--- /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,
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+ 1.14295,
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+ 1.3036,
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+ 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,
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+ 0.294492,
+ -0.255401,
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+ 0.34611,
+ 0.370172,
+ -0.29446,
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+ 0.321012,
+ 0.303055,
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+ -1.94298,
+ -1.17325,
+ -0.470769,
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+ 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()
