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Triangulation of Kodiak Island in Alaska in 1929. In surveying, triangulation is the process of determining the location of a point by measuring only angles to it from known points at either end of a fixed baseline by using trigonometry, rather than measuring distances to the point directly as in trilateration. The point can then be fixed as ...
Equivalent narcotic depth (END) (historically also equivalent nitrogen depth) is used in technical diving as a way of estimating the narcotic effect of a breathing gas mixture, such as nitrox, heliox or trimix. The method is used, for a given breathing gas mix and dive depth, to calculate the equivalent depth which would produce about the same ...
In trigonometry, the Snellius–Pothenot problem is a problem first described in the context of planar surveying.Given three known points A, B, C, an observer at an unknown point P observes that the line segment AC subtends an angle α and the segment CB subtends an angle β; the problem is to determine the position of the point P.
[3] [4] [5] The triangulation starts with a triangulated hexagon at a starting point. This hexagon is then surrounded by new triangles, following given rules, until the surface of consideration is triangulated. If the surface consists of several components, the algorithm has to be started several times using suitable starting points.
The Riemann-Hurwitz formula allows to determine the genus of a compact, connected Riemann surface without using explicit triangulation. The proof needs the existence of triangulations for surfaces in an abstract sense: Let F : X → Y {\displaystyle F:X\rightarrow Y} be a non-constant holomorphic function on a surface with known genus.
Control point — The primary/base control used for preliminary measurements; it may consist of any known point capable of establishing accurate control of distance and direction (i.e. coordinates, elevation, bearings, etc.).
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A triangulation of a set of points in the Euclidean space is a simplicial complex that covers the convex hull of , and whose vertices belong to . [1] In the plane (when P {\displaystyle {\mathcal {P}}} is a set of points in R 2 {\displaystyle \mathbb {R} ^{2}} ), triangulations are made up of triangles, together with their edges and vertices.