function angleWithTangentDirection = computeAngle(frame,vec)
    % frame: 3x3 matrix
    % vec : vector to project on frame.
    vec = reshape(vec,[3,1]);
    fframe  = frame*vec;
    if (abs(fframe(3)) > eps)
        angleWithTangentDirection = (atan(fframe(3)/fframe(2)));
    else
        angleWithTangentDirection = single(0);
    end
end