Quote -  What BB told me:

If we blend as in that tutorial, we do:

A: Blend(S, T * S, f) = (1-f) * S + f * T * S

If we use Texture_Strength equal to f, we have:

B: S * Blend(1, T, f)

I will now prove that these two setups are the same:

B
{ substitute definition of B }
= S * Blend(1, T, f)
{ substitute the definition of Blend }
= S * ((1-f) * 1 + f * T)
{ (1-f) * 1 = 1 - f }
= S * ((1 - f) + f * T)
{ distribution of multiplication over addition }
= (1 - f) * S + f * T * S
{ definition of A }
= A

Voila. B = A.

That is the proof that a Blended multiplication of skin (S) and tattoo (T) is the same as a multiplication of S with T using the texture strength as an adjustment of the intensity of the effect. But the Blended value is still starting with the premise of S * T: Blend(S, S * T, f)

Isaoshi was talking about a technique that doesn't start with multiplication of S and T: Blend(S, T, f)

That's totally different. In that sort of blend, there is no product of S and T at all.

I'm not arguing which is better (more useful) nor which is more correct (physically). Just saying they're different.

When you have the term S * T, then there is no way to make, for example, a white tattoo. More specifically, there is no way to produce a color that has any component higher than the original skin color, unless you have hyper-colors in the tatoo.  Whereas, Blend(S, T, f) can produce white quite easily. Blend is a variation on addition, not multiplication. It's a weighted sum, in fact. However, a weighted sum of S versus S * T is a different thing than just a weighted sum of S versus T.

Now we could discuss instead whether tattoo ink math is addition or multiplication or some combination, but I don't think I actually know the math. I've never seen it discussed.

Somebody want to volunteer to let me inject you with white paint and see what happens?

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Renderosity forum reply notifications are wonky. If I read a follow-up in a thread, but I don't myself reply, then notifications no longer happen AT ALL on that thread. So if I seem to be ignoring a question, that's why. (Updated September 23, 2019)