def test_Ex9_intersection():
# Two paths A and B are given by two pairs of positions:
# Enter elements as lat/long in deg:
n_EA1_E = lat_lon2n_E(rad(10), rad(20))
n_EA2_E = lat_lon2n_E(rad(30), rad(40))
n_EB1_E = lat_lon2n_E(rad(50), rad(60))
n_EB2_E = lat_lon2n_E(rad(70), rad(80))
# Find the intersection between the two paths, n_EC_E:
n_EC_E_tmp = unit(np.cross(np.cross(n_EA1_E, n_EA2_E, axis=0),
np.cross(n_EB1_E, n_EB2_E, axis=0), axis=0))
# n_EC_E_tmp is one of two solutions, the other is -n_EC_E_tmp. Select
# the one that is closet to n_EA1_E, by selecting sign from the dot
# product between n_EC_E_tmp and n_EA1_E:
n_EC_E = np.sign(np.dot(n_EC_E_tmp.T, n_EA1_E)) * n_EC_E_tmp
# When displaying the resulting position for humans, it is more
# convenient to see lat, long:
lat_EC, long_EC = n_E2lat_lon(n_EC_E)
msg = 'Ex9, Intersection: lat, long = {} {} deg'
print(msg.format(deg(lat_EC), deg(long_EC)))
assert_array_almost_equal(deg(lat_EC), 40.31864307)
assert_array_almost_equal(deg(long_EC), 55.90186788)
def plot_mean_position():
"""
Example
-------
>>> plot_mean_position()
Ex7, Average lat=[ 67.23615295], lon=[-6.91751117]
"""
positions = np.array([
(90, 0),
(60, 10),
(50, -20),
])
lats, lons = positions.T
nvecs = lat_lon2n_E(rad(lats), rad(lons))
# Find the horizontal mean position:
n_EM_E = unit(np.sum(nvecs, axis=1).reshape((3, 1)))
lat, lon = n_E2lat_lon(n_EM_E)
lat, lon = deg(lat), deg(lon)
print(('Ex7, Average lat={0}, lon={1}'.format(lat, lon)))
map1 = Basemap(projection='ortho',
lat_0=int(lat),
lon_0=int(lon),
resolution='l')
plot_world(map1)
x, y = map1(lon, lat)
map1.scatter(x, y, linewidth=5, marker='o', color='r')
x1, y1 = map1(lons, lats)
# print(len(lons), x1, y1)
map1.scatter(x1, y1, linewidth=5, marker='o', color='k')
plt.title('Figure of mean position (red dot) compared to positions '
'A, B, and C (black dots).')
def test_Ex10_cross_track_distance():
# Position A1 and A2 and B are given as n_EA1_E, n_EA2_E, and n_EB_E:
# Enter elements as lat/long in deg:
n_EA1_E = lat_lon2n_E(rad(0), rad(0))
n_EA2_E = lat_lon2n_E(rad(10), rad(0))
n_EB_E = lat_lon2n_E(rad(1), rad(0.1))
radius = 6371e3 # m, mean Earth radius
# Find the cross track distance from path A to position B.
# SOLUTION:
# Find the unit normal to the great circle:
c_E = unit(np.cross(n_EA1_E, n_EA2_E, axis=0))
# Find the great circle cross track distance:
s_xt = -np.arcsin(np.dot(c_E.T, n_EB_E)) * radius
# Find the Euclidean cross track distance:
d_xt = -np.dot(c_E.T, n_EB_E) * radius
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_Ex10_cross_track_distance():
# Position A1 and A2 and B are given as n_EA1_E, n_EA2_E, and n_EB_E:
# Enter elements as lat/long in deg:
n_EA1_E = lat_lon2n_E(rad(0), rad(0))
n_EA2_E = lat_lon2n_E(rad(10), rad(0))
n_EB_E = lat_lon2n_E(rad(1), rad(0.1))
r_Earth = 6371e3 # m, mean Earth radius
# Find the cross track distance from path A to position B.
# SOLUTION:
# Find the unit normal to the great circle:
c_E = unit(np.cross(n_EA1_E, n_EA2_E, axis=0))
# Find the great circle cross track distance:
s_xt = (np.arccos(np.dot(c_E.T, n_EB_E)) - np.pi / 2) * r_Earth
# Find the Euclidean cross track distance:
d_xt = -np.dot(c_E.T, n_EB_E) * r_Earth
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 plot_mean_position():
positions = np.array([(90, 0),
(60, 10),
(50, -20),
])
lats, lons = positions.T
nvecs = lat_lon2n_E(rad(lats), rad(lons))
# Find the horizontal mean position:
n_EM_E = unit(np.sum(nvecs, axis=1).reshape((3, 1)))
lat, lon = n_E2lat_lon(n_EM_E)
lat, lon = deg(lat), deg(lon)
print('Ex7, Average lat={0}, lon={1}'.format(lat, lon))
map1 = Basemap(projection='ortho', lat_0=int(lat), lon_0=int(lon),
resolution='l')
plot_world(map1)
x, y = map1(lon, lat)
map1.scatter(x, y, linewidth=5, marker='o', color='r')
x1, y1 = map1(lons, lats)
print(len(lons), x1, y1)
map1.scatter(x1, y1, linewidth=5, marker='o', color='k')
plt.title('Figure of mean position (red dot) compared to positions '
'A, B, and C (black dots).')
def plot_mean_position():
"""
Example
-------
>>> plot_mean_position()
Ex7, Average lat=67.2, lon=-6.9
>>> plt.show() # doctest: +SKIP
>>> plt.close()
"""
positions = np.array([
(90, 0),
(60, 10),
(50, -20),
])
lats, lons = np.transpose(positions)
nvecs = lat_lon2n_E(rad(lats), rad(lons))
# Find the horizontal mean position:
n_EM_E = unit(np.sum(nvecs, axis=1).reshape((3, 1)))
lat, lon = n_E2lat_lon(n_EM_E)
lat, lon = deg(lat), deg(lon)
print('Ex7, Average lat={0:2.1f}, lon={1:2.1f}'.format(lat[0], lon[0]))
plotter = _init_plotter(lat, lon)
plotter(lon, lat, linewidth=5, marker='o', color='r')
plotter(lons, lats, linewidth=5, marker='o', color='k')
plt.title('Figure of mean position (red dot) compared to \npositions '
'A, B, and C (black dots).')
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, long_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, long_EC, -z_EC))
assert_array_almost_equal(lat_EC, 53.32637826)
assert_array_almost_equal(long_EC, 63.46812344)
assert_array_almost_equal(z_EC, -406.00719607)
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)
def test_Ex9_intersect():
# Two paths A and B are given by two pairs of positions:
# Enter elements as lat/long in deg:
n_EA1_E = lat_lon2n_E(rad(10), rad(20))
n_EA2_E = lat_lon2n_E(rad(30), rad(40))
n_EB1_E = lat_lon2n_E(rad(50), rad(60))
n_EB2_E = lat_lon2n_E(rad(70), rad(80))
# Find the intersection between the two paths, n_EC_E:
n_EC_E_tmp = unit(
np.cross(np.cross(n_EA1_E, n_EA2_E, axis=0),
np.cross(n_EB1_E, n_EB2_E, axis=0),
axis=0))
# n_EC_E_tmp is one of two solutions, the other is -n_EC_E_tmp. Select
# the one that is closet to n_EA1_E, by selecting sign from the dot
# product between n_EC_E_tmp and n_EA1_E:
n_EC_E = np.sign(np.dot(n_EC_E_tmp.T, n_EA1_E)) * n_EC_E_tmp
# When displaying the resulting position for humans, it is more
# convenient to see lat, long:
lat_EC, long_EC = n_E2lat_lon(n_EC_E)
msg = 'Ex9, Intersection: lat, long = {} {} deg'
print(msg.format(deg(lat_EC), deg(long_EC)))
assert_array_almost_equal(deg(lat_EC), 40.31864307)
assert_array_almost_equal(deg(long_EC), 55.90186788)
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:
n_EB_E_t0 = lat_lon2n_E(rad(89), rad(0))
n_EB_E_t1 = lat_lon2n_E(rad(89), rad(180))
# 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:
n_EB_E_ti = unit(n_EB_E_t0 +
(ti - t0) * (n_EB_E_t1 - n_EB_E_t0) / (t1 - t0))
# When displaying the resulting position for humans, it is more
# convenient to see lat, long:
lat_EB_ti, long_EB_ti = n_E2lat_lon(n_EB_E_ti)
msg = 'Ex6, Interpolated position: lat, long = {} {} deg'
print(msg.format(deg(lat_EB_ti), deg(long_EB_ti)))
assert_array_almost_equal(deg(lat_EB_ti), 89.7999805)
assert_array_almost_equal(deg(long_EB_ti), 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:
n_EB_E_t0 = lat_lon2n_E(rad(89), rad(0))
n_EB_E_t1 = lat_lon2n_E(rad(89), rad(180))
# 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:
n_EB_E_ti = unit(n_EB_E_t0 + (ti - t0) * (n_EB_E_t1 - n_EB_E_t0) /
(t1 - t0))
# When displaying the resulting position for humans, it is more
# convenient to see lat, long:
lat_EB_ti, long_EB_ti = n_E2lat_lon(n_EB_E_ti)
msg = 'Ex6, Interpolated position: lat, long = {} {} deg'
print(msg.format(deg(lat_EB_ti), deg(long_EB_ti)))
assert_array_almost_equal(deg(lat_EB_ti), 89.7999805)
assert_array_almost_equal(deg(long_EB_ti), 180.)
def find_c_point_from_precalc(to_point, point1, point2, c12, p1h, p2h, dp1p2):
tpn = to_point.nv
ctp = cross(tpn, c12, axis=0)
try:
c = unit(cross(ctp, c12, axis=0))
except Exception:
print((to_point, point1, point2))
raise
sutable_c = None
for co in (c, 0 - c):
co_rs = co.reshape((3, ))
dp1co = arccos(arccos_limit(dot(p1h, co_rs)))
dp2co = arccos(arccos_limit(dot(p2h, co_rs)))
if abs(dp1co + dp2co - dp1p2) < 0.000001:
sutable_c = co
break
if sutable_c is not None:
c_point_lat, c_point_lng = n_E2lat_lon(sutable_c)
c_point = Point(lat=rad2deg(c_point_lat[0]),
lng=rad2deg(c_point_lng[0]))
c_dist = distance(to_point, c_point)
else:
c_dist, c_point = min(
((distance(to_point, p), p) for p in (point1, point2)),
key=itemgetter(0))
return find_c_point_result(c_dist, c_point)
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)
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)
def find_closest_point_pair(points,
to_point,
req_min_dist=20,
stop_after_dist=50):
tpn = to_point.nv
min_distance = None
min_point_pair = None
min_c_point = None
for point1, point2 in pairs(points):
p1 = point1.nv
p2 = point2.nv
c12 = cross(p1, p2, axis=0)
ctp = cross(tpn, c12, axis=0)
c = unit(cross(ctp, c12, axis=0))
p1h = p1.reshape((3, ))
p2h = p2.reshape((3, ))
dp1p2 = arccos(dot(p1h, p2h))
sutable_c = None
for co in (c, 0 - c):
co_rs = co.reshape((3, ))
dp1co = arccos(dot(p1h, co_rs))
dp2co = arccos(dot(p2h, co_rs))
if abs(dp1co + dp2co - dp1p2) < 0.000001:
sutable_c = co
break
if sutable_c is not None:
c_point_lat, c_point_lng = n_E2lat_lon(sutable_c)
c_point = Point(lat=rad2deg(c_point_lat[0]),
lng=rad2deg(c_point_lng[0]))
c_dist = distance(to_point, c_point)
else:
c_dist, c_point = min(
((distance(to_point, p), p) for p in (point1, point2)))
if min_distance is None or c_dist < min_distance:
min_distance = c_dist
min_point_pair = (point1, point2)
min_c_point = c_point
if min_distance < req_min_dist and c_dist > stop_after_dist:
break
return min_point_pair, min_c_point, min_distance
def test_Ex7_mean_position():
# Three positions A, B and C are given:
# Enter elements as lat/long in deg:
n_EA_E = lat_lon2n_E(rad(90), rad(0))
n_EB_E = lat_lon2n_E(rad(60), rad(10))
n_EC_E = lat_lon2n_E(rad(50), rad(-20))
# Find the horizontal mean position:
n_EM_E = unit(n_EA_E + n_EB_E + n_EC_E)
# The result is best viewed with a figure that shows the n-vectors
# relative to an Earth-model:
print('Ex7, See figure')
# plot_Earth_figure(n_EA_E,n_EB_E,n_EC_E,n_EM_E)
assert_array_almost_equal(n_EM_E.ravel(),
[0.384117, -0.046602, 0.922107])
# Alternatively:
n_EM_E = mean_horizontal_position(np.hstack((n_EA_E, n_EB_E, n_EC_E)))
assert_array_almost_equal(n_EM_E.ravel(),
[0.384117, -0.046602, 0.922107])
def test_Ex7_mean_position():
# Three positions A, B and C are given:
# Enter elements as lat/long in deg:
n_EA_E = lat_lon2n_E(rad(90), rad(0))
n_EB_E = lat_lon2n_E(rad(60), rad(10))
n_EC_E = lat_lon2n_E(rad(50), rad(-20))
# Find the horizontal mean position:
n_EM_E = unit(n_EA_E + n_EB_E + n_EC_E)
# The result is best viewed with a figure that shows the n-vectors
# relative to an Earth-model:
print('Ex7, See figure')
# plot_Earth_figure(n_EA_E,n_EB_E,n_EC_E,n_EM_E)
assert_array_almost_equal(n_EM_E.ravel(),
[0.384117, -0.046602, 0.922107])
# Alternatively:
n_EM_E = mean_horizontal_position(np.hstack((n_EA_E, n_EB_E, n_EC_E)))
assert_array_almost_equal(n_EM_E.ravel(),
[0.384117, -0.046602, 0.922107])
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:
p_BC_B = np.r_[3000, 2000, 100].reshape((-1, 1))
# Position and orientation of B is given:
n_EB_E = unit([[1], [2], [3]]) # unit to get unit length of vector
z_EB = -400
R_NB = zyx2R(rad(10), rad(20), rad(30))
# the three angles are yaw, pitch, and roll
# A custom reference ellipsoid is given (replacing WGS-84):
a, f = 6378135, 1.0 / 298.26 # (WGS-72)
# Find the position of C.
# SOLUTION:
# Step1: Find R_EN:
R_EN = n_E2R_EN(n_EB_E)
# Step2: Find R_EB, from R_EN and R_NB:
R_EB = np.dot(R_EN, R_NB) # Note: closest frames cancel
# Step3: Decompose the delta vector in E:
p_BC_E = np.dot(R_EB, p_BC_B)
# no transpose of R_EB, since the vector is in B
# Step4: Find the position of C, using the functions that goes from one
# position and a delta, to a new position:
n_EC_E, z_EC = n_EA_E_and_p_AB_E2n_EB_E(n_EB_E, p_BC_E, z_EB, a, f)
# When displaying the resulting position for humans, it is more
# convenient to see lat, long:
lat_EC, long_EC = n_E2lat_lon(n_EC_E)
# Here we also assume that the user wants output height (= - depth):
msg = 'Ex2, Pos C: lat, long = {},{} deg, height = {} m'
print(msg.format(deg(lat_EC), deg(long_EC), -z_EC))
assert_array_almost_equal(deg(lat_EC), 53.32637826)
assert_array_almost_equal(deg(long_EC), 63.46812344)
assert_array_almost_equal(z_EC, -406.00719607)
def interpolate(path, ti):
"""
Return the interpolated point along the path
Parameters
----------
path: tuple of n-vectors (positionA, po)
ti: real scalar
interpolation time assuming position A and B is at t0=0 and t1=1,
respectively.
Returns
-------
point: Nvector
point of interpolation along path
"""
n_EB_E_t0, n_EB_E_t1 = path
n_EB_E_ti = unit(n_EB_E_t0 + ti * (n_EB_E_t1 - n_EB_E_t0),
norm_zero_vector=nan)
return n_EB_E_ti
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:
p_BC_B = np.r_[3000, 2000, 100].reshape((-1, 1))
# Position and orientation of B is given:
n_EB_E = unit([[1], [2], [3]]) # unit to get unit length of vector
z_EB = -400
R_NB = zyx2R(rad(10), rad(20), rad(30))
# the three angles are yaw, pitch, and roll
# A custom reference ellipsoid is given (replacing WGS-84):
a, f = 6378135, 1.0 / 298.26 # (WGS-72)
# Find the position of C.
# SOLUTION:
# Step1: Find R_EN:
R_EN = n_E2R_EN(n_EB_E)
# Step2: Find R_EB, from R_EN and R_NB:
R_EB = np.dot(R_EN, R_NB) # Note: closest frames cancel
# Step3: Decompose the delta vector in E:
p_BC_E = np.dot(R_EB, p_BC_B)
# no transpose of R_EB, since the vector is in B
# Step4: Find the position of C, using the functions that goes from one
# position and a delta, to a new position:
n_EC_E, z_EC = n_EA_E_and_p_AB_E2n_EB_E(n_EB_E, p_BC_E, z_EB, a, f)
# When displaying the resulting position for humans, it is more
# convenient to see lat, long:
lat_EC, long_EC = n_E2lat_lon(n_EC_E)
# Here we also assume that the user wants output height (= - depth):
msg = 'Ex2, Pos C: lat, long = {},{} deg, height = {} m'
print(msg.format(deg(lat_EC), deg(long_EC), -z_EC))
assert_array_almost_equal(deg(lat_EC), 53.32637826)
assert_array_almost_equal(deg(long_EC), 63.46812344)
assert_array_almost_equal(z_EC, -406.00719607)
def test_small_and_large_cross_track_distance(self):
radius = 6371e3 # m, mean Earth radius
n_EA1_E = lat_lon2n_E(rad(5), rad(10))
n_EA2_E = lat_lon2n_E(rad(10), rad(10))
n_EB0_E = lat_lon2n_E(rad(7), rad(10.1))
path = (n_EA1_E, n_EA2_E)
n_EB1_E = closest_point_on_great_circle(path, n_EB0_E)
for s_xt0 in [np.pi / 3 * radius, 10., 0.1, 1e-4, 1e-8]:
distance_rad = s_xt0 / radius
n_EB_E = n_EA_E_distance_and_azimuth2n_EB_E(
n_EB1_E, distance_rad, np.pi / 2)
n_EB2_E = closest_point_on_great_circle(path, n_EB_E)
s_xt = great_circle_distance(n_EB1_E, n_EB_E, radius)
c_E = unit(np.cross(n_EA1_E, n_EA2_E, axis=0))
s_xt2 = (np.arccos(np.dot(c_E.T, n_EB_E)) - np.pi / 2) * radius
s_xt3 = cross_track_distance(path,
n_EB_E,
method='greatcircle',
radius=radius)
s_xt4 = np.arctan2(
-np.dot(c_E.T, n_EB_E),
np.linalg.norm(np.cross(c_E, n_EB_E, axis=0), axis=0)) * radius
assert_array_almost_equal(n_EB2_E, n_EB1_E)
assert_array_almost_equal(s_xt, s_xt0)
assert_array_almost_equal(s_xt2, s_xt0)
assert_array_almost_equal(s_xt3, s_xt0)
assert_array_almost_equal(s_xt4, s_xt0)
rtol = 10**(-min(9 + np.log10(s_xt0), 15))
self.assertTrue(np.abs(s_xt - s_xt0) / s_xt0 < rtol, 's_xt fails')
self.assertTrue(
np.abs(s_xt2 - s_xt0) / s_xt0 < rtol, 's_xt2 fails')
self.assertTrue(
np.abs(s_xt3 - s_xt0) / s_xt0 < rtol, 's_xt3 fails')
self.assertTrue(
np.abs(s_xt4 - s_xt0) / s_xt0 < rtol, 's_xt4 fails')
def getMiddlePointFromList(positions):
n_EM_E = nv.unit(sum(positions))
lat, lon = nv.n_E2lat_lon(n_EM_E)
lat, lon = degrees(lat[0]), degrees(lon[0])
return lat, lon
