Régression parabolique non triviale

[leon1789]

pour ton dessin, tu tiens bien compte du sommet en (191 ; 291) ?

[sylvain231]

oui mais la parabole a le bon sommet c'est l'angle qui n'est pas bon

[sylvain231]

ce qui est bizarre c'est que sur la parabole plate le theta est bon

[leon1789]

problème de signe :

Code: Tout sélectionner

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;

[sylvain231]

peux-tu m'envoyer l'image que tu as de la parabole plate STP car moi ça colle pas au niveau de l'ouverture ?

[leon1789]

as-tu corrigé avec ma ligne de code ci-dessus ?

[sylvain231]

ah oui là ça colle parfaitement !

[sylvain231]

mais c'est Ben qui s'était trompé dans le signe en premier, moi j'ai recopié, du coup je n'obtenais jamais les mêmes résultats que vous, ouf on y est arrivé !

[sylvain231]

je teste sur d'autres cas pour valider

[sylvain231]

ah j'ai trouvé un ensemble de points pour lesquels ça foire :

[267.482, 285.125]
[270.767, 288.156]
[279.041, 281.463]
[297.873, 287.311]
[296.95, 278.617]
[300.955, 281]
[271.478, 291.526]
[308.361, 284.636]
[312.525, 288.363]
[256.566, 288.298]
[312.581, 287.3]
[261.177, 292.503]
[259.556, 279.944]
[313.525, 279.519]
[264.735, 294.106]
[314.178, 294.834]
[245.998, 281.875]
[324.267, 286.539]
[251.241, 283.043]
[247.328, 294.931]
[330.708, 280.901]
[247.969, 279.694]
[326.908, 278.465]
[245.711, 286.321]
[240.133, 280.027]
[329.768, 296.736]
[248.547, 294.807]
[341.837, 292.7]
[335.604, 277.726]
[248.832, 292.95]
[344.93, 296.523]
[227.99, 297.168]
[350.353, 286.725]
[233.201, 288.092]
[362.114, 278.857]
[227.542, 294.123]
[366.041, 290.84]
[230.65, 283.977]
[226.301, 297.004]
[360.336, 285.247]
[374.28, 282.959]
[234.264, 285.711]
[236.231, 287.489]
[359.8, 278.9]
[222.586, 294.937]
[367.932, 289.673]
[225.639, 285.616]
[371.935, 279.974]
[218.128, 280.043]
[222.87, 279.895]
[383.229, 290.114]
[395.42, 285.705]
[221.632, 299.671]
[392.265, 293.834]
[391.034, 281.913]
[223.666, 284.68]
[212.066, 299.573]
[401.484, 283.612]
[212.072, 288.658]
[415.035, 284.583]
[222.008, 285.454]
[218.825, 292.231]
[407.697, 299.358]
[211.833, 301.132]
[413.215, 281.647]
[205.717, 298.745]
[207.695, 297.523]
[414.048, 287.043]
[211.844, 299.872]
[212.759, 282.816]
[416.342, 301.338]
[423.256, 291.924]
[208.061, 298.804]
[438.614, 293.92]
[431.543, 288.965]
[438.403, 293.146]
[431.161, 286.239]
[450.916, 291.396]
[211.25, 294.032]
[210.966, 289.622]
[449.317, 285.215]
[443.112, 295.719]
[453.402, 300.993]
[207.455, 293.061]
[208.529, 291.364]
[213.392, 304.663]
[200.486, 287.087]
[480.236, 291.841]
[196.158, 300.716]
[207.314, 299.155]
[482.622, 305.217]
[484.274, 305.396]
[200.374, 301.177]
[202.411, 292.301]
[482.002, 291.443]
[200.144, 303.281]
[203.505, 306.447]
[482.737, 291.867]
[193.109, 303.664]
[500.254, 299.925]
[198.549, 300.557]
[503.011, 291.274]
[201.566, 290.327]
[191.766, 293.79]
[201.34, 308.187]
[196.012, 306.33]
[207.89, 305.62]
[206.46, 308.99]
[192.98, 299.776]
[206.256, 302.84]
[207.823, 311.247]
[205.701, 310.005]
[206.973, 311.493]
[194.84, 313.51]
[207.34, 314.717]
[212.993, 312.28]
[198.166, 319.767]
[200.617, 306.003]
[204.75, 319.95]
[212.673, 310.185]
[208.976, 319.994]
[202.67, 321.019]
[206.421, 308.965]
[217.924, 308.631]
[209.052, 306.252]
[204.235, 310.981]
[213.244, 304.967]
[215.96, 305.491]
[214.196, 304.961]
[211.805, 305.767]
[212.828, 319.209]
[211.973, 318.979]
[206.937, 325.574]
[221.408, 320.187]
[222.701, 310.429]
[211.348, 317.789]
[228.102, 322.596]
[228.357, 326.18]
[218.2, 318.81]
[224.679, 326.736]
[218.712, 324.204]
[231.277, 315.864]
[216.799, 316.763]
[224.554, 323.022]
[221.09, 332.011]
[226.868, 322.045]
[222.381, 332.471]
[234.031, 324.791]
[244.863, 326.893]
[246.266, 320.569]
[230.009, 324.407]
[248.026, 328.286]
[234.652, 339.021]
[240.475, 326.302]
[246.63, 332.16]
[258.97, 331.047]
[254.178, 335.346]
[269.673, 329.477]
[261.492, 342.916]
[266.265, 332.608]
[276.594, 344.054]
[270.005, 344.092]
[274.673, 350.974]
[286.818, 349.891]
[284.758, 347.257]
[282.444, 351.998]
[286.284, 335.915]
[277.264, 348.244]
[287.799, 337.497]
[285.46, 345.831]
[291.811, 340.665]
[308.726, 346.951]
[296.154, 359.792]
[301.711, 357.62]
[318.017, 358.877]
[321.479, 354.404]
[315.924, 362.266]
[324.928, 350.587]
[328.778, 364.563]
[333.935, 355.975]
[335.449, 350.727]
[343.1, 354.779]
[333.89, 354.862]
[332.888, 355.435]
[334.498, 372.022]
[336.535, 367.462]
[346.141, 368.725]
[346.866, 372.731]
[344.535, 375.471]
[351.613, 360.781]
[364.466, 376.102]
[371.239, 367.614]
[377.703, 380.301]
[366.553, 363.81]
[390.86, 371.134]
[376.333, 387.168]
[394.05, 380.387]
[388.948, 376.592]
[407.356, 374.739]
[398.114, 384.353]
[401.716, 376.877]
[422.619, 376.088]
[408.631, 383.479]
[411.149, 379.654]
[425.453, 395.791]
[423.555, 379.449]
[427.992, 399.568]
[435.561, 401.473]
[432.725, 389.115]
[448.947, 385.852]
[467.686, 393.596]
[457.138, 392.665]
[458.754, 406.317]
[478.914, 410.185]
[487.105, 404.066]
[475.926, 409.209]
[481.975, 412.716]
[489.667, 406.101]
[473.577, 398.661]
[480.364, 404.728]
[479.291, 403.739]
[487.364, 416.235]
[493.849, 413.834]

[sylvain231]

autre ensemble où ça foire :
[202.55, 300.401]
[204.664, 306.736]
[208.678, 295.852]
[203.028, 291.776]
[216.623, 289.748]
[203.014, 299.954]
[197.975, 306.908]
[235.505, 305.353]
[240.204, 297.416]
[225.05, 297.851]
[207.399, 303.646]
[201.553, 306.371]
[236.984, 297.103]
[193.354, 308.415]
[244.705, 310.29]
[191.203, 304.652]
[202.177, 296.045]
[245.734, 306.002]
[238.153, 301.42]
[246.781, 300.924]
[248.659, 310.395]
[247.307, 306.44]
[201.266, 305.708]
[193.236, 306.229]
[198.788, 294.878]
[211.842, 293.96]
[255.991, 312.111]
[195.93, 294.657]
[198.265, 309.247]
[208.242, 302.406]
[270.47, 307.42]
[283.832, 296.533]
[208.039, 298.055]
[288.692, 315.087]
[210.432, 298.317]
[325.094, 319.051]
[227.066, 316.031]
[248.261, 308.95]
[361.271, 323.896]
[366.271, 322.137]
[372.789, 325.268]
[385.449, 315.275]
[370.391, 316.178]
[267.015, 321.102]
[394.935, 328.532]
[396.128, 322.581]
[275.113, 320.374]
[422.954, 325.092]
[424.477, 316.54]
[300.43, 336.02]
[434.116, 319.33]
[294.644, 320.411]
[296.493, 330.57]
[321.379, 332.753]
[472.012, 322.071]
[312.976, 335.645]
[486.986, 326.467]
[330.879, 326.325]
[341.902, 337.084]
[352.284, 334.586]
[370.271, 335.267]
[379.755, 343.1]
[384.096, 342.293]
[388.992, 347.203]
[422.226, 345.177]
[423.724, 346.961]
[450.314, 369.318]
[463.542, 362.208]
[469.757, 369.424]
[466.886, 370.204]
[485.574, 367.42]
[495.365, 363.63]

[sylvain231]

ah apparemment c'est dû à mon bruit trop important, sur cet exemple ça marche :

[204.49, 298.379]
[203.988, 298.274]
[218.101, 299.1]
[202.273, 298.759]
[224.844, 298.638]
[201.346, 298.695]
[200.747, 299.159]
[228.636, 299.728]
[229.911, 299.242]
[231.423, 300.327]
[199.73, 299.108]
[200.72, 299.488]
[234.228, 299.554]
[199.706, 301.179]
[238.895, 299.8]
[199.276, 299.692]
[200.827, 300.3]
[243.886, 301.279]
[244.003, 300.407]
[245.431, 301.616]
[245.427, 301.391]
[251.371, 302.264]
[202.423, 301.655]
[202.527, 301.334]
[202.168, 302.113]
[202.299, 302.437]
[258.284, 302.96]
[203.488, 302.641]
[204.107, 303.232]
[205.362, 304.008]
[273.669, 303.96]
[279.652, 305.772]
[212.916, 306.828]
[290.18, 305.388]
[219.666, 306.969]
[317.424, 308.794]
[231.231, 312.058]
[241.126, 314.324]
[355.024, 313.846]
[369.971, 316.879]
[375.153, 318.014]
[377.395, 317.405]
[379.589, 318.731]
[263.25, 320.107]
[399.86, 320.049]
[405.548, 322.312]
[274.599, 321.461]
[424.491, 325.352]
[426.297, 323.547]
[294.457, 326.527]
[442.744, 326.75]
[299.309, 327.114]
[302.222, 328.877]
[310.729, 330.754]
[476.86, 332.524]
[317.976, 331.6]
[486.412, 333.535]
[331.244, 335.662]
[349.036, 338.495]
[362.037, 341.822]
[365.601, 342.966]
[380.761, 346.206]
[383.22, 345.7]
[392.692, 347.906]
[418.669, 352.863]
[429.179, 355.398]
[448.169, 360.368]
[460.575, 361.648]
[467.647, 364.054]
[475.83, 366.019]
[481.548, 367.704]
[491.168, 369.06]

[sylvain231]

ah il est trop sensible au bruit dès que la parabole est serrée et qu'il y a un bruit ne serait-ce que de 2, il cherche une parabole plate exemple :

[206.025, 297.865]
[201.614, 299.851]
[218.181, 300.491]
[202.591, 297.605]
[222.44, 297.475]
[201.907, 300.593]
[198.977, 299.545]
[228.985, 298.681]
[230.028, 301.744]
[233.44, 301.796]
[201.98, 299.288]
[199.75, 301.99]
[235.44, 299.543]
[198.844, 300.356]
[236.253, 300.917]
[202.14, 302.004]
[199.757, 301.779]
[241.471, 301.199]
[243.957, 299.397]
[245.444, 300.222]
[246.98, 300.112]
[250.479, 301.184]
[201.862, 302.216]
[204.171, 302.215]
[204.406, 303.078]
[201.105, 302.675]
[258.227, 302.964]
[202.667, 303.384]
[205.879, 302.193]
[203.922, 303.954]
[273.245, 302.408]
[279.165, 305.838]
[213.126, 307.3]
[291.154, 306.928]
[220.189, 307.985]
[318.436, 311.574]
[231.611, 310.234]
[243.32, 312.099]
[356.3, 316.299]
[368.778, 315.49]
[373.462, 318.121]
[375.565, 316.778]
[380.539, 319.681]
[261.034, 319.741]
[400.991, 321.837]
[405.993, 321.512]
[273.457, 320.75]
[424.893, 324.352]
[424.699, 326.118]
[293.927, 325.031]
[440.613, 326.803]
[298.374, 328.884]
[304.173, 327.315]
[310.385, 332.266]
[476.794, 331.134]
[318.171, 333.799]
[485.97, 334.951]
[331.508, 333.877]
[349.029, 337.435]
[360.556, 341.798]
[367.086, 341.405]
[383.244, 343.989]
[382.582, 345.376]
[393.137, 349.173]
[417.974, 352.707]
[428.409, 354.238]
[448.34, 359.016]
[461.19, 363.619]
[468.543, 363.518]
[478.581, 364.477]
[483.305, 366.196]
[491.182, 370.956]

[sylvain231]

en fait quand le a est égal à 2 il faut un bruit de 0 pour que ça marche même avec un bruit de 1 il trouve une parabole plate dans 50% des cas et avec un bruit de 3 dans 100% des cas
je pense qu'on ne va pas couper à prendre les points à gauche du sommet et les points à droite sinon il confondra toujours une parabole très serrée avec une parabole plate

[leon1789]

C'est pour cela qu'il faut estimer le bon theta autrement, d'où l'idée du segment de Lycéen.
Ou alors, faire carrément autrement, d'où mon idée matricielle (qui reste à terminer).

[sylvain231]

cette méthode de Ben est la meilleure qu'on ait trouvée jusqu'ici, je la garde sous le coude, mais pas encore assez bonne, lyceen95 peux-tu nous détailler ta méthode STP ?

[sylvain231]

je pense qu'on peut pas couper à séparer les points à gauche de ceux d'à droite car la distance sera toujours trop petite en cas de a serré et le logiciel sera toujours tenté par une parabole plate

[leon1789]

Maintenant que ton code de graphe est ok,
tu peux retester les deux méthodes dont on a parlées hier :

minimiser fonctionne pour les paraboles plates.

minimiser fonctionne pour les paraboles serrées.

Tu as déjà les codes pour ces deux méthodes, et ils fonctionnent car on avait les mêmes résultats sur les valeurs numériques.

[sylvain231]

Après, on enclenche la force brute, avec des faibles variations autour de cette direction et autour de ce coefficient a.

>> tu parle de calculer la distance des points à la courbe avec la méthode de Ben, pfiu ça va nous faire un programme hyper-complexe avec ta méthode plus l'implémentation de la distance mais si ça marche tant mieux !

[sylvain231]

Léon tu peux me redonner les références des deux algos car je ne sais pas à quoi ils correspondent ?