81 lines
2.8 KiB
Python
81 lines
2.8 KiB
Python
import numpy as np
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from ellipsoide import EllipsoidTriaxial
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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_approx(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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"""
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Berechung einer Näherungslösung der ersten Hauptaufgabe
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:param ell: Ellipsoid
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:param p0: Anfangspunkt
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:param alpha0: Azimut im Anfangspunkt
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:param s: Strecke bis zum Endpunkt
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:param ds: Länge einzelner Streckenelemente
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:param all_points: Ausgabe aller Punkte als Array?
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:return: Endpunkt, Azimut im Endpunkt, optional alle Punkte
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"""
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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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s_curr = 0.0
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while s_curr < s:
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ds_step = min(ds, s - s_curr)
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if ds_step < 1e-8:
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break
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p1 = points[-1]
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alpha1 = alphas[-1]
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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.point_onto_ellipsoid(p2)
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ds_step = np.linalg.norm(p2 - p1)
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points.append(p2)
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dalpha = 1e-6
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l2 = louville_constant(ell, p2, alpha1)
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dl_dalpha = (louville_constant(ell, p2, alpha1+dalpha) - l2) / dalpha
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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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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: NDArray, p0: NDArray, p1: NDArray):
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"""
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Anzeigen der Punkte
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:param points: Array aller approximierten Punkte
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:param p0: Startpunkt
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:param p1: wahrer Endpunkt
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"""
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fig = go.Figure()
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fig.add_scatter3d(x=points[:, 0], y=points[:, 1], z=points[:, 2],
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mode='lines', line=dict(color="red", width=3), name="Approx")
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fig.add_scatter3d(x=[p0[0]], y=[p0[1]], z=[p0[2]],
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mode='markers', marker=dict(color="green"), name="P0")
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fig.add_scatter3d(x=[p1[0]], y=[p1[1]], z=[p1[2]],
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mode='markers', marker=dict(color="green"), name="P1")
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fig.update_layout(
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scene=dict(xaxis_title='X [km]',
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yaxis_title='Y [km]',
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zaxis_title='Z [km]',
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aspectmode='data'),
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title="CHAMP")
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fig.show()
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if __name__ == '__main__':
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ell = EllipsoidTriaxial.init_name("BursaSima1980round")
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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, maxM=60, maxPartCircum=32)
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P1_app, alpha1_app, points = gha1_approx(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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