def test_latitudes():
ell = Ellipsoid('GRS80')
lat = np.arange(-90, 90, 0.1, dtype=float)
sph_lat, _, sph_radius = geodetic_to_spherical(lat,
lon=0.0,
height=0.0,
ell=ell)
np.testing.assert_array_almost_equal(ell.geocentric_latitude(lat),
sph_lat,
decimal=8)
reduced_latitude = np.degrees(
np.arctan(np.tan(np.radians(sph_lat)) / (1 - ell.f)))
np.testing.assert_array_almost_equal(ell.reduced_latitude(lat),
reduced_latitude,
decimal=8)
# compare with series from
# J. P. Snyder, Map projections - a working manual, 1926, page 16
latr = np.radians(lat)
s2lat = (ell.e2 / 3 + 31 * ell.e2**2 / 180 +
59 * ell.e2**3 / 560) * np.sin(2 * latr)
s4lat = (17 * ell.e2**2 / 360 + 61 * ell.e2**3 / 1260) * np.sin(4 * latr)
s6lat = (383 * ell.e2**3 / 45360) * np.sin(6 * latr)
authalic_latitude = np.degrees(latr - s2lat + s4lat - s6lat)
np.testing.assert_array_almost_equal(ell.authalic_latitude(lat),
authalic_latitude,
decimal=6)
def test_inv():
ell = Ellipsoid('WGS84')
# check meridian arc
np.testing.assert_almost_equal(ell.meridian_arc_distance(0.0, 90),
ell.quadrant_distance,
decimal=4)
# check equatorial circle
circle_length = 2 * np.pi * ell.a
np.testing.assert_almost_equal(ell.parallel_arc_distance(0.0, 0.0, 90.),
circle_length / 4,
decimal=5)
# Load short test data from Geographiclib
# https://geographiclib.sourceforge.io/html/geodesic.html#testgeod
path = os.path.dirname(os.path.abspath(__file__))
fname = os.path.join(path, 'data/GeodTest-short.dat.gz')
(lat1, lon1, azi1, lat2, lon2, azi2,
dist12) = np.loadtxt(fname,
usecols=(0, 1, 2, 3, 4, 5, 6),
unpack=True,
dtype=np.float64)
b_azi1, b_azi2, b_dist12 = ell.inv(lat1, lon1, lat2, lon2)
# NOTE: Loss of precision
np.testing.assert_array_almost_equal(b_azi1, azi1, decimal=3)
np.testing.assert_array_almost_equal(b_azi2, azi2 - 180., decimal=3)
np.testing.assert_array_almost_equal(b_dist12, dist12, decimal=8)
def test_fwd():
ell = Ellipsoid('WGS84')
# Load short test data from Geographiclib
# https://geographiclib.sourceforge.io/html/geodesic.html#testgeod
path = os.path.dirname(os.path.abspath(__file__))
fname = os.path.join(path, 'data/GeodTest-short.dat.gz')
(lat1, lon1, azi1, lat2, lon2, azi2,
dist12) = np.loadtxt(fname,
usecols=(0, 1, 2, 3, 4, 5, 6),
unpack=True,
dtype=np.float64)
# test forward
b_lat2, b_lon2, b_azi2 = ell.fwd(lat1 * u.deg, lon1 * u.deg, azi1 * u.deg,
dist12 * u.m)
np.testing.assert_array_almost_equal(b_lat2.to('degree').value,
lat2,
decimal=8)
np.testing.assert_array_almost_equal(b_lon2.to('degree').value,
lon2,
decimal=8)
np.testing.assert_array_almost_equal(b_azi2.to('degree').value,
azi2 - 180.,
decimal=8)
def test_against_GRS80():
# Moritz, H., 1980. Geodetic reference system 1980.
# Bulletin géodésique, 54(3), pp.395-405.
ell = Ellipsoid('GRS80')
np.testing.assert_equal(ell.a.value, 6378137.0)
np.testing.assert_almost_equal(ell.b.value, 6356752.3141, decimal=4)
np.testing.assert_almost_equal(ell.linear_eccentricity.value,
521854.0097,
decimal=4)
np.testing.assert_almost_equal(ell.polar_curvature_radius.value,
6399593.6259,
decimal=4)
np.testing.assert_almost_equal(ell.eccentricity_squared.value,
0.00669438002290,
decimal=14)
np.testing.assert_almost_equal(ell.second_eccentricity_squared.value,
0.00673949677548,
decimal=14)
np.testing.assert_almost_equal(ell.flattening.value,
0.00335281068118,
decimal=14)
np.testing.assert_almost_equal(ell.reciprocal_flattening.value,
298.257222101,
decimal=9)
np.testing.assert_almost_equal(ell.quadrant_distance.value,
10001965.7293,
decimal=4)
np.testing.assert_almost_equal(ell.surface_area.value * 1e-014,
5.10065622,
decimal=8)
np.testing.assert_almost_equal(ell.volume.value * 1e-021,
1.08320732,
decimal=8)
# mean radius
kind = 'arithmetic'
np.testing.assert_almost_equal(ell.mean_radius(kind).value,
6371008.7714,
decimal=4)
kind = 'same_area'
np.testing.assert_almost_equal(ell.mean_radius(kind).value,
6371007.1810,
decimal=4)
kind = 'same_volume'
np.testing.assert_almost_equal(ell.mean_radius(kind).value,
6371000.7900,
decimal=4)
def test_radiuses():
ell = Ellipsoid('GRS80')
# geodetic latitude
lat = np.arange(-90, 90, 0.1, dtype=float)
x, y, _ = geodetic_to_cartesian(lat, lon=0.0, height=0.0, ell=ell)
np.testing.assert_array_almost_equal(ell.circle_radius(lat),
np.sqrt(x**2 + y**2),
decimal=5)
sph_lat, _, sph_radius = geodetic_to_spherical(lat,
lon=0.0,
height=0.0,
ell=ell)
np.testing.assert_array_almost_equal(ell.polar_equation(sph_lat),
sph_radius,
decimal=5)
def test_short_long_names():
ell = Ellipsoid()
assert ell.a == ell.equatorial_radius
assert ell.b == ell.polar_radius
assert ell.f == ell.flattening
assert ell.e2 == ell.eccentricity_squared
assert ell.e == ell.eccentricity
assert ell.e12 == ell.second_eccentricity_squared
assert ell.e1 == ell.second_eccentricity
def test_latitude_dependend_values():
# From
# Deakin, R.E. and Hunter, M.N., 2010. Geometric geodesy part A. Lecture
# Notes, School of Mathematical & Geospatial Sciences, RMIT University,
# Melbourne, Australia.
# pp. 87 - 88
ell = Ellipsoid('GRS80')
lat = -(37 + 48 / 60 + 33.1234 / 3600) * u.deg
np.testing.assert_almost_equal(ell._w(lat).value, 0.998741298, decimal=9)
np.testing.assert_almost_equal(ell._v(lat).value, 1.002101154, decimal=9)
np.testing.assert_almost_equal(ell.meridian_curvature_radius(lat).value,
6359422.962,
decimal=3)
np.testing.assert_almost_equal(
ell.prime_vertical_curvature_radius(lat).value, 6386175.289, decimal=3)
np.testing.assert_almost_equal(ell.mean_curvature(lat).value,
1 / 6372785.088,
decimal=16)
np.testing.assert_almost_equal(ell.meridian_arc_distance(0.0 * u.deg,
lat).value,
4186320.340,
decimal=3)
def gravity_ell(self,
lat: u.deg,
height: u.m,
ell: Ellipsoid,
elastic: bool = True) -> u.m / u.s**2:
"""Return permanent tidal gravity variation along the ellipsoidal normal.
Parameters
----------
lat : ~astropy.units.Quantity
Geodetic latitude.
height : ~astropy.units.Quantity
Geodetic height.
ell : ~pygeoid.coordinates.ellipsoid.Ellipsoid
Reference ellipsoid to which geodetic coordinates are referenced to.
elastic : bool, optional
If True then the Earth is elastic (deformable)
and gravity change is multiplied by the gravimetric factor
specified in the class instance.
Returns
-------
delta_g : ~astropy.units.Quantity
Permanent tidal potential gravity variation.
"""
pvcr = ell.prime_vertical_curvature_radius(lat.radian) * u.m
delta_g = 2 / 3 * self.coeff / self.r0**2 * (
(pvcr *
(3 - 2 * ell.e2) + 3 * height) * np.sin(lat)**2 - (pvcr + height))
if elastic:
delta_g *= self.gravimetric_factor
return -delta_g
def test_init():
with pytest.raises(ValueError):
ell = Ellipsoid('xxx')
import pytest
import numpy as np
from pygeoid.coordinates.ellipsoid import Ellipsoid
from pygeoid.coordinates.transform import *
ell = Ellipsoid('GRS80')
# test data
n_test = 10 # * 2
r_ = np.geomspace(1, 1e8, num=n_test)
r_ = np.append(-r_[::-1], r_)
x, y, z = np.meshgrid(r_, r_, r_, indexing='ij') * u.m
def test_cartesian_to_geodetic_and_back():
lat, lon, height = cartesian_to_geodetic(x, y, z, ell)
b_x, b_y, b_z = geodetic_to_cartesian(lat, lon, height, ell)
np.testing.assert_array_almost_equal(b_x.value, x.value, decimal=5)
np.testing.assert_array_almost_equal(b_y.value, y.value, decimal=5)
np.testing.assert_array_almost_equal(b_z.value, z.value, decimal=5)
def test_cartesian_to_spherical_and_back():
lat, lon, radius = cartesian_to_spherical(x, y, z)
b_x, b_y, b_z = spherical_to_cartesian(lat, lon, radius)
np.testing.assert_array_almost_equal(b_x.value, x.value, decimal=5)
np.testing.assert_array_almost_equal(b_y.value, y.value, decimal=5)
np.testing.assert_array_almost_equal(b_z.value, z.value, decimal=5)
