What is a Voronoi diagram?

A Voronoi diagram is a mathematical partition of a plane into specific regions based on distance to a set of objects, often called seeds or sites. Each region, or Voronoi cell, contains all the points closer to its specific seed than to any other. Named after mathematician Georgy Voronoy, these diagrams find extensive applications across science, technology, and visual art.

What we know

• A Voronoi diagram partitions a plane into regions close to each of a given set of objects called seeds, sites, or generators. [2]
• The Voronoi diagram of a set of points is dual to that set's Delaunay triangulation. [2]
• In weighted Voronoi diagrams, each site has a weight that influences the distance computation, allowing larger sites to claim bigger cells. [3]
• The concept is named after the mathematician Georgy Voronoy, and the resulting cells are also known as Thiessen polygons. [1, 2]

Where to go next

• whoWho was Georgy Voronoy?
• how we knowWhat is a Delaunay triangulation?
• a case in pointHow do weighted Voronoi diagrams work?
• the bigger pictureWhat is a mathematical diagram?
• how it workedHow does crystal growth model through Voronoi diagrams?
• an unexpected connectionHow do mathematics and visual art meet through cell partitions?Although Voronoi diagrams are deeply rooted in mathematical geometry and plane partitioning, they are also actively utilized in visual art.

Sources

• [1]Voronoi diagram (Wikidata Q757267) · CC0 1.0
• [2]Voronoi diagram · CC BY-SA 4.0
• [3]Weighted Voronoi diagram · CC BY-SA 4.0
• [4]Mathematical diagram · CC BY-SA 4.0
• [5]Georgy Voronoy · CC BY-SA 4.0

Your path

1. What is a small modular reactor?
2. /What is a Voronoi diagram?