Voronoi Diagrams for European Cities

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A Voronoi diagram partitions the plane into regions based on the distances to a specific subset of points. With more points, there are more regions and the regions are smaller. This Demonstration generates a Voronoi diagram using major cities for up to three countries or capitals of countries for more than three countries.


Hover over the red dots to see the name of the city.


Contributed by: Trey Taylor (July 2016)
Mathematica Summer Camp 2016
Open content licensed under CC BY-NC-SA



Given a set of points in the plane, the corresponding Voronoi diagram partitions the plane into convex polygons such that each polygon contains exactly one point of , say , and every point in is closer to than to any other point in .

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