geodesic function

geodesic and inverse geodesic problem

Highly accurate estimate of the 'geodesic problem' (find location and azimuth at arrival when departing from a location, given an direction (azimuth) at departure and distance) and the 'inverse geodesic problem' (find the distance between two points and the azimuth of departure and arrival for the shortest path. Computations are for an ellipsoid (default is WGS84 ellipsoid).

This is a direct implementation of the the GeographicLib code by C.F.F. Karney that is also used in several other functions in this package (for example, in distGeo and areaPolygon). 1.1

geodesic(p, azi, d, a=6378137, f=1/298.257223563, ...)

geodesic_inverse(p1, p2, a=6378137, f=1/298.257223563, ...)

Arguments

• p: longitude/latitude of point(s). Can be a vector of two numbers, a matrix of 2 columns (first column is longitude, second column is latitude) or a SpatialPoints* object
• p1: as above
• p2: as above
• azi: numeric. Azimuth of departure in degrees
• d: numeric. Distance in meters
• a: numeric. Major (equatorial) radius of the ellipsoid. The default value is for WGS84
• f: numeric. Ellipsoid flattening. The default value is for WGS84
• ...: additional arguments (none implemented)

Returns

Three column matrix with columns 'longitude', 'latitude', 'azimuth' (geodesic); or 'distance' (in meters), 'azimuth1' (of departure), 'azimuth2' (of arrival) (geodesic_inverse)

Details

Parameters from the WGS84 ellipsoid are used by default. It is the best available global ellipsoid, but for some areas other ellipsoids could be preferable, or even necessary if you work with a printed map that refers to that ellipsoid. Here are parameters for some commonly used ellipsoids.

	ellipsoid	a	f
	WGS84	6378137	1/298.257223563
	GRS80	6378137	1/298.257222101
	GRS67	6378160	1/298.25
	Airy 1830	6377563.396	1/299.3249646
	Bessel 1841	6377397.155	1/299.1528434
	Clarke 1880	6378249.145	1/293.465
	Clarke 1866	6378206.4	1/294.9786982
	International 1924	6378388	1/297
	Krasovsky 1940	6378245	1/298.2997381

more info: https://en.wikipedia.org/wiki/Reference_ellipsoid

Author(s)

This function calls GeographicLib code by C.F.F. Karney

References

C.F.F. Karney, 2013. Algorithms for geodesics, J. Geodesy 87: 43-55. tools:::Rd_expr_doi("10.1007/s00190-012-0578-z") . Addenda: https://geographiclib.sourceforge.io/geod-addenda.html. Also see https://geographiclib.sourceforge.io/

See Also

distGeo

Examples

geodesic(cbind(0,0), 30, 1000000)
geodesic_inverse(cbind(0,0), cbind(90,90))