373 lines
14 KiB
Python
373 lines
14 KiB
Python
import numpy as np
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import winkelumrechnungen as wu
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import ausgaben as aus
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import jacobian_Ligas
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from GHA_triaxial.panou import p_q
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class EllipsoidBiaxial:
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def __init__(self, a: float, b: float):
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self.a = a
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self.b = b
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self.c = a ** 2 / b
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self.e = np.sqrt(a ** 2 - b ** 2) / a
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self.e_ = np.sqrt(a ** 2 - b ** 2) / b
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@classmethod
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def init_name(cls, name: str):
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if name == "Bessel":
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a = 6377397.15508
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b = 6356078.96290
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return cls(a, b)
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elif name == "Hayford":
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a = 6378388
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f = 1/297
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b = a - a * f
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return cls(a, b)
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elif name == "Krassowski":
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a = 6378245
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f = 298.3
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b = a - a * f
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return cls(a, b)
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elif name == "WGS84":
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a = 6378137
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f = 298.257223563
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b = a - a * f
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return cls(a, b)
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@classmethod
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def init_af(cls, a: float, f: float):
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b = a - a * f
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return cls(a, b)
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V = lambda self, phi: np.sqrt(1 + self.e_ ** 2 * np.cos(phi) ** 2)
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M = lambda self, phi: self.c / self.V(phi) ** 3
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N = lambda self, phi: self.c / self.V(phi)
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beta2psi = lambda self, beta: np.arctan(self.a / self.b * np.tan(beta))
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beta2phi = lambda self, beta: np.arctan(self.a ** 2 / self.b ** 2 * np.tan(beta))
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psi2beta = lambda self, psi: np.arctan(self.b / self.a * np.tan(psi))
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psi2phi = lambda self, psi: np.arctan(self.a / self.b * np.tan(psi))
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phi2beta = lambda self, phi: np.arctan(self.b ** 2 / self.a ** 2 * np.tan(phi))
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phi2psi = lambda self, phi: np.arctan(self.b / self.a * np.tan(phi))
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phi2p = lambda self, phi: self.N(phi) * np.cos(phi)
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def cart2ell(self, Eh, Ephi, x, y, z):
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p = np.sqrt(x**2+y**2)
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# print(f"p = {round(p, 5)} m")
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lamb = np.arctan(y/x)
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phi_null = np.arctan(z/p*(1-self.e**2)**-1)
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hi = [0]
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phii = [phi_null]
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i = 0
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while True:
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N = self.a*(1-self.e**2*np.sin(phii[i])**2)**(-1/2)
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h = p/np.cos(phii[i])-N
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phi = np.arctan(z/p*(1-(self.e**2*N)/(N+h))**(-1))
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hi.append(h)
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phii.append(phi)
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dh = abs(hi[i]-h)
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dphi = abs(phii[i]-phi)
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i = i+1
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if dh < Eh:
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if dphi < Ephi:
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break
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for i in range(len(phii)):
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# print(f"P3[{i}]: {aus.gms('phi', phii[i], 5)}\th = {round(hi[i], 5)} m")
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pass
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return phi, lamb, h
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def ell2cart(self, phi, lamb, h):
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W = np.sqrt(1 - self.e**2 * np.sin(phi)**2)
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N = self.a / W
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x = (N+h) * np.cos(phi) * np.cos(lamb)
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y = (N+h) * np.cos(phi) * np.sin(lamb)
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z = (N * (1-self.e**2) + h) * np.sin(lamb)
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return x, y, z
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class EllipsoidTriaxial:
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def __init__(self, ax: float, ay: float, b: float):
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self.ax = ax
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self.ay = ay
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self.b = b
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self.ex = np.sqrt((self.ax**2 - self.b**2) / self.ax**2)
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self.ey = np.sqrt((self.ay**2 - self.b**2) / self.ay**2)
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self.ee = np.sqrt((self.ax**2 - self.ay**2) / self.ax**2)
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self.ex_ = np.sqrt((self.ax**2 - self.b**2) / self.b**2)
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self.ey_ = np.sqrt((self.ay**2 - self.b**2) / self.b**2)
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self.ee_ = np.sqrt((self.ax**2 - self.ay**2) / self.ay**2)
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self.Ex = np.sqrt(self.ax**2 - self.b**2)
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self.Ey = np.sqrt(self.ay**2 - self.b**2)
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self.Ee = np.sqrt(self.ax**2 - self.ay**2)
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@classmethod
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def init_name(cls, name: str):
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if name == "BursaFialova1993":
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ax = 6378171.36
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ay = 6378101.61
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b = 6356751.84
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return cls(ax, ay, b)
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elif name == "BursaSima1980":
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ax = 6378172
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ay = 6378102.7
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b = 6356752.6
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return cls(ax, ay, b)
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elif name == "Eitschberger1978":
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ax = 6378173.435
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ay = 6378103.9
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b = 6356754.4
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return cls(ax, ay, b)
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elif name == "Bursa1972":
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ax = 6378173
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ay = 6378104
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b = 6356754
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return cls(ax, ay, b)
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elif name == "Bursa1970":
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ax = 6378173
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ay = 6378105
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b = 6356754
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return cls(ax, ay, b)
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elif name == "Bessel-biaxial":
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ax = 6377397.15509
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ay = 6377397.15508
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b = 6356078.96290
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return cls(ax, ay, b)
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def ell2cart(self, beta, lamb, u):
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"""
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Panou 2014 12ff.
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:param beta: ellipsoidische Breite
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:param lamb: ellipsoidische Länge
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:param u: Höhe
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:return: kartesische Koordinaten
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"""
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s1 = u**2 - self.b**2
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s2 = -self.ay**2 * np.sin(beta)**2 - self.b**2 * np.cos(beta)**2
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s3 = -self.ax**2 * np.sin(lamb)**2 - self.ay**2 * np.cos(lamb)**2
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# print(s1, s2, s3)
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xe = np.sqrt(((self.ax**2+s1) * (self.ax**2+s2) * (self.ax**2+s3)) /
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((self.ax**2-self.ay**2) * (self.ax**2-self.b**2)))
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ye = np.sqrt(((self.ay**2+s1) * (self.ay**2+s2) * (self.ay**2+s3)) /
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((self.ay**2-self.ax**2) * (self.ay**2-self.b**2)))
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ze = np.sqrt(((self.b**2+s1) * (self.b**2+s2) * (self.b**2+s3)) /
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((self.b**2-self.ax**2) * (self.b**2-self.ax**2)))
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x = np.sqrt(u**2 + self.Ex**2) * np.sqrt(np.cos(beta)**2 + self.Ee**2/self.Ex**2 * np.sin(beta)**2) * np.cos(lamb)
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y = np.sqrt(u**2 + self.Ey**2) * np.cos(beta) * np.sin(lamb)
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z = u * np.sin(beta) * np.sqrt(1 - self.Ee**2/self.Ex**2 * np.cos(lamb)**2)
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return x, y, z
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def ell2cart_P(self, lamb, beta):
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"""
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Panou 2013, 241
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:param lamb: ellipsoidische Länge
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:param beta: reduzierte ellipsoidische Breite
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:return: kartesische Koordinaten x y z
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"""
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x = self.ax * np.sqrt(np.cos(beta) ** 2 + self.Ee ** 2 / self.Ex ** 2 * np.sin(beta) ** 2) * np.cos(lamb)
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y = self.ay * np.cos(beta) * np.sin(lamb)
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z = self.b * np.sin(beta) * np.sqrt(1 - self.Ee ** 2 / self.Ex ** 2 * np.cos(lamb) ** 2)
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return x, y, z
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def cart2ell(self, x, y, z):
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"""
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Panou 2014 15ff.
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:param x:
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:param y:
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:param z:
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:return:
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"""
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c2 = self.ax**2 + self.ay**2 + self.b**2 - x**2 - y**2 - z**2
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c1 = (self.ax**2 * self.ay**2 + self.ax**2 * self.b**2 + self.ay**2 * self.b**2 -
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(self.ay**2+self.b**2) * x**2 - (self.ax**2 + self.b**2) * y**2 - (self.ax**2 + self.ay**2) * z**2)
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c0 = (self.ax**2 * self.ay**2 * self.b**2 - self.ay**2 * self.b**2 * x**2 -
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self.ax**2 * self.b**2 * y**2 - self.ax**2 * self.ay**2 * z**2)
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p = (c2**2 - 3*c1) / 9
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q = (9*c1*c2 - 27*c0 - 2*c2**3) / 54
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omega = np.arccos(q / np.sqrt(p**3))
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s1 = 2 * np.sqrt(p) * np.cos(omega/3) - c2/3
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s2 = 2 * np.sqrt(p) * np.cos(omega/3 - 2*np.pi/3) - c2/3
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s3 = 2 * np.sqrt(p) * np.cos(omega/3 - 4*np.pi/3) - c2/3
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# print(s1, s2, s3)
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beta = np.arctan(np.sqrt((-self.b**2 - s2) / (self.ay**2 + s2)))
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lamb = np.arctan(np.sqrt((-self.ay**2 - s3) / (self.ax**2 + s3)))
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u = np.sqrt(self.b**2 + s1)
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return beta, lamb, u
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def cart2geod(self, mode: str, xG, yG, zG, maxIter=30, maxLoa=0.005):
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"""
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Ligas 2012
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:param mode:
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:param xG:
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:param yG:
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:param zG:
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:param maxIter:
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:param maxLoa:
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:return:
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"""
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rG = np.sqrt(xG**2 + yG**2 + zG**2)
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pE = np.array([self.ax * xG / rG, self.ax * yG / rG, self.ax * zG / rG], dtype=np.float64)
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E = 1 / self.ax**2
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F = 1 / self.ay**2
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G = 1 / self.b**2
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i = 0
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loa = np.inf
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while i < maxIter and loa > maxLoa:
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if mode == "ligas1":
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invJ, fxE = jacobian_Ligas.case1(E, F, G, np.array([xG, yG, zG]), pE)
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elif mode == "ligas2":
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invJ, fxE = jacobian_Ligas.case2(E, F, G, np.array([xG, yG, zG]), pE)
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elif mode == "ligas3":
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invJ, fxE = jacobian_Ligas.case3(E, F, G, np.array([xG, yG, zG]), pE)
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pEi = pE.reshape(-1, 1) - invJ @ fxE.reshape(-1, 1)
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pEi = pEi.reshape(1, -1).flatten()
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loa = np.sqrt((pEi[0]-pE[0])**2 + (pEi[1]-pE[1])**2 + (pEi[2]-pE[2])**2)
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pE = pEi
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i += 1
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phi = np.arctan((1-self.ee**2) / (1-self.ex**2) * pE[2] / np.sqrt((1-self.ee**2)**2 * pE[0]**2 + pE[1]**2))
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lamb = np.arctan(1/(1-self.ee**2) * pE[1]/pE[0])
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h = np.sign(zG-pE[2]) * np.sign(pE[2]) * np.sqrt((pE[0]-xG)**2 + (pE[1]-yG)**2 + (pE[2]-zG)**2)
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return phi, lamb, h
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def geod2cart(self, phi, lamb, h):
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"""
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Ligas 2012, 250
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:param phi:
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:param lamb:
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:param h:
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:return:
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"""
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v = self.ax / np.sqrt(1 - self.ex**2*np.sin(phi)**2-self.ee**2*np.cos(phi)**2*np.sin(lamb)**2)
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xG = (v + h) * np.cos(phi) * np.cos(lamb)
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yG = (v * (1-self.ee**2) + h) * np.cos(phi) * np.sin(lamb)
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zG = (v * (1-self.ex**2) + h) * np.sin(phi)
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return xG, yG, zG
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def para2cart(self, u, v):
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"""
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Panou, Korakitits 2020, 4
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:param u:
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:param v:
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:return:
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"""
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x = self.ax * np.cos(u) * np.cos(v)
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y = self.ay * np.cos(u) * np.cos(v)
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z = self.b * np.sin(u)
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def cart2para(self, x, y, z):
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"""
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Panou, Korakitits 2020, 4
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:param x:
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:param y:
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:param z:
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:return:
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"""
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u_check1 = z*np.sqrt(1 - self.ee**2)
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u_check2 = np.sqrt(x**2 * (1-self.ee**2) + y**2) * np.sqrt(1-self.ex**2)
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if u_check1 <= u_check2:
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u = np.arctan(u_check1 / u_check2)
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else:
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u = np.pi/2 * np.arctan(u_check2 / u_check1)
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v_check1 = y
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v_check2 = x*np.sqrt(1-self.ee**2)
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if v_check1 <= v_check2:
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v = 2 * np.arctan(v_check1 / (v_check2 + np.sqrt(x**2*(1-self.ee**2)+y**2)))
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else:
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v = np.pi/2 - 2 * np.arctan(v_check2 / (v_check1 + np.sqrt(x**2*(1-self.ee**2)+y**2)))
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return u, v
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def p_q(self, x, y, z):
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H = x ** 2 + y ** 2 / (1 - self.ee ** 2) ** 2 + z ** 2 / (1 - self.ex ** 2) ** 2
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n = np.array([x / np.sqrt(H), y / ((1 - self.ee ** 2) * np.sqrt(H)), z / ((1 - ell.ex ** 2) * np.sqrt(H))])
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beta, lamb, u = self.cart2ell(x, y, z)
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carts = self.ell2cart(beta, lamb, u)
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B = self.Ex ** 2 * np.cos(beta) ** 2 + self.Ee ** 2 * np.sin(beta) ** 2
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L = self.Ex ** 2 - self.Ee ** 2 * np.cos(lamb) ** 2
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c1 = x ** 2 + y ** 2 + z ** 2 - (self.ax ** 2 + self.ay ** 2 + self.b ** 2)
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c0 = (self.ax ** 2 * self.ay ** 2 + self.ax ** 2 * self.b ** 2 + self.ay ** 2 * self.b ** 2 -
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(self.ay ** 2 + self.b ** 2) * x ** 2 - (self.ax ** 2 + self.b ** 2) * y ** 2 - (
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self.ax ** 2 + self.ay ** 2) * z ** 2)
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t2 = (-c1 + np.sqrt(c1 ** 2 - 4 * c0)) / 2
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t1 = c0 / t2
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t2e = self.ax ** 2 * np.sin(lamb) ** 2 + self.ay ** 2 * np.cos(lamb) ** 2
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t1e = self.ay ** 2 * np.sin(beta) ** 2 + self.b ** 2 * np.cos(beta) ** 2
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F = self.Ey ** 2 * np.cos(beta) ** 2 + self.Ee ** 2 * np.sin(lamb) ** 2
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p1 = -np.sqrt(L / (F * t2)) * self.ax / self.Ex * np.sqrt(B) * np.sin(lamb)
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p2 = np.sqrt(L / (F * t2)) * self.ay * np.cos(beta) * np.cos(lamb)
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p3 = 1 / np.sqrt(F * t2) * (self.b * self.Ee ** 2) / (2 * self.Ex) * np.sin(beta) * np.sin(2 * lamb)
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# p1 = -np.sign(y) * np.sqrt(L / (F * t2)) * self.ax / (self.Ex * self.Ee) * np.sqrt(B) * np.sqrt(t2 - self.ay ** 2)
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# p2 = np.sign(x) * np.sqrt(L / (F * t2)) * self.ay / (self.Ey * self.Ee) * np.sqrt((ell.ay ** 2 - t1) * (self.ax ** 2 - t2))
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# p3 = np.sign(x) * np.sign(y) * np.sign(z) * 1 / np.sqrt(F * t2) * self.b / (self.Ex * self.Ey) * np.sqrt(
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# (t1 - self.b ** 2) * (t2 - self.ay ** 2) * (self.ax ** 2 - t2))
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p = np.array([p1, p2, p3])
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q = np.array([n[1] * p[2] - n[2] * p[1],
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n[2] * p[0] - n[0] * p[2],
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n[1] * p[1] - n[1] * p[0]])
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return {"H": H, "n": n, "beta": beta, "lamb": lamb, "u": u, "B": B, "L": L, "c1": c1, "c0": c0, "t1": t1,
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"t2": t2,
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"F": F, "p": p, "q": q}
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def louvilleConstant(ell, x, y, z):
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values = p_q(ell, x, y, z)
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pass
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if __name__ == "__main__":
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ellips = EllipsoidTriaxial.init_name("Eitschberger1978")
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# carts = ellips.ell2cart(wu.deg2rad(10), wu.deg2rad(30), 6378172)
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# ells = ellips.cart2ell(carts[0], carts[1], carts[2])
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# print(aus.gms("beta", ells[0], 3), aus.gms("lambda", ells[1], 3), "u =", ells[2])
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# ells2 = ellips.cart2ell(5712200, 2663400, 1106000)
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# carts2 = ellips.ell2cart(ells2[0], ells2[1], ells2[2])
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# print(aus.xyz(carts2[0], carts2[1], carts2[2], 10))
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# stellen = 20
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# geod1 = ellips.cart2geod("ligas1", 5712200, 2663400, 1106000)
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# print(aus.gms("phi", geod1[0], stellen), aus.gms("lambda", geod1[1], stellen), "h =", geod1[2])
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# geod2 = ellips.cart2geod("ligas2", 5712200, 2663400, 1106000)
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# print(aus.gms("phi", geod2[0], stellen), aus.gms("lambda", geod2[1], stellen), "h =", geod2[2])
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# geod3 = ellips.cart2geod("ligas3", 5712200, 2663400, 1106000)
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# print(aus.gms("phi", geod3[0], stellen), aus.gms("lambda", geod3[1], stellen), "h =", geod3[2])
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# cart1 = ellips.geod2cart(geod1[0], geod1[1], geod1[2])
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# print(aus.xyz(cart1[0], cart1[1], cart1[2], 10))
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# cart2 = ellips.geod2cart(geod2[0], geod2[1], geod2[2])
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# print(aus.xyz(cart2[0], cart2[1], cart2[2], 10))
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# cart3 = ellips.geod2cart(geod3[0], geod3[1], geod3[2])
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# print(aus.xyz(cart3[0], cart3[1], cart3[2], 10))
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# test_cart = ellips.geod2cart(0.175, 0.444, 100)
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# print(aus.xyz(test_cart[0], test_cart[1], test_cart[2], 10))
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ellips.louvilleConstant(5712200, 2663400, 1106000)
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pass
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