A Voronoi diagram is a geometric representation of a partition of a plane into regions based
on the distance to a set of points, called seeds.
It is named after Russian mathematician Georgy Voronoi, who introduced the concept in 1908.
The Voronoi diagram of a set of points is a collection of polygons that divide the plane into
regions such that each region contains exactly one seed point and consists of all points in
the plane that are closer to that seed point than to any other seed point.
The Voronoi diagram is dual to the Delaunay triangulation of the same set of points.
Voronoi diagrams are used in a wide range of applications, including computer graphics,
image processing, geographical information systems, and robotics. They can be used to visualize data,
optimize logistics, and perform spatial analysis.
To construct a Voronoi diagram, one can start by drawing a circle around each seed point with
radius equal to the distance to the nearest neighboring seed point. The intersection points of
these circles form the vertices of the Voronoi diagram. The edges of the Voronoi diagram are formed
by the segments that connect the vertices, and the regions of the Voronoi diagram are the bounded
areas between the edges.
There are several algorithms for constructing Voronoi diagrams, including the Fortune's algorithm,
the divisible-by-two algorithm, and the incremental algorithm, Delaunay-triangulation. Each of these algorithms has its own
advantages and disadvantages, and the choice of algorithm depends on the specific application.
@Safidy Rat