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:
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:
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.
See also: Delaunay triangulation
Topology generalizes this notion in a natural way as follows. A triangulation of a topological space X is a simplicial complex K, homeomorphic to X, together with a homeomorphism h:K->X.
Triangulation is useful in determining the properties of a topological space.
Some identities often used:
See: Parallax.