Berechnungen Kugel
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96
kugel.py
96
kugel.py
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import numpy as np
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from numpy import sqrt, arctan2, sin, cos, arcsin, arccos
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from numpy.typing import NDArray
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from typing import Tuple
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import winkelumrechnungen as wu
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def cart2sph(x, y, z):
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r = np.sqrt(x**2 + y**2 + z**2)
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phi = np.atan2(z, np.sqrt(x**2 + y**2))
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lamb = np.atan2(y, x)
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def cart2sph(point: NDArray) -> Tuple[float, float, float]:
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x, y, z = point
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r = sqrt(x**2 + y**2 + z**2)
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phi = arctan2(z, sqrt(x**2 + y**2))
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lamb = arctan2(y, x)
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return r, np.rad2deg(phi), np.rad2deg(lamb)
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return r, phi, lamb
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def sph2cart(r, phi, lamb):
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phi_rad = np.deg2rad(phi)
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lamb_rad = np.deg2rad(lamb)
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def sph2cart(r: float, phi: float, lamb: float) -> NDArray:
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x = r * cos(phi) * cos(lamb)
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y = r * cos(phi) * sin(lamb)
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z = r * sin(phi)
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x = r * np.cos(phi_rad) * np.cos(lamb_rad)
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y = r * np.cos(phi_rad) * np.sin(lamb_rad)
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z = r * np.sin(phi_rad)
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return x, y, z
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return np.array([x, y, z])
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def kugel_erste_gha(R, phi_1, lamb_1, s_d, a_12):
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def gha1(R, phi0, lamb0, s, alpha0):
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s_ = s / R
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s = s_d / R
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lamb_1_rad = np.deg2rad(lamb_1)
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phi_1_rad = np.deg2rad(phi_1)
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a_12_rad = np.deg2rad(a_12)
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lamb1 = lamb0 + arctan2(sin(s_) * sin(alpha0),
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cos(phi0) * cos(s_) - sin(phi0) * sin(s_) * cos(alpha0))
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sin_satz = np.sin(s) * np.sin(a_12_rad)
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sin_kos = np.cos(phi_1_rad) * np.cos(s) - np.sin(phi_1_rad) * np.sin(s) * np.cos(a_12_rad)
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delta_lam = np.atan2(sin_satz, sin_kos)
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lamb_2_rad = lamb_1_rad + delta_lam
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phi1 = arcsin(sin(phi0) * cos(s_) + cos(phi0) * sin(s_) * cos(alpha0))
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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))
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sin_satz_2 = -np.cos(phi_1_rad) * np.sin(a_12_rad)
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sin_kos_2 = np.sin(s) * np.sin(phi_1_rad) - np.cos(s) * np.cos(phi_1_rad) * np.cos(a_12_rad)
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a_21_rad = np.atan2(sin_satz_2, sin_kos_2)
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if a_21_rad < 0:
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a_21_rad += 2 * np.pi
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return np.rad2deg(phi_2_rad), np.rad2deg(lamb_2_rad), np.rad2deg(a_21_rad)
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return phi1, lamb1
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def kugel_zweite_gha(R, phi_1, lamb_1, phi_2, lamb_2):
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phi_1_rad = np.deg2rad(phi_1)
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lamb_1_rad = np.deg2rad(lamb_1)
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phi_2_rad = np.deg2rad(phi_2)
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lamb_2_rad = np.deg2rad(lamb_2)
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def gha2(R, phi0, lamb0, phi1, lamb1):
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s_ = arccos(sin(phi0) * sin(phi1) + cos(phi0) * cos(phi1) * cos(lamb1 - lamb0))
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s = R * s_
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sin_satz_1 = np.cos(phi_2_rad) * np.sin(lamb_2_rad - lamb_1_rad)
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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)
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a_12_rad = np.atan2(sin_satz_1, sin_kos_1)
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alpha0 = arctan2(cos(phi1) * sin(lamb1 - lamb0),
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cos(phi0) * sin(phi1) - sin(phi0) * cos(phi1) * cos(lamb1 - lamb0))
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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)
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s = np.acos(kos)
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s_d = R * s
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alpha1 = arctan2(-cos(phi0) * sin(lamb1 - lamb0),
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cos(phi1) * sin(phi0) - sin(phi1) * cos(phi0) * cos(lamb1 - lamb0))
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if alpha1 < 0:
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alpha1 += 2 * np.pi
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sin_satz_2 = -np.cos(phi_1_rad) * np.sin(lamb_2_rad - lamb_1_rad)
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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)
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a_21_rad = np.atan2(sin_satz_2, sin_kos_2)
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if a_21_rad < 0:
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a_21_rad += 2 * np.pi
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return s_d, np.rad2deg(a_12_rad), np.rad2deg(a_21_rad)
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return alpha0, alpha1, s
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if __name__ == "__main__":
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R = 6378815.904 # Bern
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phi_1 = 10
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lamb_1 = 40
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a_12 = 100
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phi0 = wu.deg2rad(10)
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lamb0 = wu.deg2rad(40)
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alpha0 = wu.deg2rad(100)
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s = 10000
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phi_2, lamb_2, _ = kugel_erste_gha(R, phi_1, lamb_1, s, a_12)
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phi1, lamb1 = gha1(R, phi0, lamb0, s, alpha0)
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alpha0_g, alpha1, s_g = gha2(R, phi0, lamb0, phi1, lamb1)
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phi1 = wu.rad2deg(phi1)
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lamb1 = wu.rad2deg(lamb1)
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alpha0_g = wu.rad2deg(alpha0_g)
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alpha1 = wu.rad2deg(alpha1)
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print(kugel_erste_gha(R, phi_1, lamb_1, s, a_12))
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print(kugel_zweite_gha(R, phi_1, lamb_1, phi_2, lamb_2))
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pass
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