Voronoidiagrammin

Voronoidiagrammin, also known as a Voronoi diagram, is a partitioning of a plane into regions based on distance to a specified set of points, known as seeds, sites, or generators. The diagram was named after the Russian mathematician Georgy Voronoy, who developed the concept in the early 20th century. Each region in a Voronoi diagram consists of all points closer to a particular seed than to any other seed. If two or more seeds are equidistant from a point, that point is typically assigned to the region of one of the seeds, or to a shared boundary.

Voronoi diagrams have numerous applications in various fields, including computational geometry, physics, biology, and geography. In computational geometry, they are used for solving problems such as finding the closest pair of points, constructing convex hulls, and computing Delaunay triangulations. In physics, Voronoi diagrams are used to model the structure of materials and to simulate the behavior of particles. In biology, they are used to study the distribution of species and to model the growth of cells. In geography, Voronoi diagrams are used to analyze the distribution of resources and to model the spread of diseases.

Voronoi diagrams can be constructed using various algorithms, including the Fortune's algorithm and the incremental algorithm. The choice of algorithm depends on the specific application and the size of the input data. Voronoi diagrams can also be generalized to higher dimensions and to non-Euclidean spaces, such as spherical and hyperbolic spaces. In these cases, the definition of distance and the properties of the diagram may change.