Voronoi Diagram
Voronoi regions for a set of points
About this calculator
The Voronoi Diagram Calculator partitions the plane around a set of points (sites) into regions, where every location in a region is closer to its own site than to any other. It computes each region as an exact convex polygon by intersecting perpendicular-bisector half-planes, reports the area of every region and which sites are neighbours, and draws a colour-coded diagram. Useful for nearest-neighbour analysis, facility-location and coverage problems, computational-geometry study, and generative art.
Common examples
- Two points (0,0) and (2,0) → the plane splits along x = 1 into two equal half-regions sharing one edge
- Square corners 0,0 2,0 2,2 0,2 → four equal quadrants meeting at the centre, 4 Voronoi edges
- Square plus centre 1,1 5,1 5,5 1,5 3,3 → the centre borders all four corners (8 edges total)
- Three collinear points 0,0 1,0 2,0 → three parallel strips separated by 2 edges
Frequently asked questions
What is a Voronoi diagram?
Given a set of points called sites, a Voronoi diagram divides the plane into one region per site. Every location inside a site's region is closer to that site than to any other. The boundaries between regions lie on the perpendicular bisectors of neighbouring sites.
Why are the regions shown inside a box?
Regions belonging to sites on the outer edge of the point set are unbounded — they extend to infinity. To show and measure them, the calculator clips every region to a bounding box padded around your points, so the reported areas are the areas within that box.
How is each region computed?
Each region is the intersection of half-planes: for every other site, keep the side of the perpendicular bisector nearer to the current site. Intersecting these half-planes (and the bounding box) yields an exact convex polygon, so the region areas add up to the full box area.