🧩 Voronoi Diagram Generator

A Voronoi diagram takes a set of seed points and partitions the plane into cells — one cell per seed. A cell contains every location that is closer to its own seed than to any other seed. The result is a mosaic of regions whose boundaries lie exactly halfway between neighboring seeds. It is named after the mathematician Georgy Voronoy, who formalized the construction in 1908.

Voronoi diagrams answer "which point is nearest?" questions, so they turn up everywhere. They power nearest-facility and store-catchment analysis, model cell-phone tower coverage, describe territories and resource competition in ecology, and generate organic procedural textures and game maps. In computational geometry they are also a foundation for mesh generation and spatial interpolation.

A Voronoi diagram has a twin: the Delaunay triangulation is its dual graph. Connect every pair of seeds whose Voronoi cells share an edge, and you get the Delaunay triangulation of those seeds; conversely, the Voronoi diagram can be recovered from the triangulation. The two encode the same neighbor relationships from opposite directions — explore the companion construction with our Delaunay Triangulation tool.