donnees;

n_tests = 1000;

% Estimation du rayon et de la position du centre :
[C_estime,R_estime] = estimation_2(x_donnees_bruitees,y_donnees_bruitees,n_tests);

% Affichage du cercle estime :
n_points_cercle = 100;
theta_cercle = 2*pi/n_points_cercle:2*pi/n_points_cercle:2*pi;
x_cercle_estime = C_estime(1)+R_estime*cos(theta_cercle);
y_cercle_estime = C_estime(2)+R_estime*sin(theta_cercle);
plot(x_cercle_estime([1:end 1]),y_cercle_estime([1:end 1]),'b','LineWidth',3);
lg = legend(' Cercle initial', ...
		' Donnees bruitees', ...
		' Cercle estime', ...
		'Location','Best');

 function [C_estime,R_estime] = estimation_2(x_donnees_bruitees,y_donnees_bruitees,n_tests);
    
    G = mean( [ x_donnees_bruitees.' y_donnees_bruitees.' ] );
    R_moyen = mean( sqrt((x_donnees_bruitees.'-G(1)).^2 + (y_donnees_bruitees.'-G(2)).^2) );
    
    x = repmat(x_donnees_bruitees.', 1, n_tests, n_tests);
    y = repmat(y_donnees_bruitees.', 1, n_tests, n_tests);

    x_rand = repmat((rand(1, n_tests)*2 - 1) + G(1), length(x_donnees_bruitees), 1, n_tests);
    y_rand = repmat((rand(1, n_tests)*2 - 1) + G(2), length(y_donnees_bruitees), 1, n_tests);
    
    r_rand = rand(1, 1, n_tests) - 1/2 + R_moyen;
    R = repmat(r_rand, length(x_donnees_bruitees), n_tests, 1);
    
    dist = (sqrt((x-x_rand).^2 + (y-y_rand).^2) - R).^2;
    
    somme = reshape(sum(dist), [n_tests, n_tests]);
    
    [min_val, idx] = min(somme(:));
    [row, col] = ind2sub(size(somme), idx);
    
    C_estime = [ x_rand(1, row ) y_rand(1, row ) ];
    R_estime = r_rand(col);
end