alpha blending: order independence and reversion

alpha.py

a0 = 0.3
a1 = 0.7
a2 = 0.9
a3 = 0.1

c0 = 0.1
c1 = 0.2
c2 = 0.3
c3 = 0.4

# forward alpha blending
x = c0*a0
x = x*(1 - a1) + c1*a1
x = x*(1 - a2) + c2*a2
x = x*(1 - a3) + c3*a3

# backward alpha blending
y = 0
k = 1
y = y + a3*c3*k
k = k*(1 - a3)
y = y + a2*c2*k
k = k*(1 - a2)
y = y + a1*c1*k
k = k*(1 - a1)
y = y + a0*c0*k
k = k*(1 - a0)

assert(abs(x - y) < 1e-5)

print(x, y)