Illustration
As a simple illustration, consider a group of shops in a flat city. Suppose we want to estimate the number of customers of a given shop. With all else being equal (price, products, quality of service, etc.), it is reasonable to assume that customers choose their preferred shop simply by distance considerations: they will go to the shop located nearest to them. In this case the Voronoi cell of a given shop can be used for giving a rough estimate on the number of potential customers going to this shop (which is modeled by point in our flat city).
So far it was assumed that the distance between points in the city are measured using the standard distance, that is, the familiar Euclidean distance: . However, if we consider the case where customers only go to the shops by a vehicle and the traffic paths are parallel to the and axes, as in Manhattan, then a more realistic distance function will be the distance, namely .
Read more about this topic: Voronoi Diagram
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