Régression parabolique non triviale

[sylvain231]

Bonjour, mais comment veux-tu faire en ne parcourant qu'une seule fois la liste de points ?
De plus si tu teste sur ma liste de points et mon sommet tu verras que la parabole est vraiment très loin des points

[leon1789]

200,300

ok, mais vos abscisses ne dépassent 191 et vos ordonnées 291.
Vos 269 points sont "loin" de (200; 300) , ça ne donne pas la "bonne" parabole...

[Ben314]

Bonjour, mais comment veux-tu faire en ne parcourant qu'une seule fois la liste de points ?
De plus si tu teste sur ma liste de points et mon sommet tu verras que la parabole est vraiment très loin des points

Ben tu les calcule une seule fois et tu stocke les résultat, soit dans des variables "simples" nommées E00, E01, etc, soit dans un tableau si tu préfère (en langage machine ça sera la même chose de toute façon vu que tu aura que des référence constantes aux éléments du tableau, le compilateur calculera à l'avance les adresses correspondantes)

Sinon, je pense qu'il y a un bug dans ton programme au moment du calcul du coefficient : le et le au dessus sont calculé avec un theta qui est celui de la fin de la boucle (donc 2xPi) et pas avec le théta qui a donné le minimum (donc l'angle doit être bon, mais pas le coefficient. de la parabole)

EDIT : (mini mini mini détail....) Quand tu cherche le mini de la fonction , tu peut te contenter de balayer l'intervalle vu que, si tu as une parabole dans un repère , si tu fait un demi tour (=rotation d'angle ) tu tombe sur le repère dans lequel la même parabole a pour équation (et on le voie dans la grosse formule où le passage de à ne change pas le résultat.

[sylvain231]

oui en effet pour le a et d'accord pour l'optimisation mais ça ne marche pas mieux

[leon1789]

J'ai fait des calculs avec le sommet (191, 291), qui me parait bien mieux visuellement que (200,300).
La parabole obtenue :

0 = 0.414*x^2 + 130*x - 0.99*x*y + 9997.95 - 154.7*y + 0.591*y^2




t := -2.268

a := 1.969

[sylvain231]

tu obtiens quoi comme a et theta ?

[sylvain231]

si tu as un code Python ou autre ça m'intéresserait que tu me le donnes que je compare avec le mien j'ai peut-être fait une erreur quelque part

voici mon code pour l'instant :

Code: Tout sélectionner

void Parabole::fit(std::vector<cv::Point2d> points, cv::Point2d sommet) {
    this->sommet = sommet;
    points = translatePoint2ds(points, sommet);
    double bestTheta = 0;
    double minimum= std::numeric_limits<double>::infinity();
    double E02 = E(points, 0, 2);
    double E11 = E(points, 1, 1);
    double E20 = E(points, 2, 0);
    double E21 = E(points, 2, 1);
    double E30 = E(points, 3, 0);
    double E12 = E(points, 1, 2);
    double E03 = E(points, 0, 3);
    double E40 = E(points, 4, 0);
    double E31 = E(points, 3, 1);
    double E22 = E(points, 2, 2);
    double E13 = E(points, 1, 3);
    double E04 = E(points, 0, 4);
    for (double theta = 0; theta < 2 * CV_PI; theta += CV_PI / 1000) {
        double c = cos(theta);
        double s = sin(theta);
        double delta = E02 * pow(c, 2) + 2 * E11 * c * s + E20 * pow(s, 2) -
            (pow(E21 * pow(c, 3) + (E30 - 2 * E12) * pow(c, 2) * s + (E03 - 2 * E21) * c * pow(s, 2) + E12 * pow(s, 3), 2))
                / (E40 * pow(c, 4) - 4 * E31 * pow(c, 3) * s + 6 * E22 * pow(c, 2) * pow(s, 2) - 4 * E13 * c * pow(s, 3) + E04 * pow(s, 4));
        if (delta < minimum) {
            minimum = delta;
            bestTheta = theta;
        }
    }
    double c = cos(bestTheta);
    double s = sin(bestTheta);
    this->theta_radians = bestTheta;
    this->theta = bestTheta * 180 / CV_PI;
    this->a= (E21 * pow(c, 3) + (E30 - 2 * E12) * pow(c, 2) * s + (E03 - 2 * E21) * c * pow(s, 2) + E12 * pow(s, 3))
        / (E40 * pow(c, 4) - 4 * E31 * pow(c, 3) * s + 6 * E22 * pow(c, 2) * pow(s, 2) - 4 * E13 * c * pow(s, 3) + E04 * pow(s, 4));

}

[leon1789]

tu obtiens quoi comme a et theta ?

Je l'ai ajouté à la fin du message.

[sylvain231]

c'est très proche des valeurs théoriques mais je comprend pas quelle est la différence avec mon code ?!

[Ben314]

En comparant vos valeur des , ça permettrais de mieux localiser
Si c'est pas compliqué, de tracer la fonction aiderais aussi (peut-être) à voir où est le bug.

[sylvain231]

en fait moi le theta est bon mais pas le a bizarre !

[sylvain231]

ah non sur un autre exemple le theta est complètement foireux, j'aurais besoin de voir ton code STP

[sylvain231]

j'ai ajouté des infos de débogage, voici la sortie du programme, en premier les points de départ (qui sont générés aléatoirement en début de programme donc je ne peux pas retrouver facilement ceux que j'avais tout à l'heure), en second les E, en troisième les delta, et enfin le theta en degrés et le a, si tu as besoin d'autres affichages dis-le moi

Code: Tout sélectionner

avant1
avant
apres
[-3, 112]
[0, 117]
[1, 117]
[2, 118]
[6, 122]
[7, 122]
[8, 123]
[11, 126]
[12, 127]
[15, 130]
[16, 130]
[18, 133]
[19, 133]
[22, 135]
[23, 136]
[24, 138]
[25, 138]
[27, 140]
[28, 141]
[30, 143]
[32, 144]
[33, 145]
[34, 146]
[37, 149]
[5, 150]
[38, 150]
[6, 150]
[6, 151]
[7, 151]
[7, 151]
[40, 152]
[8, 152]
[8, 152]
[41, 152]
[9, 153]
[9, 153]
[10, 153]
[10, 154]
[43, 154]
[11, 154]
[11, 155]
[12, 155]
[44, 155]
[12, 155]
[13, 156]
[13, 156]
[14, 157]
[46, 157]
[14, 157]
[15, 157]
[15, 158]
[16, 158]
[48, 158]
[16, 159]
[17, 159]
[17, 159]
[18, 160]
[49, 160]
[18, 160]
[19, 161]
[19, 161]
[51, 161]
[20, 161]
[20, 162]
[52, 162]
[21, 162]
[21, 163]
[54, 164]
[55, 165]
[57, 167]
[58, 167]
[60, 169]
[61, 170]
[31, 171]
[31, 171]
[62, 171]
[32, 171]
[32, 172]
[63, 172]
[33, 172]
[66, 174]
[67, 175]
[39, 177]
[39, 177]
[69, 177]
[40, 178]
[40, 178]
[70, 178]
[71, 179]
[44, 181]
[74, 181]
[45, 182]
[45, 182]
[75, 182]
[46, 182]
[76, 183]
[76, 184]
[77, 185]
[49, 185]
[50, 185]
[50, 186]
[54, 189]
[54, 189]
[57, 191]
[57, 192]
[60, 194]
[88, 194]
[61, 194]
[89, 195]
[90, 196]
[63, 196]
[91, 197]
[64, 197]
[92, 197]
[66, 199]
[67, 199]
[94, 199]
[95, 200]
[69, 200]
[95, 201]
[69, 201]
[97, 202]
[71, 203]
[98, 203]
[99, 204]
[74, 205]
[100, 205]
[101, 206]
[76, 206]
[76, 207]
[103, 207]
[78, 208]
[104, 208]
[105, 209]
[80, 210]
[106, 210]
[107, 211]
[82, 211]
[109, 212]
[84, 213]
[110, 213]
[86, 214]
[111, 214]
[112, 215]
[87, 215]
[88, 216]
[113, 216]
[89, 217]
[113, 217]
[114, 218]
[90, 218]
[91, 218]
[115, 219]
[92, 219]
[116, 219]
[94, 220]
[117, 220]
[118, 221]
[95, 221]
[119, 222]
[97, 223]
[120, 223]
[98, 224]
[121, 224]
[99, 225]
[122, 225]
[123, 226]
[101, 226]
[124, 227]
[102, 227]
[125, 228]
[104, 228]
[127, 229]
[104, 229]
[128, 229]
[106, 230]
[129, 230]
[107, 231]
[107, 231]
[130, 231]
[108, 232]
[131, 232]
[109, 232]
[132, 233]
[110, 233]
[111, 234]
[133, 234]
[134, 235]
[113, 235]
[114, 236]
[135, 236]
[115, 237]
[136, 237]
[136, 237]
[115, 237]
[137, 238]
[138, 239]
[118, 239]
[119, 240]
[139, 240]
[120, 241]
[140, 241]
[140, 241]
[120, 241]
[121, 242]
[142, 242]
[122, 243]
[143, 243]
[123, 243]
[124, 244]
[144, 244]
[144, 244]
[145, 245]
[126, 246]
[146, 246]
[146, 246]
[127, 246]
[128, 247]
[147, 247]
[147, 247]
[129, 248]
[129, 248]
[148, 248]
[149, 249]
[130, 249]
[131, 250]
[150, 250]
[150, 250]
[132, 251]
[151, 251]
[151, 251]
[133, 251]
[152, 252]
[135, 252]
[153, 253]
[153, 253]
[136, 253]
[137, 254]
[155, 254]
[137, 254]
[155, 254]
[138, 255]
[139, 255]
[156, 255]
[156, 255]
[139, 256]
[140, 256]
[157, 257]
[157, 257]
[141, 257]
[159, 258]
[142, 258]
[143, 259]
[160, 259]
[160, 259]
[144, 260]
[145, 260]
[161, 260]
[161, 260]
[146, 261]
[146, 261]
[163, 262]
[163, 262]
[148, 262]
[148, 262]
[148, 263]
[164, 263]
[164, 263]
[150, 264]
[150, 264]
[150, 264]
[166, 265]
[166, 265]
[166, 265]
[153, 266]
[167, 266]
[168, 266]
[153, 266]
[168, 266]
[153, 267]
[154, 267]
[169, 268]
[169, 268]
[169, 268]
[156, 269]
[157, 269]
[157, 269]
[171, 269]
[171, 270]
[157, 270]
[171, 270]
[158, 270]
[158, 270]
[159, 271]
[159, 271]
[159, 271]
[173, 271]
[173, 271]
[160, 271]
[173, 271]
[173, 272]
[160, 272]
[161, 272]
[161, 272]
[161, 273]
[162, 273]
[162, 273]
[175, 273]
[175, 273]
[163, 274]
[175, 274]
[175, 274]
[163, 274]
[163, 274]
[165, 276]
[166, 276]
[178, 276]
[178, 276]
[178, 276]
[166, 276]
[178, 276]
[178, 276]
[178, 276]
[167, 276]
[167, 277]
[168, 278]
[168, 278]
[169, 278]
[170, 279]
[170, 279]
[182, 280]
[182, 280]
[171, 280]
[182, 280]
[182, 280]
[182, 280]
[171, 280]
[182, 280]
[182, 280]
[182, 280]
[172, 280]
[182, 280]
[182, 280]
[183, 281]
[183, 281]
[183, 281]
[173, 281]
[183, 281]
[183, 281]
[183, 281]
[173, 281]
[183, 281]
[183, 281]
[183, 281]
[183, 281]
[184, 282]
[174, 282]
[184, 282]
[174, 282]
[175, 282]
[185, 283]
[185, 283]
[185, 283]
[185, 283]
[175, 283]
[185, 283]
[185, 283]
[185, 283]
[185, 283]
[185, 283]
[176, 283]
[185, 283]
[186, 284]
[186, 284]
[186, 284]
[186, 284]
[177, 284]
[186, 284]
[186, 284]
[186, 284]
[177, 284]
[186, 284]
[186, 284]
[178, 284]
[186, 284]
[187, 285]
[187, 285]
[178, 285]
[179, 285]
[180, 286]
[180, 286]
[181, 287]
[181, 287]
[189, 287]
[189, 287]
[189, 287]
[189, 287]
[189, 287]
[182, 287]
[189, 287]
[182, 288]
[182, 288]
[183, 288]
[183, 288]
[190, 288]
[190, 289]
[184, 289]
[190, 289]
[191, 289]
[184, 289]
[184, 289]
[184, 289]
[191, 290]
[191, 290]
[191, 290]
[192, 290]
[192, 290]
[192, 291]
[187, 291]
[192, 291]
[187, 291]
[187, 291]
[193, 291]
[187, 291]
[193, 291]
[188, 291]
[193, 292]
[188, 292]
[193, 292]
[193, 292]
[189, 292]
[189, 292]
[193, 292]
[189, 292]
[194, 292]
[194, 292]
[189, 292]
[194, 293]
[190, 293]
[194, 293]
[190, 293]
[194, 293]
[190, 293]
[194, 293]
[190, 293]
[194, 293]
[191, 293]
[194, 293]
[191, 293]
[194, 293]
[191, 293]
[194, 294]
[191, 294]
[195, 294]
[192, 294]
[195, 294]
[192, 294]
[195, 294]
[192, 294]
[192, 294]
[195, 294]
[192, 294]
[195, 294]
[193, 294]
[195, 294]
[193, 294]
[195, 294]
[193, 294]
[195, 294]
[195, 294]
[193, 295]
[195, 295]
[195, 295]
[193, 295]
[193, 295]
[195, 295]
[195, 295]
[194, 295]
[194, 295]
[195, 295]
[195, 295]
[194, 295]
[194, 295]
[194, 295]
[195, 295]
[195, 295]
[195, 295]
[194, 295]
[194, 295]
[194, 295]
[194, 295]
[195, 295]
[195, 295]
[195, 295]
[195, 295]
nombre de points : 495
E02=6127.82
E11=7220.97
E20=8611.91
E21=-1.06969e+06
E30=-1.28161e+06
E12=-901874
E03=-768153
E40=2.07636e+08
E31=1.72876e+08
E22=1.45279e+08
E13=1.23237e+08
E04=1.05514e+08
delta = 617.069
delta = 621.691
delta = 626.328
delta = 630.98
delta = 635.646
delta = 640.327
delta = 645.022
delta = 649.732
delta = 654.457
delta = 659.197
delta = 663.951
delta = 668.721
delta = 673.505
delta = 678.304
delta = 683.118
delta = 687.947
delta = 692.791
delta = 697.65
delta = 702.525
delta = 707.415
delta = 712.32
delta = 717.24
delta = 722.176
delta = 727.128
delta = 732.095
delta = 737.078
delta = 742.077
delta = 747.092
delta = 752.122
delta = 757.169
delta = 762.232
delta = 767.312
delta = 772.408
delta = 777.521
delta = 782.65
delta = 787.797
delta = 792.96
delta = 798.141
delta = 803.339
delta = 808.555
delta = 813.789
delta = 819.04
delta = 824.309
delta = 829.597
delta = 834.904
delta = 840.229
delta = 845.572
delta = 850.935
delta = 856.318
delta = 861.72
delta = 867.142
delta = 872.584
delta = 878.046
delta = 883.529
delta = 889.033
delta = 894.558
delta = 900.105
delta = 905.673
delta = 911.264
delta = 916.877
delta = 922.513
delta = 928.173
delta = 933.855
delta = 939.562
delta = 945.293
delta = 951.049
delta = 956.829
delta = 962.636
delta = 968.468
delta = 974.327
delta = 980.213
delta = 986.126
delta = 992.067
delta = 998.036
delta = 1004.03
delta = 1010.06
delta = 1016.12
delta = 1022.21
delta = 1028.33
delta = 1034.48
delta = 1040.66
delta = 1046.88
delta = 1053.13
delta = 1059.41
delta = 1065.73
delta = 1072.09
delta = 1078.48
delta = 1084.91
delta = 1091.38
delta = 1097.88
delta = 1104.43
delta = 1111.02
delta = 1117.65
delta = 1124.32
delta = 1131.03
delta = 1137.79
delta = 1144.59
delta = 1151.44
delta = 1158.34
delta = 1165.28
delta = 1172.28
delta = 1179.33
delta = 1186.42
delta = 1193.57
delta = 1200.78
delta = 1208.04
delta = 1215.36
delta = 1222.74
delta = 1230.17
delta = 1237.67
delta = 1245.23
delta = 1252.85
delta = 1260.54
delta = 1268.3
delta = 1276.13
delta = 1284.03
delta = 1292
delta = 1300.04
delta = 1308.16
delta = 1316.36
delta = 1324.64
delta = 1333
delta = 1341.45
delta = 1349.98
delta = 1358.61
delta = 1367.32
delta = 1376.13
delta = 1385.03
delta = 1394.04
delta = 1403.14
delta = 1412.35
delta = 1421.67
delta = 1431.09
delta = 1440.63
delta = 1450.29
delta = 1460.06
delta = 1469.96
delta = 1479.98
delta = 1490.13
delta = 1500.42
delta = 1510.84
delta = 1521.4
delta = 1532.11
delta = 1542.96
delta = 1553.97
delta = 1565.14
delta = 1576.47
delta = 1587.96
delta = 1599.63
delta = 1611.47
delta = 1623.5
delta = 1635.71
delta = 1648.12
delta = 1660.72
delta = 1673.53
delta = 1686.55
delta = 1699.78
delta = 1713.24
delta = 1726.93
delta = 1740.85
delta = 1755.02
delta = 1769.45
delta = 1784.13
delta = 1799.08
delta = 1814.31
delta = 1829.82
delta = 1845.62
delta = 1861.73
delta = 1878.15
delta = 1894.9
delta = 1911.97
delta = 1929.4
delta = 1947.17
delta = 1965.32
delta = 1983.84
delta = 2002.75
delta = 2022.07
delta = 2041.8
delta = 2061.97
delta = 2082.58
delta = 2103.65
delta = 2125.2
delta = 2147.24
delta = 2169.78
delta = 2192.86
delta = 2216.48
delta = 2240.65
delta = 2265.42
delta = 2290.78
delta = 2316.76
delta = 2343.39
delta = 2370.69
delta = 2398.68
delta = 2427.38
delta = 2456.82
delta = 2487.02
delta = 2518.02
delta = 2549.83
delta = 2582.5
delta = 2616.04
delta = 2650.49
delta = 2685.89
delta = 2722.26
delta = 2759.64
delta = 2798.07
delta = 2837.58
delta = 2878.21
delta = 2920
delta = 2963
delta = 3007.23
delta = 3052.76
delta = 3099.62
delta = 3147.85
delta = 3197.51
delta = 3248.64
delta = 3301.3
delta = 3355.53
delta = 3411.38
delta = 3468.91
delta = 3528.17
delta = 3589.22
delta = 3652.1
delta = 3716.87
delta = 3783.6
delta = 3852.32
delta = 3923.09
delta = 3995.96
delta = 4070.99
delta = 4148.22
delta = 4227.68
delta = 4309.44
delta = 4393.5
delta = 4479.91
delta = 4568.69
delta = 4659.84
delta = 4753.38
delta = 4849.27
delta = 4947.51
delta = 5048.04
delta = 5150.81
delta = 5255.72
delta = 5362.67
delta = 5471.49
delta = 5582.03
delta = 5694.04
delta = 5807.25
delta = 5921.34
delta = 6035.91
delta = 6150.5
delta = 6264.54
delta = 6377.38
delta = 6488.24
delta = 6596.22
delta = 6700.24
delta = 6799.04
delta = 6891.16
delta = 6974.84
delta = 7048.02
delta = 7108.27
delta = 7152.68
delta = 7177.79
delta = 7179.44
delta = 7152.66
delta = 7091.4
delta = 6988.37
delta = 6834.77
delta = 6620.08
delta = 6331.88
delta = 5956.07
delta = 5477.72
delta = 4883.25
delta = 4165.31
delta = 3331.43
delta = 2417.55
delta = 1503.31
delta = 718.467
delta = 221.88
delta = 143.544
delta = 517.087
delta = 1258.32
delta = 2211.27
delta = 3219.51
delta = 4171.46
delta = 5007.92
delta = 5708.97
delta = 6277.5
delta = 6726.92
delta = 7073.93
delta = 7334.97
delta = 7524.67
delta = 7655.5
delta = 7737.84
delta = 7780.24
delta = 7789.72
delta = 7772.05
delta = 7732
delta = 7673.55
delta = 7599.99
delta = 7514.09
delta = 7418.19
delta = 7314.28
delta = 7204.02
delta = 7088.87
delta = 6970.03
delta = 6848.55
delta = 6725.33
delta = 6601.12
delta = 6476.58
delta = 6352.25
delta = 6228.6
delta = 6106.02
delta = 5984.84
delta = 5865.34
delta = 5747.74
delta = 5632.22
delta = 5518.92
delta = 5407.97
delta = 5299.45
delta = 5193.41
delta = 5089.92
delta = 4988.98
delta = 4890.6
delta = 4794.79
delta = 4701.53
delta = 4610.8
delta = 4522.56
delta = 4436.77
delta = 4353.4
delta = 4272.4
delta = 4193.71
delta = 4117.28
delta = 4043.07
delta = 3971
delta = 3901.02
delta = 3833.08
delta = 3767.11
delta = 3703.07
delta = 3640.88
delta = 3580.5
delta = 3521.86
delta = 3464.92
delta = 3409.61
delta = 3355.89
delta = 3303.7
delta = 3253
delta = 3203.72
delta = 3155.83
delta = 3109.28
delta = 3064.02
delta = 3020.01
delta = 2977.2
delta = 2935.56
delta = 2895.05
delta = 2855.63
delta = 2817.25
delta = 2779.89
delta = 2743.51
delta = 2708.07
delta = 2673.55
delta = 2639.91
delta = 2607.12
delta = 2575.16
delta = 2543.99
delta = 2513.59
delta = 2483.94
delta = 2455
delta = 2426.76
delta = 2399.19
delta = 2372.27
delta = 2345.98
delta = 2320.29
delta = 2295.19
delta = 2270.65
delta = 2246.67
delta = 2223.22
delta = 2200.28
delta = 2177.83
delta = 2155.87
delta = 2134.37
delta = 2113.33
delta = 2092.72
delta = 2072.54
delta = 2052.76
delta = 2033.38
delta = 2014.38
delta = 1995.76
delta = 1977.5
delta = 1959.59
delta = 1942.01
delta = 1924.77
delta = 1907.84
delta = 1891.23
delta = 1874.91
delta = 1858.88
delta = 1843.14
delta = 1827.67
delta = 1812.46
delta = 1797.52
delta = 1782.82
delta = 1768.36
delta = 1754.15
delta = 1740.16
delta = 1726.39
delta = 1712.84
delta = 1699.5
delta = 1686.37
delta = 1673.43
delta = 1660.68
delta = 1648.13
delta = 1635.75
delta = 1623.55
delta = 1611.53
delta = 1599.67
delta = 1587.97
delta = 1576.44
delta = 1565.05
delta = 1553.82
delta = 1542.73
delta = 1531.79
delta = 1520.98
delta = 1510.31
delta = 1499.77
delta = 1489.36
delta = 1479.07
delta = 1468.9
delta = 1458.86
delta = 1448.92
delta = 1439.1
delta = 1429.39
delta = 1419.78
delta = 1410.28
delta = 1400.88
delta = 1391.58
delta = 1382.37
delta = 1373.26
delta = 1364.24
delta = 1355.31
delta = 1346.47
delta = 1337.71
delta = 1329.04
delta = 1320.44
delta = 1311.93
delta = 1303.49
delta = 1295.13
delta = 1286.84
delta = 1278.62
delta = 1270.48
delta = 1262.4
delta = 1254.39
delta = 1246.44
delta = 1238.56
delta = 1230.75
delta = 1222.99
delta = 1215.29
delta = 1207.66
delta = 1200.08
delta = 1192.55
delta = 1185.08
delta = 1177.67
delta = 1170.3
delta = 1162.99
delta = 1155.73
delta = 1148.52
delta = 1141.36
delta = 1134.24
delta = 1127.17
delta = 1120.15
delta = 1113.17
delta = 1106.23
delta = 1099.34
delta = 1092.49
delta = 1085.68
delta = 1078.91
delta = 1072.18
delta = 1065.49
delta = 1058.83
delta = 1052.22
delta = 1045.64
delta = 1039.1
delta = 1032.59
delta = 1026.12
delta = 1019.68
delta = 1013.28
delta = 1006.91
delta = 1000.57
delta = 994.261
delta = 987.986
delta = 981.742
delta = 975.528
delta = 969.344
delta = 963.189
delta = 957.064
delta = 950.967
delta = 944.898
delta = 938.857
delta = 932.843
delta = 926.856
delta = 920.896
delta = 914.962
delta = 909.053
delta = 903.171
delta = 897.313
delta = 891.48
delta = 885.671
delta = 879.887
delta = 874.127
delta = 868.39
delta = 862.677
delta = 856.986
delta = 851.319
delta = 845.673
delta = 840.051
delta = 834.45
delta = 828.871
delta = 823.313
delta = 817.777
delta = 812.263
delta = 806.769
delta = 801.295
delta = 795.843
delta = 790.411
delta = 784.999
delta = 779.607
delta = 774.235
delta = 768.883
delta = 763.55
delta = 758.237
delta = 752.943
delta = 747.668
delta = 742.412
delta = 737.176
delta = 731.958
delta = 726.758
delta = 721.578
delta = 716.415
delta = 711.272
delta = 706.146
delta = 701.039
delta = 695.949
delta = 690.878
delta = 685.825
delta = 680.789
delta = 675.772
delta = 670.772
delta = 665.789
delta = 660.825
delta = 655.878
delta = 650.948
delta = 646.036
delta = 641.141
delta = 636.264
delta = 631.404
delta = 626.561
delta = 621.736
delta = 616.928
delta = 612.137
delta = 607.363
delta = 602.606
delta = 597.867
delta = 593.144
delta = 588.439
delta = 583.751
delta = 579.08
delta = 574.426
delta = 569.789
delta = 565.169
delta = 560.566
delta = 555.98
delta = 551.412
delta = 546.86
delta = 542.326
delta = 537.808
delta = 533.308
delta = 528.825
delta = 524.359
delta = 519.91
delta = 515.479
delta = 511.064
delta = 506.667
delta = 502.287
delta = 497.925
delta = 493.579
delta = 489.251
delta = 484.941
delta = 480.647
delta = 476.372
delta = 472.113
delta = 467.872
delta = 463.649
delta = 459.443
delta = 455.255
delta = 451.085
delta = 446.932
delta = 442.797
delta = 438.679
delta = 434.58
delta = 430.498
delta = 426.435
delta = 422.389
delta = 418.361
delta = 414.351
delta = 410.36
delta = 406.386
delta = 402.431
delta = 398.494
delta = 394.575
delta = 390.675
delta = 386.793
delta = 382.93
delta = 379.085
delta = 375.258
delta = 371.451
delta = 367.662
delta = 363.891
delta = 360.14
delta = 356.407
delta = 352.693
delta = 348.999
delta = 345.323
delta = 341.667
delta = 338.029
delta = 334.411
delta = 330.812
delta = 327.233
delta = 323.672
delta = 320.132
delta = 316.611
delta = 313.109
delta = 309.627
delta = 306.165
delta = 302.723
delta = 299.3
delta = 295.898
delta = 292.515
delta = 289.153
delta = 285.81
delta = 282.488
delta = 279.186
delta = 275.904
delta = 272.643
delta = 269.402
delta = 266.181
delta = 262.981
delta = 259.802
delta = 256.643
delta = 253.505
delta = 250.388
delta = 247.292
delta = 244.217
delta = 241.163
delta = 238.129
delta = 235.117
delta = 232.126
delta = 229.157
delta = 226.209
delta = 223.282
delta = 220.376
delta = 217.493
delta = 214.63
delta = 211.79
delta = 208.971
delta = 206.173
delta = 203.398
delta = 200.645
delta = 197.913
delta = 195.204
delta = 192.516
delta = 189.851
delta = 187.208
delta = 184.587
delta = 181.988
delta = 179.412
delta = 176.859
delta = 174.327
delta = 171.819
delta = 169.333
delta = 166.869
delta = 164.429
delta = 162.011
delta = 159.616
delta = 157.244
delta = 154.895
delta = 152.568
delta = 150.265
delta = 147.985
delta = 145.729
delta = 143.495
delta = 141.285
delta = 139.098
delta = 136.934
delta = 134.794
delta = 132.678
delta = 130.585
delta = 128.515
delta = 126.469
delta = 124.447
delta = 122.449
delta = 120.474
delta = 118.524
delta = 116.597
delta = 114.694
delta = 112.815
delta = 110.96
delta = 109.129
delta = 107.323
delta = 105.54
delta = 103.782
delta = 102.048
delta = 100.338
delta = 98.6528
delta = 96.9918
delta = 95.3552
delta = 93.743
delta = 92.1554
delta = 90.5923
delta = 89.0538
delta = 87.5399
delta = 86.0506
delta = 84.5861
delta = 83.1463
delta = 81.7312
delta = 80.341
delta = 78.9755
delta = 77.635
delta = 76.3193
delta = 75.0286
delta = 73.7629
delta = 72.5221
delta = 71.3064
delta = 70.1157
delta = 68.9501
delta = 67.8096
delta = 66.6943
delta = 65.6041
delta = 64.5392
delta = 63.4994
delta = 62.4849
delta = 61.4957
delta = 60.5317
delta = 59.5931
delta = 58.6798
delta = 57.7919
delta = 56.9294
delta = 56.0922
delta = 55.2805
delta = 54.4942
delta = 53.7334
delta = 52.9981
delta = 52.2882
delta = 51.6039
delta = 50.9451
delta = 50.3118
delta = 49.7041
delta = 49.1219
delta = 48.5654
delta = 48.0344
delta = 47.529
delta = 47.0492
delta = 46.5951
delta = 46.1665
delta = 45.7637
delta = 45.3864
delta = 45.0348
delta = 44.7089
delta = 44.4086
delta = 44.134
delta = 43.8851
delta = 43.6618
delta = 43.4642
delta = 43.2923
delta = 43.1461
delta = 43.0256
delta = 42.9307
delta = 42.8615
delta = 42.8179
delta = 42.8001
delta = 42.8079
delta = 42.8414
delta = 42.9005
delta = 42.9853
delta = 43.0957
delta = 43.2317
delta = 43.3934
delta = 43.5807
delta = 43.7936
delta = 44.0322
delta = 44.2963
delta = 44.5859
delta = 44.9012
delta = 45.242
delta = 45.6083
delta = 46.0001
delta = 46.4175
delta = 46.8603
delta = 47.3286
delta = 47.8224
delta = 48.3416
delta = 48.8862
delta = 49.4562
delta = 50.0516
delta = 50.6724
delta = 51.3184
delta = 51.9898
delta = 52.6865
delta = 53.4084
delta = 54.1556
delta = 54.928
delta = 55.7255
delta = 56.5482
delta = 57.3961
delta = 58.269
delta = 59.167
delta = 60.0901
delta = 61.0382
delta = 62.0112
delta = 63.0092
delta = 64.0321
delta = 65.0799
delta = 66.1526
delta = 67.25
delta = 68.3722
delta = 69.5192
delta = 70.6909
delta = 71.8872
delta = 73.1082
delta = 74.3537
delta = 75.6238
delta = 76.9184
delta = 78.2375
delta = 79.581
delta = 80.9488
delta = 82.3411
delta = 83.7576
delta = 85.1984
delta = 86.6633
delta = 88.1525
delta = 89.6658
delta = 91.2031
delta = 92.7644
delta = 94.3498
delta = 95.959
delta = 97.5922
delta = 99.2491
delta = 100.93
delta = 102.634
delta = 104.362
delta = 106.114
delta = 107.89
delta = 109.688
delta = 111.511
delta = 113.356
delta = 115.226
delta = 117.118
delta = 119.034
delta = 120.972
delta = 122.934
delta = 124.919
delta = 126.927
delta = 128.958
delta = 131.012
delta = 133.089
delta = 135.188
delta = 137.311
delta = 139.455
delta = 141.623
delta = 143.813
delta = 146.025
delta = 148.26
delta = 150.517
delta = 152.797
delta = 155.098
delta = 157.422
delta = 159.768
delta = 162.136
delta = 164.526
delta = 166.938
delta = 169.371
delta = 171.826
delta = 174.303
delta = 176.802
delta = 179.322
delta = 181.864
delta = 184.427
delta = 187.011
delta = 189.617
delta = 192.244
delta = 194.892
delta = 197.561
delta = 200.251
delta = 202.961
delta = 205.693
delta = 208.446
delta = 211.219
delta = 214.013
delta = 216.827
delta = 219.662
delta = 222.517
delta = 225.393
delta = 228.289
delta = 231.205
delta = 234.141
delta = 237.097
delta = 240.073
delta = 243.069
delta = 246.085
delta = 249.12
delta = 252.176
delta = 255.25
delta = 258.345
delta = 261.459
delta = 264.592
delta = 267.744
delta = 270.916
delta = 274.106
delta = 277.316
delta = 280.545
delta = 283.793
delta = 287.059
delta = 290.345
delta = 293.649
delta = 296.971
delta = 300.312
delta = 303.672
delta = 307.05
delta = 310.446
delta = 313.86
delta = 317.293
delta = 320.744
delta = 324.213
delta = 327.699
delta = 331.204
delta = 334.726
delta = 338.266
delta = 341.824
delta = 345.399
delta = 348.992
delta = 352.602
delta = 356.229
delta = 359.874
delta = 363.536
delta = 367.215
delta = 370.912
delta = 374.625
delta = 378.355
delta = 382.102
delta = 385.866
delta = 389.646
delta = 393.443
delta = 397.257
delta = 401.088
delta = 404.934
delta = 408.797
delta = 412.677
delta = 416.573
delta = 420.485
delta = 424.413
delta = 428.357
delta = 432.317
delta = 436.293
delta = 440.285
delta = 444.293
delta = 448.317
delta = 452.356
delta = 456.411
delta = 460.482
delta = 464.568
delta = 468.67
delta = 472.787
delta = 476.92
delta = 481.068
delta = 485.231
delta = 489.409
delta = 493.603
delta = 497.812
delta = 502.036
delta = 506.275
delta = 510.53
delta = 514.799
delta = 519.083
delta = 523.382
delta = 527.696
delta = 532.025
delta = 536.369
delta = 540.728
delta = 545.101
delta = 549.489
delta = 553.892
delta = 558.309
delta = 562.742
delta = 567.189
delta = 571.65
delta = 576.126
delta = 580.617
delta = 585.123
delta = 589.643
delta = 594.177
delta = 598.726
delta = 603.29
delta = 607.869
delta = 612.462
delta = 617.069
delta = 621.691
delta = 626.328
delta = 630.98
delta = 635.646
delta = 640.327
delta = 645.022
delta = 649.732
delta = 654.457
delta = 659.197
delta = 663.951
delta = 668.721
delta = 673.505
delta = 678.304
delta = 683.118
delta = 687.947
delta = 692.791
delta = 697.65
delta = 702.525
delta = 707.415
delta = 712.32
delta = 717.24
delta = 722.176
delta = 727.128
delta = 732.095
delta = 737.078
delta = 742.077
delta = 747.092
delta = 752.122
delta = 757.169
delta = 762.232
delta = 767.312
delta = 772.408
delta = 777.521
delta = 782.65
delta = 787.797
delta = 792.96
delta = 798.141
delta = 803.339
delta = 808.555
delta = 813.789
delta = 819.04
delta = 824.309
delta = 829.597
delta = 834.904
delta = 840.229
delta = 845.572
delta = 850.935
delta = 856.318
delta = 861.72
delta = 867.142
delta = 872.584
delta = 878.046
delta = 883.529
delta = 889.033
delta = 894.558
delta = 900.105
delta = 905.673
delta = 911.264
delta = 916.877
delta = 922.513
delta = 928.173
delta = 933.855
delta = 939.562
delta = 945.293
delta = 951.049
delta = 956.829
delta = 962.636
delta = 968.468
delta = 974.327
delta = 980.213
delta = 986.126
delta = 992.067
delta = 998.036
delta = 1004.03
delta = 1010.06
delta = 1016.12
delta = 1022.21
delta = 1028.33
delta = 1034.48
delta = 1040.66
delta = 1046.88
delta = 1053.13
delta = 1059.41
delta = 1065.73
delta = 1072.09
delta = 1078.48
delta = 1084.91
delta = 1091.38
delta = 1097.88
delta = 1104.43
delta = 1111.02
delta = 1117.65
delta = 1124.32
delta = 1131.03
delta = 1137.79
delta = 1144.59
delta = 1151.44
delta = 1158.34
delta = 1165.28
delta = 1172.28
delta = 1179.33
delta = 1186.42
delta = 1193.57
delta = 1200.78
delta = 1208.04
delta = 1215.36
delta = 1222.74
delta = 1230.17
delta = 1237.67
delta = 1245.23
delta = 1252.85
delta = 1260.54
delta = 1268.3
delta = 1276.13
delta = 1284.03
delta = 1292
delta = 1300.04
delta = 1308.16
delta = 1316.36
delta = 1324.64
delta = 1333
delta = 1341.45
delta = 1349.98
delta = 1358.61
delta = 1367.32
delta = 1376.13
delta = 1385.03
delta = 1394.04
delta = 1403.14
delta = 1412.35
delta = 1421.67
delta = 1431.09
delta = 1440.63
delta = 1450.29
delta = 1460.06
delta = 1469.96
delta = 1479.98
delta = 1490.13
delta = 1500.42
delta = 1510.84
delta = 1521.4
delta = 1532.11
delta = 1542.96
delta = 1553.97
delta = 1565.14
delta = 1576.47
delta = 1587.96
delta = 1599.63
delta = 1611.47
delta = 1623.5
delta = 1635.71
delta = 1648.12
delta = 1660.72
delta = 1673.53
delta = 1686.55
delta = 1699.78
delta = 1713.24
delta = 1726.93
delta = 1740.85
delta = 1755.02
delta = 1769.45
delta = 1784.13
delta = 1799.08
delta = 1814.31
delta = 1829.82
delta = 1845.62
delta = 1861.73
delta = 1878.15
delta = 1894.9
delta = 1911.97
delta = 1929.4
delta = 1947.17
delta = 1965.32
delta = 1983.84
delta = 2002.75
delta = 2022.07
delta = 2041.8
delta = 2061.97
delta = 2082.58
delta = 2103.65
delta = 2125.2
delta = 2147.24
delta = 2169.78
delta = 2192.86
delta = 2216.48
delta = 2240.65
delta = 2265.42
delta = 2290.78
delta = 2316.76
delta = 2343.39
delta = 2370.69
delta = 2398.68
delta = 2427.38
delta = 2456.82
delta = 2487.02
delta = 2518.02
delta = 2549.83
delta = 2582.5
delta = 2616.04
delta = 2650.49
delta = 2685.89
delta = 2722.26
delta = 2759.64
delta = 2798.07
delta = 2837.58
delta = 2878.21
delta = 2920
delta = 2963
delta = 3007.23
delta = 3052.76
delta = 3099.62
delta = 3147.85
delta = 3197.51
delta = 3248.64
delta = 3301.3
delta = 3355.53
delta = 3411.38
delta = 3468.91
delta = 3528.17
delta = 3589.22
delta = 3652.1
delta = 3716.87
delta = 3783.6
delta = 3852.32
delta = 3923.09
delta = 3995.96
delta = 4070.99
delta = 4148.22
delta = 4227.68
delta = 4309.44
delta = 4393.5
delta = 4479.91
delta = 4568.69
delta = 4659.84
delta = 4753.38
delta = 4849.27
delta = 4947.51
delta = 5048.04
delta = 5150.81
delta = 5255.72
delta = 5362.67
delta = 5471.49
delta = 5582.03
delta = 5694.04
delta = 5807.25
delta = 5921.34
delta = 6035.91
delta = 6150.5
delta = 6264.54
delta = 6377.38
delta = 6488.24
delta = 6596.22
delta = 6700.24
delta = 6799.04
delta = 6891.16
delta = 6974.84
delta = 7048.02
delta = 7108.27
delta = 7152.68
delta = 7177.79
delta = 7179.44
delta = 7152.66
delta = 7091.4
delta = 6988.37
delta = 6834.77
delta = 6620.08
delta = 6331.88
delta = 5956.07
delta = 5477.72
delta = 4883.25
delta = 4165.31
delta = 3331.43
delta = 2417.55
delta = 1503.31
delta = 718.467
delta = 221.88
delta = 143.544
delta = 517.087
delta = 1258.32
delta = 2211.27
delta = 3219.51
delta = 4171.46
delta = 5007.92
delta = 5708.97
delta = 6277.5
delta = 6726.92
delta = 7073.93
delta = 7334.97
delta = 7524.67
delta = 7655.5
delta = 7737.84
delta = 7780.24
delta = 7789.72
delta = 7772.05
delta = 7732
delta = 7673.55
delta = 7599.99
delta = 7514.09
delta = 7418.19
delta = 7314.28
delta = 7204.02
delta = 7088.87
delta = 6970.03
delta = 6848.55
delta = 6725.33
delta = 6601.12
delta = 6476.58
delta = 6352.25
delta = 6228.6
delta = 6106.02
delta = 5984.84
delta = 5865.34
delta = 5747.74
delta = 5632.22
delta = 5518.92
delta = 5407.97
delta = 5299.45
delta = 5193.41
delta = 5089.92
delta = 4988.98
delta = 4890.6
delta = 4794.79
delta = 4701.53
delta = 4610.8
delta = 4522.56
delta = 4436.77
delta = 4353.4
delta = 4272.4
delta = 4193.71
delta = 4117.28
delta = 4043.07
delta = 3971
delta = 3901.02
delta = 3833.08
delta = 3767.11
delta = 3703.07
delta = 3640.88
delta = 3580.5
delta = 3521.86
delta = 3464.92
delta = 3409.61
delta = 3355.89
delta = 3303.7
delta = 3253
delta = 3203.72
delta = 3155.83
delta = 3109.28
delta = 3064.02
delta = 3020.01
delta = 2977.2
delta = 2935.56
delta = 2895.05
delta = 2855.63
delta = 2817.25
delta = 2779.89
delta = 2743.51
delta = 2708.07
delta = 2673.55
delta = 2639.91
delta = 2607.12
delta = 2575.16
delta = 2543.99
delta = 2513.59
delta = 2483.94
delta = 2455
delta = 2426.76
delta = 2399.19
delta = 2372.27
delta = 2345.98
delta = 2320.29
delta = 2295.19
delta = 2270.65
delta = 2246.67
delta = 2223.22
delta = 2200.28
delta = 2177.83
delta = 2155.87
delta = 2134.37
delta = 2113.33
delta = 2092.72
delta = 2072.54
delta = 2052.76
delta = 2033.38
delta = 2014.38
delta = 1995.76
delta = 1977.5
delta = 1959.59
delta = 1942.01
delta = 1924.77
delta = 1907.84
delta = 1891.23
delta = 1874.91
delta = 1858.88
delta = 1843.14
delta = 1827.67
delta = 1812.46
delta = 1797.52
delta = 1782.82
delta = 1768.36
delta = 1754.15
delta = 1740.16
delta = 1726.39
delta = 1712.84
delta = 1699.5
delta = 1686.37
delta = 1673.43
delta = 1660.68
delta = 1648.13
delta = 1635.75
delta = 1623.55
delta = 1611.53
delta = 1599.67
delta = 1587.97
delta = 1576.44
delta = 1565.05
delta = 1553.82
delta = 1542.73
delta = 1531.79
delta = 1520.98
delta = 1510.31
delta = 1499.77
delta = 1489.36
delta = 1479.07
delta = 1468.9
delta = 1458.86
delta = 1448.92
delta = 1439.1
delta = 1429.39
delta = 1419.78
delta = 1410.28
delta = 1400.88
delta = 1391.58
delta = 1382.37
delta = 1373.26
delta = 1364.24
delta = 1355.31
delta = 1346.47
delta = 1337.71
delta = 1329.04
delta = 1320.44
delta = 1311.93
delta = 1303.49
delta = 1295.13
delta = 1286.84
delta = 1278.62
delta = 1270.48
delta = 1262.4
delta = 1254.39
delta = 1246.44
delta = 1238.56
delta = 1230.75
delta = 1222.99
delta = 1215.29
delta = 1207.66
delta = 1200.08
delta = 1192.55
delta = 1185.08
delta = 1177.67
delta = 1170.3
delta = 1162.99
delta = 1155.73
delta = 1148.52
delta = 1141.36
delta = 1134.24
delta = 1127.17
delta = 1120.15
delta = 1113.17
delta = 1106.23
delta = 1099.34
delta = 1092.49
delta = 1085.68
delta = 1078.91
delta = 1072.18
delta = 1065.49
delta = 1058.83
delta = 1052.22
delta = 1045.64
delta = 1039.1
delta = 1032.59
delta = 1026.12
delta = 1019.68
delta = 1013.28
delta = 1006.91
delta = 1000.57
delta = 994.261
delta = 987.986
delta = 981.742
delta = 975.528
delta = 969.344
delta = 963.189
delta = 957.064
delta = 950.967
delta = 944.898
delta = 938.857
delta = 932.843
delta = 926.856
delta = 920.896
delta = 914.962
delta = 909.053
delta = 903.171
delta = 897.313
delta = 891.48
delta = 885.671
delta = 879.887
delta = 874.127
delta = 868.39
delta = 862.677
delta = 856.986
delta = 851.319
delta = 845.673
delta = 840.051
delta = 834.45
delta = 828.871
delta = 823.313
delta = 817.777
delta = 812.263
delta = 806.769
delta = 801.295
delta = 795.843
delta = 790.411
delta = 784.999
delta = 779.607
delta = 774.235
delta = 768.883
delta = 763.55
delta = 758.237
delta = 752.943
delta = 747.668
delta = 742.412
delta = 737.176
delta = 731.958
delta = 726.758
delta = 721.578
delta = 716.415
delta = 711.272
delta = 706.146
delta = 701.039
delta = 695.949
delta = 690.878
delta = 685.825
delta = 680.789
delta = 675.772
delta = 670.772
delta = 665.789
delta = 660.825
delta = 655.878
delta = 650.948
delta = 646.036
delta = 641.141
delta = 636.264
delta = 631.404
delta = 626.561
delta = 621.736
delta = 616.928
delta = 612.137
delta = 607.363
delta = 602.606
delta = 597.867
delta = 593.144
delta = 588.439
delta = 583.751
delta = 579.08
delta = 574.426
delta = 569.789
delta = 565.169
delta = 560.566
delta = 555.98
delta = 551.412
delta = 546.86
delta = 542.326
delta = 537.808
delta = 533.308
delta = 528.825
delta = 524.359
delta = 519.91
delta = 515.479
delta = 511.064
delta = 506.667
delta = 502.287
delta = 497.925
delta = 493.579
delta = 489.251
delta = 484.941
delta = 480.647
delta = 476.372
delta = 472.113
delta = 467.872
delta = 463.649
delta = 459.443
delta = 455.255
delta = 451.085
delta = 446.932
delta = 442.797
delta = 438.679
delta = 434.58
delta = 430.498
delta = 426.435
delta = 422.389
delta = 418.361
delta = 414.351
delta = 410.36
delta = 406.386
delta = 402.431
delta = 398.494
delta = 394.575
delta = 390.675
delta = 386.793
delta = 382.93
delta = 379.085
delta = 375.258
delta = 371.451
delta = 367.662
delta = 363.891
delta = 360.14
delta = 356.407
delta = 352.693
delta = 348.999
delta = 345.323
delta = 341.667
delta = 338.029
delta = 334.411
delta = 330.812
delta = 327.233
delta = 323.672
delta = 320.132
delta = 316.611
delta = 313.109
delta = 309.627
delta = 306.165
delta = 302.723
delta = 299.3
delta = 295.898
delta = 292.515
delta = 289.153
delta = 285.81
delta = 282.488
delta = 279.186
delta = 275.904
delta = 272.643
delta = 269.402
delta = 266.181
delta = 262.981
delta = 259.802
delta = 256.643
delta = 253.505
delta = 250.388
delta = 247.292
delta = 244.217
delta = 241.163
delta = 238.129
delta = 235.117
delta = 232.126
delta = 229.157
delta = 226.209
delta = 223.282
delta = 220.376
delta = 217.493
delta = 214.63
delta = 211.79
delta = 208.971
delta = 206.173
delta = 203.398
delta = 200.645
delta = 197.913
delta = 195.204
delta = 192.516
delta = 189.851
delta = 187.208
delta = 184.587
delta = 181.988
delta = 179.412
delta = 176.859
delta = 174.327
delta = 171.819
delta = 169.333
delta = 166.869
delta = 164.429
delta = 162.011
delta = 159.616
delta = 157.244
delta = 154.895
delta = 152.568
delta = 150.265
delta = 147.985
delta = 145.729
delta = 143.495
delta = 141.285
delta = 139.098
delta = 136.934
delta = 134.794
delta = 132.678
delta = 130.585
delta = 128.515
delta = 126.469
delta = 124.447
delta = 122.449
delta = 120.474
delta = 118.524
delta = 116.597
delta = 114.694
delta = 112.815
delta = 110.96
delta = 109.129
delta = 107.323
delta = 105.54
delta = 103.782
delta = 102.048
delta = 100.338
delta = 98.6528
delta = 96.9918
delta = 95.3552
delta = 93.743
delta = 92.1554
delta = 90.5923
delta = 89.0538
delta = 87.5399
delta = 86.0506
delta = 84.5861
delta = 83.1463
delta = 81.7312
delta = 80.341
delta = 78.9755
delta = 77.635
delta = 76.3193
delta = 75.0286
delta = 73.7629
delta = 72.5221
delta = 71.3064
delta = 70.1157
delta = 68.9501
delta = 67.8096
delta = 66.6943
delta = 65.6041
delta = 64.5392
delta = 63.4994
delta = 62.4849
delta = 61.4957
delta = 60.5317
delta = 59.5931
delta = 58.6798
delta = 57.7919
delta = 56.9294
delta = 56.0922
delta = 55.2805
delta = 54.4942
delta = 53.7334
delta = 52.9981
delta = 52.2882
delta = 51.6039
delta = 50.9451
delta = 50.3118
delta = 49.7041
delta = 49.1219
delta = 48.5654
delta = 48.0344
delta = 47.529
delta = 47.0492
delta = 46.5951
delta = 46.1665
delta = 45.7637
delta = 45.3864
delta = 45.0348
delta = 44.7089
delta = 44.4086
delta = 44.134
delta = 43.8851
delta = 43.6618
delta = 43.4642
delta = 43.2923
delta = 43.1461
delta = 43.0256
delta = 42.9307
delta = 42.8615
delta = 42.8179
delta = 42.8001
delta = 42.8079
delta = 42.8414
delta = 42.9005
delta = 42.9853
delta = 43.0957
delta = 43.2317
delta = 43.3934
delta = 43.5807
delta = 43.7936
delta = 44.0322
delta = 44.2963
delta = 44.5859
delta = 44.9012
delta = 45.242
delta = 45.6083
delta = 46.0001
delta = 46.4175
delta = 46.8603
delta = 47.3286
delta = 47.8224
delta = 48.3416
delta = 48.8862
delta = 49.4562
delta = 50.0516
delta = 50.6724
delta = 51.3184
delta = 51.9898
delta = 52.6865
delta = 53.4084
delta = 54.1556
delta = 54.928
delta = 55.7255
delta = 56.5482
delta = 57.3961
delta = 58.269
delta = 59.167
delta = 60.0901
delta = 61.0382
delta = 62.0112
delta = 63.0092
delta = 64.0321
delta = 65.0799
delta = 66.1526
delta = 67.25
delta = 68.3722
delta = 69.5192
delta = 70.6909
delta = 71.8872
delta = 73.1082
delta = 74.3537
delta = 75.6238
delta = 76.9184
delta = 78.2375
delta = 79.581
delta = 80.9488
delta = 82.3411
delta = 83.7576
delta = 85.1984
delta = 86.6633
delta = 88.1525
delta = 89.6658
delta = 91.2031
delta = 92.7644
delta = 94.3498
delta = 95.959
delta = 97.5922
delta = 99.2491
delta = 100.93
delta = 102.634
delta = 104.362
delta = 106.114
delta = 107.89
delta = 109.688
delta = 111.511
delta = 113.356
delta = 115.226
delta = 117.118
delta = 119.034
delta = 120.972
delta = 122.934
delta = 124.919
delta = 126.927
delta = 128.958
delta = 131.012
delta = 133.089
delta = 135.188
delta = 137.311
delta = 139.455
delta = 141.623
delta = 143.813
delta = 146.025
delta = 148.26
delta = 150.517
delta = 152.797
delta = 155.098
delta = 157.422
delta = 159.768
delta = 162.136
delta = 164.526
delta = 166.938
delta = 169.371
delta = 171.826
delta = 174.303
delta = 176.802
delta = 179.322
delta = 181.864
delta = 184.427
delta = 187.011
delta = 189.617
delta = 192.244
delta = 194.892
delta = 197.561
delta = 200.251
delta = 202.961
delta = 205.693
delta = 208.446
delta = 211.219
delta = 214.013
delta = 216.827
delta = 219.662
delta = 222.517
delta = 225.393
delta = 228.289
delta = 231.205
delta = 234.141
delta = 237.097
delta = 240.073
delta = 243.069
delta = 246.085
delta = 249.12
delta = 252.176
delta = 255.25
delta = 258.345
delta = 261.459
delta = 264.592
delta = 267.744
delta = 270.916
delta = 274.106
delta = 277.316
delta = 280.545
delta = 283.793
delta = 287.059
delta = 290.345
delta = 293.649
delta = 296.971
delta = 300.312
delta = 303.672
delta = 307.05
delta = 310.446
delta = 313.86
delta = 317.293
delta = 320.744
delta = 324.213
delta = 327.699
delta = 331.204
delta = 334.726
delta = 338.266
delta = 341.824
delta = 345.399
delta = 348.992
delta = 352.602
delta = 356.229
delta = 359.874
delta = 363.536
delta = 367.215
delta = 370.912
delta = 374.625
delta = 378.355
delta = 382.102
delta = 385.866
delta = 389.646
delta = 393.443
delta = 397.257
delta = 401.088
delta = 404.934
delta = 408.797
delta = 412.677
delta = 416.573
delta = 420.485
delta = 424.413
delta = 428.357
delta = 432.317
delta = 436.293
delta = 440.285
delta = 444.293
delta = 448.317
delta = 452.356
delta = 456.411
delta = 460.482
delta = 464.568
delta = 468.67
delta = 472.787
delta = 476.92
delta = 481.068
delta = 485.231
delta = 489.409
delta = 493.603
delta = 497.812
delta = 502.036
delta = 506.275
delta = 510.53
delta = 514.799
delta = 519.083
delta = 523.382
delta = 527.696
delta = 532.025
delta = 536.369
delta = 540.728
delta = 545.101
delta = 549.489
delta = 553.892
delta = 558.309
delta = 562.742
delta = 567.189
delta = 571.65
delta = 576.126
delta = 580.617
delta = 585.123
delta = 589.643
delta = 594.177
delta = 598.726
delta = 603.29
delta = 607.869
delta = 612.462
delta = 617.069
a=-3.401e-05
theta = 139.5, a = -3.401e-05, sommet =[200, 300]


[sylvain231]

ah oui j'oubliais le sommet est toujours 200,300

[leon1789]

avec le sommet forcé en (200;300) , on trouve :
t := -2.284
a := 2.388

l'équation :
0 = 0.47*x^2 + 138*x - 1.09*x*y + 9997.7 - 159.5*y + 0.63*y^2



C'est pour cela que ça me parait bizarre ce sommet.

[sylvain231]

mais moi je trouve une parabole encore plus bizarre !

[lyceen95]

Argh... je trouvais effectivement bizarre cette équation du 2nd degré. Pour un point qui est en 'dehors' de la cuvette dessinée par la parabole, il n'y a clairement qu'une normale qui passe par ce point, et c'est pas vraiment en phase avec une équation du 2nd degré.

Pour le rigolo de service, je pense savoir de qui tu parles. J'ai pris la décision il y a quelques années d'ignorer ce malade, et je m'en porte beaucoup mieux. Il se trouve que je suis allergique à la bêtise, et lire son site me donnait des poussées d'urticaire.

[sylvain231]

Pourriez-vous reprendre mes infos de débogage et vérifier si vous trouvez la même chose SVP ? Je sais je vous demande beaucoup de travail, désolé !

[sylvain231]

Rebonjour,
de quel rigolo de service parlez-vous ?
Bonne journée

[sylvain231]

mais ce n'est pas qu'une question de sommet mon problème voici l'image que j'obtiens avec les points et la parabole trouvée :