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

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

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

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

CC BY-SA 3.0
2016-04-18T08:58:40.510Z
2016-04-18T10:21:12.167Z
2016-04-18T10:21:12.167Z
wip
<p>In <a href="https://hal.inria.fr/hal-01024289/document" rel="nofollow noreferrer">Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs</a>, Eric Heitz derives the Separable Masking and Shadowing function as (P.83-84):</p>

<p><a href="https://i.sstatic.net/1F17w.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/1F17w.png" alt="enter image description here"></a></p>

<p>In the mentioned <a href="https://www.cs.cornell.edu/~srm/publications/EGSR07-btdf.pdf" rel="nofollow noreferrer">Microfacet Models for Refraction through Rough Surfaces</a> by Walter et al., Smith term is computed as:</p>

<p><a href="https://i.sstatic.net/Sxwgo.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/Sxwgo.png" alt="enter image description here"></a></p>

<p>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?</p>

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

(Asked by: username_0 on 2016-04-18)

In [Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs](https://hal.inria.fr/hal-01024289/document), Eric Heitz derives the Separable Masking and Shadowing function as (P.83-84):

[![enter image description here](https://i.sstatic.net/1F17w.png)](https://i.sstatic.net/1F17w.png)

In the mentioned [Microfacet Models for Refraction through Rough Surfaces](https://www.cs.cornell.edu/~srm/publications/EGSR07-btdf.pdf) by Walter et al., Smith term is computed as:

[![enter image description here](https://i.sstatic.net/Sxwgo.png)](https://i.sstatic.net/Sxwgo.png)

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?

**Tags:** function, masking


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## 1 answers

### Answer by username_0 on 2016-04-18. Score: 2

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

$\frac{1}{1+\Lambda (m)}=\frac{2}{1+\sqrt{1+\alpha ^{2}tan\_{2}\theta\_{m} }}$

$1+\Lambda (m)=\frac{1+\sqrt{1+\alpha ^{2}tan\_{2}\theta\_{m} }}{2}$

$\Lambda (m)=\frac{-1+\sqrt{1+\alpha ^{2}tan\_{2}\theta\_{m} }}{2}$


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