Fix reference BRDF implementation (#2386)

extensions/2.0/Khronos/KHR_materials_clearcoat/README.md

@@ -117,35 +117,33 @@ The `fresnel_coat` function is computed using the Schlick Fresnel term from the
 ```
 function fresnel_coat(normal, ior, weight, base, layer) {
   f0 = ((1-ior)/(1+ior))^2
-  fr = f0 + (1 - f0)*(1 - abs(NdotV))^5   // N = normal
+  fr = f0 + (1 - f0)*(1 - abs(dot(V, normal)))^5
   return mix(base, layer, weight * fr)
 }
 ```
 
 Applying the functions we arrive at the coated material
 
 ```
-coated_material = mix(material, clearcoat_brdf(clearcoatRughness^2), clearcoat * (0.04 + (1 - 0.04) * (1 - NdotV)^5))
+coated_material = mix(material, clearcoat_brdf(clearcoatRoughness^2), clearcoat * (0.04 + (1 - 0.04) * (1 - VdotNc)^5))
 ```
 
 and finally, substituting and simplifying, using some symbols from [Appendix B](https://www.khronos.org/registry/glTF/specs/2.0/glTF-2.0.html#appendix-b-brdf-implementation) and `Nc` for the clearcoat normal:
 
 ```
-clearcoatFresnel = 0.04 + (1 - 0.04) * (1 - abs(VdotNc))^5
-clearcoatAlpha = clearcoatRoughness^2
+clearcoat_fresnel = 0.04 + (1 - 0.04) * (1 - abs(VdotNc))^5
+clearcoat_alpha = clearcoatRoughness^2
+clearcoat_brdf = D(clearcoat_alpha) * G(clearcoat_alpha) / (4 * abs(VdotNc) * abs(LdotNc))
 
-f_clearcoat = clearcoatFresnel * D(clearcoatAlpha) * G / (4 * abs(VdotNc) * abs(LdotNc))
-
-coated_material = (f_diffuse + f_specular) * (1 - clearcoat * clearcoatFresnel) +
-                  f_clearcoat * clearcoat
+coated_material = mix(material, clearcoat_brdf, clearcoat * clearcoat_fresnel)
 ```
 
 #### Emission
 
 The clearcoat layer is on top of emission in the layering stack. Consequently, the emission is darkened by the Fresnel term.
 
 ```
-coated_emission = emission * (0.04 + (1 - 0.04) * (1 - NdotV)^5)
+coated_emission = emission * (1 - clearcoat * clearcoat_fresnel)
 ```
 
 #### Discussion

extensions/2.0/Khronos/KHR_materials_ior/README.md

@@ -103,10 +103,10 @@ Valid values for `ior` are numbers greater than or equal to 1. In addition, a va
 The extension changes the computation of the Fresnel term defined in [Appendix B](https://www.khronos.org/registry/glTF/specs/2.0/glTF-2.0.html#appendix-b-brdf-implementation) to the following:
 
 ```
-const dielectricSpecular = ((ior - 1)/(ior + 1))^2
+dielectric_f0 = ((ior - 1)/(ior + 1))^2
 ```
 
-Note that for the default index of refraction `ior = 1.5` this term evaluates to `dielectricSpecular = 0.04`.
+Note that for the default index of refraction `ior = 1.5` this term evaluates to `dielectric_f0 = 0.04`.
 
 ## Interaction with other extensions
 

extensions/2.0/Khronos/KHR_materials_sheen/README.md

@@ -91,82 +91,82 @@ 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 `f_sheen` follows the common microfacet form:
+The sheen formula follows the common microfacet form with visibility term $\mathcal{V}_s$:
+
+$$
+\text{SheenBRDF} = \frac{G_S D_S}{4 \, \left|N \cdot L \right| \, \left| N \cdot V \right|} = \mathcal{V}_S D_S
+$$
 
-*f*<sub>*sheen*</sub> = *sheenColor* * *sheenFresnel* * *sheenDistribution* * *sheenVisibility* = *sheenColor* * *F*<sub>*S*</sub> * *G*<sub>*S*</sub> * *D*<sub>*S*</sub> / (4 * abs(dot(*N*, *L*)) * abs(dot(*N*, *V*)))
 
 ### Sheen distribution
 
-The sheen distribution follows the "Charlie" sheen definition from ImageWorks [Conty and Kulla (2017)](#ContyKulla2017):
+The sheen distribution $D_s$ follows the "Charlie" sheen definition from ImageWorks [Conty and Kulla (2017)](#ContyKulla2017):
 
 ```glsl
-alphaG = sheenRoughness * sheenRoughness
-invR = 1 / alphaG
+alpha_g = sheenRoughness * sheenRoughness
+inv_r = 1 / alpha_g
 cos2h = NdotH * NdotH
 sin2h = 1 - cos2h
-sheenDistribution = (2 + invR) * pow(sin2h, invR * 0.5) / (2 * PI);
+sheen_distribution = (2 + inv_r) * pow(sin2h, inv_r * 0.5) / (2 * PI);
 ```
 
 ### Sheen visibility
 
-The "Charlie" sheen visibility is also defined in the same document:
+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:
 
 ```glsl
-float l(float x, float alphaG)
+float l(float x, float alpha_g)
 {
-    float oneMinusAlphaSq = (1.0 - alphaG) * (1.0 - alphaG);
-    float a = mix(21.5473, 25.3245, oneMinusAlphaSq);
-    float b = mix(3.82987, 3.32435, oneMinusAlphaSq);
-    float c = mix(0.19823, 0.16801, oneMinusAlphaSq);
-    float d = mix(-1.97760, -1.27393, oneMinusAlphaSq);
-    float e = mix(-4.32054, -4.85967, oneMinusAlphaSq);
+    float one_minus_alpha_sq = (1.0 - alpha_g) * (1.0 - alpha_g);
+    float a = mix(21.5473, 25.3245, one_minus_alpha_sq);
+    float b = mix(3.82987, 3.32435, one_minus_alpha_sq);
+    float c = mix(0.19823, 0.16801, one_minus_alpha_sq);
+    float d = mix(-1.97760, -1.27393, one_minus_alpha_sq);
+    float e = mix(-4.32054, -4.85967, one_minus_alpha_sq);
     return a / (1.0 + b * pow(x, c)) + d * x + e;
 }
 
-float lambdaSheen(float cosTheta, float alphaG)
+float lambda_sheen(float cos_theta, float alpha_g)
 {
-    return abs(cosTheta) < 0.5 ? exp(l(cosTheta, alphaG)) : exp(2.0 * l(0.5, alphaG) - l(1.0 - cosTheta, alphaG));
+    return abs(cos_theta) < 0.5 ? exp(l(cos_theta, alpha_g)) : exp(2.0 * l(0.5, alpha_g) - l(1.0 - cos_theta, alpha_g));
 }
 
-sheenVisibility = 1.0 / ((1.0 + lambdaSheen(NdotV, alphaG) + lambdaSheen(NdotL, alphaG)) * (4.0 * NdotV * NdotL));
+sheen_visibility = 1.0 / ((1.0 + lambda_sheen(NdotV, alpha_g) + lambda_sheen(NdotL, alpha_g)) * (4.0 * NdotV * NdotL));
 ```
 
 However, depending on device performance and resource constraints, one can use a simpler visibility term, like the one defined by [Ashikhmin and Premoze (2007)](#AshikhminPremoze2007) (but that will make the BRDF not energy conserving when using the albedo-scaling technique described below):
+
 ```glsl
-sheenVisibility = 1 / (4 * (NdotL + NdotV - NdotL * NdotV))
+sheen_visibility = 1 / (4 * (NdotL + NdotV - NdotL * NdotV))
 ```
 
-### Sheen Fresnel
-
-The Fresnel term may be omitted, i.e., *F* = 1.
-
 ### Sheen layering
 
 #### Albedo-scaling technique
 
-The sheen layer can be combined with the base layer with an albedo-scaling technique described in [Conty and Kulla (2017)](#ContyKulla2017). The base layer *f*<sub>*diffuse*</sub> + *f*<sub>*specular*</sub> from [Appendix B](https://www.khronos.org/registry/glTF/specs/2.0/glTF-2.0.html#appendix-b-brdf-implementation) is scaled with *sheenAlbedoScaling* to avoid energy gain.
-
-*f* = *f*<sub>*sheen*</sub> + (*f*<sub>*diffuse*</sub> + *f*<sub>*specular*</sub>) * *sheenAlbedoScaling*
+The sheen layer can be combined with the base layer with an albedo-scaling technique described in [Conty and Kulla (2017)](#ContyKulla2017). The base layer `material = mix(dielectric_brdf, metal_brdf, metallic)` from [Appendix B](https://www.khronos.org/registry/glTF/specs/2.0/glTF-2.0.html#appendix-b-brdf-implementation) is scaled with `sheen_albedo_scaling` to avoid energy gain.
 
 ```glsl
 float max3(vec3 v) { return max(max(v.x, v.y), v.z); }
+sheen_albedo_scaling = min(1.0 - max3(sheenColor) * E(VdotN), 1.0 - max3(sheenColor) * E(LdotN))
 
-sheenAlbedoScaling = min(1.0 - max3(sheenColor) * E(VdotN), 1.0 - max3(sheenColor) * E(LdotN))
+sheen_material = sheenColor * sheen_brdf + material * sheen_albedo_scaling
 ```
 
 The values `E(x)` can be looked up in a table which can be found in section 6.2.3 of [Enterprise PBR Shading Model](#theory-documentation-and-implementations) if you use the "Charlie" visibility term. If you use Ashikhmin instead, you can get the lookup table by using the [cmgen tool from Filament](#theory-documentation-and-implementations), with the `--ibl-dfg` and `--ibl-dfg-cloth` flags: the table is in the blue channel of the generated picture. The lookup must be done with `x = VdotN` and `y = sheenRoughness`.
 
 If you want to trade a bit of accuracy for more performance, you can use the `VdotN` term only and thus avoid doing multiple lookups for `LdotN`. The albedo scaling term is simplified to:
 ```glsl
-sheenAlbedoScaling = 1.0 - max3(sheenColor) * E(VdotN)
+sheen_albedo_scaling = 1.0 - max3(sheenColor) * E(VdotN)
 ```
 
 In this simplified form, it can be used to scale the base layer for both direct and indirect lights:
+
 ```glsl
-specular_direct *= sheenAlbedoScaling;
-diffuse_direct *= sheenAlbedoScaling;
-environmentIrradiance_indirect *= sheenAlbedoScaling
-specularEnvironmentReflectance_indirect *= sheenAlbedoScaling
+specular_direct *= sheen_albedo_scaling;
+diffuse_direct *= sheen_albedo_scaling;
+environment_irradiance_indirect *= sheen_albedo_scaling
+specular_environment_reflectance_indirect *= sheen_albedo_scaling
 ```
 
 ## Schema

extensions/2.0/Khronos/KHR_materials_specular/README.md

@@ -84,6 +84,11 @@ Factor and texture are combined by multiplication to describe a single value.
 | **specularColorFactor** | `number[3]` | The F0 color of the specular reflection (linear RGB). | No, default: `[1.0, 1.0, 1.0]`|
 | **specularColorTexture** | [`textureInfo`](https://www.khronos.org/registry/glTF/specs/2.0/glTF-2.0.html#reference-textureinfo) | A texture that defines the F0 color of the specular reflection, stored in the `RGB` channels and encoded in sRGB. This texture will be multiplied by specularColorFactor. | No |
 
+If a texture is defined:
+
+- The specular color is computed with : `specularColor = specularColorFactor * sampleLinear(specularColorTexture).rgb`.
+- The specular strength is computed with : `specular = specularFactor * sample(specularTexture).a`.
+
 The `specular` and `specularColor` parameters affect the `dielectric_brdf` of the glTF 2.0 metallic-roughness material.
 
 ```
@@ -134,41 +139,35 @@ function fresnel_mix(f0_color, ior, weight, base, layer) {
 }
 ```
 
-Therefore, the Fresnel term `F` in the final BRDF of the material changes to
+Therefore, the Fresnel term `dielectric_fresnel` in the final BRDF of the material changes to
 
 ```
-dielectricSpecularF0  = min(0.04 * specularColorFactor * specularColorTexture.rgb, float3(1.0)) *
-                        specularFactor * specularTexture.a
-dielectricSpecularF90 = specularFactor * specularTexture.a
-
-F0  = lerp(dielectricSpecularF0, baseColor.rgb, metallic)
-F90 = lerp(dielectricSpecularF90, 1, metallic)
-
-F = F0 + (F90 - F0) * (1 - VdotH)^5
+dielectric_f0  = min(0.04 * specularColor, float3(1.0)) * specular
+dielectric_f90 = specular
+dielectric_fresnel = mix(dielectric_f0, dielectric_f90, fresnel_w)
 ```
 
-Note that in `dielectricSpecularF0` we clamp the product of specular color and f0 reflectance from IOR (`0.04`), before multiplying by specular.
+Note that in `dielectric_f0` we clamp the product of specular color and f0 reflectance from IOR (`0.04`), before multiplying by `specular`.
 
-In the diffuse component we have to account for the fact that `F` is now an RGB value.
+In the diffuse component we have to account for the fact that `dielectric_fresnel` is now an RGB value. Thus we redefine `dielectric_brdf` as follows:
 
 ```
-c_diff = lerp(baseColor.rgb, black, metallic)
-diffuse = c_diff / PI
-f_diffuse = (1 - max(F.r, F.g, F.b)) * diffuse
+dielectric_fresnel_max = max_value(dielectric_fresnel)
+dielectric_brdf = dielectric_fresnel * specular_brdf + (1 - dielectric_fresnel_max) * diffuse_brdf
 ```
 
 ## Interaction with other extensions
 
 If `KHR_materials_ior` is used in combination with `KHR_materials_specular`, the constant `0.04` is replaced by the value computed from the IOR.
 
 ```
-dielectricSpecularF0 = min(((ior - outside_ior) / (ior + outside_ior))^2 * specularColorFactor * specularColorTexture.rgb, float3(1.0)) * specularFactor * specularTexture.a
-dielectricSpecularF90 = specularFactor * specularTexture.a
+dielectric_f0 = min(((ior - outside_ior) / (ior + outside_ior))^2 * specularColor, float3(1.0)) * specular
+dielectric_f90 = specular
 ```
 
 `outside_ior` is typically set to 1.0, the index of refraction of air.
 
-If `KHR_materials_transmission` is used in combination with `KHR_materials_specular`, the ratio of transmission and reflection computed from the Fresnel term also depends on `dielectricSpecularF0` and `dielectricSpecularF90`. The following images show a thin, transmissive material.
+If `KHR_materials_transmission` is used in combination with `KHR_materials_specular`, the ratio of transmission and reflection computed from the Fresnel term also depends on `dielectric_f0` and `dielectric_f90`. The following images show a thin, transmissive material.
 
 Specular from 0 to 1:
 
@@ -179,7 +178,7 @@ Specular color from [0,0,0] to [1,1,1] (top) and [0,0,0] to [1,0,0]:
 ![](figures/specular-color-thin.png)
 ![](figures/specular-color-thin-2.png)
 
-If `KHR_materials_transmission` and `KHR_materials_volume` are used in combination with `KHR_materials_specular`, specular factor and specular color have no effect on the refraction angle. The direction of the refracted light ray is only based on the index of refraction defined in `KHR_materials_ior`. The ratio of transmission and reflection computed from the Fresnel term still depends on `dielectricSpecularF0` and `dielectricSpecularF90`. The following images show a refractive material.
+If `KHR_materials_transmission` and `KHR_materials_volume` are used in combination with `KHR_materials_specular`, specular factor and specular color have no effect on the refraction angle. The direction of the refracted light ray is only based on the index of refraction defined in `KHR_materials_ior`. The ratio of transmission and reflection computed from the Fresnel term still depends on `dielectric_f0` and `dielectric_f90`. The following images show a refractive material.
 
 Specular from 0 to 1:
 
@@ -197,7 +196,7 @@ Specular color from [0,0,0] to [1,1,1] (top) and [0,0,0] to [1,0,0]:
 Material models that define F0 in terms of reflectance at normal incidence can be converted by encoding the reflectance in the specular color parameters. Typically, the reflectance ranges from 0% to 8%, given as a value in range [0,1], with 0.5 (=4%) being the default. F0 is computed from `reflectance` in the following way:
 
 ```
-dielectricSpecularF0 = 0.08 * reflectance
+dielectric_f0 = 0.08 * reflectance
 ```
 
 In contrast, `KHR_materials_specular` defines a constant factor of 0.04 to compute F0, as this corresponds to glTF's default IOR of 1.5. Therefore, by encoding an additional constant factor of 2 in `specularColorFactor`, we can convert from reflectance to specular color without any loss.

extensions/2.0/Khronos/KHR_materials_transmission/README.md

@@ -207,26 +207,26 @@ With the step function $\chi^+$ we ensure that the microsurface is only visible
 Introducing the visibility function
 
 $$
-V_T = \frac{G_T}{4 \left| N \cdot L \right| \left| N \cdot V \right|}
+\mathcal{V}_T = \frac{G_T}{4 \left| N \cdot L \right| \left| N \cdot V \right|}
 $$
 
 simplifies the original microfacet BTDF to
 
 $$
-\text{MicrofacetBTDF} = V_T D_T
+\text{MicrofacetBTDF} = \mathcal{V}_T D_T
 $$
 
 with
 
 $$
-V_T = \frac{\chi^+\left(\frac{H_T \cdot L}{N \cdot L}\right)}{\left| N \cdot L\right| + \sqrt{\alpha^2 + (1 - \alpha^2) (N \cdot L)^2}} \frac{\chi^+\left(\frac{H_T \cdot V}{N \cdot V}\right)}{\left| N \cdot V \right| + \sqrt{\alpha^2 + (1 - \alpha^2) (N \cdot V)^2}}
+\mathcal{V}_T = \frac{\chi^+\left(\frac{H_T \cdot L}{N \cdot L}\right)}{\left| N \cdot L\right| + \sqrt{\alpha^2 + (1 - \alpha^2) (N \cdot L)^2}} \frac{\chi^+\left(\frac{H_T \cdot V}{N \cdot V}\right)}{\left| N \cdot V \right| + \sqrt{\alpha^2 + (1 - \alpha^2) (N \cdot V)^2}}
 $$
 
 Thus we have the function
 
 ```
 function specular_btdf(α) {
-  return V_T * D_T
+  return Vis_T * D_T
 }
 ```
 

specification/2.0/Specification.adoc

@@ -3058,33 +3058,33 @@ 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
+Introducing the visibility function $\mathcal{V}$
 
 [latexmath]
 ++++
-V = \frac{G}{4 \, \left| N \cdot L \right| \, \left| N \cdot V \right|}
+\mathcal{V} = \frac{G}{4 \, \left| N \cdot L \right| \, \left| N \cdot V \right|}
 ++++
 
 simplifies the original microfacet BRDF to
 
 [latexmath]
 ++++
-\text{MicrofacetBRDF} = V D
+\text{MicrofacetBRDF} = \mathcal{V} D
 ++++
 
 with
 
 [latexmath]
 ++++
-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}}
+\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}}
 ++++
 
 Thus, we have the function
 
 [source,c]
 ----
 function specular_brdf(α) {
-  return V * D
+  return Vis * D
 }
 ----
 
@@ -3178,22 +3178,23 @@ Metal and dielectric are mixed according to the metalness:
 material = mix(dielectric_brdf, metal_brdf, metallic)
 ----
 
-Taking advantage of the fact that `roughness` is shared between metal and dielectric and that the Schlick Fresnel is used, we can simplify the mix and arrive at the final BRDF for the material:
+The full code is given below:
 
 [source,c]
 ----
-const black = 0
+fresnel_w = (1 - abs(VdotH))^5
 
-c_diff = lerp(baseColor.rgb, black, metallic)
-f0 = lerp(0.04, baseColor.rgb, metallic)
-α = roughness^2
+diffuse_brdf = (1 / π) * baseColor.rgb
+specular_brdf = D(roughness^2) * G(roughness^2) / (4 * abs(VdotN) * abs(LdotN))
 
-F = f0 + (1 - f0) * (1 - abs(VdotH))^5
+dielectric_f0 = 0.04
+dielectric_fresnel = dielectric_f0 + (1 - dielectric_f0) * fresnel_w
+dielectric_brdf = mix(diffuse_brdf, specular_brdf, dielectric_fresnel)
 
-f_diffuse = (1 - F) * (1 / π) * c_diff
-f_specular = F * D(α) * G(α) / (4 * abs(VdotN) * abs(LdotN))
+metal_fresnel = baseColor.rgb + (1 - baseColor.rgb) * fresnel_w
+metal_brdf = metal_fresnel * specular_brdf
 
-material = f_diffuse + f_specular
+material = mix(dielectric_brdf, metal_brdf, metallic)
 ----