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Koordinatenumrechnungen funktionieren inkl. Randfälle, GHA2_num funktioniert mit Standard Ellipsoid

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Hendrik Möllersmann
2025-11-26 11:05:18 +01:00
parent 9031a12312
commit d76859d17b
5 changed files with 181 additions and 125 deletions
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31
jacobian_Ligas.py
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@@ -35,13 +35,16 @@ def case2(E: float, F: float, G: float, pG: np.ndarray, pE: np.ndarray):
j33 = (pE[1] - pG[1]) * G - F * pE[1]
detJ = j11 * j22 * j33 - j21 * j12 * j33 + j21 * j13 * j32
invJ = 1/detJ * np.array([[j22*j33, -(j12*j33-j13*j32), -j13*j22],
[-j21*j33, j11*j33, j13*j21],
[j21*j32, -j11*j32, j11*j22-j12*j21]])
if detJ == 0:
invJ, fxE = case3(E, F, G, pG, pE)
else:
invJ = 1/detJ * np.array([[j22*j33, -(j12*j33-j13*j32), -j13*j22],
[-j21*j33, j11*j33, j13*j21],
[j21*j32, -j11*j32, j11*j22-j12*j21]])
fxE = np.array([E*pE[0]**2 + F*pE[1]**2 + G*pE[2]**2 - 1,
(pE[0]-pG[0]) * F*pE[1] - (pE[1]-pG[1]) * E*pE[0],
(pE[1]-pG[1]) * G*pE[2] - (pE[2]-pG[2]) * F*pE[1]])
fxE = np.array([E*pE[0]**2 + F*pE[1]**2 + G*pE[2]**2 - 1,
(pE[0]-pG[0]) * F*pE[1] - (pE[1]-pG[1]) * E*pE[0],
(pE[1]-pG[1]) * G*pE[2] - (pE[2]-pG[2]) * F*pE[1]])
return invJ, fxE
@@ -57,13 +60,15 @@ def case3(E: float, F: float, G: float, pG: np.ndarray, pE: np.ndarray):
j33 = (pE[1] - pG[1]) * G - F * pE[1]
detJ = -j11 * j23 * j32 - j21 * j12 * j33 + j21 * j13 * j32
if detJ == 0:
invJ, fxE = case2(E, F, G, pG, pE)
else:
invJ = 1/detJ * np.array([[-j23*j32, -(j12*j33-j13*j32), j12*j23],
[-j21*j33, j11*j33, -(j11*j23-j13*j21)],
[j21*j32, -j11*j32, -j12*j21]])
invJ = 1/detJ * np.array([[-j23*j32, -(j12*j33-j13*j32), j12*j23],
[-j21*j33, j11*j33, -(j11*j23-j13*j21)],
[j21*j32, -j11*j32, -j12*j21]])
fxE = np.array([E*pE[0]**2 + F*pE[1]**2 + G*pE[2]**2 - 1,
(pE[0]-pG[0]) * G*pE[2] - (pE[2]-pG[2]) * E*pE[0],
(pE[1]-pG[1]) * G*pE[2] - (pE[2]-pG[2]) * F*pE[1]])
fxE = np.array([E*pE[0]**2 + F*pE[1]**2 + G*pE[2]**2 - 1,
(pE[0]-pG[0]) * G*pE[2] - (pE[2]-pG[2]) * E*pE[0],
(pE[1]-pG[1]) * G*pE[2] - (pE[2]-pG[2]) * F*pE[1]])
return invJ, fxE