Let $${\textstyle X}$$ be a metric space with distance function $${\textstyle d}$$. Let $${\textstyle K}$$ be a set of indices and let $${\textstyle (P_{k})_{k\in K}}$$ be a tuple (indexed collection) of nonempty subsets (the … See more

Voronoi tessellations of regular lattices of points in two or three dimensions give rise to many familiar tessellations.
• A 2D lattice gives an irregular honeycomb tessellation, with equal hexagons with point symmetry; in the case of a regular triangular … See more

Although a normal Voronoi cell is defined as the set of points closest to a single point in S, an nth-order Voronoi cell is defined as the set of points having a particular set of n points in S as its n nearest neighbors. Higher-order Voronoi diagrams also … See more

As a simple illustration, consider a group of shops in a city. Suppose we want to estimate the number of customers of a given shop. With all … See more

• The dual graph for a Voronoi diagram (in the case of a Euclidean space with point sites) corresponds to the Delaunay triangulation for the same set of points.
• The See more

Informal use of Voronoi diagrams can be traced back to Descartes in 1644. Peter Gustav Lejeune Dirichlet used two-dimensional and three-dimensional Voronoi diagrams in his study of quadratic forms in 1850. British physician John Snow used … See more

As implied by the definition, Voronoi cells can be defined for metrics other than Euclidean, such as the Mahalanobis distance See more