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Näherungslösung GHA 2

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Hendrik Möllersmann
2026-01-11 16:05:15 +01:00
parent 4d5b6fcc3e
commit 6cc7245b0f
7 changed files with 260 additions and 235 deletions
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91
ellipsoide.py
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@@ -1,9 +1,10 @@
import numpy as np
from numpy import sin, cos, arctan, arctan2, sqrt, pi, arccos
import winkelumrechnungen as wu
import ausgaben as aus
import jacobian_Ligas
import matplotlib.pyplot as plt
from typing import Tuple
from numpy.typing import NDArray
class EllipsoidBiaxial:
@@ -162,18 +163,40 @@ class EllipsoidTriaxial:
b = 1 / sqrt(2)
return cls(ax, ay, b)
def func_H(self, x: float, y: float, z: float):
def func_H(self, point: NDArray) -> float:
"""
Berechnung H
Panou, Korakitis 2019 [43]
:param point: Punkt
:return: H
"""
x, y, z = point
return x ** 2 + y ** 2 / (1 - self.ee ** 2) ** 2 + z ** 2 / (1 - self.ex ** 2) ** 2
def func_n(self, x: float, y: float, z: float, H: float = None):
def func_n(self, point: NDArray, H: float = None) -> NDArray:
"""
Berechnung normalen Vektor
Panou, Korakitis 2019 [9-12]
:param point: Punkt
:param H:
:return:
"""
if H is None:
H = self.func_H(x, y, z)
H = self.func_H(point)
sqrtH = sqrt(H)
x, y, z = point
return np.array([x / sqrtH,
y / ((1 - self.ee ** 2) * sqrtH),
z / ((1 - self.ex ** 2) * sqrtH)])
def func_t12(self, x, y, z):
def func_t12(self, point: NDArray) -> Tuple[float, float]:
"""
Berechnung Wurzeln
Panou, Korakitis 2019 [9-12]
:param point: Punkt
:return: Wurzeln t1, t2
"""
x, y, z = point
c1 = x ** 2 + y ** 2 + z ** 2 - (self.ax ** 2 + self.ay ** 2 + self.b ** 2)
c0 = (self.ax ** 2 * self.ay ** 2 + self.ax ** 2 * self.b ** 2 + self.ay ** 2 * self.b ** 2 -
(self.ay ** 2 + self.b ** 2) * x ** 2 - (self.ax ** 2 + self.b ** 2) * y ** 2 - (
@@ -184,7 +207,7 @@ class EllipsoidTriaxial:
t1 = c0 / t2
return t1, t2
def ellu2cart(self, beta: float, lamb: float, u: float) -> np.ndarray:
def ellu2cart(self, beta: float, lamb: float, u: float) -> NDArray:
"""
Panou 2014 12ff.
Elliptische Breite+Länge sind nicht gleich der geodätischen
@@ -201,7 +224,7 @@ class EllipsoidTriaxial:
return np.array([x, y, z])
def cart2ellu(self, point: np.ndarray) -> tuple[float, float, float]:
def cart2ellu(self, point: NDArray) -> Tuple[float, float, float]:
"""
Panou 2014 15ff.
:param point: Punkt in kartesischen Koordinaten
@@ -232,7 +255,7 @@ class EllipsoidTriaxial:
return beta, lamb, u
def ell2cart(self, beta: float | np.ndarray, lamb: float | np.ndarray) -> np.ndarray:
def ell2cart(self, beta: float | NDArray, lamb: float | NDArray) -> NDArray:
"""
Panou, Korakitis 2019 2
:param beta: elliptische Breite [rad]
@@ -268,7 +291,7 @@ class EllipsoidTriaxial:
return xyz
def ell2cart_bektas(self, beta: float | np.ndarray, omega: float | np.ndarray):
def ell2cart_bektas(self, beta: float | NDArray, omega: float | NDArray) -> NDArray:
"""
Bektas 2015
:param beta:
@@ -281,14 +304,13 @@ class EllipsoidTriaxial:
return np.array([x, y, z])
def ell2cart_karney(self, beta: float | np.ndarray, lamb: float | np.ndarray) -> np.ndarray:
def ell2cart_karney(self, beta: float | NDArray, lamb: float | NDArray) -> NDArray:
"""
Karney 2025 Geographic Lib
:param beta:
:param lamb:
:return:
"""
e = sqrt(self.ax**2 - self.b**2) / self.ay
k = sqrt(self.ay**2 - self.b**2) / sqrt(self.ax**2 - self.b**2)
k_ = sqrt(self.ax**2 - self.ay**2) / sqrt(self.ax**2 - self.b**2)
X = self.ax * cos(lamb) * sqrt(k**2*cos(beta)**2+k_**2)
@@ -296,11 +318,12 @@ class EllipsoidTriaxial:
Z = self.b * sin(beta) * sqrt(k**2 + k_**2 * sin(lamb)**2)
return np.array([X, Y, Z])
def cart2ell(self, point, eps=1e-12, maxI = 100) -> tuple[float, float]:
def cart2ell(self, point: NDArray, eps: float = 1e-12, maxI: int = 100) -> Tuple[float, float]:
"""
Panou, Korakitis 2019 3f. (num)
:param point:
:param eps:
:param maxI:
:return:
"""
x, y, z = point
@@ -323,10 +346,10 @@ class EllipsoidTriaxial:
(self.b * self.Ee ** 2) / (2 * self.Ex) * sin(beta) * sin(2 * lamb) / sqrt(L)]])
N = J.T @ J
det = N[0,0] * N[1,1] - N[0,1] * N[1,0]
det = N[0, 0] * N[1, 1] - N[0, 1] * N[1, 0]
if abs(det) < eps:
det = eps
N_inv = 1 / det * np.array([[N[1,1], -N[0,1]], [-N[1,0], N[0,0]]])
N_inv = 1 / det * np.array([[N[1, 1], -N[0, 1]], [-N[1, 0], N[0, 0]]])
delta_ell = N_inv @ J.T @ delta_l
beta += delta_ell[0]
lamb += delta_ell[1]
@@ -344,7 +367,7 @@ class EllipsoidTriaxial:
return beta, lamb
def cart2ell_panou(self, point: np.ndarray) -> tuple[float, float]:
def cart2ell_panou(self, point: NDArray) -> Tuple[float, float]:
"""
Panou, Korakitis 2019 2f. (analytisch -> Näherung)
:param point: Punkt in kartesischen Koordinaten
@@ -371,7 +394,7 @@ class EllipsoidTriaxial:
# ---- Allgemeiner Fall -----
t1, t2 = self.func_t12(x, y, z)
t1, t2 = self.func_t12(point)
num_beta = max(t1 - self.b ** 2, 0)
den_beta = max(self.ay ** 2 - t1, 0)
@@ -401,7 +424,7 @@ class EllipsoidTriaxial:
return beta, lamb
def cart2ell_bektas(self, point, eps=1e-12, maxI = 100) -> tuple[float, float]:
def cart2ell_bektas(self, point: NDArray, eps: float = 1e-12, maxI: int = 100) -> Tuple[float, float]:
"""
Bektas 2015
:param point:
@@ -430,7 +453,7 @@ class EllipsoidTriaxial:
return phi, lamb
def geod2cart(self, phi: float | np.ndarray, lamb: float | np.ndarray, h: float) -> np.ndarray:
def geod2cart(self, phi: float | NDArray, lamb: float | NDArray, h: float) -> NDArray:
"""
Ligas 2012, 250
:param phi: geodätische Breite [rad]
@@ -444,7 +467,7 @@ class EllipsoidTriaxial:
zG = (v * (1-self.ex**2) + h) * sin(phi)
return np.array([xG, yG, zG])
def cart2geod(self, point: np.ndarray, mode: str = "ligas3", maxIter: int = 30, maxLoa: float = 0.005) -> tuple[float, float, float]:
def cart2geod(self, point: NDArray, mode: str = "ligas3", maxIter: int = 30, maxLoa: float = 0.005) -> Tuple[float, float, float]:
"""
Ligas 2012
:param mode: ligas1, ligas2, oder ligas3
@@ -513,7 +536,7 @@ class EllipsoidTriaxial:
return phi, lamb, h
def para2cart(self, u: float | np.ndarray, v: float | np.ndarray) -> np.ndarray:
def para2cart(self, u: float | NDArray, v: float | NDArray) -> NDArray:
"""
Panou, Korakitits 2020, 4
:param u: Parameter u
@@ -526,7 +549,7 @@ class EllipsoidTriaxial:
z = np.broadcast_to(z, np.shape(x))
return np.array([x, y, z])
def cart2para(self, point: np.ndarray) -> tuple[float, float]:
def cart2para(self, point: NDArray) -> Tuple[float, float]:
"""
Panou, Korakitits 2020, 4
:param point: Punkt in kartesischen Koordinaten
@@ -551,31 +574,31 @@ class EllipsoidTriaxial:
return u, v
def ell2para(self, beta: float, lamb: float) -> tuple[float, float]:
def ell2para(self, beta: float, lamb: float) -> Tuple[float, float]:
cart = self.ell2cart(beta, lamb)
return self.cart2para(cart)
def para2ell(self, u: float, v: float) -> tuple[float, float]:
def para2ell(self, u: float, v: float) -> Tuple[float, float]:
cart = self.para2cart(u, v)
return self.cart2ell(cart)
def para2geod(self, u: float, v: float, mode: str = "ligas3", maxIter: int = 30, maxLoa: float = 0.005) -> tuple[float, float, float]:
def para2geod(self, u: float, v: float, mode: str = "ligas3", maxIter: int = 30, maxLoa: float = 0.005) -> Tuple[float, float, float]:
cart = self.para2cart(u, v)
return self.cart2geod(cart, mode, maxIter, maxLoa)
def geod2para(self, phi: float, lamb: float, h: float) -> tuple[float, float]:
def geod2para(self, phi: float, lamb: float, h: float) -> Tuple[float, float]:
cart = self.geod2cart(phi, lamb, h)
return self.cart2para(cart)
def ell2geod(self, beta: float, lamb: float, mode: str = "ligas3", maxIter: int = 30, maxLoa: float = 0.005) -> tuple[float, float, float]:
def ell2geod(self, beta: float, lamb: float, mode: str = "ligas3", maxIter: int = 30, maxLoa: float = 0.005) -> Tuple[float, float, float]:
cart = self.ell2cart(beta, lamb)
return self.cart2geod(cart, mode, maxIter, maxLoa)
def geod2ell(self, phi: float, lamb: float, h: float) -> tuple[float, float]:
def geod2ell(self, phi: float, lamb: float, h: float) -> Tuple[float, float]:
cart = self.geod2cart(phi, lamb, h)
return self.cart2ell(cart)
def point_on(self, point: np.ndarray) -> bool:
def point_on(self, point: NDArray) -> bool:
"""
Test, ob ein Punkt auf dem Ellipsoid liegt.
:param point: kartesische 3D-Koordinaten
@@ -587,17 +610,17 @@ class EllipsoidTriaxial:
else:
return False
def cartonell(self, point: np.ndarray) -> tuple[np.ndarray, float, float, float]:
def cartonell(self, point: NDArray) -> NDArray:
"""
Berechnung des Lotpunktes auf einem Ellipsoiden
:param point: Punkt in kartesischen Koordinaten, der gelotet werden soll
:return: Lotpunkt in kartesischen Koordinaten, geodätische Koordinaten des Punktes
:return: Lotpunkt in kartesischen Koordinaten
"""
phi, lamb, h = self.cart2geod(point, "ligas3")
x, y, z = self. geod2cart(phi, lamb, 0)
return np.array([x, y, z]), phi, lamb, h
p = self. geod2cart(phi, lamb, 0)
return p
def cartellh(self, point: np.ndarray, h: float) -> np.ndarray:
def cartellh(self, point: NDArray, h: float) -> NDArray:
"""
Punkt auf Ellipsoid hoch loten
:param point: Punkt auf dem Ellipsoid
@@ -635,7 +658,7 @@ if __name__ == "__main__":
cart_geod = ell.geod2cart(geod[0], geod[1], geod[2])
diff_geod3 = np.linalg.norm(point - cart_geod, axis=-1)
diff_list.append([v_deg, u_deg, diff_ell, diff_para, diff_geod3]) #
diff_list.append([v_deg, u_deg, diff_ell, diff_para, diff_geod3])
diffs_ell.append([diff_ell])
diffs_para.append([diff_para])
diffs_geod.append([diff_geod3])