Näherungslösung GHA 2

GHA_triaxial/approx_gha1.py

@@ -1,12 +1,10 @@
 import numpy as np
-from numpy import sin, cos, arcsin, arccos, arctan2
 from ellipsoide import EllipsoidTriaxial
-import matplotlib.pyplot as plt
 from panou import louville_constant, func_sigma_ell, gha1_ana
 import plotly.graph_objects as go
 import winkelumrechnungen as wu
 
-def gha1(ell: EllipsoidTriaxial, p0: np.ndarray, alpha0: float, s: float, ds: int):
+def gha1(ell: EllipsoidTriaxial, p0: np.ndarray, alpha0: float, s: float, ds: float, all_points: bool = False) -> Tuple[NDArray, float] | Tuple[NDArray, float, NDArray]:
     l0 = louville_constant(ell, p0, alpha0)
     points = [p0]
     alphas = [alpha0]
@@ -17,10 +15,9 @@ def gha1(ell: EllipsoidTriaxial, p0: np.ndarray, alpha0: float, s: float, ds: in
             break
         p1 = points[-1]
         alpha1 = alphas[-1]
-        x1, y1, z1 = p1
+        sigma = func_sigma_ell(ell, p1, alpha1)
-        sigma = func_sigma_ell(ell, x1, y1, z1, alpha1)
         p2 = p1 + ds_step * sigma
-        p2, _, _, _ = ell.cartonell(p2)
+        p2 = ell.cartonell(p2)
         ds_step = np.linalg.norm(p2 - p1)
 
         points.append(p2)
@@ -30,7 +27,11 @@ def gha1(ell: EllipsoidTriaxial, p0: np.ndarray, alpha0: float, s: float, ds: in
         alpha2 = alpha1 + (l0 - l2) / dl_dalpha
         alphas.append(alpha2)
         s_curr += ds_step
+
+    if all_points:
         return points[-1], alphas[-1], np.array(points)
+    else:
+        return points[-1], alphas[-1]
 
 def show_points(points, p0, p1):
     fig = go.Figure()
@@ -57,7 +58,7 @@ if __name__ == '__main__':
     P0 = ell.para2cart(0, 0)
     alpha0 = wu.deg2rad(90)
     s = 1000000
-    P1_ana, alpha1_ana = gha1_ana(ell, P0, alpha0, s, 60, maxPartCircum=32)
+    P1_ana, alpha1_ana = gha1_ana(ell, P0, alpha0, s, maxM=60, maxPartCircum=32)
-    P1_app, alpha1_app, points = gha1(ell, P0, alpha0, s, 5000)
+    P1_app, alpha1_app, points = gha1(ell, P0, alpha0, s, ds=5000, all_points=True)
     show_points(points, P0, P1_ana)
     print(np.linalg.norm(P1_app - P1_ana))

GHA_triaxial/approx_gha2.py

@@ -0,0 +1,111 @@
+import numpy as np
+from numpy import arctan2
+from ellipsoide import EllipsoidTriaxial
+from panou import pq_ell
+from panou_2013_2GHA_num import gha2_num
+import plotly.graph_objects as go
+import winkelumrechnungen as wu
+from numpy.typing import NDArray
+from typing import Tuple
+
+def sigma2alpha(sigma: NDArray, point: NDArray) -> float:
+    """
+    Berechnung des Richtungswinkels an einem Punkt anhand der Ableitung zu den kartesischen Koordinaten
+    :param sigma: Ableitungsvektor ver kartesischen Koordinaten
+    :param point: Punkt
+    :return: Richtungswinkel
+    """
+    ""
+    p, q = pq_ell(ell, point)
+    P = float(p @ sigma)
+    Q = float(q @ sigma)
+
+    alpha = arctan2(P, Q)
+    return alpha
+
+def gha2(ell: EllipsoidTriaxial, p0: NDArray, p1: NDArray, ds: float, all_points: bool = False) -> Tuple[float, float, float] | Tuple[float, float, float, NDArray]:
+    """
+    Numerische Approximation für die zweite Hauptaufgabe
+    :param ell: Ellipsoid
+    :param p0: Startpunkt
+    :param p1: Endpunkt
+    :param ds: maximales Streckenelement
+    :param all_points: Alle Punkte ausgeben?
+    :return:
+    """
+    points = np.array([p0, p1])
+    while True:
+        new_points = []
+
+        for i in range(len(points)-1):
+            new_points.append(points[i])
+
+            pi = points[i] + 1/2 * (points[i+1] - points[i])
+            pi = ell.cartonell(pi)
+
+            new_points.append(pi)
+
+        new_points.append(points[-1])
+        points = np.array(new_points)
+
+        elements = np.array([np.linalg.norm(points[i] - points[i+1]) for i in range(len(points)-1)])
+
+        if np.average(elements) < ds:
+            break
+
+    p0i = ell.cartonell(p0 + ds/100 * (points[1] - p0) / np.linalg.norm(points[1] - p0))
+    sigma0 = (p0i - p0) / np.linalg.norm(p0i - p0)
+    alpha0 = sigma2alpha(sigma0, p0)
+
+    p1i = ell.cartonell(p1 - ds/100 * (p1 - points[-2]) / np.linalg.norm(p1 - points[-2]))
+    sigma1 = (p1 - p1i) / np.linalg.norm(p1 - p1i)
+    alpha1 = sigma2alpha(sigma1, p1)
+
+    s = np.sum(np.array([np.linalg.norm(points[i] - points[i+1]) for i in range(len(points)-1)]))
+
+    if all_points:
+        return alpha0, alpha1, s, np.array(points)
+    else:
+        return alpha0, alpha1, s
+
+def show_points(points: NDArray, points_app: NDArray, p0: NDArray, p1: NDArray):
+    fig = go.Figure()
+
+    fig.add_scatter3d(x=points[:, 0], y=points[:, 1], z=points[:, 2],
+                      mode='lines', line=dict(color="green", width=3), name="Analytisch")
+    fig.add_scatter3d(x=points_app[:, 0], y=points_app[:, 1], z=points_app[:, 2],
+                      mode='lines', line=dict(color="red", width=3), name="Approximiert")
+    fig.add_scatter3d(x=[p0[0]], y=[p0[1]], z=[p0[2]],
+                      mode='markers', marker=dict(color="black"), name="P0")
+    fig.add_scatter3d(x=[p1[0]], y=[p1[1]], z=[p1[2]],
+                      mode='markers', marker=dict(color="black"), name="P1")
+
+    fig.update_layout(
+        scene=dict(xaxis_title='X [km]',
+                   yaxis_title='Y [km]',
+                   zaxis_title='Z [km]',
+                   aspectmode='data'))
+
+    fig.show()
+
+
+if __name__ == '__main__':
+    ell = EllipsoidTriaxial.init_name("KarneyTest2024")
+
+    beta0, lamb0 = (0.2, 0.1)
+    P0 = ell.ell2cart(beta0, lamb0)
+    beta1, lamb1 = (0.7, 0.3)
+    P1 = ell.ell2cart(beta1, lamb1)
+
+    alpha0_app, alpha1_app, s_app, points = gha2(ell, P0, P1, ds=1e-4, all_points=True)
+
+    alpha0, alpha1, s, betas, lambs = gha2_num(ell, beta0, lamb0, beta1, lamb1, n=5000, all_points=True)
+    points_ana = []
+    for beta, lamb in zip(betas, lambs):
+        points_ana.append(ell.ell2cart(beta, lamb))
+    points_ana = np.array(points_ana)
+
+    show_points(points_ana, points, P0, P1)
+    print(f"Differenz s: {s_app - s} m")
+    print(f"Differenz alpha0: {wu.rad2deg(alpha0_app - alpha0)}°")
+    print(f"Differenz alpha1: {wu.rad2deg(alpha1_app - alpha1)}°")

GHA_triaxial/approx_louville.py

@@ -1,108 +0,0 @@
-import numpy as np
-from numpy import sin, cos, arcsin, arccos, arctan2
-from ellipsoide import EllipsoidTriaxial
-import matplotlib.pyplot as plt
-
-dbeta_dc = lambda ell, beta, lamb, alpha: -2 * ell.Ey**2 * sin(alpha)**2 * cos(beta) * sin(beta)
-dlamb_dc = lambda ell, beta, lamb, alpha: -2 * ell.Ee**2 * cos(alpha)**2 * sin(lamb) * cos(lamb)
-dalpha_dc = lambda ell, beta, lamb, alpha:  (2 * sin(alpha) * cos(alpha) *
-                                             (ell.Ey**2 * cos(beta)**2 + ell.Ee**2 * sin(lamb)**2))
-
-lamb2_sphere = lambda r, phi1, lamb1, a12, s: lamb1 + arctan2(sin(s/r) * sin(a12),
-                                                              cos(phi1) * cos(s/r) - sin(s/r) * cos(a12))
-phi2_sphere = lambda r, phi1, lamb1, a12, s: arcsin(sin(phi1) * cos(s/r) + cos(phi1) * sin(s/r) * cos(a12))
-
-a12_sphere = lambda phi1, lamb1, phi2, lamb2: arctan2(cos(phi2) * sin(lamb2 - lamb1),
-                                                      cos(phi1) * cos(phi2) -
-                                                      sin(phi1) * cos(phi2) * cos(lamb2 - lamb1))
-s_sphere = lambda r, phi1, lamb1, phi2, lamb2: r * arccos(sin(phi1) * sin(phi2) +
-                                                          cos(phi1) * cos(phi2) * cos(lamb2 - lamb1))
-
-louville = lambda beta, lamb, alpha: (ell.Ey**2 * cos(beta)**2 * sin(alpha)**2 -
-                                          ell.Ee**2 * sin(lamb)**2 * cos(alpha)**2)
-
-def points_approx_gha2(r: float, phi1: np.ndarray, lamb1: np.ndarray, phi2: np.ndarray, lamb2: np.ndarray, num: int = None, step_size: float = 10000):
-    s_approx = s_sphere(r, phi1, lamb1, phi2, lamb2)
-    if num is not None:
-        step_size = s_approx / (num+1)
-    a_approx = a12_sphere(phi1, lamb1, phi2, lamb2)
-
-    points = [np.array([phi1, lamb1, a_approx])]
-    current_s = step_size
-    while current_s < s_approx:
-        phi_n = phi2_sphere(r, phi1, lamb1, a_approx, current_s)
-        lamb_n = lamb2_sphere(r, phi1, lamb1, a_approx, current_s)
-        points.append(np.array([phi_n, lamb_n, a_approx]))
-        current_s += step_size
-    points.append(np.array([phi2, lamb2, a_approx]))
-    return points
-
-
-def num_update(ell: EllipsoidTriaxial, points, diffs):
-    for i, (beta, lamb, alpha) in enumerate(points):
-        dalpha = dalpha_dc(ell, beta, lamb, alpha)
-        if i == 0 or i == len(points) - 1:
-            grad = np.array([0, 0, dalpha])
-        else:
-            dbeta = dbeta_dc(ell, beta, lamb, alpha)
-            dlamb = dlamb_dc(ell, beta, lamb, alpha)
-            grad = np.array([dbeta, dlamb, dalpha])
-
-        delta = -diffs[i] * grad / np.dot(grad, grad)
-        points[i] += delta
-    return points
-
-
-def gha2(ell: EllipsoidTriaxial, p1: np.ndarray, p2: np.ndarray, maxI: int):
-    beta1, lamb1 = ell.cart2ell(p1)
-    beta2, lamb2 = ell.cart2ell(p2)
-    points = points_approx_gha2(ell.ax, beta1, lamb1, beta2, lamb2, 5)
-
-    for j in range(maxI):
-        constants = [louville(point[0], point[1], point[2]) for point in points]
-        mean_constant = np.mean(constants)
-        diffs = constants - mean_constant
-        if np.mean(np.abs(diffs)) > 10:
-            points = num_update(ell, points, diffs)
-        else:
-            break
-        for k in range(maxI):
-
-
-            last_diff_alpha = points[-2][-1] - points[-3][-1]
-            alpha_extrap = points[-2][-1] + last_diff_alpha
-            if abs(alpha_extrap - points[-1][-1]) > 0.0005:
-                pass
-            else:
-                break
-            pass
-    pass
-    return points
-
-def show_points(ell: EllipsoidTriaxial, points):
-    points_cart = []
-    for point in points:
-        points_cart.append(ell.ell2cart(point[0], point[1]))
-    points_cart = np.array(points_cart)
-
-    fig = plt.figure()
-    ax = fig.add_subplot(111, projection='3d')
-
-    ax.plot(points_cart[:, 0], points_cart[:, 1], points_cart[:, 2])
-    ax.scatter(points_cart[:, 0], points_cart[:, 1], points_cart[:, 2])
-
-    ax.set_xlabel('X')
-    ax.set_ylabel('Y')
-    ax.set_zlabel('Z')
-
-    plt.show()
-
-
-if __name__ == "__main__":
-    ell = EllipsoidTriaxial.init_name("Eitschberger1978")
-    p1 = np.array([4189000, 812000, 4735000])
-    p2 = np.array([4090000, 868000, 4808000])
-    p1, phi1, lamb1, h1 = ell.cartonell(p1)
-    p2, phi2, lamb2, h2 = ell.cartonell(p2)
-    points = gha2(ell, p1, p2, 10)
-    show_points(ell, points)

GHA_triaxial/panou.py

@@ -8,21 +8,22 @@ from math import comb
 import GHA_triaxial.numeric_examples_panou as ne_panou
 import GHA_triaxial.numeric_examples_karney as ne_karney
 from ellipsoide import EllipsoidTriaxial
-from typing import Callable
+from typing import Callable, Tuple, List
+from numpy.typing import NDArray
 
 
-def pq_ell(ell: EllipsoidTriaxial, x: float, y: float, z: float) -> tuple[np.ndarray, np.ndarray]:
+def pq_ell(ell: EllipsoidTriaxial, point: NDArray) -> Tuple[NDArray, NDArray]:
     """
     Berechnung von p und q in elliptischen Koordinaten
     Panou, Korakitits 2019
-    :param x: x
+    :param ell: Ellipsoid
-    :param y: y
+    :param point: Punkt
-    :param z: z
     :return: p und q
     """
-    n = ell.func_n(x, y, z)
+    x, y, z = point
+    n = ell.func_n(point)
 
-    beta, lamb = ell.cart2ell(np.array([x, y, z]))
+    beta, lamb = ell.cart2ell(point)
     B = ell.Ex ** 2 * cos(beta) ** 2 + ell.Ee ** 2 * sin(beta) ** 2
     L = ell.Ex ** 2 - ell.Ee ** 2 * cos(lamb) ** 2
 
@@ -49,7 +50,7 @@ def buildODE(ell: EllipsoidTriaxial) -> Callable:
     :param ell: Ellipsoid
     :return: DGL-System
     """
-    def ODE(s: float, v: np.ndarray) -> np.ndarray:
+    def ODE(s: float, v: NDArray) -> NDArray:
         """
         DGL-System
         :param s: unabhängige Variable
@@ -58,7 +59,7 @@ def buildODE(ell: EllipsoidTriaxial) -> Callable:
         """
         x, dxds, y, dyds, z, dzds = v
 
-        H = ell.func_H(x, y, z)
+        H = ell.func_H(np.array([x, y, z]))
         h = dxds**2 + 1/(1-ell.ee**2)*dyds**2 + 1/(1-ell.ex**2)*dzds**2
 
         ddx = -(h/H)*x
@@ -68,7 +69,7 @@ def buildODE(ell: EllipsoidTriaxial) -> Callable:
         return np.array([dxds, ddx, dyds, ddy, dzds, ddz])
     return ODE
 
-def gha1_num(ell: EllipsoidTriaxial, point: np.ndarray, alpha0: float, s: float, num: int) -> tuple[np.ndarray, float, list]:
+def gha1_num(ell: EllipsoidTriaxial, point: NDArray, alpha0: float, s: float, num: int, all_points: bool = False) -> Tuple[NDArray, float] | Tuple[NDArray, float, List]:
     """
     Panou, Korakitits 2019
     :param ell:
@@ -76,12 +77,14 @@ def gha1_num(ell: EllipsoidTriaxial, point: np.ndarray, alpha0: float, s: float,
     :param alpha0:
     :param s:
     :param num:
+    :param all_points:
     :return:
     """
     phi, lam, _ = ell.cart2geod(point, "ligas3")
-    x0, y0, z0 = ell.geod2cart(phi, lam, 0)
+    p0 = ell.geod2cart(phi, lam, 0)
+    x0, y0, z0 = p0
 
-    p, q = pq_ell(ell, x0, y0, z0)
+    p, q = pq_ell(ell, p0)
     dxds0 = p[0] * sin(alpha0) + q[0] * cos(alpha0)
     dyds0 = p[1] * sin(alpha0) + q[1] * cos(alpha0)
     dzds0 = p[2] * sin(alpha0) + q[2] * cos(alpha0)
@@ -93,7 +96,9 @@ def gha1_num(ell: EllipsoidTriaxial, point: np.ndarray, alpha0: float, s: float,
     _, werte = rk.rk4(ode, 0, v_init, s, num)
     x1, dx1ds, y1, dy1ds, z1, dz1ds = werte[-1]
 
-    p1, q1 = pq_ell(ell, x1, y1, z1)
+    point1 = np.array([x1, y1, z1])
+
+    p1, q1 = pq_ell(ell, point1)
     sigma = np.array([dx1ds, dy1ds, dz1ds])
     P = float(p1 @ sigma)
     Q = float(q1 @ sigma)
@@ -103,21 +108,23 @@ def gha1_num(ell: EllipsoidTriaxial, point: np.ndarray, alpha0: float, s: float,
     if alpha1 < 0:
         alpha1 += 2 * np.pi
 
-    return np.array([x1, y1, z1]), alpha1, werte
+    if all_points:
+        return point1, alpha1, werte
+    else:
+        return point1, alpha1
 
 # ---------------------------------------------------------------------------------------------------------------------
 
-def pq_para(ell: EllipsoidTriaxial, x: float, y: float, z: float) -> tuple[np.ndarray, np.ndarray]:
+def pq_para(ell: EllipsoidTriaxial, point: NDArray) -> Tuple[NDArray, NDArray]:
     """
     Berechnung von p und q in parametrischen Koordinaten
     Panou, Korakitits 2020
-    :param x: x
+    :param ell: Ellipsoid
-    :param y: y
+    :param point: Punkt
-    :param z: z
     :return: p und q
     """
-    n = ell.func_n(x, y, z)
+    n = ell.func_n(point)
-    u, v = ell.cart2para(np.array([x, y, z]))
+    u, v = ell.cart2para(point)
 
     # 41-47
     G = sqrt(1 - ell.ex ** 2 * cos(u) ** 2 - ell.ee ** 2 * sin(u) ** 2 * sin(v) ** 2)
@@ -136,7 +143,7 @@ def pq_para(ell: EllipsoidTriaxial, x: float, y: float, z: float) -> tuple[np.nd
 
     return p, q
 
-def gha1_ana_step(ell: ellipsoide.EllipsoidTriaxial, point, alpha0, s, maxM):
+def gha1_ana_step(ell: EllipsoidTriaxial, point: NDArray, alpha0: float, s: float, maxM: int) -> Tuple[NDArray, float]:
     """
     Panou, Korakitits 2020, 5ff.
     :param ell:
@@ -153,7 +160,7 @@ def gha1_ana_step(ell: ellipsoide.EllipsoidTriaxial, point, alpha0, s, maxM):
     y_m = [y]
     z_m = [z]
 
-    p, q = pq_para(ell, x, y, z)
+    p, q = pq_para(ell, point)
 
     # 48-50
     x_m.append(p[0] * sin(alpha0) + q[0] * cos(alpha0))
@@ -208,7 +215,8 @@ def gha1_ana_step(ell: ellipsoide.EllipsoidTriaxial, point, alpha0, s, maxM):
     for c in reversed(c_m):
         z_s = z_s * s + c
 
-    p_s, q_s = pq_para(ell, x_s, y_s, z_s)
+    p1 = np.array([x_s, y_s, z_s])
+    p_s, q_s = pq_para(ell, p1)
 
     # 57-59
     dx_s = 0
@@ -234,10 +242,10 @@ def gha1_ana_step(ell: ellipsoide.EllipsoidTriaxial, point, alpha0, s, maxM):
     if alpha1 < 0:
         alpha1 += 2 * np.pi
 
-    return np.array([x_s, y_s, z_s]), alpha1
+    return p1, alpha1
 
 
-def gha1_ana(ell: EllipsoidTriaxial, point: np.ndarray, alpha0: float, s: float, maxM: int, maxPartCircum: int = 4) -> tuple[np.ndarray, float]:
+def gha1_ana(ell: EllipsoidTriaxial, point: NDArray, alpha0: float, s: float, maxM: int, maxPartCircum: int = 4) -> Tuple[NDArray, float]:
     if s > np.pi / maxPartCircum * ell.ax:
         s /= 2
         point_step, alpha_step = gha1_ana(ell, point, alpha0, s, maxM, maxPartCircum)
@@ -251,14 +259,14 @@ def gha1_ana(ell: EllipsoidTriaxial, point: np.ndarray, alpha0: float, s: float,
 
     return point_end, alpha_end
 
-def alpha_para2ell(ell: EllipsoidTriaxial, u: float, v: float, alpha_para: float) -> tuple[float, float, float]:
+def alpha_para2ell(ell: EllipsoidTriaxial, u: float, v: float, alpha_para: float) -> Tuple[float, float, float]:
-    x, y, z = ell.para2cart(u, v)
+    point = ell.para2cart(u, v)
     beta, lamb = ell.para2ell(u, v)
 
-    p_para, q_para = pq_para(ell, x, y, z)
+    p_para, q_para = pq_para(ell, point)
     sigma_para = p_para * sin(alpha_para) + q_para * cos(alpha_para)
 
-    p_ell, q_ell = pq_ell(ell, x, y, z)
+    p_ell, q_ell = pq_ell(ell, point)
     alpha_ell = arctan2(p_ell @ sigma_para, q_ell @ sigma_para)
     sigma_ell = p_ell * sin(alpha_ell) + q_ell * cos(alpha_ell)
 
@@ -267,49 +275,42 @@ def alpha_para2ell(ell: EllipsoidTriaxial, u: float, v: float, alpha_para: float
 
     return beta, lamb, alpha_ell
 
-def alpha_ell2para(ell: EllipsoidTriaxial, beta: float, lamb: float, alpha_ell: float) -> tuple[float, float, float]:
+def alpha_ell2para(ell: EllipsoidTriaxial, beta: float, lamb: float, alpha_ell: float) -> Tuple[float, float, float]:
-    x, y, z = ell.ell2cart(beta, lamb)
+    point = ell.ell2cart(beta, lamb)
     u, v = ell.ell2para(beta, lamb)
 
-    p_ell, q_ell = pq_ell(ell, x, y, z)
+    p_ell, q_ell = pq_ell(ell, point)
     sigma_ell = p_ell * sin(alpha_ell) + q_ell * cos(alpha_ell)
 
-    p_para, q_para = pq_para(ell, x, y, z)
+    p_para, q_para = pq_para(ell, point)
     alpha_para = arctan2(p_para @ sigma_ell, q_para @ sigma_ell)
     sigma_para = p_para * sin(alpha_para) + q_para * cos(alpha_para)
 
     if np.linalg.norm(sigma_para - sigma_ell) > 1e-12:
         raise Exception("Alpha Umrechnung fehlgeschlagen")
-        print("Alpha Umrechnung fehlgeschlagen:", np.linalg.norm(sigma_para - sigma_ell))
 
     return u, v, alpha_para
 
-def func_sigma_ell(ell, x, y, z, alpha):
+def func_sigma_ell(ell: EllipsoidTriaxial, point: NDArray, alpha: float) -> NDArray:
-    p, q = pq_ell(ell, x, y, z)
+    p, q = pq_ell(ell, point)
     sigma = p * sin(alpha) + q * cos(alpha)
     return sigma
 
-def func_sigma_para(ell, x, y, z, alpha):
+def func_sigma_para(ell: EllipsoidTriaxial, point: NDArray, alpha: float) -> NDArray:
-    p, q = pq_para(ell, x, y, z)
+    p, q = pq_para(ell, point)
     sigma = p * sin(alpha) + q * cos(alpha)
     return sigma
 
 
-def louville_constant(ell: EllipsoidTriaxial, p0: np.ndarray, alpha: float) -> float:
+def louville_constant(ell: EllipsoidTriaxial, p0: NDArray, alpha: float) -> float:
     beta, lamb = ell.cart2ell(p0)
     l = ell.Ey**2 * cos(beta)**2 * sin(alpha)**2 - ell.Ee**2 * sin(lamb)**2 * cos(alpha)**2
-    # x, y, z = p0
-    # t1, t2 = ell.func_t12(x, y, z)
-    # l_cart = ell.ay**2 - (t1 * sin(alpha)**2 + t2 * cos(alpha)**2)
-    # if abs(l - l_cart) > 1e-12:
-    #     # raise Exception("Louville constant fehlgeschlagen")
-    #     print("Diff zwischen constant:", abs(l - l_cart))
     return l
 
-def louville_l2c(ell, l):
+def louville_l2c(ell: EllipsoidTriaxial, l: float) -> float:
     return sqrt((l + ell.Ee**2) / ell.Ex**2)
 
-def louville_c2l(ell, c):
+def louville_c2l(ell: EllipsoidTriaxial, c: float) -> float:
     return ell.Ex**2 * c**2 - ell.Ee**2
 
 
@@ -322,7 +323,7 @@ if __name__ == "__main__":
     #     beta0, lamb0, beta1, lamb1, _, alpha0_ell, alpha1_ell, s = example
     #     P0 = ell.ell2cart(beta0, lamb0)
     #
-    #     P1_num, alpha1_num, _ = gha1_num(ell, P0, alpha0_ell, s, 100)
+    #     P1_num, alpha1_num = gha1_num(ell, P0, alpha0_ell, s, 100)
     #     beta1_num, lamb1_num = ell.cart2ell(P1_num)
     #
     #     _, _, alpha0_para = alpha_ell2para(ell, beta0, lamb0, alpha0_ell)
@@ -342,7 +343,7 @@ if __name__ == "__main__":
         beta0, lamb0, alpha0_ell, beta1, lamb1, alpha1_ell, s = example
         P0 = ell.ell2cart(beta0, lamb0)
 
-        P1_num, alpha1_num, _ = gha1_num(ell, P0, alpha0_ell, s, 5000)
+        P1_num, alpha1_num = gha1_num(ell, P0, alpha0_ell, s, 5000)
         beta1_num, lamb1_num = ell.cart2ell(P1_num)
 
         try:
@@ -357,5 +358,3 @@ if __name__ == "__main__":
     mask_360 = (diffs_karney > 359) & (diffs_karney < 361)
     diffs_karney[mask_360] = np.abs(diffs_karney[mask_360] - 360)
     print(diffs_karney)
-
-    pass

GHA_triaxial/panou_2013_2GHA_num.py

@@ -4,9 +4,13 @@ import runge_kutta as rk
 import GHA_triaxial.numeric_examples_karney as ne_karney
 import GHA_triaxial.numeric_examples_panou as ne_panou
 import winkelumrechnungen as wu
+from typing import Tuple
+from numpy.typing import NDArray
 
 # Panou 2013
-def gha2_num(ell: EllipsoidTriaxial, beta_1, lamb_1, beta_2, lamb_2, n=16000, epsilon=10**-12, iter_max=30):
+def gha2_num(ell: EllipsoidTriaxial, beta_1: float, lamb_1: float, beta_2: float, lamb_2: float,
+             n: int = 16000, epsilon: float = 10**-12, iter_max: int = 30, all_points: bool = False
+             ) -> Tuple[float, float, float]| Tuple[float, float, float, NDArray, NDArray]:
     """
 
     :param ell: triaxiales Ellipsoid
@@ -17,6 +21,7 @@ def gha2_num(ell: EllipsoidTriaxial, beta_1, lamb_1, beta_2, lamb_2, n=16000, ep
     :param n: Anzahl Schritte
     :param epsilon:
     :param iter_max: Maximale Anzhal Iterationen
+    :param all_points:
     :return:
     """
 
@@ -25,7 +30,6 @@ def gha2_num(ell: EllipsoidTriaxial, beta_1, lamb_1, beta_2, lamb_2, n=16000, ep
     def arccot(x):
         return np.arctan2(1.0, x)
 
-
     def BETA_LAMBDA(beta, lamb):
 
         BETA = (ell.ay**2 * np.sin(beta)**2 + ell.b**2 * np.cos(beta)**2) / (ell.Ex**2 - ell.Ey**2 * np.sin(beta)**2)
@@ -60,7 +64,6 @@ def gha2_num(ell: EllipsoidTriaxial, beta_1, lamb_1, beta_2, lamb_2, n=16000, ep
         G_beta_lamb = - LAMBDA_ * ell.Ey**2 * np.sin(2*beta)
         G_lamb_lamb = LAMBDA__ * (ell.Ey**2 * np.cos(beta)**2 + ell.Ee**2 * np.sin(lamb)**2) + 2 * LAMBDA_ * ell.Ee**2 * np.sin(2*lamb) + 2 * LAMBDA * ell.Ee**2 * np.cos(2*lamb)
 
-
         return (BETA, LAMBDA, E, G,
                 BETA_, LAMBDA_, BETA__, LAMBDA__,
                 E_beta, E_lamb, G_beta, G_lamb,
@@ -244,15 +247,21 @@ def gha2_num(ell: EllipsoidTriaxial, beta_1, lamb_1, beta_2, lamb_2, n=16000, ep
             + (ell.Ee**2 / ell.Ex**2) * np.cos(lamb0) ** 2 * np.cos(alpha_1) ** 2
         )
 
+        if all_points:
             return alpha_1, alpha_2, s, beta_arr, lamb_arr
+        else:
+            return alpha_1, alpha_2, s
 
-    if lamb_1 == lamb_2:
+    else: # lamb_1 == lamb_2
 
         N = n
         dbeta = beta_2 - beta_1
 
         if abs(dbeta) < 10**-15:
+            if all_points:
                 return 0, 0, 0, np.array([]), np.array([])
+            else:
+                return 0, 0, 0
 
         lamb_0 = 0
 
@@ -369,7 +378,10 @@ def gha2_num(ell: EllipsoidTriaxial, beta_1, lamb_1, beta_2, lamb_2, n=16000, ep
         else:
             s = np.trapz(integrand, dx=h)
 
+        if all_points:
             return alpha_1, alpha_2, s, beta_arr, lamb_arr
+        else:
+            return alpha_1, alpha_2, s
 
 
 if __name__ == "__main__":
@@ -390,7 +402,6 @@ if __name__ == "__main__":
     # a1, a2, s = gha2_num(ell, beta1, lamb1, beta2, lamb2, n=5000)
     # print(s)
 
-
     # ell = EllipsoidTriaxial.init_name("BursaSima1980round")
     # diffs_panou = []
     # examples_panou = ne_panou.get_random_examples(4)
@@ -421,8 +432,4 @@ if __name__ == "__main__":
     # diffs_karney = np.array(diffs_karney)
     # print(diffs_karney)
 
-
     pass
-
-
-

dashboard.py

@@ -150,7 +150,6 @@ def figure_lines(fig, line, color):
     return fig
 
 
-
 app.layout = html.Div(
     style={"fontFamily": "Arial", "padding": "5px", "width": "70%", "margin-left": "auto"},
     children=[
@@ -254,7 +253,6 @@ def fill_inputs_from_dropdown(selected_ell):
     if not selected_ell:
         return None, None, None
 
-
     ell = EllipsoidTriaxial.init_name(selected_ell)
     ax = ell.ax
     ay = ell.ay
@@ -408,14 +406,14 @@ def calc_and_plot(n1, n2,
         alpha_rad = wu.deg2rad(float(a_deg))
         s_val = float(s)
 
-        p1 = tuple(map(float, ell.ell2cart(beta_rad, lamb_rad)))
+        p1 = ell.ell2cart(beta_rad, lamb_rad)
         out1 = []
 
         if "analytisch" in method1:
             # ana
-            (x2, y2, z2), alpha2 = gha1_ana(ell, p1, alpha_rad, s_val, 70)
+            p2_ana, alpha2 = gha1_ana(ell, p1, alpha_rad, s_val, 70)
-            p2_ana = (float(x2), float(y2), float(z2))
+            x2, y2, z2 = p2_ana
-            beta2, lamb2 = ell.cart2ell([x2, y2, z2])
+            beta2, lamb2 = ell.cart2ell(p2_ana)
 
             # out1 += f"kartesisch: x₂={p2[0]:.5f} m, y₂={p2[1]:.5f} m, z₂={p2[2]:.5f} m; ellipsoidisch: {aus.gms("β₂", beta2, 5)}, {aus.gms("λ₂", lamb2, 5)},"
             out1.append(
@@ -430,8 +428,7 @@ def calc_and_plot(n1, n2,
 
         if "numerisch" in method1:
             # num
-            (x1, y1, z1), alpha1, werte = gha1_num(ell, p1, alpha_rad, s_val, 10000)
+            p2_num, alpha1, werte = gha1_num(ell, p1, alpha_rad, s_val, 10000, all_points=True)
-            p2_num = x1, y1, z1
             beta2_num, lamb2_num = ell.cart2ell(p2_num)
 
             out1.append(
@@ -448,7 +445,6 @@ def calc_and_plot(n1, n2,
             for x1, _, y1, _, z1, _ in werte:
                 geo_line_num1.append([x1, y1, z1])
 
-
         if "stochastisch" in method1:
             # stoch
             p2_stoch = "noch nicht implementiert.."
@@ -488,15 +484,14 @@ def calc_and_plot(n1, n2,
             alpha_1, alpha_2, s12, beta_arr, lamb_arr = gha2_num(
                 ell,
                 np.deg2rad(float(beta21)), np.deg2rad(float(lamb21)),
-                np.deg2rad(float(beta22)), np.deg2rad(float(lamb22))
+                np.deg2rad(float(beta22)), np.deg2rad(float(lamb22)),
+                all_points=True
             )
             geo_line_num = []
             for beta, lamb in zip(beta_arr, lamb_arr):
                 point = ell.ell2cart(beta, lamb)
                 geo_line_num.append(point)
 
-
-
             out2.append(
                 html.Div([
                     html.Strong("Numerisch: "),
@@ -504,7 +499,6 @@ def calc_and_plot(n1, n2,
                 ])
             )
 
-
         if "stochastisch" in method2:
             # stoch
             a_stoch = "noch nicht implementiert.."
@@ -525,8 +519,6 @@ def calc_and_plot(n1, n2,
             fig = figure_lines(fig, geo_line_num, "#ff8c00")
         fig = figure_points(fig, [("P1", p1, "black"), ("P2", p2, "red")])
         
-
-        
         return "", out2, fig
 
     return no_update, no_update, no_update

ellipsoide.py

@@ -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
@@ -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)
+        p = self. geod2cart(phi, lamb, 0)
-        return np.array([x, y, z]), phi, lamb, h
+        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])