Angle along great circle on spherical surface

Smallest angle between two points on the surface of a sphere, measured along the surface of the sphere

Usage

orthodrome(lat1, lon1, lat2, lon2)

haversine(lat1, lon1, lat2, lon2)

vincenty(lat1, lon1, lat2, lon2)

Arguments

lat1, lat2

numeric vector. latitudes of point 1 and 2 (in radians)

lon1, lon2

numeric vector. longitudes of point 1 and 2 (in radians)

Value

numeric. angle in radians

Details

"orthodrome"

based on the spherical law of cosines

"haversine"

uses haversine formula that is optimized for 64-bit floating-point numbers

"vincenty"

uses Vincenty formula for an ellipsoid with equal major and minor axes

References

• Imboden, C. & Imboden, D. (1972). Formel fuer Orthodrome und Loxodrome bei der Berechnung von Richtung und Distanz zwischen Beringungs- und Wiederfundort. Die Vogelwarte 26, 336-346.

• Sinnott, Roger W. (1984). Virtues of the Haversine. Sky and telescope 68(2), 158. Vincenty, T. (1975). Direct and inverse solutions of geodesics on the ellipsoid with application of nested equations. Survey Review, 23(176), 88<U+2013>93. doi:10.1179/sre.1975.23.176.88 .

• http://www.movable-type.co.uk/scripts/latlong.html

• http://www.edwilliams.org/avform147.htm

Examples

berlin <- c(52.52, 13.41)
calgary <- c(51.04, -114.072)
orthodrome(berlin[1], berlin[2], calgary[1], calgary[2])
#> [1] 0.8595483
haversine(berlin[1], berlin[2], calgary[1], calgary[2])
#> [1] 0.8595483
vincenty(berlin[1], berlin[2], calgary[1], calgary[2])
#> [1] 0.8595483