Voronoy

Voronoi is a term that can refer to several related concepts, primarily associated with Russian mathematician Georgy Voronoy. The most common reference is to Voronoi diagrams, also known as Voronoi tessellations or partitions.

A Voronoi diagram is a partitioning of a plane into regions based on distance to a set of points. For each point in the set, there is a corresponding region consisting of all points closer to that point than to any other. These regions are convex polygons, and the boundaries between them are formed by perpendicular bisectors of the lines connecting pairs of points.

Voronoi diagrams have numerous applications in various fields, including computer graphics, image processing, geographical information systems, and crystallography. They can be used for tasks such as nearest neighbor searches, spatial interpolation, and facility location problems.

Georgy Voronoy (1868–1908) was a Russian mathematician who made significant contributions to number theory and the theory of quadratic forms. The Voronoi diagram is named in his honor due to his work on the theory of congruences and the geometric properties of lattices. His research laid the groundwork for understanding these spatial partitioning structures. The concept of Voronoi tessellations is a fundamental tool in computational geometry and has broad practical utility.