def LatLonHgt2XYZ(self, lat, lon, h):
"""LatLonHgt2XYZ(lat, lon, h) --> (x, y, z)
lat is the latitude (deg)
lon is the longitude (deg)
h is the heigh (m)
(x, y, z) is a tuple of ECEF coordinates (m)
"""
N = self.N(lat)
cos_lat = cosd(lat)
return (cos_lat * cosd(lon) * (N + h), cos_lat * sind(lon) * (N + h),
sind(lat) * ((1 - self.e2) * N + h))
def bearing(lat1, lon1, lat2, lon2):
"""hdg = bearing(lat1, lon1, lat2, lon2)
lat1, lon1 are the latitude and longitude of the starting point
lat2, lon2 are the latitude and longitude of the ending point
hdg is the bearing (heading), in degrees, linking the start to the end.
"""
from isceobj.Util.geo.trig import sind, cosd, arctand2
dlat = (lat2 - lat1)
dlon = (lon2 - lon1)
y = sind(dlon) * cosd(lat2)
x = cosd(lat1) * sind(lat2) - sind(lat1) * cosd(lat2) * cosd(dlon)
return arctand2(y, x)
def common2conformal(self, lat):
"""Convert common latiude (deg) to conformal latiude (deg) """
sinoe = np.sqrt(self.e2)
sinphi = sind(lat)
return (2. * arctand(
np.sqrt((1. + sinphi) / (1. - sinphi) *
((1. - sinphi * sinoe) / (1. + sinphi * sinoe))**sinoe)) -
90.0)
def great_circle(self, lat1, lon1, lat2, lon2):
"""s, alpha1, alpha2 = great_circle(lat1, lon1, lat2, lon2)
(lat1, lon1) p1's location
(lat2, lon2) p2's location
s distance along great circle
alpha1 heading at p1
alpha2 heading at p2
"""
phi1, L1, phi2, L2 = lat1, lon1, lat2, lon2
a = self.a
f = self.f
b = (1 - f) * a
U1 = self.common2reduced(phi1) # aka beta1
U2 = self.common2reduced(phi2)
L = L2 - L1
lam = L
delta_lam = 100000.
while abs(delta_lam) > 1.e-10:
sin_sigma = ((cosd(U2) * sind(lam))**2 +
(cosd(U1) * sind(U2) -
sind(U1) * cosd(U2) * cosd(lam))**2)**0.5
cos_sigma = sind(U1) * sind(U2) + cosd(U1) * cosd(U2) * cosd(lam)
sigma = arctan2(sin_sigma, cos_sigma)
sin_alpha = cosd(U1) * cosd(U2) * sind(lam) / sin_sigma
cos2_alpha = 1 - sin_alpha**2
cos_2sigma_m = cos_sigma - 2 * sind(U1) * sind(U2) / cos2_alpha
C = (f / 16.) * cos2_alpha * (4. + f * (4 - 3 * cos2_alpha))
lam_new = (np.radians(L) + (1 - C) * f * sin_alpha *
(sigma + C * sin_sigma * (cos_2sigma_m + C * cos_sigma *
(-1 + 2 * cos_2sigma_m**2))))
lam_new *= 180 / np.pi
delta_lam = lam_new - lam
lam = lam_new
pass
u2 = cos2_alpha * (a**2 - b**2) / b**2
A_ = 1 + u2 / 16384 * (4096 + u2 * (-768 + u2 * (320 - 175 * u2)))
B_ = u2 / 1024 * (256 + u2 * (-128 + u2 * (74 - 47 * u2)))
delta_sigma = B_ * sin_sigma * (cos_2sigma_m - (1 / 4.) * B_ *
(cos_sigma *
(-1 + 2 * cos_2sigma_m**2)) -
(1 / 6.) * B_ * cos_2sigma_m *
(-3 + 4 * sin_sigma**2) *
(-3 + 4 * cos_2sigma_m**2))
s = b * A_ * (sigma - delta_sigma)
alpha_1 = 180 * arctan2(
cosd(U2) * sind(lam),
cosd(U1) * sind(U2) - sind(U1) * cosd(U2) * cosd(lam)) / np.pi
alpha_2 = 180 * arctan2(
cosd(U1) * sind(lam),
-sind(U1) * cosd(U2) + cosd(U1) * sind(U2) * cosd(lam)) / np.pi
return s, alpha_1, alpha_2
def R(self, lat):
return (((self.a**2 * cosd(lat))**2 + (self.b**2 * sind(lat))**2) /
((self.a * cosd(lat))**2 + (self.b * sind(lat))**2))**0.5
def local_radius_of_curvature(self, lat, hdg):
"""local_radius_of_curvature(lat, hdg)"""
return 1. / (cosd(hdg)**2 / self.M(lat) + sind(hdg)**2 / self.N(lat))
def normal_radius_of_curvature(self, lat):
"""East Radius (eastRad): Normal radius of curvature (N), meters for
latitude in degrees """
return (self.a**2 / ((self.a * cosd(lat))**2 +
(self.b * sind(lat))**2)**0.5)
def meridional_radius_of_curvature(self, lat):
"""North Radius (northRad): Meridional radius of curvature (M),
meters for latitude in degress """
return ((self.a * self.b)**2 / ((self.a * cosd(lat))**2 +
(self.b * sind(lat))**2)**1.5)
def n_vector(self):
"""Compute a Vector instance representing the N-Vector"""
from isceobj.Util.geo.trig import sind, cosd
return euclid.Vector(
cosd(self.lat) * cosd(self.lon),
cosd(self.lat) * sind(self.lon), sind(self.lat))
