These two methods seem unintuitive to me. Is there a physics explanation that can explain why light may act as the methods suggest?
I think I might just be missing something really obvious, but why is it that we need the "(1-a_B)" in the expression for C'?
I am also curious if there is an explanation from physics about why this produces what we "expect" to see. Do we have models of materials that absorb X% of light? In which case we want our resulting alpha value to correspond to the % of light that the two materials over each other would let through.
It seems like the results of premultiplication and non-premultiplication are only differing by 1/alpha_c = 1/(alpha_b + (1-alpha_b)*alpha_a). It makes sense that B over A is not the same as A over B, but why does incorporating this factor eliminate fringing? This gets even more confusing for the example on the next slide where alpha_a is 1, isn't this factor just 1 then?
After "un_premultiply" to get the final color, is the alpha value of C still equal to alpha_c?
It seems like the reason this approach works is that we keep track of the alpha values, which we don’t do in the approach on the previous slide. But we could also track these values without “premultiplying”, e.g. just storing (r, g, b, a) and then the r, g, b values are actually the real ones we want, and so we wouldn’t need to divide by alpha in the end. Are there advantages/disadvantages of these two approaches?
Is this only a devision by alpha, mathematically? The issue never appears in project 1, since alpha is always 255 after blending...
What is the alpha of the overlap area? Is it also calculated by B' + (1-alpha)A'? Or is this formula only for calculating RGB value?
It looks like operations we use when we deal with homogenous space. Is there any mathematical connections between them?
Is this operator mathematically reasoned about rigorously? Properties such as being closed over composition aren't trivial. Even if they are, is there an intuitive geometric explanation for why the over operator with pre-multiplied alpha has such properties?
What's the mathmatical connection of this with homogenous space?