5.2.13. nvector.core.p_EB_E2n_EB_E

p_EB_E2n_EB_E(p_EB_E, a=6378137, f=0.0033528106647474805, R_Ee=None)

Converts Cartesian position vector in meters to n-vector.

Parameters

p_EB_E: 3 x n array

Cartesian position vector(s) from E to B, decomposed in E.

a: real scalar, default WGS-84 ellipsoid.

Semi-major axis of the Earth ellipsoid given in [m].

f: real scalar, default WGS-84 ellipsoid.

Flattening [no unit] of the Earth ellipsoid. If f==0 then spherical Earth with radius a is used in stead of WGS-84.

R_Ee3 x 3 array

rotation matrix defining the axes of the coordinate frame E.

Returns

n_EB_E: 3 x n array

n-vector(s) [no unit] of position B, decomposed in E.

depth: 1 x n array

Depth(s) [m] of system B, relative to the ellipsoid (depth = -height)

See also

n_EB_E2p_EB_E, n_EA_E_and_p_AB_E2n_EB_E, n_EA_E_and_n_EB_E2p_AB_E

Notes

The position of B (typically body) relative to E (typically Earth) is given into this function as cartesian position vector p_EB_E, in meters. (“ECEF-vector”). The function converts to n-vector, n_EB_E and its depth, depth. The calculation is excact, taking the ellipsity of the Earth into account. It is also non-singular as both n-vector and p-vector are non-singular (except for the center of the Earth). The default ellipsoid model used is WGS-84, but other ellipsoids/spheres might be specified.

Examples

Example 3: “ECEF-vector to geodetic latitude”

Position B is given as an “ECEF-vector” p_EB_E (i.e. a vector from E, the center of the Earth, to B, decomposed in E). Find the geodetic latitude, longitude and height (latEB, lonEB and hEB), assuming WGS-84 ellipsoid.

Solution:

>>> import numpy as np
>>> import nvector as nv
>>> from nvector import deg
>>> wgs84 = dict(a=6378137.0, f=1.0/298.257223563)
>>> p_EB_E = 6371e3 * np.vstack((0.9, -1, 1.1))  # m

>>> n_EB_E, z_EB = nv.p_EB_E2n_EB_E(p_EB_E, **wgs84)

>>> lat_EB, lon_EB = nv.n_E2lat_lon(n_EB_E)
>>> h = -z_EB
>>> lat, lon = deg(lat_EB), deg(lon_EB)

>>> msg = 'Ex3: Pos B: lat, lon = {:4.4f}, {:4.4f} deg, height = {:9.3f} m'
>>> msg.format(lat[0], lon[0], h[0])
'Ex3: Pos B: lat, lon = 39.3787, -48.0128 deg, height = 4702059.834 m'