+++ /dev/null
-import numpy as np
-import scipy as sp
-import scipy.linalg
-
-
-def compute_PCA(X, n_components=1):
- X_meaned = X - np.mean(X, axis=0)
- cov_mat = np.cov(X_meaned, rowvar=False)
- eigen_values, eigen_vectors = np.linalg.eigh(cov_mat)
- # sort the eigenvalues in descending order
- sorted_index = np.argsort(eigen_values)[::-1]
- sorted_eigenvalue = eigen_values[sorted_index]
- # similarly sort the eigenvectors
- sorted_eigenvectors = eigen_vectors[:, sorted_index]
- eigenvector_subset = sorted_eigenvectors[:, 0:n_components]
- return eigenvector_subset.T
-
-
-def fitPlane3D(points):
- pca = compute_PCA(points, n_components=3)
- normal = pca[2]
- affine_point = np.mean(points @ normal)
- return normal, affine_point
-
-
-def fitCircle2D(points, pp, bb):
- A = np.ones((points.shape[0], 3))
- B = np.zeros((points.shape[0]))
- A[:, 0] = points[:, 0]
- A[:, 1] = points[:, 1]
- B = points[:, 0] ** 2 + points[:, 1] ** 2
- print(np.abs(B - bb).max())
- fit, residual, rnk, s = np.linalg.lstsq(A, B, rcond=None)
- print(fit, residual, rnk, s)
- a, b, c = fit
- xc = a / 2
- yc = b / 2
- r = np.sqrt(4 * c + a**2 + b**2) / 2
- return np.array([xc, yc]), r
-
-
-def gram_schmidt(v1, v2):
- u1 = v1 / np.linalg.norm(v1) # Normalisation de v1
- u2 = v2 - np.dot(u1, v2) * u1 # Projection de v2 sur u1
- u2 = u2 / np.linalg.norm(u2) # Normalisation de u2
- return u1, u2
-
-
-def get_normal_plane_vectors(v):
- # Normalisation du vecteur v
- v_normalized = v / np.linalg.norm(v)
- # Construction d'une matrice à partir du vecteur normalisé
- v_matrix = np.array([v_normalized])
- # Calcul de l'espace nul de la matrice
- null_space_matrix = sp.linalg.null_space(v_matrix)
- # Sélection de deux vecteurs indépendants de l'espace nul
- u1 = null_space_matrix[:, 0]
- u2 = null_space_matrix[:, 1]
- v1, v2 = gram_schmidt(u1, u2)
- if np.cross(v1, v2) @ v < 0: # les vecteurs doivent former une base directe
- v1 = -v1
- return v1, v2
-
-
-def compute_parameters_torus(k1, k2, coords, normals, mm, pp, bb):
- var_1 = np.var(k1)
- var_2 = np.var(k2)
- if var_1 > var_2:
- minor_curv = np.mean(k2)
- else:
- minor_curv = np.mean(k1)
- minor_radius = 1 / minor_curv
- major_radius_points = coords - normals * minor_radius
- P_mean = np.mean(major_radius_points, axis=0)
- major_radius_points = major_radius_points - P_mean
- print(np.abs(major_radius_points - mm).max())
- normal, affine_point = fitPlane3D(major_radius_points)
- u, v = get_normal_plane_vectors(normal)
- p_matrix = np.array([u, v]).T
- p_major_radius_points = major_radius_points @ p_matrix
- print(np.abs(p_major_radius_points - pp).max())
- centre_2D, major_radius = fitCircle2D(p_major_radius_points, pp, bb)
- centre = centre_2D[0] * u + centre_2D[1] * v + P_mean
- parameters = {}
- parameters.update(
- {
- "minor_radius": minor_radius,
- "major_radius": major_radius,
- "centre": centre,
- }
- )
- print(parameters)
-
-
-def main():
- compute_parameters_torus(
- np.array(K1),
- np.array(K2),
- np.array(COORDS),
- np.array(NORMALS),
- np.array(MM),
- np.array(PP),
- np.array(BB),
- )
-
-
-BB = [
- 1.29988,
- 1.32834,
- 1.31073,
- 1.30217,
- 1.3004,
- 1.32802,
- 1.40886,
- 1.38819,
- 1.15329,
- 1.33224,
- 1.29239,
- 1.23342,
- 1.30238,
- 1.36314,
- 1.32608,
- 1.25758,
- 1.16688,
- 1.13991,
- 1.23348,
- 1.18219,
- 1.2203,
- 1.25984,
- 1.31467,
- 1.29754,
- 1.32701,
- 1.37341,
- 1.3835,
- 1.39346,
- 1.36699,
- 1.38513,
- 1.39164,
- 1.37848,
- 1.33759,
- 1.40887,
- 1.34163,
- 1.33346,
- 1.38385,
- 1.22564,
- 1.23029,
- 1.30197,
- 1.28674,
- 1.368,
- 1.3454,
- 1.34928,
- 1.30838,
- 1.27381,
- 1.24746,
- 1.22588,
- 1.21466,
- 1.18031,
- 1.08016,
- 1.18529,
- 1.23115,
- 1.2101,
- 1.22234,
- 1.21161,
- 1.18967,
- 1.20307,
- 1.23042,
- 1.24136,
- 1.25018,
- 1.22214,
- 1.268,
- 1.33643,
- 1.29568,
- 1.28693,
- 1.25032,
- 1.01616,
- 1.28119,
- 1.24947,
- 1.21533,
- 1.24026,
- 1.20846,
- 1.26105,
- 1.24038,
- 1.27136,
- 1.29468,
- 1.28342,
- 1.28925,
- 1.29826,
- 1.28555,
- 1.29329,
- 1.22736,
- 1.2337,
- 1.30764,
- 1.32819,
- 1.37281,
- 1.40958,
- 1.42911,
- 1.42011,
- 1.41975,
- 1.38649,
- 1.33099,
- 1.28097,
- 1.24976,
- 1.2287,
- 1.22615,
- 1.21312,
- 1.15805,
- 1.10605,
- 1.21257,
- 1.28317,
- 1.2835,
- 1.26095,
- 1.19331,
- 1.27272,
- 1.27796,
- 1.27132,
- 1.34219,
- 1.37059,
- 1.40964,
- 1.44505,
- 1.43081,
- 1.40872,
- 1.36834,
- 1.30892,
- 1.2686,
- 1.26305,
- 1.30879,
- 1.27939,
- 1.28073,
- 1.31929,
- 1.2598,
- 1.22048,
- 1.21601,
- 1.1966,
- 1.20778,
- 1.1939,
- 1.21448,
- 1.23422,
- 1.26638,
- 1.23913,
- 1.17684,
- 1.23806,
- 1.24665,
- 1.24903,
- 1.09784,
- 1.22823,
- 1.22897,
- 1.2352,
- 1.25402,
- 1.21612,
- 1.17462,
- 1.10981,
- 1.21096,
- 1.2808,
- 1.31638,
- 1.37202,
- 1.37594,
- 1.39594,
- 1.45298,
- 1.38753,
- 1.36049,
- 1.36021,
- 1.33335,
- 1.33825,
- 1.40989,
- 1.43406,
- 1.37539,
- 1.40051,
- 1.42711,
- 1.41021,
- 1.38393,
- 1.40263,
- 1.43309,
- 1.36506,
- 1.39896,
- 1.3855,
- 1.35028,
- 1.37377,
- 1.34695,
- 1.35958,
- 1.2953,
- 1.31097,
- 1.35788,
- 1.31656,
- 1.37928,
- 1.28303,
- 1.29909,
- 1.26879,
- 1.2514,
- 1.25047,
- 1.22388,
- 1.23911,
- 1.2314,
- 1.22712,
- 1.23376,
- 1.21774,
- 1.18743,
- 1.19656,
- 1.22343,
- 1.24818,
- 1.23516,
- 1.23684,
- 1.24645,
- 1.27108,
- 1.30362,
- 1.34807,
- 1.28548,
- 1.39272,
- 1.41669,
- 1.37402,
- 1.24369,
- 1.33271,
- 1.38335,
- 1.28888,
- 1.38451,
- 1.37468,
- 1.3168,
- 1.20807,
- 1.29194,
- 1.3191,
- 1.32651,
- 1.31312,
- 1.35904,
- 1.3144,
- 1.36248,
- 1.43151,
- 1.44124,
- 1.36247,
- 1.36509,
- 1.39602,
- 1.37578,
- 1.36368,
- 1.32171,
- 1.29417,
- 1.26564,
- 1.28197,
- 1.26516,
- 1.22019,
- 1.2104,
- 1.18011,
- 1.13635,
- 1.18086,
- 1.20877,
- 1.20591,
- 1.21808,
- 1.21509,
- 1.26505,
- 1.30837,
- 1.35343,
- 1.3891,
- 1.40041,
- 1.31966,
- 1.1857,
- 1.21441,
- 1.35452,
- 1.31039,
- 1.30165,
- 1.34868,
- 1.3405,
- 1.30601,
- 1.42104,
- 1.41801,
- 1.46154,
- 1.38631,
- 1.14847,
- 1.37646,
- 1.30515,
- 1.32861,
- 1.37463,
- 1.3204,
- 1.25174,
- 1.25007,
- 1.25577,
- 1.23818,
- 1.29151,
- 1.28852,
- 1.28247,
- 1.33274,
- 1.25059,
- 1.27221,
-]
-
-
-MM = [
- [1.05218, 0.439126, 0.0275596],
- [1.04785, 0.479983, 0.0294504],
- [1.12058, 0.234585, -0.00338201],
- [1.14104, 0.0127689, -0.0230176],
- [1.10571, -0.278786, -0.0472263],
- [1.07081, -0.425854, -0.0136113],
- [0.973353, -0.679294, -0.00261489],
- [0.640175, -0.98912, -0.00373311],
- [0.422407, -0.987409, 0.0715977],
- [-0.11622, -1.14838, 0.0373057],
- [-0.550639, -0.994583, 0.0282317],
- [-0.895716, -0.656575, 0.040941],
- [-1.05574, -0.433309, 0.0359594],
- [-1.01146, -0.583157, 0.0247077],
- [-1.15094, 0.0372052, 0.0163754],
- [-1.01934, 0.467392, 0.0344462],
- [-0.83607, 0.683944, 0.0474789],
- [-0.388598, 0.994402, 0.0386861],
- [-0.376419, 1.04489, -0.00144792],
- [-0.543529, 0.941692, -0.00744857],
- [-0.842668, 0.714298, -0.00428732],
- [-1.05887, 0.372359, -0.00547966],
- [-1.13206, 0.181956, -0.0015887],
- [-1.13864, -0.0321948, -0.00396496],
- [-1.12858, -0.230919, -0.0113774],
- [-1.00934, -0.595529, -0.00810085],
- [-0.718267, -0.931445, -0.0117962],
- [-0.385443, -1.11574, -0.0123723],
- [-0.0539776, -1.16793, -0.0202157],
- [0.105231, -1.17218, -0.0408898],
- [0.410452, -1.10595, -0.0270756],
- [0.606503, -1.00526, -0.0440616],
- [0.785018, -0.849263, -0.0435556],
- [0.78877, -0.886978, 0.00841919],
- [0.871132, -0.763444, 0.0422807],
- [0.95679, -0.646559, 0.0131272],
- [0.866666, -0.795453, 0.00141778],
- [0.847868, -0.711831, -0.0310192],
- [0.479959, -0.999919, -0.0550382],
- [-0.00704338, -1.14099, -0.0486256],
- [-0.545948, -0.994314, -0.0562787],
- [-0.729652, -0.914116, -0.0411991],
- [-1.09297, -0.388389, -0.0242567],
- [-1.14937, -0.168063, -0.0071695],
- [-1.09596, 0.327538, -0.00916765],
- [-0.825938, 0.769174, 0.00684957],
- [-0.413614, 1.03749, 0.000622491],
- [-0.312815, 1.06207, 0.0267459],
- [0.268776, 1.06883, 0.0292164],
- [0.392152, 1.01317, 0.0337524],
- [0.415459, 0.952647, 0.0341705],
- [0.220656, 1.06612, -0.00531312],
- [0.477553, 1.00155, -0.00656638],
- [0.704037, 0.845239, -0.0170485],
- [0.669049, 0.880179, -0.0321375],
- [0.421781, 1.01673, -0.0435539],
- [0.130592, 1.0829, -0.0535263],
- [-0.158514, 1.08535, -0.0333546],
- [-0.383671, 1.0408, -0.0291968],
- [-0.592747, 0.943422, -0.0185954],
- [-0.782805, 0.798408, -0.030715],
- [-0.933645, 0.592057, -0.0458696],
- [-1.08669, 0.295286, -0.0471632],
- [-1.14381, 0.167624, 0.0202696],
- [-1.12565, 0.169003, 0.0224448],
- [-1.1224, 0.164695, 0.00799367],
- [-1.11346, 0.102613, -0.00635569],
- [-0.87524, 0.500256, -0.0801847],
- [-0.825179, 0.774767, 0.00149167],
- [-0.57715, 0.95727, 0.00146035],
- [-0.245189, 1.07481, 0.00174283],
- [0.0715746, 1.11136, 0.00141126],
- [0.475719, 0.991036, 0.00349609],
- [0.54847, 0.979916, -0.00175501],
- [0.759303, 0.814767, 0.0126634],
- [0.905798, 0.671487, 0.00192825],
- [1.03956, 0.462593, 0.000498079],
- [1.10652, 0.243004, 0.00831135],
- [1.13246, 0.0825571, 0.0249298],
- [1.11721, -0.223999, 0.041278],
- [1.1327, -0.0507068, 0.0136722],
- [1.12516, -0.165256, 0.00246041],
- [1.10166, 0.11705, -0.0100355],
- [1.10996, 0.0405934, -0.029513],
- [1.14152, -0.0674168, -0.0127305],
- [1.0266, -0.523655, -0.0313335],
- [0.701, -0.938803, -0.0317084],
- [0.184108, -1.17288, -0.0215941],
- [-0.00457635, -1.19544, 0.000479688],
- [-0.586835, -1.03718, 0.0017773],
- [0.40389, -1.12099, -0.00529045],
- [0.894697, -0.765514, -0.000273007],
- [1.14658, -0.127762, -0.00997137],
- [1.01077, 0.509221, 0.00198446],
- [0.589978, 0.94957, 0.0050153],
- [0.0948726, 1.10441, -0.0152223],
- [-0.459667, 1.00742, -0.0251474],
- [0.0601388, 1.09978, -0.0186445],
- [-0.0396568, 1.07542, -0.031587],
- [0.552557, 0.894844, -0.0605588],
- [0.639852, 0.896196, -0.0377235],
- [1.06158, 0.395243, 0.00743376],
- [1.12049, -0.167594, 0.0453045],
- [1.11863, -0.0983217, 0.0254323],
- [1.09233, 0.0119581, 0.0153559],
- [1.03052, 0.459064, -0.0028931],
- [1.04139, 0.439849, -0.000810073],
- [1.04791, 0.41619, 0.00694441],
- [1.12727, -0.267333, 0.00192907],
- [0.870498, -0.782861, 0.0210384],
- [0.430566, -1.10647, 0.0145657],
- [-0.138371, -1.1941, -0.0235351],
- [-0.120929, -1.19003, -0.00798896],
- [0.589052, -1.0304, -0.00669611],
- [1.00562, -0.597545, -0.00804835],
- [1.14292, -0.0511787, -0.0212672],
- [1.01783, 0.482296, -0.00862175],
- [1.0124, 0.487948, -0.00419105],
- [1.10109, 0.310459, -0.00117018],
- [1.11781, 0.172919, 0.00343219],
- [1.03052, 0.467714, 0.000731203],
- [1.05078, 0.463836, -0.00942715],
- [0.927494, 0.632111, 0.0114052],
- [0.622723, 0.912519, 0.0428227],
- [0.368572, 1.0393, 0.0268776],
- [0.131449, 1.08594, 0.0507237],
- [-0.116833, 1.09274, 0.0315559],
- [-0.362512, 1.03073, 0.0528684],
- [-0.598413, 0.925375, 0.0335415],
- [-0.806751, 0.763742, 0.0389321],
- [-0.975683, 0.560694, 0.0234728],
- [0.711067, 0.856453, 0.00522918],
- [0.698304, 0.830188, -0.0108496],
- [0.843059, 0.726166, 0.00228899],
- [0.27213, 1.08286, 0.000884279],
- [0.0116246, 1.11754, -0.0001197],
- [0.149865, 1.03701, -0.0203214],
- [-0.20027, 1.09001, 0.00676326],
- [-0.472005, 1.00308, 0.00833057],
- [-0.703639, 0.860276, 0.00983825],
- [-0.923985, 0.632659, 0.010136],
- [-0.892113, 0.648345, -0.0490424],
- [-0.52618, 0.947538, -0.0408892],
- [-0.454733, 0.950303, -0.0271215],
- [-1.09885, -0.0595824, -0.0416295],
- [-1.09124, -0.300023, -0.0094494],
- [-1.05459, -0.45189, 0.0055773],
- [-0.934393, -0.706345, 0.00420015],
- [-0.741821, -0.908647, 0.00347728],
- [-0.442203, -1.09563, 0.00305888],
- [-0.440351, -1.12208, -0.00519117],
- [-0.533432, -1.05023, 0.0312364],
- [-0.744989, -0.897486, 0.052304],
- [-0.920372, -0.716316, 0.0324806],
- [-1.04354, -0.494303, 0.0497827],
- [-1.12861, -0.253905, 0.0229736],
- [-0.919225, -0.751607, 0.00334249],
- [-0.566044, -1.0553, 0.0277849],
- [-0.306417, -1.13205, 0.0542941],
- [-0.0585354, -1.182, 0.0251293],
- [0.148655, -1.18533, 0.00308894],
- [0.465147, -1.09264, 0.00454079],
- [0.359912, -1.12002, 0.0296904],
- [0.152287, -1.17452, 0.0348313],
- [-0.181576, -1.18327, 0.00186421],
- [-0.0541688, -1.1671, 0.00387793],
- [-0.643362, -0.992493, 0.00806684],
- [-0.847912, -0.816419, 0.00882942],
- [-1.11133, -0.339428, 0.00792329],
- [-1.00369, -0.60528, 0.00759492],
- [-0.942388, -0.677389, -0.00297831],
- [-1.06965, 0.464152, -0.000192445],
- [-1.12914, -0.142646, 0.00580705],
- [-1.06569, 0.418651, 0.00105227],
- [-1.1625, -0.0804709, -0.000631652],
- [-1.14585, -0.0593998, 0.0415459],
- [-1.12885, -0.323918, 0.0451808],
- [-1.06294, 0.39131, 0.0352204],
- [-0.959726, 0.614781, 0.0314496],
- [-0.61342, 0.944757, -0.0299485],
- [-0.169997, 1.10566, 0.00355667],
- [0.32253, 1.07073, -0.00887087],
- [0.913211, 0.624429, -0.0192011],
- [0.87408, 0.689269, -0.005635],
- [0.532473, 0.973591, -0.0122005],
- [-0.0261654, 1.10745, -0.00841875],
- [0.283174, 1.07405, -0.00787649],
- [0.601846, 0.924947, -0.00342465],
- [0.804858, 0.734601, 0.00810469],
- [0.764176, 0.782688, 0.0232811],
- [0.739081, 0.822915, 0.0294241],
- [0.647241, 0.910635, 0.00801974],
- [0.0883295, 1.10786, 0.00786736],
- [0.110928, 1.10659, -0.00992521],
- [-0.416901, 1.03569, -0.00469693],
- [-0.862549, 0.726024, -0.00955877],
- [-1.11829, 0.230413, -0.0187427],
- [-1.11354, -0.328809, -0.00972923],
- [-1.1251, 0.140273, -0.0251003],
- [-0.943174, -0.709331, -0.00817972],
- [-0.420061, -1.11366, -0.0152201],
- [-0.920783, -0.725388, -0.0141649],
- [-0.939932, -0.600206, -0.0438578],
- [-0.676287, -0.935598, -0.0114071],
- [-0.205092, -1.15812, -0.0349525],
- [-0.249685, -1.10748, -0.0225875],
- [0.192646, -1.16077, -0.00506834],
- [0.347275, -1.11984, -0.0300476],
- [0.785808, -0.836197, -0.0397711],
- [1.06014, -0.29003, -0.0244352],
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- [5.93572, -4.20071, -9.54763],
- [5.81917, -3.72382, -9.47279],
- [6.14726, -3.49904, -9.76234],
- [6.20615, -3.10271, -9.73281],
- [6.47149, -2.88504, -9.79933],
- [6.67462, -2.51198, -9.74836],
- [7.15771, -2.21947, -9.73866],
- [7.49, -2.51567, -9.86033],
- [7.68398, -2.88407, -9.80282],
- [7.72653, -3.14512, -9.63843],
- [7.65011, -3.29507, -9.45402],
- [6.99354, -3.30864, -9.78878],
- [7.17375, -3.05875, -9.8027],
- [7.4604, -3.39034, -9.4042],
- [7.44938, -3.49966, -9.18179],
- [7.39391, -3.6156, -9.04594],
- [7.37512, -3.75899, -8.99327],
- [7.4124, -3.88455, -9.09707],
- [7.50261, -4.00354, -9.19962],
- [7.28756, -3.73398, -9.39182],
- [7.16158, -3.6145, -9.59259],
- [6.96414, -3.85591, -9.75004],
- [7.17441, -4.73743, -9.86297],
- [6.87926, -4.463, -9.8609],
- [7.45515, -4.0934, -9.45453],
- [7.57417, -4.56878, -9.80543],
- [7.80318, -4.12368, -9.41891],
- [8.06683, -4.01939, -9.52276],
- [7.86509, -4.84323, -9.8629],
- [8.10042, -5.20919, -9.77159],
- [8.54486, -5.14021, -9.70138],
- [8.72929, -4.79936, -9.79213],
- [8.35701, -4.09101, -9.76565],
- [9.04054, -4.65031, -9.71191],
- [8.8527, -3.96673, -9.86262],
- [9.33277, -4.66289, -9.43009],
- [9.53836, -4.48282, -9.02],
- [9.27973, -3.83155, -9.73959],
- [8.96315, -3.54227, -9.85275],
- [8.96291, -3.1104, -9.82202],
- [9.23635, -2.97828, -9.64669],
- [9.15544, -2.53438, -9.43305],
- [9.57796, -3.26749, -9.31634],
- [9.42193, -2.88861, -8.677],
- [9.58572, -3.23298, -8.77023],
- [9.68577, -3.66446, -9.02],
- [9.15625, -2.44519, -8.73391],
- [8.97805, -2.19975, -9.02],
-]
-
-K1 = [
- 1.19742,
- 1.10354,
- 1.14907,
- 1.15043,
- 1.22354,
- 1.22235,
- 1.13188,
- 0.981901,
- 1.03604,
- 0.709188,
- 1.09286,
- 1.07003,
- 1.26782,
- 1.3122,
- 1.26756,
- 1.3689,
- 1.15674,
- 1.17528,
- 1.28998,
- 1.23027,
- 1.12868,
- 1.15578,
- 1.25699,
- 1.1553,
- 1.17413,
- 1.15094,
- 1.15178,
- 1.21847,
- 1.2516,
- 1.17151,
- 1.17063,
- 1.33213,
- 1.18518,
- 1.0682,
- 1.17914,
- 1.21917,
- 1.2068,
- 1.0939,
- 1.13594,
- 1.19896,
- 1.12807,
- 1.30628,
- 1.21965,
- 1.52805,
- 1.20057,
- 1.28683,
- 1.29944,
- 1.33911,
- 1.28139,
- 1.18256,
- 1.10645,
- 1.06408,
- 1.0965,
- 1.18692,
- 1.10563,
- 1.21843,
- 1.22667,
- 1.13631,
- 1.20817,
- 1.13895,
- 1.19749,
- 1.15447,
- 1.18275,
- 1.09933,
- 1.18072,
- 1.16824,
- 0.99584,
- 1.09059,
- 1.01944,
- 1.18948,
- 1.03335,
- 1.1381,
- 1.03862,
- 1.21733,
- 1.2433,
- 1.19621,
- 1.13219,
- 1.18533,
- 1.15925,
- 1.182,
- 1.21103,
- 1.10658,
- 1.0942,
- 1.17147,
- 1.42773,
- 1.30786,
- 1.29743,
- 1.31306,
- 1.23611,
- 1.3494,
- 1.26301,
- 1.28029,
- 1.32776,
- 1.1564,
- 1.28499,
- 1.14503,
- 1.21632,
- 1.147,
- 1.50722,
- 1.18236,
- 1.31852,
- 1.17454,
- 1.24319,
- 1.09401,
- 1.18864,
- 1.10312,
- 0.931669,
- 0.876142,
- 1.2934,
- 1.21907,
- 1.30991,
- 1.51383,
- 1.09556,
- 1.30842,
- 1.29534,
- 1.19195,
- 0.962355,
- 0.963581,
- 1.25778,
- 1.14618,
- 1.08882,
- 1.19339,
- 1.24819,
- 1.2945,
- 1.17345,
- 1.27354,
- 1.1939,
- 1.23823,
- 1.13651,
- 1.20865,
- 1.20307,
- 1.13204,
- 1.11798,
- 1.11248,
- 1.21338,
- 1.30081,
- 1.05123,
- 1.24533,
- 1.23076,
- 1.24697,
- 1.21668,
- 1.34948,
- 1.06382,
- 1.0813,
- 1.27874,
- 1.01942,
- 1.12397,
- 1.25103,
- 1.16397,
- 1.08262,
- 1.30112,
- 1.22445,
- 1.26206,
- 1.17346,
- 1.26302,
- 1.22153,
- 1.0977,
- 1.08502,
- 1.29874,
- 1.1887,
- 1.17321,
- 1.1826,
- 1.17089,
- 1.2635,
- 1.20194,
- 1.09826,
- 1.21022,
- 1.23322,
- 1.18322,
- 1.21803,
- 1.12576,
- 1.04465,
- 1.09941,
- 1.26061,
- 1.19788,
- 1.29197,
- 1.10013,
- 1.27175,
- 1.09435,
- 1.09918,
- 1.08359,
- 1.0781,
- 1.2261,
- 1.16435,
- 1.25847,
- 1.17829,
- 1.24583,
- 1.07368,
- 1.12846,
- 1.06213,
- 1.22504,
- 1.30253,
- 1.4652,
- 1.27216,
- 1.2538,
- 1.31984,
- 1.22178,
- 1.59261,
- 1.36179,
- 1.30396,
- 1.36935,
- 0.996679,
- 1.21832,
- 1.06071,
- 1.33719,
- 1.05711,
- 1.01937,
- 1.28109,
- 1.19835,
- 1.14849,
- 1.22351,
- 1.02332,
- 1.07756,
- 1.20856,
- 1.21726,
- 1.10843,
- 1.20263,
- 1.09455,
- 1.09018,
- 1.1698,
- 1.09742,
- 1.20776,
- 1.10128,
- 1.21941,
- 1.10173,
- 1.14295,
- 1.22707,
- 1.25119,
- 1.15338,
- 1.15773,
- 1.1574,
- 1.18209,
- 1.16355,
- 1.2526,
- 1.20632,
- 1.06499,
- 1.08241,
- 1.30988,
- 1.30657,
- 1.43131,
- 1.2878,
- 1.29887,
- 1.35942,
- 1.55406,
- 1.24562,
- 1.14184,
- 1.13441,
- 1.08653,
- 1.24455,
- 1.05094,
- 1.32982,
- 1.16057,
- 1.03679,
- 1.18101,
- 1.25019,
- 1.17951,
- 1.03869,
- 1.3036,
- 1.02111,
- 1.24628,
- 1.06374,
- 1.18218,
- 1.11238,
- 1.2232,
- 1.10736,
- 1.1374,
- 1.26377,
- 1.24702,
- 1.34437,
- 1.09683,
- 1.25885,
- 1.03085,
-]
-K2 = [
- 0.495172,
- 0.456066,
- 0.41051,
- 0.483741,
- 0.451438,
- 0.335015,
- 0.13779,
- 0.0845594,
- -0.625154,
- -0.718537,
- -0.614467,
- -0.637731,
- -1.56218,
- -2.5706,
- -2.85071,
- -2.20399,
- -1.17888,
- -1.02953,
- -0.445578,
- 0.051206,
- 0.0952012,
- 0.114029,
- -0.62022,
- 0.0170489,
- 0.307267,
- 0.338932,
- 0.345823,
- 0.330729,
- 0.308163,
- 0.441216,
- 0.502429,
- 0.416836,
- 0.479956,
- 0.485236,
- 0.440744,
- 0.334737,
- -0.0410915,
- -0.455159,
- -0.752267,
- -1.04928,
- -1.06893,
- -2.29096,
- -2.26737,
- -3.1572,
- -3.08108,
- -3.20892,
- -3.27129,
- -2.89255,
- -2.53226,
- -1.5429,
- -0.436992,
- 0.108906,
- 0.372582,
- 0.322518,
- 0.474249,
- 0.456065,
- 0.457558,
- 0.482369,
- 0.45976,
- 0.491782,
- 0.436978,
- 0.442762,
- 0.432519,
- 0.478053,
- 0.453599,
- 0.223272,
- -0.132486,
- -0.689866,
- 0.0370908,
- 0.0362719,
- 0.10264,
- 0.163657,
- 0.154541,
- 0.372946,
- 0.432424,
- 0.319959,
- 0.250292,
- 0.368056,
- 0.481423,
- 0.406364,
- 0.292489,
- 0.0673104,
- -0.29432,
- -0.939232,
- -1.927,
- -2.18706,
- -2.47478,
- -2.65895,
- -3.12768,
- -3.2165,
- -3.31111,
- -3.16634,
- -3.1795,
- -2.78982,
- -2.82076,
- -2.61436,
- -2.2993,
- -1.76414,
- -1.41035,
- -1.06146,
- -2.19168,
- -2.71668,
- -2.05913,
- -0.924032,
- -0.372202,
- -0.0289572,
- -0.472779,
- -1.33054,
- -2.76354,
- -2.53466,
- -2.94761,
- -2.80399,
- -3.08119,
- -3.09044,
- -2.86859,
- -2.63001,
- -1.46378,
- -0.541119,
- 0.523248,
- 0.146024,
- -0.0599811,
- 0.406023,
- 0.408329,
- 0.460156,
- 0.495234,
- 0.446228,
- 0.505498,
- 0.42382,
- 0.487574,
- 0.421683,
- 0.508657,
- 0.294492,
- -0.255401,
- 0.144412,
- 0.34611,
- 0.370172,
- -0.29446,
- 0.330497,
- 0.321012,
- 0.303055,
- 0.319245,
- -1.94298,
- -1.17325,
- -0.470769,
- -0.900235,
- -0.145793,
- 0.156298,
- 0.109494,
- 0.10749,
- 0.1456,
- 0.340028,
- 0.495982,
- 0.438926,
- 0.499742,
- 0.444352,
- 0.518762,
- 0.494655,
- 0.479316,
- 0.443408,
- 0.500227,
- 0.394569,
- 0.330562,
- 0.48503,
- 0.451944,
- 0.327074,
- 0.12035,
- 0.351572,
- 0.359925,
- 0.363342,
- 0.361338,
- -0.130087,
- 0.0808711,
- 0.204982,
- 0.366471,
- 0.412965,
- 0.457275,
- 0.482909,
- 0.458812,
- 0.485696,
- 0.494342,
- 0.477924,
- 0.4715,
- 0.312006,
- 0.135443,
- 0.392,
- 0.343122,
- 0.354555,
- 0.083377,
- -0.373596,
- -0.99949,
- -2.46905,
- -3.16248,
- -3.25642,
- -3.24827,
- -3.01846,
- -2.82295,
- -2.46904,
- -1.7479,
- -1.72326,
- -2.94808,
- -2.84588,
- -1.33981,
- -0.83769,
- -0.344284,
- -2.09224,
- -0.34194,
- -0.169117,
- -1.71205,
- -1.37899,
- -0.428884,
- -1.12172,
- 0.0145813,
- 0.0721618,
- 0.314444,
- 0.301532,
- 0.475807,
- 0.452342,
- 0.49173,
- 0.481624,
- 0.437383,
- 0.488331,
- 0.419365,
- 0.50285,
- 0.417895,
- 0.472651,
- 0.448635,
- 0.294955,
- 0.347867,
- 0.331375,
- 0.349691,
- 0.370979,
- 0.0744396,
- -0.476447,
- -1.13098,
- -1.83794,
- -0.380967,
- -0.380265,
- -2.09781,
- -2.89157,
- -3.2824,
- -3.26186,
- -3.17371,
- -2.93098,
- -2.45546,
- -1.26459,
- -0.664481,
- 0.0233179,
- -0.0243138,
- -1.74989,
- -0.359187,
- -1.86717,
- -1.40881,
- 0.0160553,
- 0.310217,
- 0.373326,
- 0.344446,
- -0.388131,
- 0.349189,
- 0.100287,
- 0.429005,
- 0.464987,
- 0.349951,
- 0.130455,
- 0.246086,
- 0.425423,
- 0.423052,
- 0.475293,
- 0.513705,
- 0.534168,
- 0.49863,
- 0.471324,
- 0.499803,
-]
-
-if __name__ == "__main__":
- main()
