How does mixing shaders work?

Question

Hello i am having trouble understanding how the 'mix shader' node actually works and more specifically why mix 2 identical nodes? For example: why is there a different result between using a glossy shader then mixing 2 glossy shaders with the same color and the same average roughness? what does mix shader actually do? average(with factor) the pixel color returned by each shader? i see people mixing 2 glossy shaders claiming it looks better since it gives a different roughness distribution, but i am curious to what is happening behind the scenes and what is actually the 100% PBR way.

related resources:

What's the point of mixing the same shader types?

https://www.youtube.com/watch?v=nsem2HjwZQU

https://www.blenderguru.com/articles/making-better-materials

Answer 1

The easy part of the answer is that the 100% PBR way is to not use the mix shader because the mix shader does not preserve the physical properties of light.

The mix shader works, put crudely, by adding the output of the two BSDF nodes that are its inputs, in a ratio controlled by the value of Fac. Call the Shader that plugs into the top input $T$. Call the Shader that plugs into the bottom input $B$. Then the output of the mix shader is $Fac * B + (1 - Fac) * T$

The mix shader is used for a lot of purposes, but they all rely on using some input to control the Fac value. Many of these purposes were overcome by the Principled BSDF shader; but you still see examples. There's a common glass shader that uses a Fresnel or Layer Weight node to set FAC to mix between a glossy and a transparent shader, for example.

Even with the Principled BSDF shader available, some effects are still better produced by mixing two shaders to overcome limitations of the Cycles render engine.

Mixing two identical shaders is an artistic tradeoff that gives up actual photorealism for an effect that might better simulate the look that the artist wants. It's not a way to achieve PBR.

Answer 2

Mix shader is not complicated. It finds the color returned by each shader and interpolates between the two (in linear space) by the factor given. It's really just a mixRGB. Indeed, if we use it in Eevee, it's identical to shader to RGB -> mixRGB. (In Cycles, of course, this mixRGB has to happen for further ray bounces and has to preserve information like ray type and ray direction.)

Why is it different to mix shader two different roughnesses than to use a single, average roughness? I think the best parallel would be to imagine mixing two circles of different diameter:

When we take two white circles of different sizes and mix their colors, is it the same thing as taking one white circle of average size? Clearly not.

The same thing is true of roughnesses. Let's look at the same thing with a single lamp on spheres, but mixing roughnesses this time:

If we take a wide, dull highlight (1.0 roughness) and mix it with a tight, bright highlight (0.0 roughness) we're mixing two circles of different sizes. It is not the same thing as taking a medium highlight (0.5 roughness.) And the colors make it more clear what the difference is between mixing two different elements, and just taking the average of those elements.