Triangulierte

Triangulierte is the past participle and an attributive form of the German verb triangulieren. It describes something that has been determined, constructed, or divided by triangulation, or that consists of triangles. The term is commonly used as an adjective in reference to networks, surfaces, or models produced through triangulation.

In surveying and geodesy, triangulation is a method to determine positions by measuring angles in a network of triangles derived from a known baseline. A trianguliertes Netz comprises interconnected triangles whose side lengths and angles allow the calculation of coordinates for network points. Historically, this approach supported large-scale mapping and the establishment of geographic control before the advent of precise distance measurement tools. Triangulierte nets remain relevant in legacy datasets and certain regional geodetic systems.

In geometry, computer graphics and related fields, triangulation refers to partitioning a polygon or a polyhedral surface into triangles. A trianguliertes Netz or triangulated mesh underpins 3D modeling, computer-aided design, finite element analysis, and rendering. Delaunay-Triangulation and other triangulation schemes are central to achieving desirable geometric properties, such as avoiding skinny triangles and improving numerical stability.

Etymology and usage notes: triangulieren derives from the idea of triangles and angles, with the Latin root triangulus (three-cornered). In German, triangulierte is used to describe objects or results produced by this process, for example a trianguliertes Netz, triangulierte Oberfläche, or triangulierte Messdaten. The concept spans practical measurement, theoretical geometry, and digital modeling.