Régression parabolique non triviale

[sylvain231]

Léon : quel logiciel as-tu utilisé Mathematica ?

[Ben314]

pour le b je l'ai rajouté dans le post (et j'ai rajouté la valeur du delta_min que je trouve dans le post suivant)

Sinon, l'hurluberlu, c'est DzLogique ?

(Et je comprend pas comment ça se fait que Léon trouve pas pareil avec la même méthode . . . )

[sylvain231]

non ça ne marche pas avec l'équation de la parabole de Léon ou avec la tienne
je te poste la sortie de mon programme avec la formule de Léon :

Code: Tout sélectionner

avant1
avant
apres
[199, 299]
[199, 300]
[199, 300]
[199, 300]
[199, 300]
[199, 300]
[199, 300]
[199, 301]
[199, 301]
[199, 301]
[199, 302]
[199, 302]
[199, 303]
[199, 303]
[199, 303]
[198, 305]
[199, 305]
[198, 306]
[198, 306]
[197, 309]
[198, 309]
[197, 311]
[198, 312]
[197, 313]
[197, 313]
[196, 317]
[197, 318]
[196, 319]
[196, 319]
[195, 320]
[195, 322]
[194, 326]
[194, 334]
[194, 335]
[192, 337]
[192, 341]
[192, 344]
[190, 351]
[191, 351]
[188, 358]
[189, 361]
[186, 370]
[188, 371]
[186, 371]
[186, 372]
[186, 374]
[185, 387]
[183, 390]
[182, 391]
[182, 392]
[184, 395]
[183, 398]
[182, 402]
[182, 405]
[179, 408]
[181, 409]
[180, 419]
[177, 419]
[178, 425]
[176, 428]
[177, 431]
[174, 435]
[173, 443]
[175, 444]
[170, 461]
[168, 472]
[169, 478]
[164, 492]
[163, 497]
nombre de points : 69
sommet = [200, 300]
E02=6447.8
E11=-1185.88
E20=218.957
E21=29378.3
E30=-5414.67
E12=-159723
E03=870115
E40=148892
E31=-806615
E22=4.37644e+06
E13=-2.37821e+07
E04=1.29441e+08
theta = 0 delta = 15034.6
theta = 0.18 delta = 27038.1
theta = 0.36 delta = 39424
theta = 0.54 delta = 52211.6
theta = 0.72 delta = 65420.1
theta = 0.9 delta = 79069
theta = 1.08 delta = 93177.5
theta = 1.26 delta = 107765
theta = 1.44 delta = 122850
theta = 1.62 delta = 138453
theta = 1.8 delta = 154592
theta = 1.98 delta = 171287
theta = 2.16 delta = 188558
theta = 2.34 delta = 206422
theta = 2.52 delta = 224900
theta = 2.7 delta = 244010
theta = 2.88 delta = 263771
theta = 3.06 delta = 284203
theta = 3.24 delta = 305324
theta = 3.42 delta = 327154
theta = 3.6 delta = 349711
theta = 3.78 delta = 373013
theta = 3.96 delta = 397081
theta = 4.14 delta = 421931
theta = 4.32 delta = 447584
theta = 4.5 delta = 474057
theta = 4.68 delta = 501369
theta = 4.86 delta = 529538
theta = 5.04 delta = 558582
theta = 5.22 delta = 588521
theta = 5.4 delta = 619371
theta = 5.58 delta = 651151
theta = 5.76 delta = 683878
theta = 5.94 delta = 717571
theta = 6.12 delta = 752247
theta = 6.3 delta = 787924
theta = 6.48 delta = 824619
theta = 6.66 delta = 862350
theta = 6.84 delta = 901133
theta = 7.02 delta = 940986
theta = 7.2 delta = 981926
theta = 7.38 delta = 1.02397e+06
theta = 7.56 delta = 1.06713e+06
theta = 7.74 delta = 1.11143e+06
theta = 7.92 delta = 1.15689e+06
theta = 8.1 delta = 1.20351e+06
theta = 8.28 delta = 1.25132e+06
theta = 8.46 delta = 1.30033e+06
theta = 8.64 delta = 1.35056e+06
theta = 8.82 delta = 1.40202e+06
theta = 9 delta = 1.45474e+06
theta = 9.18 delta = 1.50871e+06
theta = 9.36 delta = 1.56396e+06
theta = 9.54 delta = 1.62051e+06
theta = 9.72 delta = 1.67837e+06
theta = 9.9 delta = 1.73755e+06
theta = 10.08 delta = 1.79807e+06
theta = 10.26 delta = 1.85994e+06
theta = 10.44 delta = 1.92318e+06
theta = 10.62 delta = 1.9878e+06
theta = 10.8 delta = 2.05381e+06
theta = 10.98 delta = 2.12123e+06
theta = 11.16 delta = 2.19007e+06
theta = 11.34 delta = 2.26035e+06
theta = 11.52 delta = 2.33207e+06
theta = 11.7 delta = 2.40526e+06
theta = 11.88 delta = 2.47991e+06
theta = 12.06 delta = 2.55605e+06
theta = 12.24 delta = 2.63369e+06
theta = 12.42 delta = 2.71283e+06
theta = 12.6 delta = 2.79349e+06
theta = 12.78 delta = 2.87569e+06
theta = 12.96 delta = 2.95943e+06
theta = 13.14 delta = 3.04472e+06
theta = 13.32 delta = 3.13158e+06
theta = 13.5 delta = 3.22001e+06
theta = 13.68 delta = 3.31002e+06
theta = 13.86 delta = 3.40163e+06
theta = 14.04 delta = 3.49485e+06
theta = 14.22 delta = 3.58968e+06
theta = 14.4 delta = 3.68613e+06
theta = 14.58 delta = 3.78422e+06
theta = 14.76 delta = 3.88395e+06
theta = 14.94 delta = 3.98532e+06
theta = 15.12 delta = 4.08836e+06
theta = 15.3 delta = 4.19306e+06
theta = 15.48 delta = 4.29944e+06
theta = 15.66 delta = 4.4075e+06
theta = 15.84 delta = 4.51724e+06
theta = 16.02 delta = 4.62868e+06
theta = 16.2 delta = 4.74183e+06
theta = 16.38 delta = 4.85668e+06
theta = 16.56 delta = 4.97325e+06
theta = 16.74 delta = 5.09154e+06
theta = 16.92 delta = 5.21156e+06
theta = 17.1 delta = 5.3333e+06
theta = 17.28 delta = 5.45679e+06
theta = 17.46 delta = 5.58201e+06
theta = 17.64 delta = 5.70899e+06
theta = 17.82 delta = 5.83771e+06
theta = 18 delta = 5.96819e+06
theta = 18.18 delta = 6.10042e+06
theta = 18.36 delta = 6.23442e+06
theta = 18.54 delta = 6.37018e+06
theta = 18.72 delta = 6.50771e+06
theta = 18.9 delta = 6.64701e+06
theta = 19.08 delta = 6.78808e+06
theta = 19.26 delta = 6.93093e+06
theta = 19.44 delta = 7.07555e+06
theta = 19.62 delta = 7.22195e+06
theta = 19.8 delta = 7.37012e+06
theta = 19.98 delta = 7.52008e+06
theta = 20.16 delta = 7.67181e+06
theta = 20.34 delta = 7.82533e+06
theta = 20.52 delta = 7.98062e+06
theta = 20.7 delta = 8.1377e+06
theta = 20.88 delta = 8.29655e+06
theta = 21.06 delta = 8.45718e+06
theta = 21.24 delta = 8.61958e+06
theta = 21.42 delta = 8.78376e+06
theta = 21.6 delta = 8.94971e+06
theta = 21.78 delta = 9.11744e+06
theta = 21.96 delta = 9.28692e+06
theta = 22.14 delta = 9.45818e+06
theta = 22.32 delta = 9.6312e+06
theta = 22.5 delta = 9.80597e+06
theta = 22.68 delta = 9.9825e+06
theta = 22.86 delta = 1.01608e+07
theta = 23.04 delta = 1.03408e+07
theta = 23.22 delta = 1.05226e+07
theta = 23.4 delta = 1.07061e+07
theta = 23.58 delta = 1.08913e+07
theta = 23.76 delta = 1.10783e+07
theta = 23.94 delta = 1.1267e+07
theta = 24.12 delta = 1.14574e+07
theta = 24.3 delta = 1.16495e+07
theta = 24.48 delta = 1.18433e+07
theta = 24.66 delta = 1.20388e+07
theta = 24.84 delta = 1.2236e+07
theta = 25.02 delta = 1.24348e+07
theta = 25.2 delta = 1.26354e+07
theta = 25.38 delta = 1.28375e+07
theta = 25.56 delta = 1.30414e+07
theta = 25.74 delta = 1.32469e+07
theta = 25.92 delta = 1.3454e+07
theta = 26.1 delta = 1.36628e+07
theta = 26.28 delta = 1.38732e+07
theta = 26.46 delta = 1.40852e+07
theta = 26.64 delta = 1.42987e+07
theta = 26.82 delta = 1.45139e+07
theta = 27 delta = 1.47306e+07
theta = 27.18 delta = 1.49489e+07
theta = 27.36 delta = 1.51688e+07
theta = 27.54 delta = 1.53902e+07
theta = 27.72 delta = 1.56131e+07
theta = 27.9 delta = 1.58376e+07
theta = 28.08 delta = 1.60635e+07
theta = 28.26 delta = 1.6291e+07
theta = 28.44 delta = 1.65199e+07
theta = 28.62 delta = 1.67503e+07
theta = 28.8 delta = 1.69821e+07
theta = 28.98 delta = 1.72154e+07
theta = 29.16 delta = 1.74501e+07
theta = 29.34 delta = 1.76862e+07
theta = 29.52 delta = 1.79237e+07
theta = 29.7 delta = 1.81625e+07
theta = 29.88 delta = 1.84028e+07
theta = 30.06 delta = 1.86444e+07
theta = 30.24 delta = 1.88873e+07
theta = 30.42 delta = 1.91315e+07
theta = 30.6 delta = 1.93771e+07
theta = 30.78 delta = 1.96239e+07
theta = 30.96 delta = 1.98719e+07
theta = 31.14 delta = 2.01213e+07
theta = 31.32 delta = 2.03718e+07
theta = 31.5 delta = 2.06236e+07
theta = 31.68 delta = 2.08766e+07
theta = 31.86 delta = 2.11307e+07
theta = 32.04 delta = 2.1386e+07
theta = 32.22 delta = 2.16425e+07
theta = 32.4 delta = 2.19001e+07
theta = 32.58 delta = 2.21588e+07
theta = 32.76 delta = 2.24185e+07
theta = 32.94 delta = 2.26793e+07
theta = 33.12 delta = 2.29412e+07
theta = 33.3 delta = 2.32041e+07
theta = 33.48 delta = 2.3468e+07
theta = 33.66 delta = 2.37329e+07
theta = 33.84 delta = 2.39988e+07
theta = 34.02 delta = 2.42656e+07
theta = 34.2 delta = 2.45333e+07
theta = 34.38 delta = 2.48019e+07
theta = 34.56 delta = 2.50714e+07
theta = 34.74 delta = 2.53418e+07
theta = 34.92 delta = 2.5613e+07
theta = 35.1 delta = 2.5885e+07
theta = 35.28 delta = 2.61578e+07
theta = 35.46 delta = 2.64314e+07
theta = 35.64 delta = 2.67057e+07
theta = 35.82 delta = 2.69807e+07
theta = 36 delta = 2.72565e+07
theta = 36.18 delta = 2.75329e+07
theta = 36.36 delta = 2.781e+07
theta = 36.54 delta = 2.80878e+07
theta = 36.72 delta = 2.83661e+07
theta = 36.9 delta = 2.8645e+07
theta = 37.08 delta = 2.89245e+07
theta = 37.26 delta = 2.92046e+07
theta = 37.44 delta = 2.94851e+07
theta = 37.62 delta = 2.97662e+07
theta = 37.8 delta = 3.00477e+07
theta = 37.98 delta = 3.03296e+07
theta = 38.16 delta = 3.0612e+07
theta = 38.34 delta = 3.08948e+07
theta = 38.52 delta = 3.11779e+07
theta = 38.7 delta = 3.14614e+07
theta = 38.88 delta = 3.17452e+07
theta = 39.06 delta = 3.20293e+07
theta = 39.24 delta = 3.23137e+07
theta = 39.42 delta = 3.25983e+07
theta = 39.6 delta = 3.28831e+07
theta = 39.78 delta = 3.31681e+07
theta = 39.96 delta = 3.34533e+07
theta = 40.14 delta = 3.37387e+07
theta = 40.32 delta = 3.40242e+07
theta = 40.5 delta = 3.43097e+07
theta = 40.68 delta = 3.45953e+07
theta = 40.86 delta = 3.4881e+07
theta = 41.04 delta = 3.51667e+07
theta = 41.22 delta = 3.54523e+07
theta = 41.4 delta = 3.5738e+07
theta = 41.58 delta = 3.60235e+07
theta = 41.76 delta = 3.6309e+07
theta = 41.94 delta = 3.65944e+07
theta = 42.12 delta = 3.68796e+07
theta = 42.3 delta = 3.71647e+07
theta = 42.48 delta = 3.74496e+07
theta = 42.66 delta = 3.77342e+07
theta = 42.84 delta = 3.80186e+07
theta = 43.02 delta = 3.83028e+07
theta = 43.2 delta = 3.85866e+07
theta = 43.38 delta = 3.88701e+07
theta = 43.56 delta = 3.91533e+07
theta = 43.74 delta = 3.94361e+07
theta = 43.92 delta = 3.97185e+07
theta = 44.1 delta = 4.00005e+07
theta = 44.28 delta = 4.0282e+07
theta = 44.46 delta = 4.05631e+07
theta = 44.64 delta = 4.08437e+07
theta = 44.82 delta = 4.11237e+07
theta = 45 delta = 4.14032e+07
theta = 45.18 delta = 4.16821e+07
theta = 45.36 delta = 4.19604e+07
theta = 45.54 delta = 4.2238e+07
theta = 45.72 delta = 4.2515e+07
theta = 45.9 delta = 4.27914e+07
theta = 46.08 delta = 4.3067e+07
theta = 46.26 delta = 4.33419e+07
theta = 46.44 delta = 4.36161e+07
theta = 46.62 delta = 4.38894e+07
theta = 46.8 delta = 4.4162e+07
theta = 46.98 delta = 4.44338e+07
theta = 47.16 delta = 4.47047e+07
theta = 47.34 delta = 4.49747e+07
theta = 47.52 delta = 4.52438e+07
theta = 47.7 delta = 4.5512e+07
theta = 47.88 delta = 4.57793e+07
theta = 48.06 delta = 4.60456e+07
theta = 48.24 delta = 4.63109e+07
theta = 48.42 delta = 4.65752e+07
theta = 48.6 delta = 4.68384e+07
theta = 48.78 delta = 4.71006e+07
theta = 48.96 delta = 4.73618e+07
theta = 49.14 delta = 4.76218e+07
theta = 49.32 delta = 4.78807e+07
theta = 49.5 delta = 4.81384e+07
theta = 49.68 delta = 4.8395e+07
theta = 49.86 delta = 4.86504e+07
theta = 50.04 delta = 4.89046e+07
theta = 50.22 delta = 4.91575e+07
theta = 50.4 delta = 4.94092e+07
theta = 50.58 delta = 4.96596e+07
theta = 50.76 delta = 4.99088e+07
theta = 50.94 delta = 5.01566e+07
theta = 51.12 delta = 5.04032e+07
theta = 51.3 delta = 5.06483e+07
theta = 51.48 delta = 5.08921e+07
theta = 51.66 delta = 5.11346e+07
theta = 51.84 delta = 5.13756e+07
theta = 52.02 delta = 5.16152e+07
theta = 52.2 delta = 5.18534e+07
theta = 52.38 delta = 5.20901e+07
theta = 52.56 delta = 5.23254e+07
theta = 52.74 delta = 5.25592e+07
theta = 52.92 delta = 5.27915e+07
theta = 53.1 delta = 5.30223e+07
theta = 53.28 delta = 5.32516e+07
theta = 53.46 delta = 5.34793e+07
theta = 53.64 delta = 5.37055e+07
theta = 53.82 delta = 5.39302e+07
theta = 54 delta = 5.41532e+07
theta = 54.18 delta = 5.43747e+07
theta = 54.36 delta = 5.45946e+07
theta = 54.54 delta = 5.48129e+07
theta = 54.72 delta = 5.50295e+07
theta = 54.9 delta = 5.52446e+07
theta = 55.08 delta = 5.5458e+07
theta = 55.26 delta = 5.56697e+07
theta = 55.44 delta = 5.58799e+07
theta = 55.62 delta = 5.60883e+07
theta = 55.8 delta = 5.62952e+07
theta = 55.98 delta = 5.65003e+07
theta = 56.16 delta = 5.67038e+07
theta = 56.34 delta = 5.69056e+07
theta = 56.52 delta = 5.71057e+07
theta = 56.7 delta = 5.73042e+07
theta = 56.88 delta = 5.7501e+07
theta = 57.06 delta = 5.76961e+07
theta = 57.24 delta = 5.78895e+07
theta = 57.42 delta = 5.80812e+07
theta = 57.6 delta = 5.82713e+07
theta = 57.78 delta = 5.84597e+07
theta = 57.96 delta = 5.86465e+07
theta = 58.14 delta = 5.88316e+07
theta = 58.32 delta = 5.9015e+07
theta = 58.5 delta = 5.91968e+07
theta = 58.68 delta = 5.93769e+07
theta = 58.86 delta = 5.95555e+07
theta = 59.04 delta = 5.97324e+07
theta = 59.22 delta = 5.99077e+07
theta = 59.4 delta = 6.00814e+07
theta = 59.58 delta = 6.02536e+07
theta = 59.76 delta = 6.04242e+07
theta = 59.94 delta = 6.05932e+07
theta = 60.12 delta = 6.07608e+07
theta = 60.3 delta = 6.09268e+07
theta = 60.48 delta = 6.10914e+07
theta = 60.66 delta = 6.12545e+07
theta = 60.84 delta = 6.14162e+07
theta = 61.02 delta = 6.15765e+07
theta = 61.2 delta = 6.17355e+07
theta = 61.38 delta = 6.18931e+07
theta = 61.56 delta = 6.20494e+07
theta = 61.74 delta = 6.22044e+07
theta = 61.92 delta = 6.23583e+07
theta = 62.1 delta = 6.25109e+07
theta = 62.28 delta = 6.26625e+07
theta = 62.46 delta = 6.28129e+07
theta = 62.64 delta = 6.29623e+07
theta = 62.82 delta = 6.31107e+07
theta = 63 delta = 6.32582e+07
theta = 63.18 delta = 6.34048e+07
theta = 63.36 delta = 6.35505e+07
theta = 63.54 delta = 6.36956e+07
theta = 63.72 delta = 6.38399e+07
theta = 63.9 delta = 6.39837e+07
theta = 64.08 delta = 6.41269e+07
theta = 64.26 delta = 6.42697e+07
theta = 64.44 delta = 6.44121e+07
theta = 64.62 delta = 6.45542e+07
theta = 64.8 delta = 6.46961e+07
theta = 64.98 delta = 6.4838e+07
theta = 65.16 delta = 6.49799e+07
theta = 65.34 delta = 6.51219e+07
theta = 65.52 delta = 6.52641e+07
theta = 65.7 delta = 6.54068e+07
theta = 65.88 delta = 6.55499e+07
theta = 66.06 delta = 6.56937e+07
theta = 66.24 delta = 6.58383e+07
theta = 66.42 delta = 6.59839e+07
theta = 66.6 delta = 6.61305e+07
theta = 66.78 delta = 6.62784e+07
theta = 66.96 delta = 6.64278e+07
theta = 67.14 delta = 6.65789e+07
theta = 67.32 delta = 6.67318e+07
theta = 67.5 delta = 6.68868e+07
theta = 67.68 delta = 6.70441e+07
theta = 67.86 delta = 6.7204e+07
theta = 68.04 delta = 6.73667e+07
theta = 68.22 delta = 6.75324e+07
theta = 68.4 delta = 6.77016e+07
theta = 68.58 delta = 6.78745e+07
theta = 68.76 delta = 6.80514e+07
theta = 68.94 delta = 6.82326e+07
theta = 69.12 delta = 6.84187e+07
theta = 69.3 delta = 6.86099e+07
theta = 69.48 delta = 6.88067e+07
theta = 69.66 delta = 6.90096e+07
theta = 69.84 delta = 6.9219e+07
theta = 70.02 delta = 6.94355e+07
theta = 70.2 delta = 6.96597e+07
theta = 70.38 delta = 6.98922e+07
theta = 70.56 delta = 7.01336e+07
theta = 70.74 delta = 7.03846e+07
theta = 70.92 delta = 7.0646e+07
theta = 71.1 delta = 7.09186e+07
theta = 71.28 delta = 7.12034e+07
theta = 71.46 delta = 7.15012e+07
theta = 71.64 delta = 7.18132e+07
theta = 71.82 delta = 7.21405e+07
theta = 72 delta = 7.24843e+07
theta = 72.18 delta = 7.2846e+07
theta = 72.36 delta = 7.3227e+07
theta = 72.54 delta = 7.3629e+07
theta = 72.72 delta = 7.40538e+07
theta = 72.9 delta = 7.45033e+07
theta = 73.08 delta = 7.49796e+07
theta = 73.26 delta = 7.54851e+07
theta = 73.44 delta = 7.60225e+07
theta = 73.62 delta = 7.65946e+07
theta = 73.8 delta = 7.72047e+07
theta = 73.98 delta = 7.78563e+07
theta = 74.16 delta = 7.85536e+07
theta = 74.34 delta = 7.93009e+07
theta = 74.52 delta = 8.01034e+07
theta = 74.7 delta = 8.09666e+07
theta = 74.88 delta = 8.18972e+07
theta = 75.06 delta = 8.29022e+07
theta = 75.24 delta = 8.39901e+07
theta = 75.42 delta = 8.51701e+07
theta = 75.6 delta = 8.64532e+07
theta = 75.78 delta = 8.78516e+07
theta = 75.96 delta = 8.93796e+07
theta = 76.14 delta = 9.10533e+07
theta = 76.32 delta = 9.28915e+07
theta = 76.5 delta = 9.49159e+07
theta = 76.68 delta = 9.7151e+07
theta = 76.86 delta = 9.96248e+07
theta = 77.04 delta = 1.02369e+08
theta = 77.22 delta = 1.05417e+08
theta = 77.4 delta = 1.08805e+08
theta = 77.58 delta = 1.12565e+08
theta = 77.76 delta = 1.16717e+08
theta = 77.94 delta = 1.21251e+08
theta = 78.12 delta = 1.26084e+08
theta = 78.3 delta = 1.30985e+08
theta = 78.48 delta = 1.354e+08
theta = 78.66 delta = 1.38108e+08
theta = 78.84 delta = 1.36555e+08
theta = 79.02 delta = 1.25775e+08
theta = 79.2 delta = 9.77237e+07
theta = 79.38 delta = 4.49362e+07
theta = 79.56 delta = -2.62925e+07
theta = 79.74 delta = -8.88538e+07
theta = 79.92 delta = -1.2081e+08
theta = 80.1 delta = -1.25391e+08
theta = 80.28 delta = -1.15908e+08
theta = 80.46 delta = -1.01826e+08
theta = 80.64 delta = -8.75302e+07
theta = 80.82 delta = -7.45874e+07
theta = 81 delta = -6.33607e+07
theta = 81.18 delta = -5.37707e+07
theta = 81.36 delta = -4.56057e+07
theta = 81.54 delta = -3.8639e+07
theta = 81.72 delta = -3.26671e+07
theta = 81.9 delta = -2.75193e+07
theta = 82.08 delta = -2.30559e+07
theta = 82.26 delta = -1.91636e+07
theta = 82.44 delta = -1.57511e+07
theta = 82.62 delta = -1.27443e+07
theta = 82.8 delta = -1.00827e+07
theta = 82.98 delta = -7.71687e+06
theta = 83.16 delta = -5.60616e+06
theta = 83.34 delta = -3.71671e+06
theta = 83.52 delta = -2.02031e+06
theta = 83.7 delta = -493246
theta = 83.88 delta = 884540
theta = 84.06 delta = 2.13009e+06
theta = 84.24 delta = 3.25798e+06
theta = 84.42 delta = 4.28074e+06
theta = 84.6 delta = 5.20919e+06
theta = 84.78 delta = 6.05271e+06
theta = 84.96 delta = 6.81951e+06
theta = 85.14 delta = 7.51674e+06
theta = 85.32 delta = 8.15072e+06
theta = 85.5 delta = 8.727e+06
theta = 85.68 delta = 9.2505e+06
theta = 85.86 delta = 9.72562e+06
theta = 86.04 delta = 1.01562e+07
theta = 86.22 delta = 1.05459e+07
theta = 86.4 delta = 1.08976e+07
theta = 86.58 delta = 1.12144e+07
theta = 86.76 delta = 1.14986e+07
theta = 86.94 delta = 1.17526e+07
theta = 87.12 delta = 1.19786e+07
theta = 87.3 delta = 1.21783e+07
theta = 87.48 delta = 1.23535e+07
theta = 87.66 delta = 1.25059e+07
theta = 87.84 delta = 1.26367e+07
theta = 88.02 delta = 1.27475e+07
theta = 88.2 delta = 1.28393e+07
theta = 88.38 delta = 1.29134e+07
theta = 88.56 delta = 1.29707e+07
theta = 88.74 delta = 1.30122e+07
theta = 88.92 delta = 1.30388e+07
theta = 89.1 delta = 1.30513e+07
theta = 89.28 delta = 1.30505e+07
theta = 89.46 delta = 1.30371e+07
theta = 89.64 delta = 1.30117e+07
theta = 89.82 delta = 1.29749e+07
theta = 90 delta = 1.29275e+07
theta = 90.18 delta = 1.28698e+07
theta = 90.36 delta = 1.28024e+07
theta = 90.54 delta = 1.27257e+07
theta = 90.72 delta = 1.26403e+07
theta = 90.9 delta = 1.25465e+07
theta = 91.08 delta = 1.24447e+07
theta = 91.26 delta = 1.23353e+07
theta = 91.44 delta = 1.22187e+07
theta = 91.62 delta = 1.20952e+07
theta = 91.8 delta = 1.1965e+07
theta = 91.98 delta = 1.18286e+07
theta = 92.16 delta = 1.16861e+07
theta = 92.34 delta = 1.15379e+07
theta = 92.52 delta = 1.13843e+07
theta = 92.7 delta = 1.12254e+07
theta = 92.88 delta = 1.10614e+07
theta = 93.06 delta = 1.08927e+07
theta = 93.24 delta = 1.07194e+07
theta = 93.42 delta = 1.05418e+07
theta = 93.6 delta = 1.03599e+07
theta = 93.78 delta = 1.01741e+07
theta = 93.96 delta = 9.98443e+06
theta = 94.14 delta = 9.79113e+06
theta = 94.32 delta = 9.59436e+06
theta = 94.5 delta = 9.39426e+06
theta = 94.68 delta = 9.19099e+06
theta = 94.86 delta = 8.9847e+06
theta = 95.04 delta = 8.77552e+06
theta = 95.22 delta = 8.56359e+06
theta = 95.4 delta = 8.34905e+06
theta = 95.58 delta = 8.13201e+06
theta = 95.76 delta = 7.9126e+06
theta = 95.94 delta = 7.69093e+06
theta = 96.12 delta = 7.46712e+06
theta = 96.3 delta = 7.24129e+06
theta = 96.48 delta = 7.01353e+06
theta = 96.66 delta = 6.78395e+06
theta = 96.84 delta = 6.55265e+06
theta = 97.02 delta = 6.31973e+06
theta = 97.2 delta = 6.08529e+06
theta = 97.38 delta = 5.84941e+06
theta = 97.56 delta = 5.61218e+06
theta = 97.74 delta = 5.37369e+06
theta = 97.92 delta = 5.13403e+06
theta = 98.1 delta = 4.89327e+06
theta = 98.28 delta = 4.65151e+06
theta = 98.46 delta = 4.40881e+06
theta = 98.64 delta = 4.16525e+06
theta = 98.82 delta = 3.92091e+06
theta = 99 delta = 3.67586e+06
theta = 99.18 delta = 3.43016e+06
theta = 99.36 delta = 3.1839e+06
theta = 99.54 delta = 2.93713e+06
theta = 99.72 delta = 2.68993e+06
theta = 99.9 delta = 2.44235e+06
theta = 100.08 delta = 2.19446e+06
theta = 100.26 delta = 1.94632e+06
theta = 100.44 delta = 1.698e+06
theta = 100.62 delta = 1.44955e+06
theta = 100.8 delta = 1.20103e+06
theta = 100.98 delta = 952488
theta = 101.16 delta = 703992
theta = 101.34 delta = 455593
theta = 101.52 delta = 207343
theta = 101.7 delta = -40705.4
theta = 101.88 delta = -288501
theta = 102.06 delta = -535993
theta = 102.24 delta = -783132
theta = 102.42 delta = -1.02987e+06
theta = 102.6 delta = -1.27616e+06
theta = 102.78 delta = -1.52195e+06
theta = 102.96 delta = -1.76721e+06
theta = 103.14 delta = -2.01187e+06
theta = 103.32 delta = -2.25591e+06
theta = 103.5 delta = -2.49928e+06
theta = 103.68 delta = -2.74192e+06
theta = 103.86 delta = -2.98381e+06
theta = 104.04 delta = -3.22491e+06
theta = 104.22 delta = -3.46516e+06
theta = 104.4 delta = -3.70453e+06
theta = 104.58 delta = -3.94299e+06
theta = 104.76 delta = -4.1805e+06
theta = 104.94 delta = -4.417e+06
theta = 105.12 delta = -4.65249e+06
theta = 105.3 delta = -4.8869e+06
theta = 105.48 delta = -5.12021e+06
theta = 105.66 delta = -5.35239e+06
theta = 105.84 delta = -5.5834e+06
theta = 106.02 delta = -5.8132e+06
theta = 106.2 delta = -6.04177e+06
theta = 106.38 delta = -6.26907e+06
theta = 106.56 delta = -6.49506e+06
theta = 106.74 delta = -6.71972e+06
theta = 106.92 delta = -6.94303e+06
theta = 107.1 delta = -7.16493e+06
theta = 107.28 delta = -7.38542e+06
theta = 107.46 delta = -7.60445e+06
theta = 107.64 delta = -7.822e+06
theta = 107.82 delta = -8.03805e+06
theta = 108 delta = -8.25256e+06
theta = 108.18 delta = -8.46551e+06
theta = 108.36 delta = -8.67686e+06
theta = 108.54 delta = -8.88661e+06
theta = 108.72 delta = -9.09471e+06
theta = 108.9 delta = -9.30115e+06
theta = 109.08 delta = -9.5059e+06
theta = 109.26 delta = -9.70894e+06
theta = 109.44 delta = -9.91024e+06
theta = 109.62 delta = -1.01098e+07
theta = 109.8 delta = -1.03076e+07
theta = 109.98 delta = -1.05035e+07
theta = 110.16 delta = -1.06976e+07
theta = 110.34 delta = -1.08899e+07
theta = 110.52 delta = -1.10804e+07
theta = 110.7 delta = -1.12689e+07
theta = 110.88 delta = -1.14555e+07
theta = 111.06 delta = -1.16403e+07
theta = 111.24 delta = -1.1823e+07
theta = 111.42 delta = -1.20038e+07
theta = 111.6 delta = -1.21827e+07
theta = 111.78 delta = -1.23595e+07
theta = 111.96 delta = -1.25343e+07
theta = 112.14 delta = -1.27071e+07
theta = 112.32 delta = -1.28779e+07
theta = 112.5 delta = -1.30466e+07
theta = 112.68 delta = -1.32132e+07
theta = 112.86 delta = -1.33777e+07
theta = 113.04 delta = -1.35402e+07
theta = 113.22 delta = -1.37005e+07
theta = 113.4 delta = -1.38586e+07
theta = 113.58 delta = -1.40147e+07
theta = 113.76 delta = -1.41686e+07
theta = 113.94 delta = -1.43203e+07
theta = 114.12 delta = -1.44698e+07
theta = 114.3 delta = -1.46172e+07
theta = 114.48 delta = -1.47624e+07
theta = 114.66 delta = -1.49053e+07
theta = 114.84 delta = -1.5046e+07
theta = 115.02 delta = -1.51845e+07
theta = 115.2 delta = -1.53208e+07
theta = 115.38 delta = -1.54548e+07
theta = 115.56 delta = -1.55866e+07
theta = 115.74 delta = -1.57161e+07
theta = 115.92 delta = -1.58433e+07
theta = 116.1 delta = -1.59683e+07
theta = 116.28 delta = -1.60909e+07
theta = 116.46 delta = -1.62113e+07
theta = 116.64 delta = -1.63294e+07
theta = 116.82 delta = -1.64452e+07
theta = 117 delta = -1.65587e+07
theta = 117.18 delta = -1.66699e+07
theta = 117.36 delta = -1.67787e+07
theta = 117.54 delta = -1.68853e+07
theta = 117.72 delta = -1.69895e+07
theta = 117.9 delta = -1.70914e+07
theta = 118.08 delta = -1.7191e+07
theta = 118.26 delta = -1.72883e+07
theta = 118.44 delta = -1.73832e+07
theta = 118.62 delta = -1.74758e+07
theta = 118.8 delta = -1.75661e+07
theta = 118.98 delta = -1.7654e+07
theta = 119.16 delta = -1.77396e+07
theta = 119.34 delta = -1.78229e+07
theta = 119.52 delta = -1.79038e+07
theta = 119.7 delta = -1.79824e+07
theta = 119.88 delta = -1.80587e+07
theta = 120.06 delta = -1.81326e+07
theta = 120.24 delta = -1.82042e+07
theta = 120.42 delta = -1.82735e+07
theta = 120.6 delta = -1.83405e+07
theta = 120.78 delta = -1.84052e+07
theta = 120.96 delta = -1.84675e+07
theta = 121.14 delta = -1.85275e+07
theta = 121.32 delta = -1.85852e+07
theta = 121.5 delta = -1.86407e+07
theta = 121.68 delta = -1.86938e+07
theta = 121.86 delta = -1.87446e+07
theta = 122.04 delta = -1.87931e+07
theta = 122.22 delta = -1.88394e+07
theta = 122.4 delta = -1.88834e+07
theta = 122.58 delta = -1.89251e+07
theta = 122.76 delta = -1.89645e+07
theta = 122.94 delta = -1.90017e+07
theta = 123.12 delta = -1.90366e+07
theta = 123.3 delta = -1.90693e+07
theta = 123.48 delta = -1.90998e+07
theta = 123.66 delta = -1.9128e+07
theta = 123.84 delta = -1.91541e+07
theta = 124.02 delta = -1.91779e+07
theta = 124.2 delta = -1.91995e+07
theta = 124.38 delta = -1.92189e+07
theta = 124.56 delta = -1.92361e+07
theta = 124.74 delta = -1.92512e+07
theta = 124.92 delta = -1.92641e+07
theta = 125.1 delta = -1.92749e+07
theta = 125.28 delta = -1.92835e+07
theta = 125.46 delta = -1.929e+07
theta = 125.64 delta = -1.92944e+07
theta = 125.82 delta = -1.92967e+07
theta = 126 delta = -1.92969e+07
theta = 126.18 delta = -1.9295e+07
theta = 126.36 delta = -1.92911e+07
theta = 126.54 delta = -1.92851e+07
theta = 126.72 delta = -1.9277e+07
theta = 126.9 delta = -1.9267e+07
theta = 127.08 delta = -1.92549e+07
theta = 127.26 delta = -1.92408e+07
theta = 127.44 delta = -1.92247e+07
theta = 127.62 delta = -1.92067e+07
theta = 127.8 delta = -1.91867e+07
theta = 127.98 delta = -1.91648e+07
theta = 128.16 delta = -1.91409e+07
theta = 128.34 delta = -1.91152e+07
theta = 128.52 delta = -1.90875e+07
theta = 128.7 delta = -1.9058e+07
theta = 128.88 delta = -1.90265e+07
theta = 129.06 delta = -1.89933e+07
theta = 129.24 delta = -1.89582e+07
theta = 129.42 delta = -1.89213e+07
theta = 129.6 delta = -1.88826e+07
theta = 129.78 delta = -1.88421e+07
theta = 129.96 delta = -1.87999e+07
theta = 130.14 delta = -1.87559e+07
theta = 130.32 delta = -1.87102e+07
theta = 130.5 delta = -1.86628e+07
theta = 130.68 delta = -1.86137e+07
theta = 130.86 delta = -1.85629e+07
theta = 131.04 delta = -1.85104e+07
theta = 131.22 delta = -1.84563e+07
theta = 131.4 delta = -1.84006e+07
theta = 131.58 delta = -1.83433e+07
theta = 131.76 delta = -1.82845e+07
theta = 131.94 delta = -1.8224e+07
theta = 132.12 delta = -1.8162e+07
theta = 132.3 delta = -1.80985e+07
theta = 132.48 delta = -1.80335e+07
theta = 132.66 delta = -1.7967e+07
theta = 132.84 delta = -1.78991e+07
theta = 133.02 delta = -1.78297e+07
theta = 133.2 delta = -1.77589e+07
theta = 133.38 delta = -1.76866e+07
theta = 133.56 delta = -1.7613e+07
theta = 133.74 delta = -1.7538e+07
theta = 133.92 delta = -1.74617e+07
theta = 134.1 delta = -1.73841e+07
theta = 134.28 delta = -1.73052e+07
theta = 134.46 delta = -1.7225e+07
theta = 134.64 delta = -1.71435e+07
theta = 134.82 delta = -1.70608e+07
theta = 135 delta = -1.69769e+07
theta = 135.18 delta = -1.68918e+07
theta = 135.36 delta = -1.68055e+07
theta = 135.54 delta = -1.6718e+07
theta = 135.72 delta = -1.66295e+07
theta = 135.9 delta = -1.65398e+07
theta = 136.08 delta = -1.64491e+07
theta = 136.26 delta = -1.63572e+07
theta = 136.44 delta = -1.62644e+07
theta = 136.62 delta = -1.61705e+07
theta = 136.8 delta = -1.60756e+07
theta = 136.98 delta = -1.59797e+07
theta = 137.16 delta = -1.58829e+07
theta = 137.34 delta = -1.57852e+07
theta = 137.52 delta = -1.56865e+07
theta = 137.7 delta = -1.5587e+07
theta = 137.88 delta = -1.54866e+07
theta = 138.06 delta = -1.53853e+07
theta = 138.24 delta = -1.52832e+07
theta = 138.42 delta = -1.51804e+07
theta = 138.6 delta = -1.50767e+07
theta = 138.78 delta = -1.49723e+07
theta = 138.96 delta = -1.48672e+07
theta = 139.14 delta = -1.47613e+07
theta = 139.32 delta = -1.46548e+07
theta = 139.5 delta = -1.45476e+07
theta = 139.68 delta = -1.44397e+07
theta = 139.86 delta = -1.43312e+07
theta = 140.04 delta = -1.42222e+07
theta = 140.22 delta = -1.41125e+07
theta = 140.4 delta = -1.40023e+07
theta = 140.58 delta = -1.38916e+07
theta = 140.76 delta = -1.37803e+07
theta = 140.94 delta = -1.36686e+07
theta = 141.12 delta = -1.35564e+07
theta = 141.3 delta = -1.34437e+07
theta = 141.48 delta = -1.33307e+07
theta = 141.66 delta = -1.32172e+07
theta = 141.84 delta = -1.31033e+07
theta = 142.02 delta = -1.29891e+07
theta = 142.2 delta = -1.28746e+07
theta = 142.38 delta = -1.27597e+07
theta = 142.56 delta = -1.26445e+07
theta = 142.74 delta = -1.25291e+07
theta = 142.92 delta = -1.24134e+07
theta = 143.1 delta = -1.22975e+07
theta = 143.28 delta = -1.21814e+07
theta = 143.46 delta = -1.20651e+07
theta = 143.64 delta = -1.19486e+07
theta = 143.82 delta = -1.1832e+07
theta = 144 delta = -1.17152e+07
theta = 144.18 delta = -1.15983e+07
theta = 144.36 delta = -1.14814e+07
theta = 144.54 delta = -1.13644e+07
theta = 144.72 delta = -1.12473e+07
theta = 144.9 delta = -1.11303e+07
theta = 145.08 delta = -1.10132e+07
theta = 145.26 delta = -1.08961e+07
theta = 145.44 delta = -1.07791e+07
theta = 145.62 delta = -1.06621e+07
theta = 145.8 delta = -1.05452e+07
theta = 145.98 delta = -1.04284e+07
theta = 146.16 delta = -1.03118e+07
theta = 146.34 delta = -1.01952e+07
theta = 146.52 delta = -1.00788e+07
theta = 146.7 delta = -9.96257e+06
theta = 146.88 delta = -9.84652e+06
theta = 147.06 delta = -9.73068e+06
theta = 147.24 delta = -9.61507e+06
theta = 147.42 delta = -9.4997e+06
theta = 147.6 delta = -9.38459e+06
theta = 147.78 delta = -9.26976e+06
theta = 147.96 delta = -9.15523e+06
theta = 148.14 delta = -9.04101e+06
theta = 148.32 delta = -8.92712e+06
theta = 148.5 delta = -8.81357e+06
theta = 148.68 delta = -8.7004e+06
theta = 148.86 delta = -8.5876e+06
theta = 149.04 delta = -8.4752e+06
theta = 149.22 delta = -8.36321e+06
theta = 149.4 delta = -8.25166e+06
theta = 149.58 delta = -8.14055e+06
theta = 149.76 delta = -8.0299e+06
theta = 149.94 delta = -7.91973e+06
theta = 150.12 delta = -7.81005e+06
theta = 150.3 delta = -7.70088e+06
theta = 150.48 delta = -7.59222e+06
theta = 150.66 delta = -7.48411e+06
theta = 150.84 delta = -7.37654e+06
theta = 151.02 delta = -7.26954e+06
theta = 151.2 delta = -7.16312e+06
theta = 151.38 delta = -7.05729e+06
theta = 151.56 delta = -6.95207e+06
theta = 151.74 delta = -6.84746e+06
theta = 151.92 delta = -6.74349e+06
theta = 152.1 delta = -6.64016e+06
theta = 152.28 delta = -6.53749e+06
theta = 152.46 delta = -6.43549e+06
theta = 152.64 delta = -6.33416e+06
theta = 152.82 delta = -6.23354e+06
theta = 153 delta = -6.13361e+06
theta = 153.18 delta = -6.0344e+06
theta = 153.36 delta = -5.93592e+06
theta = 153.54 delta = -5.83818e+06
theta = 153.72 delta = -5.74119e+06
theta = 153.9 delta = -5.64495e+06
theta = 154.08 delta = -5.54948e+06
theta = 154.26 delta = -5.45479e+06
theta = 154.44 delta = -5.36089e+06
theta = 154.62 delta = -5.26779e+06
theta = 154.8 delta = -5.17549e+06
theta = 154.98 delta = -5.08401e+06
theta = 155.16 delta = -4.99335e+06
theta = 155.34 delta = -4.90352e+06
theta = 155.52 delta = -4.81453e+06
theta = 155.7 delta = -4.72639e+06
theta = 155.88 delta = -4.6391e+06
theta = 156.06 delta = -4.55268e+06
theta = 156.24 delta = -4.46713e+06
theta = 156.42 delta = -4.38245e+06
theta = 156.6 delta = -4.29865e+06
theta = 156.78 delta = -4.21574e+06
theta = 156.96 delta = -4.13372e+06
theta = 157.14 delta = -4.0526e+06
theta = 157.32 delta = -3.97239e+06
theta = 157.5 delta = -3.89309e+06
theta = 157.68 delta = -3.8147e+06
theta = 157.86 delta = -3.73723e+06
theta = 158.04 delta = -3.66068e+06
theta = 158.22 delta = -3.58506e+06
theta = 158.4 delta = -3.51037e+06
theta = 158.58 delta = -3.43661e+06
theta = 158.76 delta = -3.36379e+06
theta = 158.94 delta = -3.29191e+06
theta = 159.12 delta = -3.22097e+06
theta = 159.3 delta = -3.15097e+06
theta = 159.48 delta = -3.08192e+06
theta = 159.66 delta = -3.01382e+06
theta = 159.84 delta = -2.94667e+06
theta = 160.02 delta = -2.88047e+06
theta = 160.2 delta = -2.81522e+06
theta = 160.38 delta = -2.75092e+06
theta = 160.56 delta = -2.68757e+06
theta = 160.74 delta = -2.62517e+06
theta = 160.92 delta = -2.56373e+06
theta = 161.1 delta = -2.50323e+06
theta = 161.28 delta = -2.44369e+06
theta = 161.46 delta = -2.38509e+06
theta = 161.64 delta = -2.32745e+06
theta = 161.82 delta = -2.27075e+06
theta = 162 delta = -2.21499e+06
theta = 162.18 delta = -2.16017e+06
theta = 162.36 delta = -2.1063e+06
theta = 162.54 delta = -2.05336e+06
theta = 162.72 delta = -2.00135e+06
theta = 162.9 delta = -1.95027e+06
theta = 163.08 delta = -1.90012e+06
theta = 163.26 delta = -1.8509e+06
theta = 163.44 delta = -1.80259e+06
theta = 163.62 delta = -1.7552e+06
theta = 163.8 delta = -1.70871e+06
theta = 163.98 delta = -1.66313e+06
theta = 164.16 delta = -1.61845e+06
theta = 164.34 delta = -1.57467e+06
theta = 164.52 delta = -1.53177e+06
theta = 164.7 delta = -1.48975e+06
theta = 164.88 delta = -1.44861e+06
theta = 165.06 delta = -1.40834e+06
theta = 165.24 delta = -1.36894e+06
theta = 165.42 delta = -1.33039e+06
theta = 165.6 delta = -1.29268e+06
theta = 165.78 delta = -1.25582e+06
theta = 165.96 delta = -1.2198e+06
theta = 166.14 delta = -1.18459e+06
theta = 166.32 delta = -1.15021e+06
theta = 166.5 delta = -1.11663e+06
theta = 166.68 delta = -1.08386e+06
theta = 166.86 delta = -1.05187e+06
theta = 167.04 delta = -1.02067e+06
theta = 167.22 delta = -990242
theta = 167.4 delta = -960575
theta = 167.58 delta = -931661
theta = 167.76 delta = -903489
theta = 167.94 delta = -876050
theta = 168.12 delta = -849332
theta = 168.3 delta = -823325
theta = 168.48 delta = -798018
theta = 168.66 delta = -773400
theta = 168.84 delta = -749459
theta = 169.02 delta = -726183
theta = 169.2 delta = -703561
theta = 169.38 delta = -681580
theta = 169.56 delta = -660228
theta = 169.74 delta = -639493
theta = 169.92 delta = -619361
theta = 170.1 delta = -599821
theta = 170.28 delta = -580857
theta = 170.46 delta = -562459
theta = 170.64 delta = -544610
theta = 170.82 delta = -527299
theta = 171 delta = -510511
theta = 171.18 delta = -494232
theta = 171.36 delta = -478448
theta = 171.54 delta = -463144
theta = 171.72 delta = -448306
theta = 171.9 delta = -433918
theta = 172.08 delta = -419967
theta = 172.26 delta = -406436
theta = 172.44 delta = -393310
theta = 172.62 delta = -380574
theta = 172.8 delta = -368213
theta = 172.98 delta = -356210
theta = 173.16 delta = -344549
theta = 173.34 delta = -333215
theta = 173.52 delta = -322191
theta = 173.7 delta = -311461
theta = 173.88 delta = -301008
theta = 174.06 delta = -290815
theta = 174.24 delta = -280867
theta = 174.42 delta = -271145
theta = 174.6 delta = -261633
theta = 174.78 delta = -252313
theta = 174.96 delta = -243169
theta = 175.14 delta = -234183
theta = 175.32 delta = -225337
theta = 175.5 delta = -216614
theta = 175.68 delta = -207996
theta = 175.86 delta = -199465
theta = 176.04 delta = -191003
theta = 176.22 delta = -182592
theta = 176.4 delta = -174214
theta = 176.58 delta = -165851
theta = 176.76 delta = -157484
theta = 176.94 delta = -149095
theta = 177.12 delta = -140666
theta = 177.3 delta = -132178
theta = 177.48 delta = -123612
theta = 177.66 delta = -114950
theta = 177.84 delta = -106172
theta = 178.02 delta = -97261
theta = 178.2 delta = -88196.9
theta = 178.38 delta = -78961.1
theta = 178.56 delta = -69534.5
theta = 178.74 delta = -59898.2
theta = 178.92 delta = -50033.2
theta = 179.1 delta = -39920.1
theta = 179.28 delta = -29540.1
theta = 179.46 delta = -18873.8
theta = 179.64 delta = -7902.03
theta = 179.82 delta = 3394.36
theta = 180 delta = 15034.6
a=-7.22037e-05
theta = 80.1, a = -7.22037e-05, sommet =[200, 300]



et ma fonction draw refaite :

Code: Tout sélectionner

void Parabole::draw (Mat& img){
    // Itérer sur chaque pixel
    for(double y = 0; y < img.rows; y+=0.1) {
        for(double x = 0; x < img.cols; x += 0.1) {
            // Calculer X' et Y'
            double X_prime = x - sommet.x;
            double Y_prime = y - sommet.y;

            // Calculer la valeur de l'équation de la parabole
            double val = a*pow(cos(this->theta_radians)*X_prime + sin(this->theta_radians)*Y_prime, 2)
                            - sin(this->theta_radians)*X_prime - cos(this->theta_radians)*Y_prime;

            // Si val est proche de 0, colorer le pixel
            if(fabs(val) < 0.1) { // Vous pouvez ajuster la tolérance
                img.at<cv::Vec3b>(y, x) = cv::Vec3b(0,0,255); // Par exemple, en blanc
            }
        }
    }
}

[leon1789]

yes Ben

Léon : quel logiciel as-tu utilisé Mathematica ?

Maple 8 ... (année 2002 ! )

[sylvain231]

Léon peux-tu nous refaire les formules détaillées avec tes changements de signe et tes corrections STP ?

[sylvain231]

allé courage je suis sûr qu'on va y arriver !

[leon1789]

j'ai écrit les formules principales ici :
superieur/regression-parabolique-non-triviale-t278846-80.html#p1548878

n = 269

Xt est la liste des Xt[i] (abscisses des points tournés) : cos(t)*X[i] - sin(t)*Y[i]

Yt est la liste des Yt[i] (ordonnées des points tournés) : sin(t)*X[i] + cos(t)*Y[i]

[sylvain231]

oui mais ça c'est du Maple c'est optimisé pour les maths on a des fonctions prédéfinies pour minimiser etc, en C++ il faut tout détailler

[leon1789]

Pour cerner l'erreur (ou les erreurs) , prend MA valeur de t (attention au Sommet : (200,300) ou (191, 291) ),
puis avec ce t calcule TA valeur de a : est-ce la même que moi ?

[leon1789]

j'ai trouvé cet article est-il intéressant ?(...)

C'est peut-être lié à cela
superieur/regression-parabolique-non-triviale-t278846-20.html#p1548698

[lyceen95]

Le rigolo de service, c'est quelqu'un qui s'est fait bannir de tous les forums d'entraide francophones ; chacun en tire les conclusions qu'il veut.

[sylvain231]

j'ai adapté mon code à celui de Léon c'est beaucoup mieux : le theta est bon mais pas le a, je vous donne mon code :

Code: Tout sélectionner

std::vector<Point2d> translatePoint2ds(const std::vector<Point2d>& points, const Point2d& sommet) {
    std::vector<Point2d> translatedPoint2ds;
    for (const auto& point : points) {
        translatedPoint2ds.push_back({point.x - sommet.x, point.y - sommet.y});
    }
    return translatedPoint2ds;
}

std::vector<Point2d> rotatePoint2ds(const std::vector<Point2d>& points, double theta) {
    std::vector<Point2d> rotatedPoint2ds;
    for (const auto& point : points) {
        rotatedPoint2ds.push_back({point.x * cos(theta) - point.y * sin(theta), point.x * sin(theta) + point.y * cos(theta)});
    }
    return rotatedPoint2ds;
}
void Parabole::fit(std::vector<cv::Point2d> points, cv::Point2d sommet) {
    this->sommet = sommet;
    int n = points.size();
    cout << "sommet = " << sommet << endl;
    points = translatePoint2ds(points, sommet);
    double bestTheta = 0;
    double minimum= std::numeric_limits<double>::infinity();
    cv::Mat img(6500, 6500, CV_8UC3, cv::Scalar(255, 255, 255));//crée une image blanche vide de 500x500 pixels
    vector<Point> vec;
    for (double theta = 0; theta <= CV_PI; theta += CV_PI / 1000) {

        vector<Point2d> rotated = rotatePoint2ds(points, theta);
        double E1 = 0;
        for (int i = 0; i < n; i++) {
            E1 += pow(rotated[i].y, 2);
        }
        double E2 = 0;
        for (int i = 0; i < n; i++) {
            E2 += pow(rotated[i].x, 2)* rotated[i].y;
        }
        double E3 = 0;
        for (int i = 0; i < n; i++) {
            E3 += pow(rotated[i].x, 4);
        }
        double delta = E1 - (E2 / E3);
        if (delta < minimum) {
            minimum = delta;
            bestTheta = theta;
        }
        vec.push_back(Point(6500-theta*1000,delta));
    }
    drawVectorPoints(img, vec, Scalar(0, 0, 255));
    imwrite("delta.png", img);
    this->theta_radians = bestTheta;
    this->theta = bestTheta * 180 / CV_PI;
    vector<Point2d> rotated = rotatePoint2ds(points, bestTheta);
    double E2 = 0;
    for (int i = 0; i < n; i++) {
        E2 += pow(rotated[i].x, 2) * rotated[i].y;
    }
    double E3 = 0;
    for (int i = 0; i < n; i++) {
        E3 += pow(rotated[i].x, 4);
    }
    this->a = E2 / E3;
    cout<<"a="<< this->a << endl;

}

void Parabole::draw (Mat& img){
    // Itérer sur chaque pixel
    for(double y = 0; y < img.rows; y+=0.1) {
        for(double x = 0; x < img.cols; x += 0.1) {
            // Calculer X' et Y'
            double X_prime = x - sommet.x;
            double Y_prime = y - sommet.y;

            // Calculer la valeur de l'équation de la parabole
            double val = a*pow(cos(this->theta_radians)*X_prime + sin(this->theta_radians)*Y_prime, 2)
                            - sin(this->theta_radians)*X_prime - cos(this->theta_radians)*Y_prime;

            // Si val est proche de 0, colorer le pixel
            if(fabs(val) < 0.1) { // Vous pouvez ajuster la tolérance
                img.at<cv::Vec3b>(y, x) = cv::Vec3b(0,0,255); // Par exemple, en blanc
            }
        }
    }
}



et l'image résultante :



sachant que si ça peut aider je sais dans mes points de départ lesquels sont dans une branche et lesquels sont dans l'autre

[sylvain231]

là j'obtiens un a proche de 0 au lieu de 2

[sylvain231]

je pense que comme les points sont serrés il cherche une droite, ce que je ne veux pas donc je crois qu'on ne va pas couper à lui donner les points à gauche et les points à droite, désolé ça fait du travail supplémentaire

[sylvain231]

mais je trouve la formule du a pas équilibrée si on a des X proches des Y on a du X^3/X^4 donc toujours des petits a

[leon1789]

Question d'homogénéïté :
Par définition, on a
Yt ~~ a * Xt ^2 (et non Yt ~~ Xt )
Donc
Yt * Xt^2 ~~ a * Xt ^4
Donc
a ~~ Yt * Xt^2 / Xt ^4

Après, en fonction des situations, a peut être proche de 0 , ou très grand...

[sylvain231]

et pourquoi on ne fait pas : a=Yt/Xt^2 tout simplement ?

[sylvain231]

j'ai malheureusement des cas où le theta n'est pas bon !

[leon1789]

et pourquoi on ne fait pas : a=Yt/Xt^2 tout simplement ?

Yt et Xt représentent tous les points : on a 269 équations du type Yt[i] = a Xt[i]^2

On utilise les moindres carrés pour déterminer a
(qui est géométriquement une simple projection orthogonale d'un vecteur Yt sur une droite dirigée par Xt^2, dans un espace euclidien de dimension 269)
et on obtient la formule donnée pour a :

a = add(Xt[i]^2*Yt[i], i=1..n) / add(Xt[i]^4, i=1..n) ;

[sylvain231]

je viens de m'apercevoir que c'ets Ben qui avait raison c'est bien :
double val = a*pow(cos(this->theta_radians)*X_prime + sin(this->theta_radians)*Y_prime, 2)
+ sin(this->theta_radians)*X_prime - cos(this->theta_radians)*Y_prime;
et non
double val = a*pow(cos(this->theta_radians)*X_prime + sin(this->theta_radians)*Y_prime, 2)
- sin(this->theta_radians)*X_prime - cos(this->theta_radians)*Y_prime;
donc le theta est bon !