# Why does the G1 term have a 2 in the numerator in Walter's formula, but not in Heitz's generalized formula?

In Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs, Eric Heitz derives the Separable Masking and Shadowing function as (P.83-84):

In the mentioned Microfacet Models for Refraction through Rough Surfaces by Walter et al., Smith term is computed as:

I don't see a parameterisation of Λ that could make appear the generic form (Heitz version) from the specific form derived by Walter. What am I missing?

## 1 Answer

Actually I just had to solve the following equation to find a solution, consistent with the presence of the "2" in the numerator:

$\frac{1}{1+\Lambda (m)}=\frac{2}{1+\sqrt{1+\alpha ^{2}tan_{2}\theta_{m} }}$

$1+\Lambda (m)=\frac{1+\sqrt{1+\alpha ^{2}tan_{2}\theta_{m} }}{2}$

$\Lambda (m)=\frac{-1+\sqrt{1+\alpha ^{2}tan_{2}\theta_{m} }}{2}$