Photoshop Fill Opacity blend mode.

I'm trying to figure out how Fill Opacity in Photoshop works. I know there are 8 special blending modes which works differently with Opacity and Fill Opacity. Assuming source color is S and background color is B I need a formula to count a pixel if opacity for S is set to 100% but Fill Opacity is not 100%. For now I need a formula for Color Dodge blend when source color's Fill Opacity is not 100%.
Color Dodge formula is B/(1-S) if Fill Opacity is 100% as I know.

Thanks for any help!

 

In the past I played with photoshop blends in Unity shader, link to source code:

Code (CSharp):

1. https://github.com/przemyslawzaworski/Unity3D-CG-programming/blob/master/photoshop_blends.shader

To emulate opacity you need add transparency, as I understand.

 

Wait, wait, wait. It's a shader with photoshop blend modes where alpha is not taken into account. I know formulae I need for this. My problem is to find a blend formula for Fill Opacity, there are 8 blend modes which work with Opacity differently than with Fill Opacity. May be question in my first post wasn't pretty clear so I'll provide a screenshot explaining what I'm looking for.



I'm blending that diffused sphere with backdrop. To the left is an initial sphere. Up-Right is a result of ColorDodge blending with 60% opacity and 100% Fill Opacity. Bottom-Right is ColorDodge blending with 100% opacity and 60% FillOpacity. I know how to count a pixel when it is a regular opacity goes in, but how to count a pixel when Fill is not 100% is my problem here.

 

To me it looks like it's doing this:

color = lerp(B, BlendFunc(B, S, Fill), Opacity)

If I was to guess, for color dodge this is:

color = lerp(B, B / (1 - S * Fill), Opacity)

 

Bgolus.. you have saved my day again! I don't know how to thank you, really It worked as I wanted.

 

Bgolus. Do you even happen to know why this formula is exact copy of PS's only when a channel is not very near to FF. For example for FA it is exactly the same, but for FF in a channel it differs (a value is a little less than in PS). I upgraded my formula to this (Opacity 100%)

Code (CSharp):

1.  
2. fixed ColorDodge(fixed _b, fixed _s, fixed _fill) {
3.     if(_s * _fill < 1) {
4.         return min(1, _b / (1 - _s * _fill));
5.     }
6.     return 1;
7. }
8.  

May be I'm missing smth?

 

1 - 1 = 0
x / 0 = badness

I suspect Photoshop is doing the same test for 1 you are.

 

I mean I have a slight difference near to FF from Photoshop when using this upgraded formula above...)

 

Oh, yeah, no idea. Could be some factor of floating point math, or photoshop could be doing some different kind of blend when near 1.

 

I tried to figure out what kind of math near 1 PS uses but did not figure it out. Anyway the difference is small so this formula is ok. Let it be as it is. You helped me a lot anyway!