Näherungslösung GHA 2
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@@ -1,12 +1,10 @@
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import numpy as np
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from numpy import sin, cos, arcsin, arccos, arctan2
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from ellipsoide import EllipsoidTriaxial
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import matplotlib.pyplot as plt
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from panou import louville_constant, func_sigma_ell, gha1_ana
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import plotly.graph_objects as go
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import winkelumrechnungen as wu
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def gha1(ell: EllipsoidTriaxial, p0: np.ndarray, alpha0: float, s: float, ds: int):
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def gha1(ell: EllipsoidTriaxial, p0: np.ndarray, alpha0: float, s: float, ds: float, all_points: bool = False) -> Tuple[NDArray, float] | Tuple[NDArray, float, NDArray]:
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l0 = louville_constant(ell, p0, alpha0)
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points = [p0]
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alphas = [alpha0]
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@@ -17,10 +15,9 @@ def gha1(ell: EllipsoidTriaxial, p0: np.ndarray, alpha0: float, s: float, ds: in
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break
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p1 = points[-1]
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alpha1 = alphas[-1]
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x1, y1, z1 = p1
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sigma = func_sigma_ell(ell, x1, y1, z1, alpha1)
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sigma = func_sigma_ell(ell, p1, alpha1)
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p2 = p1 + ds_step * sigma
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p2, _, _, _ = ell.cartonell(p2)
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p2 = ell.cartonell(p2)
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ds_step = np.linalg.norm(p2 - p1)
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points.append(p2)
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@@ -30,7 +27,11 @@ def gha1(ell: EllipsoidTriaxial, p0: np.ndarray, alpha0: float, s: float, ds: in
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alpha2 = alpha1 + (l0 - l2) / dl_dalpha
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alphas.append(alpha2)
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s_curr += ds_step
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return points[-1], alphas[-1], np.array(points)
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if all_points:
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return points[-1], alphas[-1], np.array(points)
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else:
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return points[-1], alphas[-1]
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def show_points(points, p0, p1):
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fig = go.Figure()
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@@ -57,7 +58,7 @@ if __name__ == '__main__':
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P0 = ell.para2cart(0, 0)
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alpha0 = wu.deg2rad(90)
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s = 1000000
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P1_ana, alpha1_ana = gha1_ana(ell, P0, alpha0, s, 60, maxPartCircum=32)
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P1_app, alpha1_app, points = gha1(ell, P0, alpha0, s, 5000)
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P1_ana, alpha1_ana = gha1_ana(ell, P0, alpha0, s, maxM=60, maxPartCircum=32)
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P1_app, alpha1_app, points = gha1(ell, P0, alpha0, s, ds=5000, all_points=True)
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show_points(points, P0, P1_ana)
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print(np.linalg.norm(P1_app - P1_ana))
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