A 50% opaque white object put on top of another 50% opaque white object is not anywhere near as white as a 100% opaque white object (blending mode normal). I tried this in Illustrator and Inkscape, and the results seem to be similar, so my question is: how are overlapping transparencies calculated? Is there a way to force either to use simple addition (30% opaque on top of 20% opaque = 50% opaque)?
2 Answers
Let the 2 otherwise identical layers have opacities 80% and 40%.
Represent the opacities as decimal numbers ie. 0,8 for 80% and 0,4 for 40%
The combined opacity as decimal number is 1 - (1-0,8)*(1- 0,4) = 1 - 0,2 * 0,6 = 1 - 0,12 = 0,88
As percentage that is 88%
The general formula for combining opacities A and B as decimal numbers:
Opacity = 1 - (1 -A)*(1 - B)
This is easy, if one thinks 1-A and 1-B as "transparencies". The combined transparency is calculated by multiplying the single layer transparencies. The opacity is = 1 - the transparency.
Your example: A=0,3 and B=0,2. The transparencies are 0,7 and 0,8
The combined opacity is 1 - 0,7 * 0,8 = 1 - 0,56 = 0,44 = 44%
ADDENDUM: The questioner wanted a way to force the combined opacity to be the sum of single layer opacities. This unfortunately is impossible. Let the layer opacities be 60% and 70%. We have no way to make something to have 130% opacity. 100% is the maximum. Nothing can be less transparent than the absolutely non-transparent.
If one has the single layer opacity = A (decimal) and wants to pile these layers to get the combined opacity = C, he needs log(1-C)/log(1-A) layers.
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Many thanks for this explanation! Do you happen to know the answer to my second question: is there a way to enforce simple addition? Alternately, how can I count the number of overlapping objects at each point?– Kamil S.May 7, 2017 at 22:15
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@KamilS. added the 2nd answer– user82991May 7, 2017 at 22:28
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Thank you. Of course, >100% makes no sense. What I want is for fifty 1% layers to have the combined opacity of 50% so as to count the number of layers by just looking at the resulting opacity. Too bad this isn't possible.– Kamil S.May 8, 2017 at 7:01
Think of transparency as light shining through.
The first layer absorbs 50% of the light, 50% comes through. So now from the remaining light, 50% will pass through the second layer, which is 25% from the original amount.
(While the formulars of user287001 are fine, I think the explanation is too complicated.)
#777777+#888888=#ffffff, in Gimp 2.10 you can achieve that using the legacy "addition" blend mode documented here: docs.gimp.org/en/gimp-concepts-layer-modes.html