geodesic: geodesic and inverse geodesic problem

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

geodesic(p, azi, d, a=6378137, f=1/298.257223563, ...)
geodesic_inverse(p1, p2, a=6378137, f=1/298.257223563, ...)

Arguments

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

as above

azi

numeric. Azimuth of departure in degrees

numeric. Distance in meters

numeric. Major (equatorial) radius of the ellipsoid. The default value is for WGS84

numeric. Ellipsoid flattening. The default value is for WGS84

...

additional arguments (none implemented)

Value

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

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/

Examples

Run this code

# NOT RUN {
geodesic(cbind(0,0), 30, 1000000)
geodesic_inverse(cbind(0,0), cbind(90,90))
# }

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