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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.
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 ...
Polygon triangulation. In computational geometry, polygon triangulation is the partition of a polygonal area (simple polygon) P into a set of triangles, [1] i.e., finding a set of triangles with pairwise non-intersecting interiors whose union is P. Triangulations may be viewed as special cases of planar straight-line graphs.
The triangulation of a parametrically defined surface is simply achieved by triangulating the area of definition (see second figure, depicting the Monkey Saddle). However, the triangles may vary in shape and extension in object space, posing a potential drawback.
Compared to any other triangulation of the points, the smallest angle in the Delaunay triangulation is at least as large as the smallest angle in any other. However, the Delaunay triangulation does not necessarily minimize the maximum angle. [6] The Delaunay triangulation also does not necessarily minimize the length of the edges.
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.
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The primary face of the subdivision is called a principal polyhedral triangle (PPT) or the breakdown structure. Calculating a single PPT allows the entire figure to be created. The frequency of a geodesic polyhedron is defined by the sum of ν = b + c. A harmonic is a subfrequency and can be any whole divisor of ν.