Q radiant energy: J
Φ radiant flux: W dQ/dt
E irradiance: W/m2 dΦ/dA
I radiant intersity: W/sr dΦ/dω
L radiance: W/(m2sr) d2Φ/dAprojdω
BRDF 双向反射分布函数
ωi 入射光= fi(θ,φ)
ωo 出射光 = fo(θ,φ)
azimuth angle φ and zenith angle θ
所以BRDF 是一个四维函数。
https://en.wikipedia.org/wiki/Bidirectional_reflectance_distribution_function
渲染方程:
dω = sinθdθdφ
推导:
--PBR,From Theory to Impllementation
Microfacet Theory
f = D()G()R()
Microfacet Distrbution Function,D
Shadowing-Masking Function,G
Beckmann Distribution with width parameter b:
Phong Distribution with exponent parameter ,p:
GGX Distribution with width parameter ,g:
Fresnel reflectance Function,R
Schlick
Local Subsurface scattering :Diffuse
https://en.wikipedia.org/wiki/Diffuse_reflection
Normalized BRDF 的推导
Lambert
Phong
Directional hemispherical reflectance
R(l) <=1
===========================================
unity的 BRDF1_Unity_PBS
BRDF = kD/pi + kS *(D*V*F)/4
I = BRDF * NdotL
- NDF (depending on UNITY_BRDF_GGX):
- V -Visiblity term -Smith
- Schlick approximaation for Fresnel --specular比例
color = diffuseColor* (gi.diffuse + light.color * diffuseTerm)
+ light.color * specularTerm * FresnelTerm
+ surfaceReduction *gi.specular * FresnelLerp