Re: [Gimp-developer] how layers actually get merged?

```Bear wrote:
> Assume there are four layers, all of which are in Normal mode and grayscale.
> for a specific pixel in each layer,
> Their intensity and alpha values(mapped to [0,1]) are
> i1,a1
> i2,a2
> i3,a3
> i4(background)
>
> the merged intensity is ((i1*a1+i2*(1-a1))*a2+i3*(1-a2))*a3+i4*(1-a3)
> am I correct? Thanks! ```
```
I hope not.  The proper expression should be

a1*i1 + (1-a1) * (a2*i2 + (1-a2) * (a3*i3 + (1-a3) * i4)).

That is, you have the expression reversed.  With your expression, the
background could show through even with opaque layers above it.

The best way to think about it is that the projection at layer n
is given by the recursive formula

P(n) = a_n * i_n + (1 - a_n) * P(n-1),

where the background is layer 0, and P(0) = i_0.

Best,
-- Bill

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