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")
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)
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)
def test_intersection_of_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.intersection(pathB)
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))
def test_Ex9_intersection():
# 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.intersection(pathB)
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)
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))
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)
def test_Ex10_cross_track_distance():
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)
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))
assert_array_almost_equal(s_xt, 11117.79911015)
assert_array_almost_equal(d_xt, 11117.79346741)
def test_compute_delta_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)
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 = 10.0
t1 = 20.0
ti = 16.0 # 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, 180.0)
# 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, 180.0)
def test_compute_delta_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)
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.)
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)
