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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.
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 ...
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 ...
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 ...
a value greater than 1 for two disjoint circles, a value of 1 for two circles that are tangent to each other and both outside each other, a value between −1 and 1 for two circles that intersect, a value of 0 for two circles that intersect each other at right angles, a value of −1 for two circles that are tangent to each other, one inside of ...
The introduction says that "[t]he great-circle distance or orthodromic distance is the shortest distance between any two points on the surface of a sphere measured along a path on the surface of the sphere (as opposed to going through the sphere's interior)".
The two dimensional Manhattan distance has "circles" i.e. level sets in the form of squares, with sides of length √ 2 r, oriented at an angle of π/4 (45°) to the coordinate axes, so the planar Chebyshev distance can be viewed as equivalent by rotation and scaling to (i.e. a linear transformation of) the planar Manhattan distance.
The distance (or perpendicular distance) from a point to a line is the shortest distance from a fixed point to any point on a fixed infinite line in Euclidean geometry. It is the length of the line segment which joins the point to the line and is perpendicular to the line. The formula for calculating it can be derived and expressed in several ways.