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:
“It is just possible that the tensions in a novel of murder are the simplest and yet most complete pattern of the tensions on which we live in this generation.”
—Raymond Chandler (1888–1959)
“In case I conk out, this is provisionally what I have to do: I must clarify obscurities; I must make clearer definite ideas or dissociations. I must find a verbal formula to combat the rise of brutality—the principle of order versus the split atom.”
—Ezra Pound (1885–1972)