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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 ...
Proximity analysis is a class of spatial analysis tools and algorithms that employ geographic distance as a central principle. [1] Distance is fundamental to geographic inquiry and spatial analysis, due to principles such as the friction of distance, Tobler's first law of geography, and Spatial autocorrelation, which are incorporated into analytical tools. [2]
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 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.
In each zone the scale factor of the central meridian reduces the diameter of the transverse cylinder to produce a secant projection with two standard lines, or lines of true scale, about 180 km on each side of, and about parallel to, the central meridian (Arc cos 0.9996 = 1.62° at the Equator). The scale is less than 1 inside the standard ...
The calculation requires measurements or observations of distances or angles to reference points whose positions are known. In 2D surveys, observations of three reference points are enough to compute a position in a two-dimensional plane. In practice, observations are subject to errors resulting from various physical and atmospheric factors ...
For example, an equation of 7.6 back = 9.2 ahead means that the feature does not have any section between mile 7.6 and mile 9.2, and the distance between mileposts 7 and 10 is only 1.4 miles. This would usually be caused by a relocation that shortened the distance by 1.6 miles.
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.