[GAMES202 笔记] Lecture 10

[GAMES 202] Lecture Note 10


Microfacet models (its usage in RTR (without multi-bounce) is not phisically accurate) and Disney Pricipled BRDFs (the model itself is not phisically accurate) are among the mostly used PBR surface materials in RTR.

For volumes: fast and approximate single/multiple scattering in volumes.

Microfacet BRDF

Fresnel Term

Given the index of refraction and the angle which the incident ray makes with the surface normal, the Fresnel equations specify the material’s corresponding reflectance (i.e. the amount of light reflected from a surface) for two different polarization states of the incident illumination. (PBRT)

Physically Accurate: The Fresnel Equation

指Reflection,即反射的部分比例。相应地根据能量守恒,透射(折射)的比例为 ,这部分光在物体内部发生吸收和散射(散射表现为漫反射,次表面散射以及透射)。注意随着波长变化,即金属颜色的反映。


In which and is the index of refractive (ior) of the incident and transmitted media, . Dielectrics have real valued ior usually in . Conductors have complex-valued ior , where is referred to as the absorption coefficient. Ior varies as the light’s wave length changes.

For unpolarized light (which is often assumed), the Fresnel reflectance is:

Due to conservation of energy, the energy transmitted by a dielectric is .

The Approximation by Schlick:

is the specular reflectance at normal incidence.

Normal Distribution Function

There are many different models to discribe NDF!

(1) Beckmann NDF

Insights: (1) is roughness, shape similar to Gaussian distribution with acts like v ariance~ (2) slope space: the acts as variant. (If we use then it doesn’t attenuate to when achieving ) (3) The result should be when integrated over the projected solid angle on the surface of upper hemisphere. (为什么积分为1?因为这就是一个概率密度函数?)

(2) GGX (or Trowbridge-Reitz, TR)

Property: Long tail (more gentle specular, “光晕”)

Extending GGX: Generalized TR, GTR [Burly.] Adjustable tail length with !

Shadowing Masking Term

Idea: self-occlusion in microfacet. generally: more occlusions when increasing or , drops to when arriving grazing angle.

Another perspective: the goes to infinity at grazing angles, amplifying Fresnel effect, but the infinity is OK because the geometry shadowing term.


Insights: Decoupling shadowing (from light direction) and masking (from view direction): .

Kulla-Conty Approximation

The Issue: Multiple bounces in Microfacet ?

Missing energy! (observed under the white furnace test) Since multiple bounces in microfacet should be considered, especially when high roughness.

To get the overall energy when uniform incident radiance:

Idea: (1) Compensate the lost energy with another BRDF lobe, which can be integrated to in uniform incident radiance. (注意此处没有考虑菲涅尔项,即表面没有吸收或透射光线,因此认为所有能量均被反射) (2) The new BRDF should be reciprocal, i.e. in the form: . (since all brdf should be reciprocal w.r.t. !) So……


For each material (BRDF), get by precomputation: (Numerical fitting is not quite precise)


If the surface transmits/absorbs energy…

这里使用cosine-weighted average Fresnel近似总共被反射的能量。这种近似代表假设光线的多次散射都是diffuse的。

这是我们考虑Fresnel项后,多次散射中除去被吸收部分后的总能量(近似)。假设每次有比例的能量是参与下一次散射的,而的能量直接可以观测到。 *这个逻辑我还是不明白…


  1. 博主
    3 年前
    2021-5-29 17:03:39


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