In mathematics, a Voronoi diagram is a special kind of decomposition of a metric space determined by distances to a specified discrete set of objects in the space, e.g., by a discrete set of points. It is named after Georgy Voronoi, also called a Voronoi tessellation, a Voronoi decomposition, or a Dirichlet tessellation (after Lejeune Dirichlet),
In the simplest case, we are given a set of points S in the plane, which are the Voronoi sites. Each site s has a Voronoi cell, also called a Dirichlet cell, V(s) consisting of all points closer to s than to any other site. The segments of the Voronoi diagram are all the points in the plane that are equidistant to the two nearest sites. The Voronoi nodes are the points equidistant to three (or more) sites.
more about Voronroi…
Voronoi diagrams were considered as early at 1644 by René Descartes and were used by Dirichlet (1850) in the investigation of positive quadratic forms. They were also studied by Voronoi (1907), who extended the investigation of Voronoi diagrams to higher dimensions. They find widespread applications in areas such as computer graphics, epidemiology, geophysics, and meteorology. A particularly notable use of a Voronoi diagram was the analysis of the 1854 cholera epidemic in London, in which physician John Snow determined a strong correlation of deaths with proximity to a particular (and infected) water pump on Broad Street.
Mesh Library// http://www.leebyron.com/else/mesh/
Mesh is a library for creating Voronoi, Delaunay and Convex Hull diagrams in Processing. After searching online for a Java package for creating Voronoi diagrams and failing to find anything simple enough to fit my needs I decided to make my own as simple as possible. I did find the wonderfully useful QuickHull3D package, which the algorithms for creating these diagrams are based on. These complete in O(n log n) time.