Ted wants to use measurements of rainfall in certain specific parts of a city to estimate rainfall in other parts of the city.

Using the values of known points on a 2D grid to estimate the values at other points is called interpolation.

A simple method of interpolation is called nearest neighbour interpolation. To estimate the value of a variable at any point, we use the variable’s value at the nearest known data point. A Voronoi diagram can help us quickly identify the nearest known data point.

If the given point lies on an edge or at a vertex, we take the average of the closest known data points.

Worked Example

Ted measured the rainfall in his city at three locations A, B and C marked on the map below:

His results were as follows:

Location	Rainfall (mm)
A	12
B	7
C	15

• Use nearest neighbour interpolation to estimate the rainfall at:
  • (-4,1)
  • (3,-2)
  • (1,-2)

Exercise

Answers