Given a set of seed points, the Voronoi diagram partitions space so that every point in a cell is closer to that cell's seed than to any other. It appears in giraffe markings, bone microstructure, city planning and epidemiology.
Voronoi cells are computed live using Fortune's sweep-line algorithm (O(n log n)). The dual graph — Delaunay triangulation — is drawn in overlay: it maximises the minimum angle of all triangles, the optimal mesh for finite-element methods and terrain rendering.
Click anywhere to add a seed point. Drag seeds to watch the tessellation update in real time. Toggle Delaunay overlay. Try the Lloyd relaxation button to iterate cells toward uniform spacing — the process that generates centroidal Voronoi diagrams.
John Snow's famous 1854 cholera map was an early Voronoi diagram: he drew boundaries around water pumps and showed that deaths clustered inside one pump's cell. Removing its handle ended the outbreak — an early triumph of spatial data analysis.