Triangulation (advanced geometry)

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 triangulation T of $mathbb\{R\}^\{n+1\}$ is a subdivision of $mathbb\{R\}^\{n+1\}$ into (n+1)-dimensional simplices such that:
#any two simplices in T intersect in a common face or not at all;
#any bounded set in $mathbb\{R\}^\{n+1\}$ intersects only finitely many simplices in T.

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.

See also

* Pseudotriangulation