In computational geometry, the Delaunay triangulation of a set P of points in the plane is a triangulation DT such that no point of P is inside the circumcircle of one of the triangles of DT.
Delaunay triangulations maximize the smallest angle of the set of angles of triangles, thus avoiding elongated triangles.
According to Delaunay's definition, the circumcircle of a triangle made up of three points of the starting set is empty if it does not contain any vertices other than its own.
Thus, the other points are authorized on the perimeter itself but not strictly inside the circumscribed circle.
The Delaunay condition asserts that a network of triangles is a Delaunay triangulation if all the circumcircles of the triangles in the network are empty.
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