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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 computational geometry and computer science, the minimum-weight triangulation problem is the problem of finding a triangulation of minimal total edge length. [1] That is, an input polygon or the convex hull of an input point set must be subdivided into triangles that meet edge-to-edge and vertex-to-vertex, in such a way as to minimize the ...
The problem of finding the Delaunay triangulation of a set of points in d-dimensional Euclidean space can be converted to the problem of finding ... For example ...
In computer vision, triangulation refers to the process of determining a point in 3D space given its projections onto two, or more, images. In order to solve this problem it is necessary to know the parameters of the camera projection function from 3D to 2D for the cameras involved, in the simplest case represented by the camera matrices.
Until 1988, whether a simple polygon can be triangulated faster than O(n log n) time was an open problem in computational geometry. [1] Then, Tarjan & Van Wyk (1988) discovered an O(n log log n)-time algorithm for triangulation, [7] later simplified by Kirkpatrick, Klawe & Tarjan (1992). [8]
Handling the direct problem is straightforward, because α 0 can be determined directly from the given quantities φ 1 and α 1; for a sample calculation, see Karney (2013). In the case of the inverse problem, λ 12 is given; this cannot be easily related to the equivalent spherical angle ω 12 because α 0 is unknown.
In the social sciences, triangulation refers to the application and combination of several research methods in the study of the same phenomenon. [1] By combining multiple observers, theories, methods, and empirical materials, researchers hope to overcome the weakness or intrinsic biases and the problems that come from single method, single-observer, and single-theory studies.