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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 study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks. The figure of the Earth is well approximated by an oblate ellipsoid, a slightly flattened sphere. A geodesic is the shortest path between two points on a curved surface, analogous to a straight line on a plane surface.
Although this formula is accurate for most distances on a sphere, it too suffers from rounding errors for the special (and somewhat unusual) case of antipodal points. A formula that is accurate for all distances is the following special case of the Vincenty formula for an ellipsoid with equal major and minor axes: [5]
The most widely used algorithm is by Vincenty, [10] who uses a series which is accurate to third order in the flattening of the ellipsoid, i.e., about 0.5 mm; however, the algorithm fails to converge for points that are nearly antipodal. (For details, see Vincenty's formulae.)
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]
An Earth ellipsoid or Earth spheroid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, ...
Vincenty's formulae: a fast algorithm to calculate the distance between two latitude/longitude points on an ellipsoid; Geohash: a public domain algorithm that encodes a decimal latitude/longitude pair as a hash string
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 .