Voronoi diagrams divide a geographical region into cells according to which facility or location is nearest. Urban planners use them to model service areas, while epidemiologists can use them to examine access to healthcare or the geographical pattern of disease cases.
Each known location is called a site. A Voronoi cell contains every point closer to its site than to any other site; therefore, the edges are sections of perpendicular bisectors between pairs of sites.
For example, suppose three hospitals are represented by sites , , and . A resident at point belongs to hospital 's cell if is less than both and . Under a nearest-facility model, hospital would serve that resident.
| Application | How the Voronoi diagram is used | Possible limitation |
|---|---|---|
| Urban planning | Divides a city into nearest-hospital, school, fire-station, or public-transport service areas | Straight-line distance may ignore roads, rivers, traffic, or capacity |
| Epidemiology | Assigns communities to their nearest clinic or testing centre and helps identify areas with poor healthcare coverage | Proximity alone does not explain infection or transmission |
| Facility placement | Large cells or distant Voronoi vertices may indicate underserved areas where a new facility could be considered | Population density and cost must also be considered |
A related IB concept is nearest-neighbour interpolation. If a monitoring station records an infection rate or pollution level, every point inside its cell may be estimated to have the site's value. This is useful but assumes that values change abruptly at cell boundaries, which may be unrealistic.
A common misconception is that Voronoi cells show actual administrative boundaries or prove where a disease originated. They show nearest-site regions under a distance model, not causation or real travel routes.
Exam technique: This is SL 3.6 content and may appear in either Paper 1 or Paper 2. Identify the containing cell and name its site, explain that edges are perpendicular bisectors, and interpret the result in context. For evaluation questions, state one realistic limitation of using straight-line distance.