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Berechnungen Biaxial

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Hendrik Möllersmann
2026-01-13 16:15:00 +01:00
parent 4b348533bb
commit 9dfb959eb0
4 changed files with 94 additions and 102 deletions
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38
ellipsoide.py
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@@ -46,24 +46,25 @@ class EllipsoidBiaxial:
M = lambda self, phi: self.c / self.V(phi) ** 3
N = lambda self, phi: self.c / self.V(phi)
beta2psi = lambda self, beta: arctan(self.a / self.b * np.tan(beta))
beta2phi = lambda self, beta: arctan(self.a ** 2 / self.b ** 2 * np.tan(beta))
beta2psi = lambda self, beta: np.arctan2(self.a * np.sin(beta), self.b * np.cos(beta))
beta2phi = lambda self, beta: np.arctan2(self.a ** 2 * np.sin(beta), self.b ** 2 * np.cos(beta))
psi2beta = lambda self, psi: arctan(self.b / self.a * np.tan(psi))
psi2phi = lambda self, psi: arctan(self.a / self.b * np.tan(psi))
psi2beta = lambda self, psi: np.arctan2(self.b * np.sin(psi), self.a * np.cos(psi))
psi2phi = lambda self, psi: np.arctan2(self.a * np.sin(psi), self.b * np.cos(psi))
phi2beta = lambda self, phi: arctan(self.b ** 2 / self.a ** 2 * np.tan(phi))
phi2psi = lambda self, phi: arctan(self.b / self.a * np.tan(phi))
phi2beta = lambda self, phi: np.arctan2(self.b**2 * np.sin(phi), self.a**2 * np.cos(phi))
phi2psi = lambda self, phi: np.arctan2(self.b * np.sin(phi), self.a * np.cos(phi))
phi2p = lambda self, phi: self.N(phi) * cos(phi)
def cart2ell(self, Eh, Ephi, x, y, z):
def bi_cart2ell(self, point: NDArrayself, Eh: float = 0.001, Ephi: float = wu.gms2rad([0, 0, 0.001])) -> Tuple[float, float, float]:
x, y, z = point
lamb = arctan2(y, x)
p = sqrt(x**2+y**2)
# print(f"p = {round(p, 5)} m")
lamb = arctan(y/x)
phi_null = arctan(z/p*(1-self.e**2)**-1)
phi_null = arctan2(z, p*(1 - self.e**2))
hi = [0]
phii = [phi_null]
@@ -71,9 +72,9 @@ class EllipsoidBiaxial:
i = 0
while True:
N = self.a*(1-self.e**2*sin(phii[i])**2)**(-1/2)
h = p/cos(phii[i])-N
phi = arctan(z/p*(1-(self.e**2*N)/(N+h))**(-1))
N = self.a / sqrt(1 - self.e**2 * sin(phii[i])**2)
h = p / cos(phii[i]) - N
phi = arctan2(z, p * (1-(self.e**2*N) / (N+h)))
hi.append(h)
phii.append(phi)
dh = abs(hi[i]-h)
@@ -82,18 +83,15 @@ class EllipsoidBiaxial:
if dh < Eh:
if dphi < Ephi:
break
for i in range(len(phii)):
# print(f"P3[{i}]: {aus.gms('phi', phii[i], 5)}\th = {round(hi[i], 5)} m")
pass
return phi, lamb, h
def ell2cart(self, phi, lamb, h):
def bi_ell2cart(self, phi: float, lamb: float, h: float) -> NDArray:
W = sqrt(1 - self.e**2 * sin(phi)**2)
N = self.a / W
x = (N+h) * cos(phi) * cos(lamb)
y = (N+h) * cos(phi) * sin(lamb)
z = (N * (1-self.e**2) + h) * sin(lamb)
return x, y, z
z = (N * (1-self.e**2) + h) * sin(phi)
return np.array([x, y, z])
class EllipsoidTriaxial:
def __init__(self, ax: float, ay: float, b: float):