draw_bezier.py

from PIL import Image, ImageDraw

X = 0
Y = 1

def position_by_ratio(p1, p2, ratio):
    # divide returns float with Python3
    return p1[X] + ((p2[X] - p1[X]) * (ratio/100)), p1[Y] + ((p2[Y] - p1[Y]) * (ratio/100))


def bezier_position_by_ratio(p1, p2, p3, p4, ratio):
    p5 = position_by_ratio(p1, p2, ratio)
    p6 = position_by_ratio(p2, p3, ratio)
    p7 = position_by_ratio(p3, p4, ratio)
    
    p8 = position_by_ratio(p5, p6, ratio)
    p9 = position_by_ratio(p6, p7, ratio)
    
    return position_by_ratio(p8, p9, ratio)

if __name__ == '__main__':
    im = Image.new('RGBA', (600, 600), (255,255,255,0))
    draw = ImageDraw.Draw(im)
    x1 = (0,600 - 0)
    x2 = (100, 600 - 550)
    x3 = (400, 600 - 400)
    x4 = (600, 600 - 50)

    _pos = x1
    for i in range(1, 101):
        pos = bezier_position_by_ratio(x1, x2, x3, x4, i)
        draw.line((_pos, pos))
        _pos = pos

    im.save('bezier.png', "PNG")