Voronoi Diagrams
Which school, defibrillator, fire station or kebab shop is closest to any point in your town? Split the map into nearest-point regions, then use the areas of the regions to answer a question you actually care about.
Where this idea comes from
Start here — these are the sources that inspired this exploration.
Introduction
Drop a set of points on a map — supermarkets, water fountains, train stations, ambulance bases — and divide the map so each region contains everywhere closest to one point. That's a Voronoi diagram, and it is how Melbourne draws school catchments and how planners site fire stations. Once you have the regions, their AREAS start answering real questions: which branch serves the largest share of the town? If sites serve equal populations, are the areas fair? Where is the most poorly-served spot — the centre of the largest circle that touches no site — and is that where the next site should go? Pick a scenario from your own life: pizza delivery zones, choosing which lifeguard chair watches which swimmers, where to stand in a doubles match, planting trees so each gets its share of ground. Then ask the question that turns this into a real investigation: is 'closest as the crow flies' actually the right rule for your scenario — and if not, what is?
Guiding Questions
- Choose a scenario and gather real points: every defibrillator, supermarket or bus stop in your area, with coordinates from an online map. Construct the diagram with perpendicular bisectors, then check it with a Voronoi tool.
- Use the areas of your regions to answer a concrete question: which site carries the biggest load? If each site can only serve so many people, which region is in trouble?
- Find the worst-served point on your map — the centre of the largest empty circle. If you could add one new site, where should it go, and how much does the worst case improve?
- Now interrogate your own model: is straight-line distance really what matters in your scenario? Decide what your scenario actually cares about, test whether the plain diagram captures it, and adapt your rule if it doesn't.
- Compare your diagram with reality — the actual school catchment, delivery zone or coverage map. Where do they disagree, and what explains the difference?