Urban transportation systems and Voronoi diagrams

One crucial factor for most urban transportation systems (suburban railway, etc) is the positioning of the stations. It is desirable to cover an area as efficiently as possible. One way to measure the efficiency of the positioning of existing or new stations is to use a Voronoi diagram. The Voronoi diagram decomposes the city map into polygonal areas each one “served” by a specific station.

You can take a look at a live demonstration of the application featuring the railway system of Athens:

http://labpower.teipir.gr/prekageo/metro_map/