triangulationcrossverifying

Triangulation is a method used to determine locations and shapes by constructing triangles with at least two known vertices and measuring angles between lines to unknown points. The core premise is that if the positions of two reference points A and B are known and the angles from A and B to a target point P are measured, the lines AP and BP intersect at P, locating the target. In practice, measurements are repeated along a network to determine multiple points and to check consistency.

In surveying and geodesy, triangulation networks use a base line of known length and a series of triangles to extend control points over large areas. It is distinct from trilateration, which relies on distance measurements rather than angles. Over time, triangulation has enabled the creation of accurate maps and coordinate systems by propagating precision from a well-measured baseline through a network.

In other fields, triangulation refers to 3D reconstruction in computer vision: with several camera views and known camera geometry, corresponding image points map to rays; their intersection estimates 3D coordinates. In navigation, signal localization and robotics, angles or direction measurements from multiple known stations help locate a device.

Limitations and history: Triangulation accuracy depends on angular measurement precision and the geometric arrangement of reference points; poorly conditioned configurations amplify errors. It has roots in classical surveying and geodesy and was a foundational technique before modern satellite geodesy; today it is complemented by trilateration and optimization methods like network adjustment.