Delaunay triangulation


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Delaunay triangulation

(mathematics, graphics)
(After B. Delaunay) For a set S of points in the Euclidean plane, the unique triangulation DT(S) of S such that no point in S is inside the circumcircle of any triangle in DT(S). DT(S) is the dual of the voronoi diagram of S.
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The Delaunay triangulation only considers one of the points which have the same values of x and y coordinates and different z coordinates.
and its Delaunay triangulation is a (k+1)-neighborly triangulation.
The Delaunay triangulation of a set of points in the plane divides the plane into a number of triangles, plus one open figure.
Since edges in a Delaunay triangulation are guaranteed not to cross one another, conflict resolution is not required and no additional geometry need be created.
The idea is the following: if we see each character, image or collection of pixels as an entity we can connect each of them with the neighboring entity by using the Delaunay triangulation.
The current clustering algorithm used in our system is based on this observation and it uses Delaunay triangulations to form clusters by growing them in each possible direction.
As mentioned previously, we apply Delaunay triangulation since it maximizes the minimum angle of the triangle and avoids the creation of extremely acute angles.
A Delaunay triangulation is one of the many ways to triangulate a set V.
The Delaunay triangulation, the planar dual to the Voronoi diagram, can be built simultaneously with the Voronoi diagram.
In this section, we review the definitions of geometric structures such as the medial axis, Voronoi diagram, and Delaunay triangulation, their representations in the computer, and the benefits they provide for river analysis.