High Quality Content by WIKIPEDIA articles! In advanced geometry, in the most general meaning, triangulation is a subdivision of a geometric object into simplices. In particular, in the plane it is a subdivision into triangles, hence the name. Different branches of geometry use slightly differing definitions of the term. A point set triangulation,i.e., a triangulation of a discrete set of points Psubsetmathbb{R}^{n+1} is a subdivision of the convex hull of the points into simplices such that any two simplices intersect in a common face or not at all and the set of points that are vertices of the subdividing simplices coincides with P. The Delaunay triangulation is a famous triangulation of a set of points where the circum-hypersphere of each simplex contains none of the points.

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