geodesic and inverse geodesic problem

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Description

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).

Usage

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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)

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: http://en.wikipedia.org/wiki/Reference_ellipsoid

Value

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

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. https://dx.doi.org/10.1007/s00190-012-0578-z. Addenda: http://geographiclib.sf.net/geod-addenda.html. Also see http://geographiclib.sourceforge.net/

See Also

distGeo

Examples

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

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