Voronoi diagrams on a sphere
A flat Voronoi diagram measures straight-line distance on a plane. The Earth is round, so for anything larger than a region — airports across a continent, weather stations around the world, a global network of offices — the right distance is the great-circle distance over the globe's surface. A spherical Voronoi diagram uses exactly that: every point on Earth is assigned to the nearest site along the shortest path over the sphere.
How to use the globe
- Start from random points, an even Fibonacci layout, or a set of major world cities.
- Click anywhere on the globe to add a point, drag points to move them, right-click to remove them.
- Drag empty space to turn the globe, or switch to the equal-area map to see the whole world at once.
- Hover a cell to read its area in km²; press Relax to even the cells out.
Why flat maps get world-scale Voronoi wrong
On a Web Mercator map — the projection of most web maps — distances are stretched more and more toward the poles. A Voronoi diagram computed on that map puts borders too close to high-latitude sites and splits cells at the date line. The spherical diagram has none of those problems: its borders are great-circle arcs and its cells wrap seamlessly around the globe. The equal-area view here keeps the true relative size of every cell.
For a city or a region, where flat distance is accurate enough and you need street-level detail, use the Voronoi map generator.
Frequently asked questions
What is a spherical Voronoi diagram?
It is a Voronoi diagram computed on the surface of a sphere instead of a flat plane. Distance is measured along great circles — the shortest path over the globe — so cell borders are great-circle arcs and the cells wrap around the poles and the date line without breaking.
Why not just draw a Voronoi diagram on a flat world map?
Every flat map distorts distance. On a Web Mercator map, cells near the poles look huge and their borders fall in the wrong place. For a whole country or the world, only a spherical diagram gives correct nearest-place regions.
How are the cell areas computed?
Each cell's area is measured on a sphere with the Earth's mean radius of 6,371 km. The Earth is slightly flattened, so real areas can differ by a fraction of a percent.
What do Relax and Even do?
Relax moves every point to the center of its cell on the sphere, step by step. Even places points on a Fibonacci spiral, one of the most uniform ways to spread points over a globe.