Add GLSL functions for PDFs (#2779)

This changelist adds explicit GLSL functions for PDFs (probability density functions) to MaterialX, making its physically based shading code clearer and more self-documenting, and providing a stepping stone towards future use of generated GLSL/ESSL/MSL in path tracers as well as rasterization renderers.

Author: jstone-lucasfilm

libraries/pbrlib/genglsl/lib/mx_environment_fis.glsl

@@ -33,7 +33,7 @@ vec3 mx_environment_radiance(vec3 N, vec3 V, vec3 X, vec2 alpha, int distributio
 
         // Sample the environment light from the given direction.
         vec3 Lw = mx_matrix_mul(tangentToWorld, L);
-        float pdf = mx_ggx_NDF(H, alpha) * G1V / (4.0 * NdotV);
+        float pdf = mx_ggx_VNDF_reflection_PDF(H, alpha, G1V, NdotV);
         float lod = mx_latlong_compute_lod(Lw, pdf, float($envRadianceMips - 1), envRadianceSamples);
         vec3 sampleColor = mx_latlong_map_lookup(Lw, $envMatrix, lod, $envRadiance);
 

libraries/pbrlib/genglsl/lib/mx_generate_prefilter_env.glsl

@@ -53,7 +53,7 @@ vec3 mx_generate_prefilter_env()
 
         // Sample the environment light from the given direction.
         vec3 Lw = mx_matrix_mul(tangentToWorld, L);
-        float pdf = mx_ggx_NDF(H, vec2(alpha)) * G1V / (4.0 * NdotV);
+        float pdf = mx_ggx_VNDF_reflection_PDF(H, vec2(alpha), G1V, NdotV);
         float lod = mx_latlong_compute_lod(Lw, pdf, float($envRadianceMips - 1), envRadianceSamples);
         vec3 sampleColor = mx_latlong_map_lookup(Lw, $envMatrix, lod, $envRadiance);
 

libraries/pbrlib/genglsl/lib/mx_microfacet.glsl

@@ -93,6 +93,18 @@ vec3 mx_cosine_sample_hemisphere(vec2 Xi)
                 cosTheta);
 }
 
+// PDF of a cosine-weighted hemisphere sample.
+float mx_cosine_hemisphere_PDF(float cosTheta)
+{
+    return max(cosTheta, 0.0) * M_PI_INV;
+}
+
+// PDF of a uniform hemisphere sample.
+float mx_uniform_hemisphere_PDF()
+{
+    return 0.5 * M_PI_INV;
+}
+
 // Construct an orthonormal basis from a unit vector.
 // https://graphics.pixar.com/library/OrthonormalB/paper.pdf
 mat3 mx_orthonormal_basis(vec3 N)

libraries/pbrlib/genglsl/lib/mx_microfacet_sheen.glsl

@@ -70,9 +70,8 @@ float mx_imageworks_sheen_dir_albedo_monte_carlo(float NdotV, float roughness)
         float reflectance = mx_imageworks_sheen_brdf(NdotL, NdotV, NdotH, roughness);
 
         // Add the radiance contribution of this sample.
-        //   uniform_pdf = 1 / (2 * PI)
         //   radiance = reflectance * NdotL / uniform_pdf;
-        radiance += reflectance * NdotL * 2.0 * M_PI;
+        radiance += reflectance * NdotL / mx_uniform_hemisphere_PDF();
     }
 
     // Return the final directional albedo.
@@ -153,7 +152,7 @@ float mx_zeltner_sheen_brdf(vec3 L, vec3 V, vec3 N, float NdotV, float roughness
     //      = Do(wo) . |M^-1| / dot(wo, wo)^2
     //      = Do(wo) . aInv^2 / dot(wo, wo)^2
     //      = Do(wo) . (aInv / dot(wo, wo))^2
-    return max(wo.z, 0.0) * M_PI_INV * mx_square(aInv / lenSqr);
+    return mx_cosine_hemisphere_PDF(wo.z) * mx_square(aInv / lenSqr);
 }
 
 vec3 mx_zeltner_sheen_importance_sample(vec2 Xi, vec3 V, vec3 N, float roughness, out float pdf)
@@ -180,7 +179,7 @@ vec3 mx_zeltner_sheen_importance_sample(vec2 Xi, vec3 V, vec3 N, float roughness
     //      = Do(w) . ||M.wo||^4 / |M| (possible because M doesn't change z component)
     //      = Do(w) . dot(w, w)^2 * aInv^2
     //      = Do(w) . (aInv * dot(w, w))^2
-    pdf = max(w.z, 0.0) * M_PI_INV * mx_square(aInv * lenSqr);
+    pdf = mx_cosine_hemisphere_PDF(w.z) * mx_square(aInv * lenSqr);
 
     mat3 fromLTC = mx_orthonormal_basis_ltc(V, N, NdotV);
     w = mx_matrix_mul(fromLTC, w);

libraries/pbrlib/genglsl/lib/mx_microfacet_specular.glsl

@@ -61,6 +61,12 @@ vec3 mx_ggx_importance_sample_VNDF(vec2 Xi, vec3 V, vec2 alpha)
     return H;
 }
 
+// PDF of a reflection direction sampled from the GGX VNDF.
+float mx_ggx_VNDF_reflection_PDF(vec3 H, vec2 alpha, float G1V, float NdotV)
+{
+    return mx_ggx_NDF(H, alpha) * G1V / (4.0 * NdotV);
+}
+
 // https://www.cs.cornell.edu/~srm/publications/EGSR07-btdf.pdf
 // Equation 34
 float mx_ggx_smith_G1(float cosTheta, float alpha)