1980: Physical based, microfacet model (Cook-Torrance)
1990: models with special effect (materials, weathering, dust)
2000: measurement, acquisition of static materials and lights
Three Levels of Detail
Non-Physics-Based Model
Phong Model: just diffused reflection
Phong BRDFA
Blinn-Phong BRDF: says that the normal isn't just surface normal. instead, the normal of a point depends on your viewing angle (due to microfacet)
Blinn-Phong BRDF
Phong vs Blinn-Phong: Blinn-Phong produce correct specular highlight
Ward Model: Gaussian blur distribution over half vector slopes (Original version had issues with energy conservation and singularities; several modified variants exist)
Limitations:
not physically-based
do not necessarily preserve energy
no Fresnel effects
can't accurately model glossy surfaces
Physically-Based Model
Torrance-Sparrow Model: originally used by physicist until Cook, Torrance, Blinn adapted for graphics. Assumes surface is composed of many micro-grooves, each of which is a perfect mirror.
fresnel: material fresnel coefficient
microfacet distribution: Fraction of microfacets facing each direction. PDF over projected solid angle.
shadowing masking: occlusion by microfacets, depend on microfacet distribution
Microfacet Model
There are many microfacet distributions:
Beckmann Distribution: slope follow a Gaussian distribution. Slope of \theta_h is \tan \theta_h
The Blinn distribution: D(\vec{w_h}) = \frac{e+2}{2\pi} (\vec{w_h} \cdot n)^e
GGX distribution: Walter et al., EGSR 2007
Anisotropic distributions: PBRTv2, Ch. 8
Beckmann Distribution
Beckmann vs GGX Distribution
Beckmann vs GGX Image
Beckmann Shadowing
Torrance-Sparrow (Blinn) Shadowing
Microfacets does not account for second bounce within microfacets itself, so there is energy loss with large angle.
Increase roughness lead to great energy loss. But there is a paper try to solve it, with huge computational cost.
The Oren-Nayar Model: assumes facets are diffuse, instead of perfect mirror.
Top: Actual Moon. Down: Moon simulated by Original Microfacets model that assumes mirror reflection
Oren-Nayar Model
Layered Material Coating
Smooth Plastic
Now, people use all sorts of equipments to get data-driven BRDFs
Sections 5.A-5.C of Eric Veach's thesis have a detailed discussion of the issues we discussed in today's recitation regarding measures, Dirac deltas, and the various ways to write out specular BSDFs. If you are interested, I encourage you to take a read: https://www.proquest.com/docview/304456010?pq-origsite=gscholar&fromopenview=true
