Voronoi Diagram Generator

Interactive visualization of Voronoi diagrams - click to add sites and see regions

How to Use:

Controls

Sites: 0 | Tip: Click anywhere on the canvas to add a new site

About Voronoi Diagrams

What is a Voronoi Diagram?

A Voronoi diagram is a partition of a plane into regions based on distance to a specific set of points (called sites). Each region consists of all points closer to one particular site than to any other site.

Properties:

  • Each region contains exactly one site
  • Voronoi edges are equidistant from two sites
  • Voronoi vertices are equidistant from three or more sites
  • Used in nearest neighbor searches, spatial analysis, and natural patterns
Distance Metrics

Euclidean Distance: The standard straight-line distance (√((x₂-x₁)² + (y₂-y₁)²))

Manhattan Distance: Distance measured along axis-aligned paths (|x₂-x₁| + |y₂-y₁|), creates diamond-shaped regions

Chebyshev Distance: Maximum of absolute differences (max(|x₂-x₁|, |y₂-y₁|)), creates square-shaped regions

Applications
  • Geographic: Service area analysis, finding nearest facilities
  • Biology: Cell growth patterns, territorial divisions
  • Computer Graphics: Texture generation, procedural content
  • Astronomy: Analyzing cosmic web structure
  • Robotics: Path planning and coverage problems