In mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, a Voronoi diagram is a special kind of decomposition of a given space, e.g., a metric space

Metric space

In mathematics, a metric space is a set where a notion of distance between elements of the set is defined.The metric space which most closely corresponds to our intuitive understanding of space is the 3-dimensional Euclidean space...

, determined by distances to a specified family of objects (subsets) in the space. These objects are usually called the sites or the generators (but other names such as "seeds" are in use) and to each such an object one associates a corresponding Voronoi cell, namely the set of all
points in the given space whose distance to the given object is not greater than their distance to the other objects.