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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 ...
Then calculate the central angle in radians between two points (,) and (,) on a sphere using the Great-circle distance method (haversine formula), with longitudes and being the same on the sphere as on the spheroid.
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 ...
Computes the great circle distance between two points, specified by the latitude and longitude, using the haversine formula. Template parameters [Edit template data] Parameter Description Type Status Latitude 1 lat1 1 Latitude of point 1 in decimal degrees Default 0 Number required Longitude 1 long1 2 Longitude of point 1 in decimal degrees Default 0 Number required Latitude 2 lat2 3 Latitude ...
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That is (unlike road distance with one-way streets) the distance between two points does not depend on which of the two points is the start and which is the destination. [12] It is positive, meaning that the distance between every two distinct points is a positive number, while the distance from any point to itself is zero. [12]
For example, to find the midpoint of the path, substitute σ = 1 ⁄ 2 (σ 01 + σ 02); alternatively to find the point a distance d from the starting point, take σ = σ 01 + d/R. Likewise, the vertex, the point on the great circle with greatest latitude, is found by substituting σ = + 1 ⁄ 2 π. It may be convenient to parameterize the ...