Editing Voronoi diagram (section)

=== Mathematics ===
*A [[point location]] data structure can be built on top of the Voronoi diagram in order to answer [[nearest neighbor search|nearest neighbor]] queries, where one wants to find the object that is closest to a given query point. Nearest neighbor queries have numerous applications. For example, one might want to find the nearest hospital or the most similar object in a [[database]]. A large application is [[vector quantization]], commonly used in [[data compression]]. 
*In [[geometry]], Voronoi diagrams can be used to find the [[Largest empty sphere|largest empty circle]] amid a set of points, and in an enclosing polygon; e.g. to build a new supermarket as far as possible from all the existing ones, lying in a certain city.
*Voronoi diagrams together with farthest-point Voronoi diagrams are used for efficient algorithms to compute the [[Roundness (object)|roundness]] of a set of points.<ref name="berg2008" /> The Voronoi approach is also put to use in the evaluation of circularity/[[roundness (object)|roundness]] while assessing the dataset from a [[coordinate-measuring machine]].
*Zeroes of iterated derivatives of a rational function on the complex plane accumulate on the edges of the Voronoi diagam of the set of the poles ([[Pólya's shires theorem]]<ref>Pólya, G. On the zeros of the derivatives of a function and its analytic character. Bulletin
of the AMS, Volume 49, Issue 3, 178-191, 1943.</ref>).