Abgabe fertig

nicht abgeben/GHA_biaxial/bessel.py

@@ -0,0 +1,36 @@
+from typing import Tuple
+
+import scipy as sp
+from ellipsoid_biaxial import EllipsoidBiaxial
+from numpy import *
+
+
+def gha1(re: EllipsoidBiaxial, phi0: float, lamb0: float, alpha0:float, s: float) -> Tuple[float, float, float]:
+    """
+    Berechnung der 1.GHA auf einem Rotationsellipsoid nach Bessel
+    :param re:
+    :param phi0:
+    :param lamb0:
+    :param alpha0:
+    :param s:
+    :return:
+    """
+    psi0 = re.phi2psi(phi0)
+    clairant = arcsin(cos(psi0) * sin(alpha0))
+    sigma0 = arcsin(sin(psi0) / cos(clairant))
+
+    sqrt_sigma = lambda sigma: sqrt(1 + re.e_ ** 2 * cos(clairant) ** 2 * sin(sigma) ** 2)
+    int_sqrt_sigma = lambda sigma: sp.integrate.quad(sqrt_sigma, sigma0, sigma)[0]
+
+    f_sigma1_i = lambda sigma1_i: (int_sqrt_sigma(sigma1_i) - s / re.b)
+
+    sigma1_0 = sigma0 + s / re.a
+    sigma1 = sp.optimize.newton(f_sigma1_i, sigma1_0)
+    psi1 = arcsin(cos(clairant) * sin(sigma1))
+    phi1 = re.psi2phi(psi1)
+    alpha1 = arcsin(sin(clairant) / cos(psi1))
+
+    f_d_lambda = lambda sigma: sin(clairant) * sqrt_sigma(sigma) / (1 - cos(clairant) ** 2 * sin(sigma) ** 2)
+    d_lambda = sqrt(1-re.e**2) * sp.integrate.quad(f_d_lambda, sigma0, sigma1)[0]
+    lamb1 = lamb0 + d_lambda
+    return phi1, lamb1, alpha1

nicht abgeben/GHA_biaxial/gauss.py

@@ -0,0 +1,101 @@
+from typing import Tuple
+
+from ellipsoid_biaxial import EllipsoidBiaxial
+from numpy import arctan, cos, sin, sqrt, tan
+
+
+def gha1(re: EllipsoidBiaxial, phi0: float, lamb0: float, alpha0: float, s: float, eps: float = 1e-12) -> Tuple[float, float, float]:
+    """
+    Berechnung der 1. Geodätische Hauptaufgabe nach Gauß´schen Mittelbreitenformeln
+    :param re: Klasse Ellipsoid
+    :param phi0: Breite Punkt 0
+    :param lamb0: Länge Punkt 0
+    :param alpha0: Azimut der geodätischen Linie in Punkt 1
+    :param s: Strecke zu Punkt 1
+    :param eps: Abbruchkriterium für Winkelgrößen
+    :return: Breite, Länge, Azimut von Punkt 21
+    """
+    t = lambda phi: tan(phi)
+    eta = lambda phi: sqrt(re.e_ ** 2 * cos(phi) ** 2)
+
+    F1 = lambda alpha, phi, s: 1 + (2 + 3 * t(phi) ** 2 + 2 * eta(phi) ** 2) / (24 * re.N(phi) ** 2) * sin(alpha) ** 2 * s ** 2 \
+                               + (t(phi)**2 - 1) * eta(phi) ** 2 / (8 * re.N(phi) ** 2) * cos(alpha) ** 2 * s ** 2
+
+    F2 = lambda alpha, phi, s: 1 + t(phi) ** 2 / (24 * re.N(phi) ** 2) * sin(alpha) ** 2 * s ** 2 \
+                               - (1 + eta(phi)**2 - 9 * eta(phi)**2 * t(phi)**2) / (24 * re.N(phi) ** 2) * cos(alpha) ** 2 * s ** 2
+
+    F3 = lambda alpha, phi, s: 1 + (1 + eta(phi) ** 2) / (12 * re.N(phi) ** 2) * sin(alpha) ** 2 * s ** 2 \
+                               + (3 + 8 * eta(phi)**2) / (24 * re.N(phi) ** 2) * cos(alpha) ** 2 * s ** 2
+
+    phi1_i = lambda alpha, phi: phi0 + cos(alpha) / re.M(phi) * s * F1(alpha, phi, s)
+    lamb1_i = lambda alpha, phi: lamb0 + sin(alpha) / (re.N(phi) * cos(phi)) * s * F2(alpha, phi, s)
+    alpha1_i = lambda alpha, phi: alpha0 + sin(alpha) * tan(phi) / re.N(phi) * s * F3(alpha, phi, s)
+
+    phi_m_i = lambda phi1: (phi0 + phi1) / 2
+    alpha_m_i = lambda alpha1: (alpha0 + alpha1) / 2
+
+    phi_m = []
+    alpha_m = []
+    phi1 = []
+    lamb1 = []
+    alpha1 = []
+
+    # 1. Näherung für P1
+    phi1.append(phi0 + cos(alpha0) / re.M(phi0) * s)
+    lamb1.append(lamb0 + sin(alpha0) / (re.N(phi0) * cos(phi0)) * s)
+    alpha1.append(alpha0 + sin(alpha0) * tan(phi0) / re.N(phi0) * s)
+
+    while True:
+        # Berechnug P_m durch Mittelbildung
+        phi_m.append(phi_m_i(phi1[-1]))
+        alpha_m.append(alpha_m_i(alpha1[-1]))
+        # Berechnung P1
+        phi1.append(phi1_i(alpha_m[-1], phi_m[-1]))
+        lamb1.append(lamb1_i(alpha_m[-1], phi_m[-1]))
+        alpha1.append(alpha1_i(alpha_m[-1], phi_m[-1]))
+
+        # Abbruchkriterium
+        if abs(phi1[-2] - phi1[-1]) < eps and \
+           abs(lamb1[-2] - lamb1[-1]) < eps and \
+           abs(alpha1[-2] - alpha1[-1]) < eps:
+            break
+    return phi1[-1], lamb1[-1], alpha1[-1]
+
+
+def gha2(re: EllipsoidBiaxial, phi0: float, lamb0: float, phi1: float, lamb1: float):
+    """
+    Berechnung der 2. Geodätische Hauptaufgabe nach Gauß´schen Mittelbreitenformeln
+    :param re: Klasse Ellipsoid
+    :param phi0: Breite Punkt 1
+    :param lamb0: Länge Punkt 1
+    :param phi1: Breite Punkt 2
+    :param lamb1: Länge Punkt 2
+    :return: Länge der geodätischen Linie, Azimut von P1 nach P2, Azimut von P2 nach P1
+    """
+
+    t = lambda phi: tan(phi)
+    eta = lambda phi: sqrt(re.e_ ** 2 * cos(phi) ** 2)
+
+    phi_0 = (phi0 + phi1) / 2
+    d_phi = phi1 - phi0
+    d_lambda = lamb1 - lamb0
+
+    f_A = lambda phi: (2 + 3*t(phi)**2 + 2*eta(phi)**2) / 24
+    f_B = lambda phi: ((t(phi)**2 - 1) * eta(phi)**2) / 8
+    # f_C = lambda phi: (t(phi)**2) / 24
+    f_D = lambda phi: (1 + eta(phi)**2 - 9 * eta(phi)**2 * t(phi)**2) / 24
+
+    F1 = lambda phi: d_phi * re.M(phi) * (1 - f_A(phi) * d_lambda ** 2 * cos(phi) ** 2 -
+                                          f_B(phi) * d_phi ** 2 / re.V(phi) ** 4)
+    F2 = lambda phi: d_lambda * re.N(phi) * cos(phi) * (1 - 1 / 24 * d_lambda ** 2 * sin(phi) ** 2 +
+                                                           f_D(phi) * d_phi ** 2 / re.V(phi) ** 4)
+
+    s = sqrt(F1(phi_0) ** 2 + F2(phi_0) ** 2)
+    A_0 = arctan(F2(phi_0) / F1(phi_0))
+    d_A = d_lambda * sin(phi_0) * (1 + (1 + eta(phi_0) ** 2) / 12 * s ** 2 * sin(A_0) ** 2 / re.N(phi_0) ** 2 +
+                                      (3 + 8 * eta(phi_0) ** 2) / 24 * s ** 2 * cos(A_0) ** 2 / re.N(phi_0) ** 2)
+
+    alpha0 = A_0 - d_A / 2
+    alpha1 = A_0 + d_A / 2
+
+    return alpha0, alpha1, s

nicht abgeben/GHA_biaxial/rk.py

@@ -0,0 +1,33 @@
+from typing import Tuple
+
+import numpy as np
+from ellipsoid_biaxial import EllipsoidBiaxial
+from numpy import cos, sin, tan
+from numpy.typing import NDArray
+
+import runge_kutta as rk
+
+
+def gha1(re: EllipsoidBiaxial, phi0: float, lamb0: float, alpha0: float, s: float, num: int) -> Tuple[float, float, float]:
+    """
+    Berechnung der 1. GHA auf einem Rotationsellipsoid mittels RK4
+    :param re:
+    :param phi0:
+    :param lamb0:
+    :param alpha0:
+    :param s:
+    :param num:
+    :return:
+    """
+    def buildODE():
+        def ODE(s: float, v: NDArray):
+            phi, lam, A = v
+            V = re.V(phi)
+            dphi = cos(A) * V ** 3 / re.c
+            dlam = sin(A) * V / (cos(phi) * re.c)
+            dA = tan(phi) * sin(A) * V / re.c
+            return np.array([dphi, dlam, dA])
+        return ODE
+
+    _, funktionswerte = rk.rk4(buildODE(), 0, np.array([phi0, lamb0, alpha0]), s, num)
+    return funktionswerte[-1][0], funktionswerte[-1][1], funktionswerte[-1][2]

nicht abgeben/Tests/alpha_conversion_test.ipynb

@@ -0,0 +1,101 @@
+{
+ "cells": [
+  {
+   "metadata": {},
+   "cell_type": "code",
+   "source": [
+    "%load_ext autoreload\n",
+    "%autoreload 2"
+   ],
+   "id": "a78faf7f4883772f",
+   "outputs": [],
+   "execution_count": null
+  },
+  {
+   "metadata": {},
+   "cell_type": "code",
+   "source": [
+    "%reload_ext autoreload\n",
+    "%autoreload 2\n",
+    "import numpy as np\n",
+    "\n",
+    "import winkelumrechnungen as wu\n",
+    "from GHA_triaxial.utils import alpha_ell2para, alpha_para2ell\n",
+    "from ellipsoid_triaxial import EllipsoidTriaxial"
+   ],
+   "id": "46aa84a937fea491",
+   "outputs": [],
+   "execution_count": null
+  },
+  {
+   "metadata": {},
+   "cell_type": "code",
+   "source": [
+    "ell = EllipsoidTriaxial.init_name(\"KarneyTest2024\")\n",
+    "diffs = []\n",
+    "for beta_deg in range(-90, 91, 15):\n",
+    "    for lamb_deg in range(-180, 180, 15):\n",
+    "        for alpha_deg in range(0, 360, 15):\n",
+    "            beta = wu.deg2rad(beta_deg)\n",
+    "            lamb = wu.deg2rad(lamb_deg)\n",
+    "            u, v = ell.ell2para(beta, lamb)\n",
+    "            alpha = wu.deg2rad(alpha_deg)\n",
+    "\n",
+    "            alpha_para_1, *_ = alpha_ell2para(ell, beta, lamb, alpha)\n",
+    "            alpha_ell_1, *_ = alpha_para2ell(ell, u, v, alpha_para_1)\n",
+    "            diff_1 = wu.deg2rad(abs(alpha_ell_1 - alpha))/3600\n",
+    "\n",
+    "            alpha_ell_2, *_ = alpha_para2ell(ell, u, v, alpha)\n",
+    "            alpha_para_2, *_ = alpha_ell2para(ell, beta, lamb, alpha_ell_2)\n",
+    "            diff_2 = wu.deg2rad(abs(alpha_para_2 - alpha))/3600\n",
+    "\n",
+    "            diffs.append((beta_deg, lamb_deg, alpha_deg, diff_1, diff_2))\n",
+    "diffs = np.array(diffs)"
+   ],
+   "id": "82fc6cbbe7d5abcb",
+   "outputs": [],
+   "execution_count": null
+  },
+  {
+   "metadata": {},
+   "cell_type": "code",
+   "source": [
+    "i_max_ell = np.argmax(diffs[:, 3])\n",
+    "max_ell = diffs[i_max_ell, 3]\n",
+    "point_max_ell = diffs[i_max_ell, :3]\n",
+    "\n",
+    "i_max_para = np.argmax(diffs[:, 4])\n",
+    "max_para = diffs[i_max_para, 4]\n",
+    "point_max_para = diffs[i_max_para, :4]\n",
+    "\n",
+    "print(f'Für elliptisches Alpha = {point_max_ell[2]}° und beta = {point_max_ell[0]}°, lamb = {point_max_ell[1]}°: diff = {max_ell}\"')\n",
+    "print(f'Für parametrisches Alpha = {point_max_para[2]}° und beta = {point_max_para[0]}°, lamb = {point_max_para[1]}°: diff = {max_ell}\"')\n",
+    "pass"
+   ],
+   "id": "97b5b8c9ca5377ab",
+   "outputs": [],
+   "execution_count": null
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

nicht abgeben/Tests/conversions_test.ipynb

@@ -0,0 +1,246 @@
+{
+ "cells": [
+  {
+   "metadata": {},
+   "cell_type": "code",
+   "source": [
+    "%load_ext autoreload\n",
+    "%autoreload 2"
+   ],
+   "id": "746c5b9e4c0226e7",
+   "outputs": [],
+   "execution_count": null
+  },
+  {
+   "cell_type": "code",
+   "id": "initial_id",
+   "metadata": {
+    "collapsed": true
+   },
+   "source": [
+    "%reload_ext autoreload\n",
+    "%autoreload 2\n",
+    "from itertools import product\n",
+    "\n",
+    "import numpy as np\n",
+    "import pandas as pd\n",
+    "import plotly.graph_objects as go\n",
+    "\n",
+    "import winkelumrechnungen as wu\n",
+    "from ellipsoid_triaxial import EllipsoidTriaxial"
+   ],
+   "outputs": [],
+   "execution_count": null
+  },
+  {
+   "metadata": {},
+   "cell_type": "code",
+   "source": [
+    "# ellips = \"KarneyTest2024\"\n",
+    "ellips = \"BursaSima1980\"\n",
+    "# ellips = \"Fiction\"\n",
+    "ell: EllipsoidTriaxial = EllipsoidTriaxial.init_name(ellips)"
+   ],
+   "id": "7b05ca89fcd7b331",
+   "outputs": [],
+   "execution_count": null
+  },
+  {
+   "metadata": {},
+   "cell_type": "code",
+   "source": [
+    "def deg_range(start, stop, step):\n",
+    "    return [float(x) for x in range(start, stop + step, step)]\n",
+    "\n",
+    "def asymptotic_range(start, direction=\"up\", max_decimals=4):\n",
+    "    values = []\n",
+    "    for d in range(0, max_decimals + 1):\n",
+    "        step = 10 ** -d\n",
+    "        if direction == \"up\":\n",
+    "            values.append(start + (1 - step))\n",
+    "        else:\n",
+    "            values.append(start - (1 - step))\n",
+    "    return values"
+   ],
+   "id": "61a6b14fef0180ad",
+   "outputs": [],
+   "execution_count": null
+  },
+  {
+   "metadata": {},
+   "cell_type": "code",
+   "source": [
+    "beta_5_85 = deg_range(5, 85, 5)\n",
+    "lambda_5_85 = deg_range(5, 85, 5)\n",
+    "beta_5_90 = deg_range(5, 90, 5)\n",
+    "lambda_5_90 = deg_range(5, 90, 5)\n",
+    "beta_0_90 = deg_range(0, 90, 5)\n",
+    "lambda_0_90 = deg_range(0, 90, 5)\n",
+    "beta_90 = [90.0]\n",
+    "lambda_90 = [90.0]\n",
+    "beta_0 = [0.0]\n",
+    "lambda_0 = [0.0]\n",
+    "beta_asym_89 = asymptotic_range(89.0, direction=\"up\")\n",
+    "lambda_asym_0 = asymptotic_range(1.0, direction=\"down\")"
+   ],
+   "id": "f7184980a4b930b7",
+   "outputs": [],
+   "execution_count": null
+  },
+  {
+   "metadata": {},
+   "cell_type": "code",
+   "source": [
+    "groups = {\n",
+    "    1: list(product(beta_5_85, lambda_5_85)),\n",
+    "    2: list(product(beta_0, lambda_0_90)),\n",
+    "    3: list(product(beta_5_85, lambda_0)),\n",
+    "    4: list(product(beta_90, lambda_5_90)),\n",
+    "    5: list(product(beta_asym_89, lambda_asym_0)),\n",
+    "    6: list(product(beta_5_85, lambda_90)),\n",
+    "    7: list(product(lambda_asym_0, lambda_0_90)),\n",
+    "    8: list(product(beta_0_90, lambda_asym_0)),\n",
+    "    9: list(product(beta_asym_89, lambda_0_90)),\n",
+    "    10: list(product(beta_0_90, beta_asym_89)),\n",
+    "}"
+   ],
+   "id": "cea9fd9cce6a4fd1",
+   "outputs": [],
+   "execution_count": null
+  },
+  {
+   "metadata": {},
+   "cell_type": "code",
+   "source": [
+    "for nr, points in groups.items():\n",
+    "    points_cart = []\n",
+    "    for point in points:\n",
+    "        beta, lamb = point\n",
+    "        cart = ell.ell2cart(wu.deg2rad(beta), wu.deg2rad(lamb))\n",
+    "        points_cart.append(cart)\n",
+    "    groups[nr] = points_cart"
+   ],
+   "id": "17a6a130782a89ce",
+   "outputs": [],
+   "execution_count": null
+  },
+  {
+   "metadata": {},
+   "cell_type": "code",
+   "source": [
+    "results = {}\n",
+    "\n",
+    "for nr, points in groups.items():\n",
+    "    group_results = {\"ell\": [],\n",
+    "                     \"para\": [],\n",
+    "                     \"geod\": []}\n",
+    "    for point in points:\n",
+    "        elli = ell.cart2ell(point)\n",
+    "        cart_elli = ell.ell2cart(elli[0], elli[1])\n",
+    "        group_results[\"ell\"].append(np.linalg.norm(point - cart_elli, axis=-1))\n",
+    "\n",
+    "        para = ell.cart2para(point)\n",
+    "        cart_para = ell.para2cart(para[0], para[1])\n",
+    "        group_results[\"para\"].append(np.linalg.norm(point - cart_para, axis=-1))\n",
+    "\n",
+    "        geod = ell.cart2geod(point, \"ligas3\")\n",
+    "        cart_geod = ell.geod2cart(geod[0], geod[1], geod[2])\n",
+    "        group_results[\"geod\"].append(np.linalg.norm(point - cart_geod, axis=-1))\n",
+    "\n",
+    "    group_results[\"ell\"] = np.array(group_results[\"ell\"])\n",
+    "    group_results[\"para\"] = np.array(group_results[\"para\"])\n",
+    "    group_results[\"geod\"] = np.array(group_results[\"geod\"])\n",
+    "    results[nr] = group_results"
+   ],
+   "id": "c3298ea233bca274",
+   "outputs": [],
+   "execution_count": null
+  },
+  {
+   "metadata": {},
+   "cell_type": "code",
+   "source": [
+    "# with open(f\"conversion_results_{ellips}.pkl\", \"wb\") as f:\n",
+    "#     pickle.dump(results, f)"
+   ],
+   "id": "e1285860be416ad3",
+   "outputs": [],
+   "execution_count": null
+  },
+  {
+   "metadata": {},
+   "cell_type": "code",
+   "source": [
+    "# with open(f\"conversion_results_{ellips}.pkl\", \"rb\") as f:\n",
+    "#     results = pickle.load(f)"
+   ],
+   "id": "d26720e34595ccbc",
+   "outputs": [],
+   "execution_count": null
+  },
+  {
+   "metadata": {},
+   "cell_type": "code",
+   "source": [
+    "df = pd.DataFrame({\n",
+    "    \"Gruppe\": [nr for nr in results.keys()],\n",
+    "    \"max_Δr_ell\": [f\"{max(result[\"ell\"]):.3g}\" for result in results.values()],\n",
+    "    \"max_Δr_para\": [f\"{max(result[\"para\"]):.3g}\" for result in results.values()],\n",
+    "    \"max_Δr_geod\": [f\"{max(result[\"geod\"]):.3g}\" for result in results.values()]\n",
+    "})"
+   ],
+   "id": "4e2e55e4699ec81e",
+   "outputs": [],
+   "execution_count": null
+  },
+  {
+   "metadata": {},
+   "cell_type": "code",
+   "source": [
+    "fig = go.Figure(data=[go.Table(\n",
+    "    header=dict(\n",
+    "        values=list(df.columns),\n",
+    "        fill_color=\"lightgrey\",\n",
+    "        align=\"left\"\n",
+    "    ),\n",
+    "    cells=dict(\n",
+    "        values=[df[col] for col in df.columns],\n",
+    "        align=\"left\"\n",
+    "    )\n",
+    ")])\n",
+    "fig.update_layout(\n",
+    "    template=\"simple_white\",\n",
+    "    width=650,\n",
+    "    height=len(groups)*20+80,\n",
+    "    margin=dict(l=20, r=20, t=20, b=20))\n",
+    "\n",
+    "fig.show()\n",
+    "# fig.write_image(f\"conversion_results_{ellips}.png\", width=650, height=len(groups)*20+80, scale=2)"
+   ],
+   "id": "c2fa82afef2d6e0e",
+   "outputs": [],
+   "execution_count": null
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}

nicht abgeben/ellipsoid_biaxial.py

@@ -0,0 +1,126 @@
+from typing import Tuple
+
+import numpy as np
+from numpy import arctan2, cos, sin, sqrt
+from numpy.typing import NDArray
+
+import winkelumrechnungen as wu
+
+
+class EllipsoidBiaxial:
+    """
+    Klasse für Rotationsellipdoide
+    """
+    def __init__(self, a: float, b: float):
+        self.a = a
+        self.b = b
+        self.c = a ** 2 / b
+        self.e = sqrt(a ** 2 - b ** 2) / a
+        self.e_ = sqrt(a ** 2 - b ** 2) / b
+
+    @classmethod
+    def init_name(cls, name: str) -> EllipsoidBiaxial:
+        """
+        Erstellen eines Rotationsellipdoids nach Namen
+        :param name: Name des Rotationsellipsoids
+        :return: Rotationsellipsoid
+        """
+        if name == "Bessel":
+            a = 6377397.15508
+            b = 6356078.96290
+            return cls(a, b)
+        elif name == "Hayford":
+            a = 6378388
+            f = 1/297
+            b = a - a * f
+            return cls(a, b)
+        elif name == "Krassowski":
+            a = 6378245
+            f = 298.3
+            b = a - a * f
+            return cls(a, b)
+        elif name == "WGS84":
+            a = 6378137
+            f = 298.257223563
+            b = a - a * f
+            return cls(a, b)
+        else:
+            raise Exception(f"EllipsoidBiaxial.init_name: Name {name} unbekannt")
+
+    @classmethod
+    def init_af(cls, a: float, f: float) -> EllipsoidBiaxial:
+        """
+        Erstellen eines Rotationsellipdoids aus der großen Halbachse und der Abplattung
+        :param a: große Halbachse
+        :param f: großen Halbachse
+        :return: Rotationsellipsoid
+        """
+        b = a - a * f
+        return cls(a, b)
+
+    V = lambda self, phi: sqrt(1 + self.e_ ** 2 * cos(phi) ** 2)
+    M = lambda self, phi: self.c / self.V(phi) ** 3
+    N = lambda self, phi: self.c / self.V(phi)
+
+    beta2psi = lambda self, beta: arctan2(self.a * sin(beta), self.b * cos(beta))
+    beta2phi = lambda self, beta: arctan2(self.a ** 2 * sin(beta), self.b ** 2 * cos(beta))
+
+    psi2beta = lambda self, psi: arctan2(self.b * sin(psi), self.a * cos(psi))
+    psi2phi = lambda self, psi: arctan2(self.a * sin(psi), self.b * cos(psi))
+
+    phi2beta = lambda self, phi: arctan2(self.b**2 * sin(phi), self.a**2 * cos(phi))
+    phi2psi = lambda self, phi: arctan2(self.b * sin(phi), self.a * cos(phi))
+
+    phi2p = lambda self, phi: self.N(phi) * cos(phi)
+
+    def bi_cart2ell(self, point: NDArray, Eh: float = 0.001, Ephi: float = wu.gms2rad([0, 0, 0.001])) -> Tuple[float, float, float]:
+        """
+        Umrechnung von kartesischen in ellipsoidische Koordinaten auf einem Rotationsellipsoid
+        # TODO: Quelle
+        :param point: Punkt in kartesischen Koordinaten
+        :param Eh: Grenzwert für die Höhe
+        :param Ephi: Grenzwert für die Breite
+        :return: ellipsoidische Breite, Länge, geodätische Höhe
+        """
+        x, y, z = point
+
+        lamb = arctan2(y, x)
+
+        p = sqrt(x**2+y**2)
+
+        phi_null = arctan2(z, p*(1 - self.e**2))
+
+        hi = [0]
+        phii = [phi_null]
+
+        i = 0
+
+        while True:
+            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)
+            dphi = abs(phii[i]-phi)
+            i += 1
+            if dh < Eh:
+                if dphi < Ephi:
+                    break
+        return phi, lamb, h
+
+    def bi_ell2cart(self, phi: float, lamb: float, h: float) -> NDArray:
+        """
+        Umrechnung von ellipsoidischen in kartesische Koordinaten auf einem Rotationsellipsoid
+        # TODO: Quelle
+        :param phi: ellipsoidische Breite
+        :param lamb: ellipsoidische Länge
+        :param h: geodätische Höhe
+        :return: Punkt in kartesischen Koordinaten
+        """
+        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(phi)
+        return np.array([x, y, z])

nicht abgeben/kugel.py

@@ -0,0 +1,100 @@
+from typing import Tuple
+
+import numpy as np
+from numpy import arccos, arcsin, arctan2, cos, pi, sin, sqrt
+from numpy.typing import NDArray
+
+import winkelumrechnungen as wu
+
+
+def cart2sph(point: NDArray) -> Tuple[float, float, float]:
+    """
+    Umrechnung von kartesischen in sphärische Koordinaten
+    # TODO: Quelle
+    :param point: Punkt in kartesischen Koordinaten
+    :return: Radius, Breite, Länge
+    """
+    x, y, z = point
+    r = sqrt(x**2 + y**2 + z**2)
+    phi = arctan2(z, sqrt(x**2 + y**2))
+    lamb = arctan2(y, x)
+
+    return r, phi, lamb
+
+
+def sph2cart(r: float, phi: float, lamb: float) -> NDArray:
+    """
+    Umrechnung von sphärischen in kartesische Koordinaten
+    # TODO: Quelle
+    :param r: Radius
+    :param phi: Breite
+    :param lamb: Länge
+    :return: Punkt in kartesischen Koordinaten
+    """
+    x = r * cos(phi) * cos(lamb)
+    y = r * cos(phi) * sin(lamb)
+    z = r * sin(phi)
+
+    return np.array([x, y, z])
+
+
+def gha1(R: float, phi0: float, lamb0: float, s: float, alpha0: float) -> Tuple[float, float]:
+    """
+    Berechnung der 1. GHA auf der Kugel
+    # TODO: Quelle
+    :param R: Radius
+    :param phi0: Breite des Startpunktes
+    :param lamb0: Länge des Startpunktes
+    :param s: Strecke
+    :param alpha0: Azimut
+    :return: Breite, Länge des Zielpunktes
+    """
+    s_ = s / R
+
+    lamb1 = lamb0 + arctan2(sin(s_) * sin(alpha0),
+                            cos(phi0) * cos(s_) - sin(phi0) * sin(s_) * cos(alpha0))
+
+    phi1 = arcsin(sin(phi0) * cos(s_) + cos(phi0) * sin(s_) * cos(alpha0))
+
+    return phi1, lamb1
+
+
+def gha2(R: float, phi0: float, lamb0: float, phi1: float, lamb1: float) -> Tuple[float, float, float]:
+    """
+    Berechnung der 2. GHA auf der Kugel
+    # TODO: Quelle
+    :param R: Radius
+    :param phi0: Breite des Startpunktes
+    :param lamb0: Länge des Startpunktes
+    :param phi1: Breite des Zielpunktes
+    :param lamb1: Länge des Zielpunktes
+    :return: Azimut im Startpunkt, Azimut im Zielpunkt, Strecke
+    """
+    s_ = arccos(sin(phi0) * sin(phi1) + cos(phi0) * cos(phi1) * cos(lamb1 - lamb0))
+    s = R * s_
+
+    alpha0 = arctan2(cos(phi1) * sin(lamb1 - lamb0),
+                     cos(phi0) * sin(phi1) - sin(phi0) * cos(phi1) * cos(lamb1 - lamb0))
+
+    alpha1 = arctan2(-cos(phi0) * sin(lamb1 - lamb0),
+                     cos(phi1) * sin(phi0) - sin(phi1) * cos(phi0) * cos(lamb1 - lamb0))
+    if alpha1 < 0:
+        alpha1 += 2 * pi
+
+    return alpha0, alpha1, s
+
+
+if __name__ == "__main__":
+    R = 6378815.904                                             # Bern
+    phi0 = wu.deg2rad(10)
+    lamb0 = wu.deg2rad(40)
+    alpha0 = wu.deg2rad(100)
+    s = 10000
+    phi1, lamb1 = gha1(R, phi0, lamb0, s, alpha0)
+    alpha0_g, alpha1, s_g = gha2(R, phi0, lamb0, phi1, lamb1)
+    phi1 = wu.rad2deg(phi1)
+    lamb1 = wu.rad2deg(lamb1)
+    alpha0_g = wu.rad2deg(alpha0_g)
+    alpha1 = wu.rad2deg(alpha1)
+
+    pass

nicht abgeben/test.py

@@ -0,0 +1,8 @@
+import numpy as np
+
+import ellipsoid_triaxial
+
+ell = ellipsoid_triaxial.EllipsoidTriaxial.init_name("KarneyTest2024")
+
+cart = ell.para2cart(0, np.pi/2)
+print(cart)