5.2.3. nvector.core.euclidean_distance

euclidean_distance(n_EA_E, n_EB_E, radius=6371009.0)

Returns Euclidean distance between positions A and B

Parameters

n_EA_E, n_EB_E: 3 x n array

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

radius: real scalar

radius of sphere.

Examples

Example 5: “Surface distance”

Find the surface distance sAB (i.e. great circle distance) between two positions A and B. The heights of A and B are ignored, i.e. if they don’t have zero height, we seek the distance between the points that are at the surface of the Earth, directly above/below A and B. The Euclidean distance (chord length) dAB should also be found. Use Earth radius 6371e3 m. Compare the results with exact calculations for the WGS-84 ellipsoid.

Solution for a sphere:

>>> import numpy as np
>>> import nvector as nv
>>> from nvector import rad

>>> n_EA_E = nv.lat_lon2n_E(rad(88), rad(0))
>>> n_EB_E = nv.lat_lon2n_E(rad(89), rad(-170))

>>> r_Earth = 6371e3  # m, mean Earth radius
>>> s_AB = nv.great_circle_distance(n_EA_E, n_EB_E, radius=r_Earth)[0]
>>> d_AB = nv.euclidean_distance(n_EA_E, n_EB_E, radius=r_Earth)[0]

>>> msg = 'Ex5: Great circle and Euclidean distance = {}'
>>> msg = msg.format('{:5.2f} km, {:5.2f} km')
>>> msg.format(s_AB / 1000, d_AB / 1000)
'Ex5: Great circle and Euclidean distance = 332.46 km, 332.42 km'

Exact solution for the WGS84 ellipsoid:

>>> wgs84 = nv.FrameE(name='WGS84')
>>> point1 = wgs84.GeoPoint(latitude=88, longitude=0, degrees=True)
>>> point2 = wgs84.GeoPoint(latitude=89, longitude=-170, degrees=True)
>>> s_12, _azi1, _azi2 = point1.distance_and_azimuth(point2)

>>> p_12_E = point2.to_ecef_vector() - point1.to_ecef_vector()
>>> d_12 = p_12_E.length
>>> msg = 'Ellipsoidal and Euclidean distance = {:5.2f} km, {:5.2f} km'
>>> msg.format(s_12 / 1000, d_12 / 1000)
'Ellipsoidal and Euclidean distance = 333.95 km, 333.91 km'