Interactive Voronoi Tessellation
Lloyd's relaxation optimization with multiple patterns, click-to-add sites, and educational visualizations.
🔶 Watch sites relax to optimal positions, click to add new sites, explore different patterns
Click on the canvas to add new sites
Voronoi Properties
- • Nearest Neighbor: Each region contains all points closest to its site
- • Dual of Delaunay: Connected to triangulation theory
- • Natural Patterns: Found in biological cell structures
- • Optimization: Lloyd's algorithm minimizes energy
Lloyd's Relaxation
- • Centroidal Voronoi: Sites move to region centroids
- • Energy Minimization: Reduces overall system energy
- • Uniform Distribution: Creates more regular spacing
- • Iterative Process: Converges to optimal configuration
Applications
Computer Graphics:
- • Procedural textures
- • Terrain generation
- • Cell shading
Computational Geometry:
- • Mesh generation
- • Spatial analysis
- • Nearest neighbor queries
Real World:
- • Ecology and biology
- • Urban planning
- • Material science