triangulation

Triangulation is a multisense term in geometry, surveying, computer vision, and social science. In general, it denotes deriving a quantity, position, or structure by forming triangles from known references. The core idea is to use triangular geometry to relate measurements to unknowns.

Geometric triangulation can refer to subdividing a polygon into triangles, a process used in mesh generation and computer graphics, or to constructing a triangulation of a finite set of points, which yields a planar straight-line graph where all faces are triangles. A triangulation of a polygon aims to avoid crossing diagonals and to respect the polygon boundary. A common variant is the Delaunay triangulation, which maximizes the minimum angle of all triangles and tends to avoid skinny triangles. Triangulations underpin finite element analysis and surface rendering.

In surveying, triangulation determines a location by measuring angles from two or more known reference points. A baseline distance between two references, combined with observed angles, yields the position of the unknown point via triangle geometry. Triangulation differs from trilateration, which uses distances rather than angles. With modern technologies such as GNSS, triangulation has largely been superseded for navigation but remains conceptually important in geodetic networks and historical surveying.

In computer vision, triangulation reconstructs a 3D point by intersecting projection rays from two calibrated cameras that observe the same scene point. Accurate triangulation requires precise camera calibration, correspondence between image points, and handling of noise.

In research methodology, triangulation refers to using multiple data sources, methods, or researchers to study a phenomenon, increasing validity by cross-checking findings.