Triangulation

In 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 Rⁿ⁺¹ is a subdivision of Rⁿ⁺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 Rⁿ⁺¹ intersects only finitely many simplices in T.

A triangulation of a discrete set of points P in Rⁿ⁺¹ is a triangulation of Rⁿ⁺¹ such that the set of points that are vertices of the subdividing simplices coincides with P.

In 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 Rⁿ⁺¹ is a subdivision of Rⁿ⁺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 Rⁿ⁺¹ intersects only finitely many simplices in T.

A triangulation of a discrete set of points P in Rⁿ⁺¹ is a triangulation of Rⁿ⁺¹ such that the set of points that are vertices of the subdividing simplices coincides with P.

The following definitions are used in Computational geometry.

A triangulation of a polygon P is its partition into triangles. In the strict sence, these triangles may have vertices only in the vertices of P. In non-strict sense, it is allowed to add more points to serve as vertices of triangles.

Also, a triangulation of a set of points P is sometimes taken to be the triangulation of the convex hull of P.