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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 ...
the inverse geodesic problem or second geodesic problem, given A and B, determine s 12, α 1, and α 2. As can be seen from Fig. 1, these problems involve solving the triangle NAB given one angle, α 1 for the direct problem and λ 12 = λ 2 − λ 1 for the inverse problem, and its two adjacent sides.
Thaddeus Vincenty (born Tadeusz Szpila; 27 October 1920 – 6 March 2002) was a Polish American geodesist who worked with the U.S. Air Force and later the National Geodetic Survey to adapt three-dimensional adjustment techniques to NAD 83. [1] He devised Vincenty's formulae, a geodesic calculation technique published in 1975 which is accurate ...
Finding the geodesic between two points on the Earth, the so-called inverse geodetic problem, was the focus of many mathematicians and geodesists over the course of the 18th and 19th centuries with major contributions by Clairaut, [5] Legendre, [6] Bessel, [7] and Helmert English translation of Astron. Nachr. 4, 241–254 (1825).
An inverse problem in science is the process of calculating from a set of observations the causal factors that produced them: for example, calculating an image in X-ray computed tomography, source reconstruction in acoustics, or calculating the density of the Earth from measurements of its gravity field. It is called an inverse problem because ...
The opposite problem occurs when the coordinates (X 1, Y 1) of one point, the distance D, and the azimuth α to another point (X 2, Y 2) are known, one can calculate its coordinates: X 2 = X 1 + D sin α Y 2 = Y 1 + D cos α {\displaystyle {\begin{aligned}X_{2}&=X_{1}+D\sin \alpha \\Y_{2}&=Y_{1}+D\cos \alpha \end{aligned}}}
Vincenty's formulae, a fast algorithm to calculate the distance between two latitude/longitude points Topics referred to by the same term This disambiguation page lists articles associated with the title Vincenty .
"Nearly antipodal points" which describes the problems of failure to converge or slow convergence for the inverse method. This includes pointers to Vincenty's efforts to correct these problems. I also include a plug for my method of solving the inverse problem via Newton's method because