78 lines
2.5 KiB
Python
78 lines
2.5 KiB
Python
import numpy as np
|
|
|
|
|
|
def cart2sph(x, y, z):
|
|
r = np.sqrt(x**2 + y**2 + z**2)
|
|
phi = np.atan2(z, np.sqrt(x**2 + y**2))
|
|
lamb = np.atan2(y, x)
|
|
|
|
return r, np.rad2deg(phi), np.rad2deg(lamb)
|
|
|
|
|
|
def sph2cart(r, phi, lamb):
|
|
phi_rad = np.deg2rad(phi)
|
|
lamb_rad = np.deg2rad(lamb)
|
|
|
|
x = r * np.cos(phi_rad) * np.cos(lamb_rad)
|
|
y = r * np.cos(phi_rad) * np.sin(lamb_rad)
|
|
z = r * np.sin(phi_rad)
|
|
|
|
return x, y, z
|
|
|
|
|
|
def kugel_erste_gha(R, phi_1, lamb_1, s_d, a_12):
|
|
|
|
s = s_d / R
|
|
lamb_1_rad = np.deg2rad(lamb_1)
|
|
phi_1_rad = np.deg2rad(phi_1)
|
|
a_12_rad = np.deg2rad(a_12)
|
|
|
|
sin_satz = np.sin(s) * np.sin(a_12_rad)
|
|
sin_kos = np.cos(phi_1_rad) * np.cos(s) - np.sin(phi_1_rad) * np.sin(s) * np.cos(a_12_rad)
|
|
delta_lam = np.atan2(sin_satz, sin_kos)
|
|
lamb_2_rad = lamb_1_rad + delta_lam
|
|
|
|
phi_2_rad = np.asin(np.sin(phi_1_rad) * np.cos(s) + np.cos(phi_1_rad) * np.sin(s) * np.cos(a_12_rad))
|
|
|
|
sin_satz_2 = -np.cos(phi_1_rad) * np.sin(a_12_rad)
|
|
sin_kos_2 = np.sin(s) * np.sin(phi_1_rad) - np.cos(s) * np.cos(phi_1_rad) * np.cos(a_12_rad)
|
|
a_21_rad = np.atan2(sin_satz_2, sin_kos_2)
|
|
if a_21_rad < 0:
|
|
a_21_rad += 2 * np.pi
|
|
|
|
return np.rad2deg(phi_2_rad), np.rad2deg(lamb_2_rad), np.rad2deg(a_21_rad)
|
|
|
|
|
|
def kugel_zweite_gha(R, phi_1, lamb_1, phi_2, lamb_2):
|
|
phi_1_rad = np.deg2rad(phi_1)
|
|
lamb_1_rad = np.deg2rad(lamb_1)
|
|
phi_2_rad = np.deg2rad(phi_2)
|
|
lamb_2_rad = np.deg2rad(lamb_2)
|
|
|
|
sin_satz_1 = np.cos(phi_2_rad) * np.sin(lamb_2_rad - lamb_1_rad)
|
|
sin_kos_1 = np.cos(phi_1_rad) * np.sin(phi_2_rad) - np.sin(phi_1_rad) * np.cos(phi_2_rad) * np.cos(lamb_2_rad - lamb_1_rad)
|
|
a_12_rad = np.atan2(sin_satz_1, sin_kos_1)
|
|
|
|
kos = np.sin(phi_1_rad) * np.sin(phi_2_rad) + np.cos(phi_1_rad) * np.cos(phi_2_rad) * np.cos(lamb_2_rad - lamb_1_rad)
|
|
s = np.acos(kos)
|
|
s_d = R * s
|
|
|
|
sin_satz_2 = -np.cos(phi_1_rad) * np.sin(lamb_2_rad - lamb_1_rad)
|
|
sin_kos_2 = np.cos(phi_2_rad) * np.sin(phi_1_rad) - np.sin(phi_2_rad) * np.cos(phi_1_rad) * np.cos(lamb_2_rad - lamb_1_rad)
|
|
a_21_rad = np.atan2(sin_satz_2, sin_kos_2)
|
|
if a_21_rad < 0:
|
|
a_21_rad += 2 * np.pi
|
|
|
|
return s_d, np.rad2deg(a_12_rad), np.rad2deg(a_21_rad)
|
|
|
|
|
|
if __name__ == "__main__":
|
|
R = 6378815.904 # Bern
|
|
phi_1 = 10
|
|
lamb_1 = 40
|
|
a_12 = 100
|
|
s = 10000
|
|
phi_2, lamb_2, _ = kugel_erste_gha(R, phi_1, lamb_1, s, a_12)
|
|
|
|
print(kugel_erste_gha(R, phi_1, lamb_1, s, a_12))
|
|
print(kugel_zweite_gha(R, phi_1, lamb_1, phi_2, lamb_2)) |