistic, Painterly and 'Toon Rendering
• Fast Matrix Multiplies using Graphics Hardware
• Voronoi Camera

[edit]

Mathematics

• Mathematical Web Sites
• Jara Software: MLLib
• Christopher Gold - Voronoi methods in geomatics--the importance of the spatial model
• Robert Erdahl - Dicings, Zonotopes, and Voronoi's conjecture on parallelohedra
• COMAP Web Links Course 2 Grade 10 Unit 5
• netlib home page
• Octave_links
• To find center, the unique point in 2 or higher-dimensional space
• Vector Quantization
• UNIT 14 - VECTOR GIS CAPABILITIES
• An Introduction to Voronoi Diagrams and Their Applications
• Continuous Location Problems
• Classification of Voronoi and Delone tiles in quasicrystals: I
• Classification of Voronoi and Delone tiles of quasicrystals: II
• Iterative reconstruction of multivariate band-limitedfunctions from irregular sampling values
• University of Pittsburgh: Department of Mathematics
• Computational geometry
• A Review of Current Geometric Tolerancing Theories
• Hybrid Segmentation of the Visible Human Data
• Unequal N HSD
• Natural Neighbour Galerkin methods (PDF)
• The Natural Element Methods in Solid Mechanics (PDF)

[edit]

Medicine

• Biomedical Structural Research
• Medial Surface Transformations for Rapid Approximation of Casting Solidification (PDF)
• k-means

[edit]

Ornamental design

• Using the Voronoi Tessellation for Grouping Words and Multi-part Symbols in Documents
• Weighted Voronoi Stippling

[edit]

Other collections

• The One-Round Voronoi Game

[edit]

Physical science

• Robotics
• John Baez
• Problems in a Digital Description of a Configuration of Atoms and Some Other Geometrical Topics in Physics
• What is GHL?

[edit]

Placement of nodes and elements

• A Replacement for Voronoi Diagrams of Near Linear Size
• Voronoi Diagrams Based on General Metrics in the Plane
• How can I arrange N points evenly on a sphere?
• VORONOI
• The Probabilistic Complexity of the Voronoi Diagram of Points on a Polyhedron
• A SIMPLE FACTOR-2/3 APPROXIMATION ALGORITHM FOR TWO-CIRCLE POINT LABELING

[edit]

Programs

• Program - A Replacement for Voronoi Diagrams of Near Linear Size
• DEMO PROGRAM FOR DELAUNAY TRIANGULATION AND VORONOI DIAGRAM
• BCRP Woodland Caribou in Alberta – Literature
• Go - Other Boards
• CSNA Web -- 'On-Line Software for Classif. ...'
• Geographic tools, DLL API's and sample programs
• Vertical Mapper: Voronoi Diagram Example

[edit]

Route Planning

• Unsupervised ontogenic networks (PDF)
• How representative are samples in a sampling network?
• Visibility Graph and Voronoi Diagram (PPT)
• Das Traveling-Salesman-Problem - Anwendungen und heuristischeNutzung von Voronoi-/Delaunay-Strukturen zur Lösung euklidischer,zweidimensionaler Traveling-Salesman-Probleme (PDF)
• Network Design
• Algorithmus von Voronoi / Reine kubische Körper (in German)
• High School Projects
• Robot Path Planning Using Generalized Voronoi Diagrams.
• Voronoi Diagrams Based on Convex Distance Functions
• Multiplicatively Weighted Crystal Growth Voronoi Diagrams (Thesis)
• Quickest Paths, Straight Skeletons, and the City Voronoi Diagram
• Drawing Graphs with NEATO
• Abstract: Incremental Construction of the Generalized Voronoi Diagram, the Generalized Voronoi Graph, and the Hierarchical Generalized Voronoi Graph

[edit]

Systems

• Online Software for Clustering
• [2]
• LEDA Overview
• SysQuake LE On The Web
• Voronoi Game-Dennis Shasha Omniheurist Course
• GeoPrO Voronoi Diagram with sites in both sides of the plane
• Voronoi Polygons
• User Manual and Supporting Information for Library of Codes for Centroidal Voronoi Point Placement and Associated Zeroth, First, and Second Moment Determination (PDF)
• V-Clip: Fast and Robust Polyhedral Collision Detection (PDF)
• Voronoi Polygons
• Optimization Softwares and Test Problems
• Takashi Ohyama's Elliptic Voronoi diagram page
• Takashi Ohyama's Farthest-Point Voronoi diagram page
• Takashi Ohyama's Voronoi diagram page
• Takashi Ohyama's area of Voronoi region (Click version) page
• Machine Vision
• SGSI - GIS Desktop Mapping and Remote Sensing {Index}
• Northwest MapInfo User's Group
• Short Descriptioin of the Software for the Two-Dimensional Voronoi Diagram
• Simulog Technologies-Meshing Software Components
• Free Software for Smalltalk
• The MGE_FIT_SECTORS package
• Bulletin - Community Instantly

[edit]

Telecommunications network

• Stochastic Geometry: a Tool for Modeling Telecommunication Networks
• Anne-Elisabeth Baert: Broadcasting Algorithm in Cellular Networks Based on Voronoï Diagram and Delaunay Triangulation
• MODELLING OF COMMUNICATION NETWORKS VIA STOCHASTIC GEOMETRY

[edit]

Terrain Modelling

• Location-Based Services And Topology
• 0.Modelling Geographical Systems: Statistical and Computational Applications
• Levels of Detail & Polygonal Simplification
• CS 760M Project - Surface Reconstruction by Voronoi Filtering - slide 0
• CS 760M Project - Surface Reconstruction by Voronoi Filtering - slide 1
• Voronoi Graphs
• Voronoi-The reasons why the GVDs are so crucial as a new way of spatial tessellations in GIS
• Nearest Neighbor Search
• SPATIAL PLANNING: VORONOI DIAGRAMS
• DC MetaData pour: Approximate decomposition of some modulated-Poisson Voronoi tessellations
• New Surfaces over Voronoi Diagrams
• Voronoi Diagrams: The Modelling of Natural and Synthetic Structures
• Cut Locus & Medial Axis in the Euclidean Space and on Surfaces
• Taxicab Geometry
• Voronoi Polygons
• The Voronoi-Delaunay methodology for modelling of flow and analysis of voids
• Boundary Functions
• Abstract-Splines over iterated Voronoi Diagrams (PDF)
• Fast Extraction of Adaptive Multiresolution Meshes with Guaranteed Properties from Volumetric Data
• VoroGlide, interactive Voronoi diagrams

[edit]

Unclassified

• Skew Voronoi Diagrams
• Voronoi Diagrams for Planar Shapes
• Strategic Directions in Computational Geometry Working Group Report
• The Free-from Light Stage (PDF)
• Distributed Services for Microsensor Networks (PDF)
• Voronoi Diagram
• Spatial Data and The Voronoi Tessellation
• Libraries and Tools for Haskell
• Data Structures in the Web
• A Block Extraction Program-Based on the Area Voronoi Diagram (PDF)
• Online Software for Clustering
• AMCA: Multi Voronoi Nets System for Market Information Processing by Marina Resta
• Non-linear resampling for edge preserving moire suppression (PDF)
• Molecular Biophysics & Biochemistry 447b3 / 747b3 Bioinformatics
• Prove-Protein Volume Evaluator
• Calyxa's Bryce Tutorials
• Variance
• Pattern Recognition on the Web
• Elastic properties of model random three-dimensional open-cell solids, J. Mech. Phys. Solids
• 40.10.6 SPATIAL PLANNING: VORONOI DIAGRAMS
• Fast Nearest Neighbor Search using Voronoi Diagram (PDF)
• Cannonballs and Honeycombs
• Voronoi-Based Region Approximation for Geographical Information Retrieval with Gazetteers
• Voronoi-Based Region Approximation for Geographical Information Retrieval with Gazetteers (PDF)
• Constraint-Based Motion Planning
• A New-Voronoi-Based Reconstruction Algorithm (PDF)
• Quasicrystal and Symmetry
• http://ise.uoregon.edu/macGIS/Beta/Docs/Voronoi.word
• Do Irregular Grids make a Difference? Relaxing the Spatial Regularity Assumption in Cellular Models of Social Dynamics
• Varinace-Based k-Clustering Algorithms by Voronoi Diagrams and Randomization
• Table of contents for Spatial tessellations: concepts and applications of Voronoi diagrams
• Transportation Voronoi Diagrams (PDF)
• Problems in a Digital Description of a Configuration of Atoms and Some Other Geometrical Topics in Physics
• Multiresolution Representation and Reconstruction of Adaptively Sampled Images (PDF)
• The One-Round Voronoi Game (PDF)
• SimplicialVIEW, a package for robust stability analysis.
• The Analysis Extension Features