def _get_rise_fall_coeff_(normalized_time):
    """
    This is a smooth function that goes from 0 to 1. It is a 5th order polynomial because it satisfies the following
    5 conditions

    value = 0 at t=0 and t=1 (2 conditions)
    first derivative = 0 at t=0 and t=1 (2 conditions)
    value = 0.5 in the middle

    :param normalized_time:
    :return:
    """
    coeff = (
        6.0 * pow(normalized_time, 5.0)
        - 15.0 * pow(normalized_time, 4.0)
        + 10.0 * pow(normalized_time, 3.0)
    )
    return coeff