def origin_fun(x,case=1):
    """
    Some functions defined on [0,1] to be expanded by Fourier basis
    :param x:The point where the function need to be evaluated
    :param case: Considered case
    :return: Corresponding function value
    """
    if case==1:
        return 32*x*x*(1-x)*(1-x)
    if case==2:
        return 20*x*(1-x)*(0.5-x)
    if case==3:
        return (1-x)*(x)
    if case==4:
        return x**3