Triangeln

Triangeln is a method used to determine geographic positions, shapes, or boundaries by constructing a network of triangles and measuring angles and, in some cases, distances. The practice relies on known reference points and the geometry of triangles to propagate position information across the network.

Principles and process: A baseline of known length is established. Angles at the baseline endpoints are measured to unknown survey points. Using trigonometry, the locations of those points are computed. In large networks, many triangles are connected to form a tessellation, and a least-squares adjustment is often applied to reduce errors across the network.

History and scope: Triangulation has played a central role in geodesy and cartography since the 18th and 19th centuries, enabling large-area mapping before satellite navigation. It remains foundational in establishing national geodetic reference systems, though modern methods supplement or replace it with satellite-based measurements and trilateration.

Variations and applications: In computer graphics and computational geometry, polygon triangulation refers to decomposing a polygon into triangles for rendering and analysis. In navigation and wireless positioning, triangulation describes locating a device by measuring angles or distances to multiple reference stations; contemporary systems often combine triangulation with other techniques for improved accuracy.

Limitations: Accuracy depends on the precision of baseline measurements, angle measurements, and the geometric arrangement of the network. Line-of-sight, terrain, and measurement errors can limit reliability, especially over long distances.

See also: polygon triangulation, geodetic triangulation, least-squares adjustment, trilateration, Delaunay triangulation.