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In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points. Applications [ edit ]
Delaunay triangulation; Bitmap resampling is the application of 2D multivariate interpolation in image processing. Three of the methods applied on the same dataset, from 25 values located at the black dots. The colours represent the interpolated values.
Illustration from an edition of 1726 Gemma Frisius's 1533 proposal to use triangulation for mapmaking Nineteenth-century triangulation network for the triangulation of Rhineland-Hesse. Triangulation today is used for many purposes, including surveying, navigation, metrology, astrometry, binocular vision, model rocketry and gun direction of weapons.
Nearest-neighbor interpolation (also known as proximal interpolation or, in some contexts, point sampling) is a simple method of multivariate interpolation in one or more dimensions. Interpolation is the problem of approximating the value of a function for a non-given point in some space when given the value of that function in points around ...
One method divides the 3D region of consideration into cubes and determines the intersections of the surface with the edges of the cubes in order to get polygons on the surface, which thereafter have to be triangulated (cutting cube method). [1] [2] The expenditure for managing the data is great. The second and simpler concept is the marching ...
Gemma Frisius described for the first time the method of triangulation still used today in surveying. It was Leonhard Euler who fully incorporated complex numbers into trigonometry. The works of the Scottish mathematicians James Gregory in the 17th century and Colin Maclaurin in the 18th century were influential in the development of ...
Vincenty's formulae are two related iterative methods used in geodesy to calculate the distance between two points on the surface of a spheroid, developed by Thaddeus Vincenty (1975a). They are based on the assumption that the figure of the Earth is an oblate spheroid, and hence are more accurate than methods that assume a spherical Earth, such ...
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.