% Create the sample data
n=20;
d1=[rand(1,n)/4+2; 3*rand(1,n)+2];
d2=[4*rand(1,n)-2; rand(1,n)/4+2];
d3=[4*rand(1,n)-2; rand(1,n)/4+5];
d4=[rand(1,n)/4-2; 3*rand(1,n)+2];
data=[d1, d2, d3, d4];
data=round(data*50);
% Do the fitting
theta=rectangleFit(data);
fprintf('data=%s\n', mat2str(data));
fprintf('theta=%s\n', mat2str(theta));
% Plot the result
plot(data(1,:), data(2,:), '.');
x1=theta(1)-theta(3);
x2=theta(1)+theta(3);
y1=theta(2)-theta(4);
y2=theta(2)+theta(4);
line([x1 x1 x2 x2 x1], [y1 y2 y2 y1 y1], 'color', 'r');
axis image
legend({'Sample data', 'Final fitting rectangle'}, 'location', 'northOutside', 'orientation', 'horizontal');