microfacet theory

Microfacet theory is based on the idea that rough surfaces can be represented as a collection of microfacets, which are tiny, flat, and ideally smooth surfaces. These microfacets are statistically distributed, and their aggregate behavior determines the macroscopic surface’s reflective properties.

The following is the form of the general microfacet specular BRDF

where we have light direction , view direction , surface normal , and half vector . The three terms are Fresnel reflectance , geometry/shadowing masking function , and normal distribution function .

Fresnel Reflectance

The Fresnel reflectance term describes the fraction of incoming light that is reflected instead of refracted

Geometric Shadowing

The geometric shadowing term take into account the shadowing and masking of microfacets.

Normal Distribution Function

The normal distribution function characterizes the concentration of microfacet normals pointing toward any given direction

References

• ‘Physics and Math of Shading’ note