% ajustement d'un cercle
R = [83	64	50	54	70	88	93	91]
theta = [0	45	90	135	180	225	270	315]

theta_rad = theta * pi/180

x = R.*cos(theta_rad)
y = R.*sin(theta_rad)

X = [sum(x) sum(y) length(R);
    sum(x.^2) sum(x.*y) sum(x);
    sum(x.*y) sum(y.^2) sum(y) ]

A = [sum(x.^2)+sum(y.^2);
     sum(x.^3)+sum(x.*y.^2);
     sum(x.^2.*y)+sum(y.^3)]
 
Q = inv(X)*A

a = Q(1) /2
b = Q(2) /2
c = Q(3)

R2 = c + a^2 + b^2
Rayon = sqrt(R2)

figure
hold on
plot (x, y, 'o')
circle (Rayon, a, b)
xlim ([-100 100])
ylim ([-100 100])
axis square
grid on

% calcul des erreurs de mesure radiale
R_reel = sqrt ((x - a).^2 + (y - b).^2)
erreur_R = R_reel - Rayon
% écart-type
sigma_R = std (erreur_R)

% erreur avec facteur de confiance de 95%
err_R_95 = sigma_R * 2.37