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Although the specular term of the Cook-Torrance BRDF is widely used in Path Tracing, it was meant initially for rasterization (it was proposed before the advent of Path Tracing). The original idea of summing weighted diffuse and specular components (i.e. $R=dR_d+sR_s, d + s \leq 1$) is not capable of representing the complex results that may emerge from the interaction between diffuse and specular material elements (e.g. refraction, Fresnel for plastics, etc).

Actually, a better physically based model for material representation would be that of layers. For instance, smooth and rough conductors could be modeled through a unique layer represented by the specular term of the Cook-Torrance BRDF. Smooth and rough dielectrics could be modeled through a unique BSDF. Plastics, on the other hand, could be modeled through the use two layers: the topmost layer representing a dielectric (a BSDF) and the second layer, underneath the dieletric, representing a diffuse material (e.g. a lambertian or Oren-Nayar BRDF). That two-layer setup for plastics is capable of simulating the Fresnel reflectance of plastics (through the dielectric layer), the plastic color (through the light reflected by the colored diffuse layer underneath the dielectric), the light absorbed by the dielectric (through the implementation of Beer's Law), etc.

The layer-based material model approximates quite well what actually happens in real life. I have already written a related answer, with more details, and that may help you (I've included some references in that answer): https://computergraphics.stackexchange.com/a/5761/5681

The original Cook-Torrance does not properly conserve energy (I've already posted a question about that here). In 2007, Walter et al. have published the paper Microfacet Models for Refraction through Rough Surfaces, where they propose a Cook-Torrance based model amenable for Path Tracing.

Regarding layered material, I've implemented the system presented in the paper by Weidlich and Wilkie, Arbitrarily layered micro-facet surfaces, where a quite general layered material model is presented. After that, more sophisticated layered material models have been proposed. One of them is A comprehensive framework for rendering layered materials , by Wenzel Jakob. There is a new paper (published in 2017, I think), that supports subsurface scattering for top layers (I will add it here when I find it).

I think that PBRT uses layer-based materials too, but I do not know how they have actually implemented it.

Although the specular term of the Cook-Torrance BRDF is widely used in Path Tracing, the original BRDF was meant initially for rasterization (it was proposed before the advent of Path Tracing). The idea of summing weighted diffuse and specular components (i.e. $R=dR_d+sR_s, d + s \leq 1$) is not capable of representing the complex results that may emerge from the interaction between diffuse and specular material elements (e.g. refraction, Fresnel for plastics, etc).

Actually, a better physically based model for material representation would be that of layers. For instance, smooth and rough conductors could be modeled through a unique layer represented by the specular term of the Cook-Torrance BRDF. Smooth and rough dielectrics could be modeled through a unique BSDF. Plastics, on the other hand, could be modeled through the use two layers: the topmost layer representing a dielectric (a BSDF) and the second layer, underneath the dieletric, representing a diffuse material (e.g. a lambertian or Oren-Nayar BRDF). That two-layer setup for plastics is capable of simulating the Fresnel reflectance of plastics (through the dielectric layer), the plastic color (through the light reflected by the colored diffuse layer underneath the dielectric), the light absorbed by the dielectric (through the implementation of Beer's Law), etc.

The layer-based material model approximates quite well what actually happens in real life. I have already written a related answer, with more details, and that may help you (I've included some references in that answer): https://computergraphics.stackexchange.com/a/5761/5681

The original Cook-Torrance does not properly conserve energy (I've already posted a question about that here). In 2007, Walter et al. have published the paper Microfacet Models for Refraction through Rough Surfaces, where they propose a Cook-Torrance based model amenable for Path Tracing.

Regarding layered material, I've implemented the system presented in the paper by Weidlich and Wilkie, Arbitrarily layered micro-facet surfaces, where a quite general layered material model is presented. After that, more sophisticated layered material models have been proposed. One of them is A comprehensive framework for rendering layered materials , by Wenzel Jakob. There is a new paper (published in 2017, I think), that supports subsurface scattering for top layers (I will add it here when I find it).

I think that PBRT uses layer-based materials too, but I do not know how they have actually implemented it.

The original approach of Cook-Torrance was meant for rasterization (it was proposed before the advent of Path Tracing). The original idea of summing weighted diffuse and specular components is not capable of simulating the intricate results that emerge from the interaction between material layers (e.g. refraction, Fresnel for plastics, etc).

Actually, a better physically based model for material representation would be that of layers. For instance, smooth and rough conductors could be modeled through a unique layer represented by the specular term of the Cook-Torrance BRDF. Smooth and rough dielectrics could be modeled through a unique BSDF. Plastics, on the other hand, could be modeled through the use two layers: the topmost layer representing a dielectric (a BSDF) and the second layer, underneath the dieletric, representing a diffuse material (e.g. a lambertian or Oren-Nayar BRDF). That two-layer setup for plastics is capable of simulating the Fresnel reflectance of plastics (through the dielectric layer), the plastic color (through the light reflected by the colored diffuse layer underneath the dielectric), the light absorbed by the dielectric (through the implementation of Beer's Law), etc.

The layer-based material model approximates quite well what actually happens in real life. I have already written a related answer, with more details, and that may help you (I've included some references in that answer): https://computergraphics.stackexchange.com/a/5761/5681

The original Cook-Torrance does not properly conserve energy (I've already posted a question about that here). In 2007, Walter et al. have published the paper Microfacet Models for Refraction through Rough Surfaces, where they propose a Cook-Torrance based model amenable for Path Tracing.

Regarding layered material, I've implemented the system presented in the paper by Weidlich and Wilkie, Arbitrarily layered micro-facet surfaces, where a quite general layered material model is presented. After that, more sophisticated layered material models have been proposed. One of them is A comprehensive framework for rendering layered materials , by Wenzel Jakob. There is a new paper (published in 2017, I think), that supports subsurface scattering for top layers (I will add it here when I find it).

I think that PBRT uses layer-based materials too, but I do not know how they have actually implemented it.

Although the specular term of the Cook-Torrance BRDF is widely used in Path Tracing, it was meant initially for rasterization (it was proposed before the advent of Path Tracing). The original idea of summing weighted diffuse and specular components (i.e. $R=dR_d+sR_s, d + s \leq 1$) is not capable of representing the complex results that may emerge from the interaction between diffuse and specular material elements (e.g. refraction, Fresnel for plastics, etc).

Actually, a better physically based model for material representation would be that of layers. For instance, smooth and rough conductors could be modeled through a unique layer represented by the specular term of the Cook-Torrance BRDF. Smooth and rough dielectrics could be modeled through a unique BSDF. Plastics, on the other hand, could be modeled through the use two layers: the topmost layer representing a dielectric (a BSDF) and the second layer, underneath the dieletric, representing a diffuse material (e.g. a lambertian or Oren-Nayar BRDF). That two-layer setup for plastics is capable of simulating the Fresnel reflectance of plastics (through the dielectric layer), the plastic color (through the light reflected by the colored diffuse layer underneath the dielectric), the light absorbed by the dielectric (through the implementation of Beer's Law), etc.

The layer-based material model approximates quite well what actually happens in real life. I have already written a related answer, with more details, and that may help you (I've included some references in that answer): https://computergraphics.stackexchange.com/a/5761/5681

The original Cook-Torrance does not properly conserve energy (I've already posted a question about that here). In 2007, Walter et al. have published the paper Microfacet Models for Refraction through Rough Surfaces, where they propose a Cook-Torrance based model amenable for Path Tracing.

Regarding layered material, I've implemented the system presented in the paper by Weidlich and Wilkie, Arbitrarily layered micro-facet surfaces, where a quite general layered material model is presented. After that, more sophisticated layered material models have been proposed. One of them is A comprehensive framework for rendering layered materials , by Wenzel Jakob. There is a new paper (published in 2017, I think), that supports subsurface scattering for top layers (I will add it here when I find it).

I think that PBRT uses layer-based materials too, but I do not know how they have actually implemented it.

The original approach of Cook-Torrance was meant for rasterization (it was proposed before the advent of Path Tracing). The original idea of summing weighted diffuse and specular components is not capable of simulating the intricate results that emerge from the interaction between material layers (e.g. refraction, Fresnel for plastics, etc).

Actually, a better physically based model for material representation would be that of layers. For instance, smooth and rough conductors could be modeled through a unique layer represented by the specular term of the Cook-Torrance BRDF. Smooth and rough dielectrics could be modeled through a unique BSDF. Plastics, on the other hand, could be modeled through the use two layers: the topmost layer representing a dielectric (a BSDF) and the second layer, underneath the dieletric, representing a diffuse material (e.g. a lambertian or Oren-Nayar BRDF). That two-layer setup for plastics is capable of simulating the Fresnel reflectance of plastics (through the dielectric layer), the plastic color (through the light reflected by the colored diffuse layer underneath the dielectric), the light absorbed by the dielectric (through the implementation of Beer's Law), etc.

The layer approach approximates quite well what actually happens in real life. I have already written a related answer, with more details, and that may help you (I've included some references in that answer): https://computergraphics.stackexchange.com/a/5761/5681

The original Cook-Torrance does not properly conserve energy (I've already posted a question about that here). In 2007, Walter et al. have published the paper Microfacet Models for Refraction through Rough Surfaces, where they propose a Cook-Torrance based model amenable for Path Tracing.

Regarding layered material, I've implemented the system presented in the paper by Weidlich and Wilkie, Arbitrarily layered micro-facet surfaces, where a quite general layered material model is presented. After that, more sophisticated layered material models have been proposed. One of them is A comprehensive framework for rendering layered materials , by Wenzel Jakob. There is a new paper (published in 2017, I think), that supports subsurface scattering for top layers (I will add it here when I find it).

The original approach of Cook-Torrance was meant for rasterization (it was proposed before the advent of Path Tracing). The original idea of summing weighted diffuse and specular components is not capable of simulating the intricate results that emerge from the interaction between material layers (e.g. refraction, Fresnel for plastics, etc).

Actually, a better physically based model for material representation would be that of layers. For instance, smooth and rough conductors could be modeled through a unique layer represented by the specular term of the Cook-Torrance BRDF. Smooth and rough dielectrics could be modeled through a unique BSDF. Plastics, on the other hand, could be modeled through the use two layers: the topmost layer representing a dielectric (a BSDF) and the second layer, underneath the dieletric, representing a diffuse material (e.g. a lambertian or Oren-Nayar BRDF). That two-layer setup for plastics is capable of simulating the Fresnel reflectance of plastics (through the dielectric layer), the plastic color (through the light reflected by the colored diffuse layer underneath the dielectric), the light absorbed by the dielectric (through the implementation of Beer's Law), etc.

The layer-based material model approximates quite well what actually happens in real life. I have already written a related answer, with more details, and that may help you (I've included some references in that answer): https://computergraphics.stackexchange.com/a/5761/5681

The original Cook-Torrance does not properly conserve energy (I've already posted a question about that here). In 2007, Walter et al. have published the paper Microfacet Models for Refraction through Rough Surfaces, where they propose a Cook-Torrance based model amenable for Path Tracing.

Regarding layered material, I've implemented the system presented in the paper by Weidlich and Wilkie, Arbitrarily layered micro-facet surfaces, where a quite general layered material model is presented. After that, more sophisticated layered material models have been proposed. One of them is A comprehensive framework for rendering layered materials , by Wenzel Jakob. There is a new paper (published in 2017, I think), that supports subsurface scattering for top layers (I will add it here when I find it).

I think that PBRT uses layer-based materials too, but I do not know how they have actually implemented it.