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Search-and-replace \mathcal{V} with \nu to fix PDF render issue (#2403)
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emackey authored May 22, 2024
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6 changes: 3 additions & 3 deletions extensions/2.0/Khronos/KHR_materials_sheen/README.md
Original file line number Diff line number Diff line change
Expand Up @@ -91,10 +91,10 @@ Not all incoming light is reflected at a micro-fiber. Some of the light may hit

All implementations should use the same calculations for the BRDF inputs. See [Appendix B](https://www.khronos.org/registry/glTF/specs/2.0/glTF-2.0.html#appendix-b-brdf-implementation) for more details on the BRDF calculations.

The sheen formula follows the common microfacet form with visibility term $\mathcal{V}_s$:
The sheen formula follows the common microfacet form with visibility term $\nu_s$:

$$
\text{SheenBRDF} = \frac{G_S D_S}{4 \, \left|N \cdot L \right| \, \left| N \cdot V \right|} = \mathcal{V}_S D_S
\text{SheenBRDF} = \frac{G_S D_S}{4 \, \left|N \cdot L \right| \, \left| N \cdot V \right|} = \nu_S D_S
$$


Expand All @@ -112,7 +112,7 @@ sheen_distribution = (2 + inv_r) * pow(sin2h, inv_r * 0.5) / (2 * PI);

### Sheen visibility

The "Charlie" sheen visibility $\mathcal{V}_s = \frac{G_s}{4 \, \left|N \cdot L \right| \, \left| N \cdot V \right|}$ is also defined in the same document:
The "Charlie" sheen visibility $\nu_s = \frac{G_s}{4 \, \left|N \cdot L \right| \, \left| N \cdot V \right|}$ is also defined in the same document:

```glsl
float l(float x, float alpha_g)
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6 changes: 3 additions & 3 deletions extensions/2.0/Khronos/KHR_materials_transmission/README.md
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Expand Up @@ -207,19 +207,19 @@ With the step function $\chi^+$ we ensure that the microsurface is only visible
Introducing the visibility function

$$
\mathcal{V}_T = \frac{G_T}{4 \left| N \cdot L \right| \left| N \cdot V \right|}
\nu_T = \frac{G_T}{4 \left| N \cdot L \right| \left| N \cdot V \right|}
$$

simplifies the original microfacet BTDF to

$$
\text{MicrofacetBTDF} = \mathcal{V}_T D_T
\text{MicrofacetBTDF} = \nu_T D_T
$$

with

$$
\mathcal{V}_T = \frac{\chi^+\left(\frac{H_T \cdot L}{N \cdot L}\right)}{\left| N \cdot L\right| + \sqrt{\alpha^2 + (1 - \alpha^2) (N \cdot L)^2}} \frac{\chi^+\left(\frac{H_T \cdot V}{N \cdot V}\right)}{\left| N \cdot V \right| + \sqrt{\alpha^2 + (1 - \alpha^2) (N \cdot V)^2}}
\nu_T = \frac{\chi^+\left(\frac{H_T \cdot L}{N \cdot L}\right)}{\left| N \cdot L\right| + \sqrt{\alpha^2 + (1 - \alpha^2) (N \cdot L)^2}} \frac{\chi^+\left(\frac{H_T \cdot V}{N \cdot V}\right)}{\left| N \cdot V \right| + \sqrt{\alpha^2 + (1 - \alpha^2) (N \cdot V)^2}}
$$

Thus we have the function
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8 changes: 4 additions & 4 deletions specification/2.0/Specification.adoc
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Expand Up @@ -3058,25 +3058,25 @@ G = \frac{2 \, \left| N \cdot L \right| \, \chi^{+}(H \cdot L)}{\left| N \cdot L

where χ^+^(*x*) denotes the Heaviside function: 1 if *x* > 0 and 0 if *x* <= 0. See <<Heitz2014,Heitz (2014)>> for a derivation of the formulas.

Introducing the visibility function latexmath:[\mathcal{V}]
Introducing the visibility function latexmath:[\nu]

[latexmath]
++++
\mathcal{V} = \frac{G}{4 \, \left| N \cdot L \right| \, \left| N \cdot V \right|}
\nu = \frac{G}{4 \, \left| N \cdot L \right| \, \left| N \cdot V \right|}
++++

simplifies the original microfacet BRDF to

[latexmath]
++++
\text{MicrofacetBRDF} = \mathcal{V} D
\text{MicrofacetBRDF} = \nu D
++++

with

[latexmath]
++++
\mathcal{V} = \frac{\, \chi^{+}(H \cdot L)}{\left| N \cdot L\right| + \sqrt{\alpha^2 + (1 - \alpha^2) (N \cdot L)^2}} \frac{\, \chi^{+}(H \cdot V)}{\left| N \cdot V \right| + \sqrt{\alpha^2 + (1 - \alpha^2) (N \cdot V)^2}}
\nu = \frac{\, \chi^{+}(H \cdot L)}{\left| N \cdot L\right| + \sqrt{\alpha^2 + (1 - \alpha^2) (N \cdot L)^2}} \frac{\, \chi^{+}(H \cdot V)}{\left| N \cdot V \right| + \sqrt{\alpha^2 + (1 - \alpha^2) (N \cdot V)^2}}
++++

Thus, we have the function
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