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Triangulation can also refer to the accurate surveying of systems of very large triangles, called triangulation networks. This followed from the work of Willebrord Snell in 1615–17, who showed how a point could be located from the angles subtended from three known points, but measured at the new unknown point rather than the previously fixed ...
Triangulation today is used for many purposes, including surveying, navigation, metrology, astrometry, binocular vision, model rocketry and, in the military, the gun direction, the trajectory and distribution of fire power of weapons. The use of triangles to estimate distances dates to antiquity.
In cartography, a triangulated irregular network is a point set triangulation of a set of two-dimensional points together with elevations for each point. Lifting each point from the plane to its elevated height lifts the triangles of the triangulation into three-dimensional surfaces, which form an approximation of a three-dimensional landform.
To aid the mapping of the country, the science of trigonometic surveying was introduced by Major Thomas Mitchell who had been brought out to the colony as Assistant Surveyor General of New South Wales. The freestanding peak of Mount Jellore was selected as the first trigonometric summit for his triangulation survey of the countryside.
Example of triangle network and its application in cartography Main article: Georeferencing After a cartographer registers key points in a digital map to the real world coordinates of those points on the ground, the map is then said to be "in control".
The Principal Triangulation of Britain was the first high-precision triangulation survey of the whole of Great Britain and Ireland, carried out between 1791 and 1853 under the auspices of the Board of Ordnance. The aim of the survey was to establish precise geographical coordinates of almost 300 significant landmarks which could be used as the ...
Practically unused in cartography because of severe polar distortion, but popular in panoramic photography, especially for architectural scenes. c. 1600: Sinusoidal = Sanson–Flamsteed = Mercator equal-area: Pseudocylindrical Equal-area, equidistant (Several; first is unknown) Meridians are sinusoids; parallels are equally spaced.
A triangulation of the square that respects the gluings, like that shown below, also defines a triangulation of the torus. A two dimensional torus, represented as the gluing of a square via the map g, identifying its opposite sites; The projective plane admits a triangulation (see CW-complexes)