The Simplest Case
In the simplest and most familiar case (shown in the first picture), we are given a finite set of points {p1,...,pn} in the Euclidean plane. In this case each site pk is simply a point and its corresponding Voronoi cell (also called Voronoi region or Dirichlet cell) Rk consisting of every point whose distance to pk is less than or equal to its distance to any other site. Each such cell is obtained from the intersection of half-spaces, and hence it is a convex polygon. The segments of the Voronoi diagram are all the points in the plane that are equidistant to the two nearest sites. The Voronoi vertices (nodes) are the points equidistant to three (or more) sites.
Read more about this topic: Voronoi Diagram
Famous quotes containing the words simplest and/or case:
“The simplest surrealist gesture consists in going out into the street, gun in hand, and taking pot shots at the crowd!”
—Surrealist slogan from the 1920s, quoted by Luis Buñuel in My Last Sigh, ch. 10 (1983)
“The circumstances with which every thing in this world is begirt, give every thing in this world its size and shape;—and by tightening it, or relaxing it, this way or that, make the thing to be, what it is—great—little—good—bad—indifferent or not indifferent, just as the case happens.”
—Laurence Sterne (1713–1768)