# Triangulation

In trigonometry and geometry, triangulation is the process of determining the location of a point by measuring angles to it from known points at either end of a fixed baseline, rather than measuring distances to the point directly (trilateration). The point can then be fixed as the third point of a triangle with one known side and two known angles.

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 points, a problem called resectioning. Surveying error is minimized if a mesh of triangles at the largest appropriate scale is established first. Points inside the triangles can all then be accurately located with reference to it. Such triangulation methods were used for accurate large-scale land surveying until the rise of global navigation satellite systems in the 1980s.

### Other articles related to "triangulation, triangulations":

Triangulation (computer Vision) - Properties of Triangulation Methods - Invariance
... In some applications, it is desirable that the triangulation is independent of the coordinate system used to represent 3D points if the triangulation problem is ... Not every triangulation method assures invariance, at least not for general types of coordinate transformations ... matrices must transform as to produce the same homogeneous image coordinates If the triangulation function is invariant to then the following relation must be valid from which ...
Triangulation (psychology)
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History - Willebrord Snell and Modern Triangulation Networks
... The modern systematic use of triangulation networks stems from the work of the Dutch mathematician Willebrord Snell, who in 1615 surveyed the distance ... to Perpignan and between 1733 and 1740 Jacques and his son César Cassini undertook the first triangulation of the whole country, including a re-surveying of the meridian arc, leading to ... Triangulation methods were by now well established for local mapmaking, but it was only towards the end of the 18th century that other countries began to establish detailed triangulation ...
Pitteway Triangulation
... In computational geometry, a Pitteway triangulation is a point set triangulation in which the nearest neighbor of any point p within the triangulation is one ... Alternatively, it is a Delaunay triangulation in which each internal edge crosses its dual Voronoi diagram edge ... Pitteway triangulations are named after Michael Pitteway, who studied them in 1973 ...