# Radiative Transfer Equation for Photorealistic Rendering

I've recently become interested in photorealistic rendering, and I've been looking at the different rendering philosophies. I read this Disney Research bachelor's thesis, which states both the radiative transfer equation (RTE)

$(\vec{w}\cdot\nabla)L(\vec{x},\vec{\omega}) = -(\sigma_{a}+\sigma_{s})L(\vec{x},\vec{\omega})+Q(\vec{x},\vec{\omega})+\sigma_{s} \int_{\Omega}L(\vec{x},\vec{\omega})\rho(\vec{\omega},\vec{\omega}')d\vec{\omega}'$

and that

Exact BSSRDFs follow trivially from exact solutions to the RTE. Unfortunately, closed form solutions of the RTE for general 3D geometry, illumination and materials are rare, which motivates analysis on simplified, lower dimensional domains.

But most shaders use BSSRDF's and(/or?) the Rendering Equation instead, even high-end shaders like Disney's Hyperion, even though the Rendering Equation supposedly doesn't take into account sub-surface scattering, polarization, etc..

So my two questions are a) what is the reason for not using the radiative transfer equation for photorealistic rendering (or an approximation like the skin-shaders used for Big Hero and Moana), and b) how are the parameters like the phase functions and coefficients found for different materials like skin, hair, water, metal, glass?