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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 ...
Consider e.g. the value of ("east displacement") when and are on either side of the ±180° meridian, or the value of ("mean latitude") for the two positions (=89°, =45°) and (=89°, =−135°). If a calculation based on latitude/longitude should be valid for all Earth positions, it should be verified that the discontinuity and the Poles are ...
where is the k-th 3-vector measurement in the reference frame, is the corresponding k-th 3-vector measurement in the body frame and is a 3 by 3 rotation matrix between the coordinate frames. [ 1 ] a k {\displaystyle a_{k}} is an optional set of weights for each observation.
To convert from geodetic coordinates to local tangent plane coordinates is a two-stage process: Convert geodetic coordinates to ECEF coordinates;
Consider two points: A at latitude φ 1 and longitude λ 1 and B at latitude φ 2 and longitude λ 2 (see Fig. 1). The connecting geodesic (from A to B ) is AB , of length s 12 , which has azimuths α 1 and α 2 at the two endpoints. [ 1 ]
The haversine formula determines the great-circle distance between two points on a sphere given their longitudes and latitudes.Important in navigation, it is a special case of a more general formula in spherical trigonometry, the law of haversines, that relates the sides and angles of spherical triangles.
A diagram illustrating great-circle distance (drawn in red) between two points on a sphere, P and Q. Two antipodal points, u and v are also shown. The great-circle distance, orthodromic distance, or spherical distance is the distance between two points on a sphere, measured along the great-circle arc between them. This arc is the shortest path ...
The distance from the pole is called the radial coordinate, radial distance or simply radius, and the angle is called the angular coordinate, polar angle, or azimuth. [1] Angles in polar notation are generally expressed in either degrees or radians (2 π rad being equal to 360°).