Now that we understand the structure of Voronoi diagrams, we're ready to go over the contexts that the IB exam will ask you to apply them in.

Nearest Neighbor Interpolation

Weather stations measure the temperature (in degrees Fahrenheit) throughout the desert based on temperatures taken in five base camps. It's not realistic to set up more stations throughout the desert due to its vast size and remote location. When scientists are studying the behavior of plants and animals in the desert, they use the measurement closest to them as an estimate for the actual temperature of a more remote location.

For example, a scientist located anywhere in the bottom right region would record the temperature as 91°, even if that is not the exact temperature at their specific location. Similarly, a scientist anywhere in the middle region would record the temperature as 82°. A scientist in between two or more regions (on an edge or vertex) would record the temperature as an average of the regions around them, adding the values of the temperatures in the nearest cells and dividing by the number of cells bordering them (two for an edge, three or more for a vertex).

This method is a simple kind of interpolation, a process by which known data points are used to estimate the value of unknown data points.