linear-to-smooth curve mapping, based on a paper https://arxiv.org/abs/2010.09714

mapping.py

def curve_mapping(x, s, t):
    """
    provides a linear-to-smooth curve mapping

    based on a paper https://arxiv.org/abs/2010.09714
    """
    epsilon = 0.000001

    if x < 0:
        return 0
    if x > 1:
        return 1
    if x < t:
        return (t * x) / (x + s * (t - x) + epsilon)

    return ((1 - t) * (x - 1)) / (1 - x - s * (t - x) + epsilon) + 1