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Geographical distance or geodetic distance is the distance measured along the surface of the Earth, or the shortest arch length. The formulae in this article calculate distances between points which are defined by geographical coordinates in terms of latitude and longitude. This distance is an element in solving the second (inverse) geodetic ...
Euclidean distance. In mathematics, the Euclidean distance between two points in Euclidean space is the length of the line segment between them. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, and therefore is occasionally called the Pythagorean distance . These names come from the ancient Greek ...
The distance from (x 0, y 0) to this line is measured along a vertical line segment of length |y 0 − (− c / b)| = |by 0 + c| / |b| in accordance with the formula. Similarly, for vertical lines (b = 0) the distance between the same point and the line is |ax 0 + c| / |a|, as measured along a horizontal line segment. Line defined by two points
d is the distance between the two points along a great circle of the sphere (see spherical distance), r is the radius of the sphere. The haversine formula allows the haversine of θ (that is, hav(θ)) to be computed directly from the latitude (represented by φ) and longitude (represented by λ) of the two points:
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 great-circle distance, orthodromic distance, or spherical distance is the distance along a great circle . It is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere (as opposed to a straight line through the sphere's interior). The distance between two points in Euclidean space is the ...
The taxicab distance, , between two points in an n -dimensional real coordinate space with fixed Cartesian coordinate system, is the sum of the lengths of the projections of the line segment between the points onto the coordinate axes. More formally, For example, in , the taxicab distance between and is.
In Euclidean space, the distance from a point to a plane is the distance between a given point and its orthogonal projection on the plane, the perpendicular distance to the nearest point on the plane. It can be found starting with a change of variables that moves the origin to coincide with the given point then finding the point on the shifted ...