# 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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Caption: Figure 3: Preliminary Delaunay triangulation of adjacent tooth surface scan lines.
Apart from regular Delaunay triangulation, we define the intermediate Delaunay complex as
The main techniques of converting these point clouds are for now Delaunay triangulation, alpha shapes and marching cubes.
Moreover, for each area, the proposed deployment algorithm has been initially compared with three other basic algorithms well-known in literature: a mesh based algorithm , a pattern based algorithm , and a Delaunay Triangulation (DT) based algorithm .
The GNSS station does not measure the distance and that is why a well-tried method of a Delaunay triangulation was used.
The Delaunay triangulation D of V, introduced by Delaunay in 1934, is a graph that is defined as follows.
Georgiopoulos, "Fingerprint identification using delaunay triangulation", In Proc.
The Delaunay triangulation only considers one of the points which have the same values of x and y coordinates and different z coordinates.
The Delaunay triangulation (DT) is the straight-line dual structure of the Voronoi diagram; see  for the clear definitions of the Delaunay triangulation and constrained Delaunay triangulation.
Then the Delaunay triangulation T := D([??]) coincides with the placing triangulation of [??].

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