"""
Created on 18. des. 2015
@author: pab
"""
import unittest
import numpy as np
from numpy.testing import assert_array_almost_equal # @UnresolvedImport
from nvector import (FrameB, FrameE, FrameN, FrameL, GeoPoint, GeoPath, unit,
delta_L)
EARTH_RADIUS_M = 6371009.0
[docs]class TestFrames(unittest.TestCase):
[docs] def test_compare_E_frames(self):
E = FrameE(name='WGS84')
E2 = FrameE(a=E.a, f=E.f)
self.assertEqual(E, E2)
self.assertEqual(E, E)
E3 = FrameE(a=E.a, f=0)
self.assertNotEqual(E, E3)
[docs] def test_compare_B_frames(self):
E = FrameE(name='WGS84')
E2 = FrameE(name='WGS72')
n_EB_E = E.Nvector(unit([[1], [2], [3]]), z=-400)
B = FrameB(n_EB_E, yaw=10, pitch=20, roll=30, degrees=True)
self.assertEqual(B, B)
self.assertNotEqual(B, E)
B2 = FrameB(n_EB_E, yaw=1, pitch=20, roll=30, degrees=True)
self.assertNotEqual(B, B2)
B3 = FrameB(n_EB_E, yaw=10, pitch=20, roll=30, degrees=True)
self.assertEqual(B, B3)
n_EC_E = E.Nvector(unit([[1], [2], [2]]), z=-400)
B4 = FrameB(n_EC_E, yaw=10, pitch=20, roll=30, degrees=True)
self.assertNotEqual(B, B4)
n_ED_E = E2.Nvector(unit([[1], [2], [3]]), z=-400)
B5 = FrameB(n_ED_E, yaw=10, pitch=20, roll=30, degrees=True)
self.assertNotEqual(B, B5)
[docs] def test_compare_N_frames(self):
wgs84 = FrameE(name='WGS84')
wgs72 = FrameE(name='WGS72')
pointA = wgs84.GeoPoint(latitude=1, longitude=2, z=3, degrees=True)
pointB = wgs72.GeoPoint(latitude=1, longitude=2, z=6, degrees=True)
frame_N = FrameN(pointA)
frame_L1 = FrameL(pointA, wander_azimuth=0)
frame_L2 = FrameL(pointA, wander_azimuth=0)
frame_L3 = FrameL(pointB, wander_azimuth=0)
self.assertEqual(frame_N, frame_N)
self.assertEqual(frame_N, frame_L1)
self.assertFalse((frame_N != frame_L1))
self.assertEqual(frame_N, frame_L2)
self.assertTrue(frame_N != frame_L3)
self.assertTrue(frame_L1 != frame_L3)
[docs] def test_compare_L_frames(self):
wgs84 = FrameE(name='WGS84')
wgs72 = FrameE(name='WGS72')
pointA = wgs84.GeoPoint(latitude=1, longitude=2, z=3, degrees=True)
pointB = wgs72.GeoPoint(latitude=1, longitude=2, z=6, degrees=True)
frame_N = FrameL(pointA)
frame_N1 = FrameL(pointA, wander_azimuth=10)
frame_N2 = FrameL(pointB, wander_azimuth=10)
self.assertEqual(frame_N, frame_N)
self.assertNotEqual(frame_N, frame_N1)
self.assertNotEqual(frame_N, frame_N2)
self.assertNotEqual(frame_N1, frame_N2)
[docs]class TestExamples(unittest.TestCase):
[docs] @staticmethod
def test_compute_delta_L_in_moving_frame_east():
wgs84 = FrameE(name='WGS84')
point_a = wgs84.GeoPoint(latitude=1, longitude=2, z=0, degrees=True)
point_b = wgs84.GeoPoint(latitude=1, longitude=2.005, z=0,
degrees=True)
sensor_position = wgs84.GeoPoint(latitude=1.000090437, longitude=2.0025, z=0,
degrees=True)
path = GeoPath(point_a, point_b)
ti = np.linspace(0, 1.0, 8)
ship_positions0 = path.interpolate(ti[:-1])
ship_positions1 = path.interpolate(ti[1:])
headings = ship_positions0.delta_to(ship_positions1).azimuth_deg
assert_array_almost_equal(headings, 90, decimal=4)
ship_positions = path.interpolate(ti)
delta = delta_L(ship_positions, sensor_position, wander_azimuth=np.pi / 2)
x, y, z = delta.pvector
azimuth = np.round(delta.azimuth_deg)
# positive angle about down-axis
print('Ex1, delta L = {0}'.format(delta.pvector.T))
print('Ex1, azimuth = {0} deg'.format(azimuth))
true_x = [278.2566243359911, 198.7547317612817, 119.25283909376164,
39.750946370747656, -39.75094637085409, -119.25283909387079,
-198.75473176137066, -278.2566243360949]
assert_array_almost_equal(x, true_x, decimal=3)
assert_array_almost_equal(y, -10, decimal=3)
assert_array_almost_equal(z, 0, decimal=2)
assert_array_almost_equal(azimuth,
[-2., -3., -5., -14., -166., -175., -177., -178.])
[docs] @staticmethod
def test_compute_delta_N_in_moving_frame_east():
wgs84 = FrameE(name='WGS84')
point_a = wgs84.GeoPoint(latitude=1, longitude=2, z=0, degrees=True)
point_b = wgs84.GeoPoint(latitude=1, longitude=2.005, z=0,
degrees=True)
sensor_position = wgs84.GeoPoint(latitude=1.0, longitude=2.0025, z=0,
degrees=True)
path = GeoPath(point_a, point_b)
ti = np.linspace(0, 1.0, 8)
ship_positions0 = path.interpolate(ti[:-1])
ship_positions1 = path.interpolate(ti[1:])
headings = ship_positions0.delta_to(ship_positions1).azimuth_deg
assert_array_almost_equal(headings, 90, decimal=4)
ship_positions = path.interpolate(ti)
delta = ship_positions.delta_to(sensor_position)
x, y, z = delta.pvector
azimuth = np.round(delta.azimuth_deg)
# positive angle about down-axis
print('Ex1, delta north, east, down = {0}'.format(delta.pvector.T))
print('Ex1, azimuth = {0} deg'.format(azimuth))
true_y = [278.2566243359911, 198.7547317612817, 119.25283909376164,
39.750946370747656, -39.75094637085409, -119.25283909387079,
-198.75473176137066, -278.2566243360949]
assert_array_almost_equal(x, 0, decimal=3)
assert_array_almost_equal(y, true_y)
assert_array_almost_equal(z, 0, decimal=2)
n2 = len(azimuth) // 2
assert_array_almost_equal(azimuth[:n2], 90)
assert_array_almost_equal(azimuth[n2:], -90)
[docs] @staticmethod
def test_compute_delta_L_in_moving_frame_north():
wgs84 = FrameE(name='WGS84')
point_a = wgs84.GeoPoint(latitude=1, longitude=2, z=0, degrees=True)
point_b = wgs84.GeoPoint(latitude=1.005, longitude=2.0, z=0,
degrees=True)
sensor_position = wgs84.GeoPoint(latitude=1.0025, longitude=2.0, z=0,
degrees=True)
path = GeoPath(point_a, point_b)
ti = np.linspace(0, 1.0, 8)
ship_positions0 = path.interpolate(ti[:-1])
ship_positions1 = path.interpolate(ti[1:])
headings = ship_positions0.delta_to(ship_positions1).azimuth_deg
assert_array_almost_equal(headings, 0, decimal=8)
ship_positions = path.interpolate(ti)
delta0 = delta_L(ship_positions, sensor_position, wander_azimuth=0)
delta = ship_positions.delta_to(sensor_position)
assert_array_almost_equal(delta0.pvector, delta.pvector)
x, y, z = delta.pvector
azimuth = np.round(np.abs(delta.azimuth_deg))
# positive angle about down-axis
print('Ex1, delta north, east, down = {0}'.format(delta.pvector.T))
print('Ex1, azimuth = {0} deg'.format(azimuth))
true_x = [276.436537069603, 197.45466985931083, 118.47280221160541,
39.49093416312986, -39.490934249581684, -118.47280298990226,
-197.454672021303, -276.4365413071498]
assert_array_almost_equal(x, true_x)
assert_array_almost_equal(y, 0, decimal=8)
assert_array_almost_equal(z, 0, decimal=2)
n2 = len(azimuth) // 2
assert_array_almost_equal(azimuth[:n2], 0)
assert_array_almost_equal(azimuth[n2:], 180)
[docs] @staticmethod
def test_Ex1_A_and_B_to_delta_in_frame_N():
wgs84 = FrameE(name='WGS84')
point_a = wgs84.GeoPoint(latitude=1, longitude=2, z=3, degrees=True)
point_b = wgs84.GeoPoint(latitude=4, longitude=5, z=6, degrees=True)
# Find the exact vector between the two positions, given in meters
# north, east, and down, i.e. find delta_N.
# SOLUTION:
delta = point_a.delta_to(point_b)
x, y, z = delta.pvector
azimuth = delta.azimuth_deg
elevation = delta.elevation_deg
print('Ex1, delta north, east, down = {0}, {1}, {2}'.format(x, y, z))
print('Ex1, azimuth = {0} deg'.format(azimuth))
assert_array_almost_equal(x, 331730.23478089)
assert_array_almost_equal(y, 332997.87498927)
assert_array_almost_equal(z, 17404.27136194)
assert_array_almost_equal(azimuth, 45.10926324)
assert_array_almost_equal(elevation, 2.12055861)
[docs] @staticmethod
def test_Ex2_B_and_delta_in_frame_B_to_C_in_frame_E():
# delta vector from B to C, decomposed in B is given:
# A custom reference ellipsoid is given (replacing WGS-84):
wgs72 = FrameE(name='WGS72')
# Position and orientation of B is given 400m above E:
n_EB_E = wgs72.Nvector(unit([[1], [2], [3]]), z=-400)
frame_B = FrameB(n_EB_E, yaw=10, pitch=20, roll=30, degrees=True)
p_BC_B = frame_B.Pvector(np.r_[3000, 2000, 100].reshape((-1, 1)))
p_BC_E = p_BC_B.to_ecef_vector()
p_EB_E = n_EB_E.to_ecef_vector()
p_EC_E = p_EB_E + p_BC_E
pointC = p_EC_E.to_geo_point()
lat_EC, lon_EC = pointC.latitude_deg, pointC.longitude_deg
z_EC = pointC.z
# Here we also assume that the user wants output height (= - depth):
msg = 'Ex2, Pos C: lat, long = {},{} deg, height = {} m'
print(msg.format(lat_EC, lon_EC, -z_EC))
assert_array_almost_equal(lat_EC, 53.32637826)
assert_array_almost_equal(lon_EC, 63.46812344)
assert_array_almost_equal(z_EC, -406.00719607)
[docs] @staticmethod
def test_Ex3_ECEF_vector_to_geodetic_latitude():
wgs84 = FrameE(name='WGS84')
# Position B is given as p_EB_E ("ECEF-vector")
position_B = 6371e3 * np.vstack((0.9, -1, 1.1)) # m
p_EB_E = wgs84.ECEFvector(position_B)
# Find position B as geodetic latitude, longitude and height
pointB = p_EB_E.to_geo_point()
lat, lon, h = pointB.latitude_deg, pointB.longitude_deg, -pointB.z
msg = 'Ex3, Pos B: lat, lon = {} {} deg, height = {} m'
print(msg.format(lat, lon, h))
assert_array_almost_equal(lat, 39.37874867)
assert_array_almost_equal(lon, -48.0127875)
assert_array_almost_equal(h, 4702059.83429485)
[docs] @staticmethod
def test_Ex4_geodetic_latitude_to_ECEF_vector():
wgs84 = FrameE(name='WGS84')
pointB = wgs84.GeoPoint(latitude=1, longitude=2, z=-3, degrees=True)
p_EB_E = pointB.to_ecef_vector()
print('Ex4: p_EB_E = {0} m'.format(p_EB_E.pvector.ravel()))
assert_array_almost_equal(p_EB_E.pvector.ravel(),
[6373290.27721828, 222560.20067474,
110568.82718179])
[docs] @staticmethod
def test_Ex5_great_circle_distance():
frame_E = FrameE(a=6371e3, f=0)
positionA = frame_E.GeoPoint(latitude=88, longitude=0, degrees=True)
positionB = frame_E.GeoPoint(latitude=89, longitude=-170, degrees=True)
s_AB, _azia, _azib = positionA.distance_and_azimuth(positionB)
p_AB_E = positionB.to_ecef_vector() - positionA.to_ecef_vector()
# The Euclidean distance is given by:
d_AB = p_AB_E.length
msg = 'Ex5, Great circle distance = {} km, Euclidean distance = {} km'
print(msg.format(s_AB / 1000, d_AB / 1000))
assert_array_almost_equal(s_AB / 1000, 332.45644411)
assert_array_almost_equal(d_AB / 1000, 332.41872486)
[docs] @staticmethod
def test_alternative_great_circle_distance():
frame_E = FrameE(a=6371e3, f=0)
positionA = frame_E.GeoPoint(latitude=88, longitude=0, degrees=True)
positionB = frame_E.GeoPoint(latitude=89, longitude=-170, degrees=True)
path = GeoPath(positionA, positionB)
s_AB = path.track_distance(method='greatcircle')
d_AB = path.track_distance(method='euclidean')
s1_AB = path.track_distance(method='exact')
msg = 'Ex5, Great circle distance = {} km, Euclidean distance = {} km'
print(msg.format(s_AB / 1000, d_AB / 1000))
assert_array_almost_equal(s_AB / 1000, 332.45644411)
assert_array_almost_equal(s1_AB / 1000, 332.45644411)
assert_array_almost_equal(d_AB / 1000, 332.41872486)
[docs] @staticmethod
def test_exact_ellipsoidal_distance():
wgs84 = FrameE(name='WGS84')
pointA = wgs84.GeoPoint(latitude=88, longitude=0, degrees=True)
pointB = wgs84.GeoPoint(latitude=89, longitude=-170, degrees=True)
s_AB, _azia, _azib = pointA.distance_and_azimuth(pointB)
p_AB_E = pointB.to_ecef_vector() - pointA.to_ecef_vector()
# The Euclidean distance is given by:
d_AB = p_AB_E.length
msg = 'Ex5, Great circle distance = {} km, Euclidean distance = {} km'
print(msg.format(s_AB / 1000, d_AB / 1000))
assert_array_almost_equal(s_AB / 1000, 333.94750946834665)
assert_array_almost_equal(d_AB / 1000, 333.90962112)
[docs] @staticmethod
def test_Ex6_interpolated_position():
# Position B at time t0 and t2 is given as n_EB_E_t0 and n_EB_E_t1:
# Enter elements as lat/long in deg:
wgs84 = FrameE(name='WGS84')
n_EB_E_t0 = wgs84.GeoPoint(89, 0, degrees=True).to_nvector()
n_EB_E_t1 = wgs84.GeoPoint(89, 180, degrees=True).to_nvector()
# The times are given as:
t0 = 10.
t1 = 20.
ti = 16. # time of interpolation
# Find the interpolated position at time ti, n_EB_E_ti
# SOLUTION:
# Using standard interpolation:
ti_n = (ti - t0) / (t1 - t0)
n_EB_E_ti = n_EB_E_t0 + ti_n * (n_EB_E_t1 - n_EB_E_t0)
# When displaying the resulting position for humans, it is more
# convenient to see lat, long:
g_EB_E_ti = n_EB_E_ti.to_geo_point()
lat_ti, lon_ti = g_EB_E_ti.latitude_deg, g_EB_E_ti.longitude_deg
msg = 'Ex6, Interpolated position: lat, long = {} deg, {} deg'
print(msg.format(lat_ti, lon_ti))
assert_array_almost_equal(lat_ti, 89.7999805)
assert_array_almost_equal(lon_ti, 180.)
# Alternative solution
path = GeoPath(n_EB_E_t0, n_EB_E_t1)
g_EB_E_ti = path.interpolate(ti_n).to_geo_point()
lat_ti, lon_ti = g_EB_E_ti.latitude_deg, g_EB_E_ti.longitude_deg
msg = 'Ex6, Interpolated position: lat, long = {} deg, {} deg'
print(msg.format(lat_ti, lon_ti))
assert_array_almost_equal(lat_ti, 89.7999805)
assert_array_almost_equal(lon_ti, 180.)
[docs] @staticmethod
def test_Ex7_mean_position():
# Three positions A, B and C are given:
# Enter elements directly:
# n_EA_E=unit(np.vstack((1, 0, -2)))
# n_EB_E=unit(np.vstack((-1, -2, 0)))
# n_EC_E=unit(np.vstack((0, -2, 3)))
# or input as lat/long in deg:
points = GeoPoint(latitude=[90, 60, 50], longitude=[0, 10, -20],
degrees=True)
nvectors = points.to_nvector()
nmean = nvectors.mean_horizontal_position()
n_EM_E = nmean.normal
assert_array_almost_equal(n_EM_E.ravel(),
[0.384117, -0.046602, 0.922107])
[docs] @staticmethod
def test_Ex8_position_A_and_azimuth_and_distance_to_B():
frame = FrameE(a=EARTH_RADIUS_M, f=0)
pointA = frame.GeoPoint(latitude=80, longitude=-90, degrees=True)
pointB, _azimuthb = pointA.displace(distance=1000, azimuth=200,
degrees=True)
pointB2, _azimuthb = pointA.displace(distance=1000,
azimuth=np.deg2rad(200))
assert_array_almost_equal(pointB.latlon, pointB2.latlon)
lat_B, lon_B = pointB.latitude_deg, pointB.longitude_deg
print('Ex8, Destination: lat, long = {0} {1} deg'.format(lat_B, lon_B))
assert_array_almost_equal(lat_B, 79.99154867)
assert_array_almost_equal(lon_B, -90.01769837)
[docs] @staticmethod
def test_Ex9_intersect():
# Two paths A and B are given by two pairs of positions:
pointA1 = GeoPoint(10, 20, degrees=True)
pointA2 = GeoPoint(30, 40, degrees=True)
pointB1 = GeoPoint(50, 60, degrees=True)
pointB2 = GeoPoint(70, 80, degrees=True)
pathA = GeoPath(pointA1, pointA2)
pathB = GeoPath(pointB1, pointB2)
pointC = pathA.intersect(pathB).to_geo_point()
lat, lon = pointC.latitude_deg, pointC.longitude_deg
msg = 'Ex9, Intersection: lat, long = {} {} deg'
print(msg.format(lat, lon))
assert_array_almost_equal(lat, 40.31864307)
assert_array_almost_equal(lon, 55.90186788)
[docs] def test_intersect_on_parallell_paths(self):
# Two paths A and B are given by two pairs of positions:
pointA1 = GeoPoint(10, 20, degrees=True)
pointA2 = GeoPoint(30, 40, degrees=True)
pointB1 = GeoPoint(10, 20, degrees=True)
pointB2 = GeoPoint(30, 40, degrees=True)
pathA = GeoPath(pointA1, pointA2)
pathB = GeoPath(pointB1, pointB2)
pointC = pathA.intersect(pathB).to_geo_point()
lat, lon = pointC.latitude_deg, pointC.longitude_deg
msg = 'Ex9, Intersection: lat, long = {} {} deg'
print(msg.format(lat, lon))
self.assertTrue(np.isnan(lat))
self.assertTrue(np.isnan(lon))
[docs] def test_Ex10_cross_track_distance(self):
frame = FrameE(a=6371e3, f=0)
# Position A1 and A2 and B as lat/long in deg:
pointA1 = frame.GeoPoint(0, 0, degrees=True)
pointA2 = frame.GeoPoint(10, 0, degrees=True)
pointB = frame.GeoPoint(1, 0.1, degrees=True)
pointB2 = frame.GeoPoint(11, 0.1, degrees=True)
pointB3 = frame.GeoPoint(-1, 0.1, degrees=True)
pathA = GeoPath(pointA1, pointA2)
# Find the cross track distance from path A to position B.
s_xt = pathA.cross_track_distance(pointB, method='greatcircle')
d_xt = pathA.cross_track_distance(pointB, method='euclidean')
msg = 'Ex10, Cross track distance = {} m, Euclidean = {} m'
print(msg.format(s_xt, d_xt))
pointC = pathA.closest_point_on_great_circle(pointB)
pointC2 = pathA.closest_point_on_great_circle(pointB2)
pointC3 = pathA.closest_point_on_path(pointB2)
pointC4 = pathA.closest_point_on_path(pointB3)
s_xt2, _az_bc, _az_cb = pointB.distance_and_azimuth(pointC)
assert_array_almost_equal(s_xt2, 11117.79911015)
assert_array_almost_equal(s_xt, 11117.79911015)
assert_array_almost_equal(d_xt, 11117.79346741)
self.assertTrue(pathA.on_path(pointC))
self.assertTrue(pathA.on_path(pointC, method='exact'))
self.assertFalse(pathA.on_path(pointC2))
self.assertFalse(pathA.on_path(pointC2, method='exact'))
self.assertEqual(pointC3, pointA2)
self.assertEqual(pointC4, pointA1)
if __name__ == "__main__":
# import sys;sys.argv = ['', 'Test.testName']
unittest.main()