Colorise parametric value using Python

colorise.py

from math import pi, cos
from functools import partial


def sinusoidal(v):
    '''
    Create a sinusoidal easing function.

    *v* is assumed to range from 0 to 1. The function will return a new value
    from 0 to 1.

    >>> sinusoidal(0)
    0.0
    >>> sinusoidal(1)
    1.0
    >>> sinusoidal(0.5)
    0.5
    >>> sinusoidal(0.75)
    0.8535533905932737
    '''
    output = cos(pi * v)
    output = (output / 2) + 0.5
    output = 1 - output
    return output


def squeeze(start, end):
    '''
    Given a "start" and "end" value, returns slope and intercept coefficients
    for a linear function which ranges from 0 to 1 and intercepts x=0 at *start*
    and x=1 at *1-end*.

    >>> squeeze(0, 0)
    (1.0, -0.0)
    >>> squeeze(0.2, 0)
    (1.25, -0.25)
    >>> squeeze(0, 0.2)
    (1.25, -0.0)
    >>> squeeze(0.2, 0.2)
    (1.6666666666666665, -0.3333333333333333)
    '''
    tan_alpha = 1 / (1-start-end)
    slope = tan_alpha
    intercept = -(start * (1 / (1-start-end)))
    return slope, intercept


def clamped_sinusoidal(v, x1=0.0, x2=0.0):
    '''
    Applies :py:func:`sinusoidal` only between *start+x1* and *end-x2*.

    Returns a sinusoidal function mapping a value in [0..1] to a new value in
    from [0..1].  The curve is "squeezed" between *0+start* and *1-end*
    effectively ramping up late, and levelling out early.

    >>> clamped_sinusoidal(0.5, 0, 0) == sinusoidal(0.5)
    True
    >>> clamped_sinusoidal(0.1, 0, 0) == sinusoidal(0.1)
    True
    >>> clamped_sinusoidal(0.9, 0, 0) == sinusoidal(0.9)
    True
    >>> clamped_sinusoidal(0.5, 0.2, 0.2)
    0.4999999999999999
    >>> clamped_sinusoidal(0.5, 0, 0.2)
    0.6913417161825448
    >>> clamped_sinusoidal(0.5, 0.2, 0)
    0.3086582838174551
    '''
    a, b = squeeze(x1, x2)
    if x1 and v <= x1:
        return 0.0
    if x2 and v >= (1-x2):
        return 1.0
    return sinusoidal(a*v+b)


def percentage_position(percentage, items):
    '''
    Returns an item from a list by a percentage position.

    Example::

        >>> percentage_position(0.0, [1, 2, 3])
        1
        >>> percentage_position(0.5, [1, 2, 3])
        2
        >>> percentage_position(0.99, [1, 2, 3])
        3
    '''
    position = (len(items)-1) * percentage
    return items[round(position)]


def main():

    print('Visualising Easing function')
    ease = partial(clamped_sinusoidal, x1=0.3, x2=0.2)

    print(' Visualising Easing Curve '.center(80, '-'))
    for n in range(30):
        progress = ease(n/30)
        print('%3s' % n, '*'*round((80*(progress))))

    print(' Example with fixed pallette '.center(80, '-'))
    colors = [
        '#ff0000',
        '#aaaa00',
        '#ffff00',
        '#aaff00',
        '#00ff00',
    ]
    print('Pallette:', colors)
    for n in range(30):
        value = ease(n / 30)
        out = percentage_position(value, colors)
        print('%3s' % n, out)

    print(' Example with a smooth transition '.center(80, '-'))
    for n in range(30):
        value = ease(n / 30)
        hue = 120 * value
        out = 'hsl(%d%%, 50%%, 50%%)' % round(hue)
        print('%3s' % n, out)


if __name__ == '__main__':
    main()