From 2ff4cff2bee1ca7a58aa3873c10bb66807c86f94 Mon Sep 17 00:00:00 2001
From: "Tammo.Weber" <tammo.weber@gmail.com>
Date: Tue, 18 Nov 2025 13:17:33 +0100
Subject: [PATCH] Kugel

---
 kugel.py | 78 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 78 insertions(+)
 create mode 100644 kugel.py

diff --git a/kugel.py b/kugel.py
new file mode 100644
index 0000000..931af68
--- /dev/null
+++ b/kugel.py
@@ -0,0 +1,78 @@
+import numpy as np
+
+
+def cart2sph(x, y, z):
+    r = np.sqrt(x**2 + y**2 + z**2)
+    phi = np.atan2(z, np.sqrt(x**2 + y**2))
+    lamb = np.atan2(y, x)
+
+    return r, np.rad2deg(phi), np.rad2deg(lamb)
+
+
+def sph2cart(r, phi, lamb):
+    phi_rad = np.deg2rad(phi)
+    lamb_rad = np.deg2rad(lamb)
+
+    x = r * np.cos(phi_rad) * np.cos(lamb_rad)
+    y = r * np.cos(phi_rad) * np.sin(lamb_rad)
+    z = r * np.sin(phi_rad)
+
+    return x, y, z
+
+
+def kugel_erste_gha(R, phi_1, lamb_1, s_d, a_12):
+
+    s = s_d / R
+    lamb_1_rad = np.deg2rad(lamb_1)
+    phi_1_rad = np.deg2rad(phi_1)
+    a_12_rad = np.deg2rad(a_12)
+
+    sin_satz = np.sin(s) * np.sin(a_12_rad)
+    sin_kos = np.cos(phi_1_rad) * np.cos(s) - np.sin(phi_1_rad) * np.sin(s) * np.cos(a_12_rad)
+    delta_lam = np.atan2(sin_satz, sin_kos)
+    lamb_2_rad = lamb_1_rad + delta_lam
+
+    phi_2_rad = np.asin(np.sin(phi_1_rad) * np.cos(s) + np.cos(phi_1_rad) * np.sin(s) * np.cos(a_12_rad))
+
+    sin_satz_2 = -np.cos(phi_1_rad) * np.sin(a_12_rad)
+    sin_kos_2 = np.sin(s) * np.sin(phi_1_rad) - np.cos(s) * np.cos(phi_1_rad) * np.cos(a_12_rad)
+    a_21_rad = np.atan2(sin_satz_2, sin_kos_2)
+    if a_21_rad < 0:
+        a_21_rad += 2 * np.pi
+
+    return np.rad2deg(phi_2_rad), np.rad2deg(lamb_2_rad), np.rad2deg(a_21_rad)
+
+
+def kugel_zweite_gha(R, phi_1, lamb_1, phi_2, lamb_2):
+    phi_1_rad = np.deg2rad(phi_1)
+    lamb_1_rad = np.deg2rad(lamb_1)
+    phi_2_rad = np.deg2rad(phi_2)
+    lamb_2_rad = np.deg2rad(lamb_2)
+
+    sin_satz_1 = np.cos(phi_2_rad) * np.sin(lamb_2_rad - lamb_1_rad)
+    sin_kos_1 = np.cos(phi_1_rad) * np.sin(phi_2_rad) - np.sin(phi_1_rad) * np.cos(phi_2_rad) * np.cos(lamb_2_rad - lamb_1_rad)
+    a_12_rad = np.atan2(sin_satz_1, sin_kos_1)
+
+    kos = np.sin(phi_1_rad) * np.sin(phi_2_rad) + np.cos(phi_1_rad) * np.cos(phi_2_rad) * np.cos(lamb_2_rad - lamb_1_rad)
+    s = np.acos(kos)
+    s_d = R * s
+
+    sin_satz_2 = -np.cos(phi_1_rad) * np.sin(lamb_2_rad - lamb_1_rad)
+    sin_kos_2 = np.cos(phi_2_rad) * np.sin(phi_1_rad) - np.sin(phi_2_rad) * np.cos(phi_1_rad) * np.cos(lamb_2_rad - lamb_1_rad)
+    a_21_rad = np.atan2(sin_satz_2, sin_kos_2)
+    if a_21_rad < 0:
+        a_21_rad += 2 * np.pi
+
+    return s_d, np.rad2deg(a_12_rad), np.rad2deg(a_21_rad)
+
+
+if __name__ == "__main__":
+    R = 6378815.904                                             # Bern
+    phi_1 = 10
+    lamb_1 = 40
+    a_12 = 100
+    s = 10000
+    phi_2, lamb_2, _ = kugel_erste_gha(R, phi_1, lamb_1, s, a_12)
+
+    print(kugel_erste_gha(R, phi_1, lamb_1, s, a_12))
+    print(kugel_zweite_gha(R, phi_1, lamb_1, phi_2, lamb_2))
\ No newline at end of file