Compositing Math In Blender (Physically Based Shading & Rendering)

So it is a long story how I got here. Interestingly the Compositing Math should be the first thing documented next to the shader description itself. And I remember I had hard times in the past to find Mental Ray (oh f* it is a fossil now...I used to use that a lot), and Arnold rendering. It is the dark side the documentations: COMPOSITING CG renders.

Now I can't remember actually where I found the source to that (because it is hard to find), but I have the receipt.

But couple of words about what Compositing Math is. 

Essentially when the energy conservation applies to the physically based shading and rendering it means the components of the surface properties absorb and reflect (and transmit) (the BRDF and or BSDF) the amount of energy that hits the surface. To solve this formula, practically it means the components are calculated combined together during rendering, and it allows that to output separately and combine those together during the compositing. So we can check what kind of passes (render elements, components, AOVs, whatever we call it) we want to access during the composition 

BUT if we want to recreate the render output (commonly referred as beauty), we need a specific set of passes. 

How do we know which passes? 

And how we can combine those? 

The answer is the Compositing Math my friends, AND also it is based on the shading and rendering architecture. So Cycles’ render passes based on the Principled BSDF (OpenPBR, Disney, Standard Surface) shader looks like this in Compositing:

• Diffuse

• Diffuse = ( Diffuse Direct + Diffuse Indirect ) × Diffuse Color

• Glossy

• Glossy = ( Glossy Direct + Glossy Indirect ) × Glossy Color

• Transmission

• Transmission = ( Transmission Direct + Transmission Indirect ) × Transmission Color

• Subsurface

• Subsurface = ( Subsurface Direct + Subsurface Indirect ) × Subsurface Color

• Volume

• Volume = Volume Direct + Volume Indirect

• Emission / Background (Environment)

• Add Emission and Environment passes directly.
  
  

Then sum:

Combined = Diffuse + Glossy + Transmission + Subsurface + Volume + Emission + Environment

However...let me know what is Your experience, whether it is a pixel perfect match or not.

And just a bit of summertime CG (knowledge) Entertainment. I always refer to this presentation because Naty Hoffman has a nice CG Explainer Voice to hear :)