Umrechnung ell cart

2025-10-21 14:19:40 +02:00
parent cc5996e174
commit dcf1780f44
3 changed files with 59 additions and 8 deletions
--- a/ellipsoide.py
+++ b/ellipsoide.py
@@ -120,8 +120,63 @@ class EllipsoidTriaxial:
            return cls(ax, ay, b)

    def ell2cart(self, beta, lamb, u):
-        s1 = u**2 - self.b**2
-        s2 = -self.ay**2 * np.sin(beta)**2 - self.b**2 * np.cos(beta)**2
-        s3 = -self.ax**2 * np.sin(lamb)**2 - self.ay**2 * np.cos(lamb)**2
+        """
+        Panou 2014 12ff.
+        :param beta: ellipsoidische Breite
+        :param lamb: ellipsoidische Länge
+        :param u: Höhe
+        :return: kartesische Koordinaten
+        """
+        beta = wu.deg2rad(beta)
+        lamb = wu.deg2rad(lamb)

-        x = np.sqrt(u**2 + self.ex**2) * np.sqrt(np.cos(beta)**2 + self.ee**2/self.ex**2 * np.sin(beta)**2)
+        # s1 = u**2 - self.b**2
+        # s2 = -self.ay**2 * np.sin(beta)**2 - self.b**2 * np.cos(beta)**2
+        # s3 = -self.ax**2 * np.sin(lamb)**2 - self.ay**2 * np.cos(lamb)**2
+        # print(s1, s2, s3)
+
+        x = np.sqrt(u**2 + self.ex**2) * np.sqrt(np.cos(beta)**2 + self.ee**2/self.ex**2 * np.sin(beta)**2) * np.cos(lamb)
+        y = np.sqrt(u**2 + self.ey**2) * np.cos(beta) * np.sin(lamb)
+        z = u * np.sin(beta) * np.sqrt(1 - self.ee**2/self.ex**2 * np.cos(lamb)**2)
+
+        return x, y, z
+
+    def cart2ell(self, x, y, z):
+        """
+        Panou 2014 15ff.
+        :param x:
+        :param y:
+        :param z:
+        :return:
+        """
+        c2 = self.ax**2 + self.ay**2 + self.b**2 - x**2 - y**2 - z**2
+        c1 = (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 - (self.ax**2 + self.ay**2) * z**2)
+        c0 = (self.ax**2 * self.ay**2 * self.b**2 - self.ay**2 * self.b**2 * x**2 -
+              self.ax**2 * self.b**2 * y**2 - self.ax**2 * self.ay**2 * z**2)
+
+        p = (c2**2 - 3*c1) / 9
+        q = (9*c1*c2 - 27*c0 - 2*c2**3) / 54
+        omega = np.arccos(q / np.sqrt(p**3))
+
+        s1 = 2 * np.sqrt(p) * np.cos(omega/3) - c2/3
+        s2 = 2 * np.sqrt(p) * np.cos(omega/3 - 2*np.pi/3) - c2/3
+        s3 = 2 * np.sqrt(p) * np.cos(omega/3 - 4*np.pi/3) - c2/3
+        # print(s1, s2, s3)
+
+        beta = np.arctan(np.sqrt((-self.b**2 - s2) / (self.ay**2 + s2)))
+        lamb = np.arctan(np.sqrt((-self.ay**2 - s3) / (self.ax**2 + s3)))
+        u = np.sqrt(self.b**2 + s1)
+
+        return beta, lamb, u
+
+
+if __name__ == "__main__":
+    ellips = EllipsoidTriaxial.init_name("Eitschberger1978")
+    # ellips = EllipsoidTriaxial.init_name("Bursa1972")
+    # carts = ellips.ell2cart(10, 30, 6378172)
+    # ells = ellips.cart2ell(carts[0], carts[1], carts[2])
+
+    carts = ellips.ell2cart(90, 0, 6356754.4)
+    # print(aus.gms("beta", ells[0], 3), aus.gms("lambda", ells[1], 3), "u =", ells[2])
+    pass