5.1.1. nvector.objects.delta_E

delta_E(point_a, point_b)

Returns cartesian delta vector from positions a to b decomposed in E.

Parameters

point_a, point_b: Nvector, GeoPoint or ECEFvector objects

position a and b, decomposed in E.

Returns

p_ab_E: ECEFvector

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

See also

n_EA_E_and_p_AB_E2n_EB_E

p_EB_E2n_EB_E

n_EB_E2p_EB_E.

Notes

The calculation is exact, 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).

Examples

Example 1: “A and B to delta”

Given two positions, A and B as latitudes, longitudes and depths relative to Earth, E.

Find the exact vector between the two positions, given in meters north, east, and down, and find the direction (azimuth) to B, relative to north. Assume WGS-84 ellipsoid. The given depths are from the ellipsoid surface. Use position A to define north, east, and down directions. (Due to the curvature of Earth and different directions to the North Pole, the north, east, and down directions will change (relative to Earth) for different places. Position A must be outside the poles for the north and east directions to be defined.)

Solution:

>>> import numpy as np
>>> import nvector as nv
>>> wgs84 = nv.FrameE(name='WGS84')
>>> pointA = wgs84.GeoPoint(latitude=1, longitude=2, z=3, degrees=True)
>>> pointB = wgs84.GeoPoint(latitude=4, longitude=5, z=6, degrees=True)

Step1: Find p_AB_N (delta decomposed in N).

>>> p_AB_N = pointA.delta_to(pointB)
>>> x, y, z = p_AB_N.pvector.ravel()
>>> 'Ex1: delta north, east, down = {0:8.2f}, {1:8.2f}, {2:8.2f}'.format(x, y, z)
'Ex1: delta north, east, down = 331730.23, 332997.87, 17404.27'

Step2: Also find the direction (azimuth) to B, relative to north:

>>> 'azimuth = {0:4.2f} deg'.format(p_AB_N.azimuth_deg)
'azimuth = 45.11 deg'
>>> 'elevation = {0:4.2f} deg'.format(p_AB_N.elevation_deg)
'elevation = 2.12 deg'
>>> 'distance = {0:4.2f} m'.format(p_AB_N.length)
'distance = 470356.72 m'