Given the n-vectors for positions A (n_EA_E) and B (n_EB_E), the output is the delta vector from A to B (p_AB_E).

n_EA_E_and_n_EB_E2p_AB_E(n_EA_E, n_EB_E, z_EA = 0, z_EB = 0,
  a = 6378137, f = 1/298.257223563)

Arguments

n_EA_E

n-vector of position A, decomposed in E (3x1 vector) (no unit)

n_EB_E

n-vector of position B, decomposed in E (3x1 vector) (no unit)

z_EA

Depth of system A, relative to the ellipsoid (z_EA = -height) (m, default 0)

z_EB

Depth of system B, relative to the ellipsoid (z_EB = -height) (m, default 0)

a

Semi-major axis of the Earth ellipsoid (m, default [WGS-84] 6378137)

f

Flattening of the Earth ellipsoid (no unit, default [WGS-84] 1/298.257223563)

Value

Position vector from A to B, decomposed in E (3x1 vector)

Details

The calculation is exact, taking the ellipticity of the Earth into account. It is also nonsingular as both n-vector and p-vector are nonsingular (except for the center of the Earth). The default ellipsoid model used is WGS-84, but other ellipsoids (or spheres) might be specified via the optional parameters a and f.

References

Kenneth Gade A Nonsingular Horizontal Position Representation. The Journal of Navigation, Volume 63, Issue 03, pp 395-417, July 2010.

See also

Examples

lat_EA <- rad(1); lon_EA <- rad(2); z_EA <- 3 lat_EB <- rad(4); lon_EB <- rad(5); z_EB <- 6 n_EA_E <- lat_lon2n_E(lat_EA, lon_EA) n_EB_E <- lat_lon2n_E(lat_EB, lon_EB) n_EA_E_and_n_EB_E2p_AB_E(n_EA_E, n_EB_E, z_EA, z_EB)
#> [1] -34798.44 331985.66 331375.96