Delaunay Triangulation - Relationship With The Voronoi Diagram

Relationship With The Voronoi Diagram

The Delaunay triangulation of a discrete point set P in general position corresponds to the dual graph of the Voronoi tessellation for P. Special cases include the existence of three points on a line and four points on circle.

  • The Delaunay triangulation with all the circumcircles and their centers (in red).

  • Connecting the centers of the circumcircles produces the Voronoi diagram (in red).

Read more about this topic:  Delaunay Triangulation

Famous quotes containing the words relationship with, relationship and/or diagram:

    Every man is in a state of conflict, owing to his attempt to reconcile himself and his relationship with life to his conception of harmony. This conflict makes his soul a battlefield, where the forces that wish this reconciliation fight those that do not and reject the alternative solutions they offer. Works of art are attempts to fight out this conflict in the imaginative world.
    Rebecca West (1892–1983)

    Living in cities is an art, and we need the vocabulary of art, of style, to describe the peculiar relationship between man and material that exists in the continual creative play of urban living. The city as we imagine it, then, soft city of illusion, myth, aspiration, and nightmare, is as real, maybe more real, than the hard city one can locate on maps in statistics, in monographs on urban sociology and demography and architecture.
    Jonathan Raban (b. 1942)

    If a fish is the movement of water embodied, given shape, then cat is a diagram and pattern of subtle air.
    Doris Lessing (b. 1919)