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The math behind blending modes

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So I have been trying to figure out exactly what's going on when changing the blending modes between layers. To do this, I am looking at the RGBA data (set to Decimal in 32bpc) in the Info window while moving my mouse about the canvas.

 

So far, my theories were correct as to how "Multiply" and "Add" get their name... but I came across a much more fundamental question. Rather mindblowing in its simplicity.

 

How is AE calculating the opacities of two overlapped images?

 

The example I have been working with is simple: two solids with Opacity=50% overlap to create an overall opacity of 75% (.75 floating point).

I am not understanding the equation of .5 + .5 = .75

Furthermore, it seems .3 + .3 = .51, .75 + .75 = .9375 etc etc.

 

I'm just curious what the math is behind this calculation.

 

 

-Chris


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