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.
The following definitions are used in Computational geometry.
A triangulation of a polygon P is its partition into triangles. In the strict sense, 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
Triangulation is useful in determining the properties of a topological space.
Triangulation is the process of finding a distance by calculating the length of one side of a triangle, given a deterministic combination of angles and sides of the triangle. It uses mathematical identities from trigonometry.
Some identities often used:
- The sum of the angles of a triangle is &pi (180 degrees).
- The law of sines
- The law of cosines
- The Pythagorean theorem
In the social sciences, triangulation is often used to indicate that more than one method is used in a study with a view to double (or triple) checking results. This is also called "cross examination". The idea is that we can be more confident with a result if different methods lead to the same result.