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  • BRDF

    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

    f_{ ext{r}}(omega _{ ext{i}},\,omega _{ ext{r}})\,=\,{frac {operatorname {d} L_{ ext{r}}(omega _{ ext{r}})}{operatorname {d} E_{ ext{i}}(omega _{ ext{i}})}}\,=\,{frac {operatorname {d} L_{ ext{r}}(omega _{ ext{r}})}{L_{ ext{i}}(omega _{ ext{i}})cos heta _{ ext{i}}\,operatorname {d} omega _{ ext{i}}}}

    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：

    L_{{{ ext{o}}}}({mathbf x},\,omega _{{{ ext{o}}}},\,lambda ,\,t)\,=\,L_{e}({mathbf x},\,omega _{{{ ext{o}}}},\,lambda ,\,t) +\,int _{Omega }f_{r}({mathbf x},\,omega _{{{ ext{i}}}},\,omega _{{{ ext{o}}}},\,lambda ,\,t)\,L_{{{ ext{i}}}}({mathbf x},\,omega _{{{ ext{i}}}},\,lambda ,\,t)\,(omega _{{{ ext{i}}}}\,cdot \,{mathbf n})\,operatorname domega _{{{ ext{i}}}}

    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

    // Main Physically Based BRDF
    // Derived from Disney work and based on Torrance-Sparrow micro-facet model
    //
    // BRDF = kD / pi + kS * (D * V * F) / 4
    // I = BRDF * NdotL
    //
    // * NDF (depending on UNITY_BRDF_GGX):
    // a) Normalized BlinnPhong
    // b) GGX
    // * Smith for Visiblity term
    // * Schlick approximation for Fresnel

    BRDF = kD/pi + kS *(D*V*F)/4

    I = BRDF * NdotL

    • NDF (depending on UNITY_BRDF_GGX):
     　　　　a) Normalized BlinnPhong
     　　　　b) 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

    // Based on Minimalist CookTorrance BRDF
    // Implementation is slightly different from original derivation: http://www.thetenthplanet.de/archives/255
    //
    // * NDF (depending on UNITY_BRDF_GGX):
    // a) BlinnPhong
    // b) [Modified] GGX
    // * Modified Kelemen and Szirmay-​Kalos for Visibility term
    // * Fresnel approximated with 1/LdotH
     
    half3 color = (diffColor + specularTerm * specColor) * light.color * nl
    + gi.diffuse * diffColor
    + surfaceReduction * gi.specular * FresnelLerpFast (specColor, grazingTerm, nv);
     
    // Old school, not microfacet based Modified Normalized Blinn-Phong BRDF
    // Implementation uses Lookup texture for performance
    //
    // * Normalized BlinnPhong in RDF form
    // * Implicit Visibility term
    // * No Fresnel term
     
     
    GI 
    gi.diffuse
    gi.specular
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  • 原文地址：https://www.cnblogs.com/minggoddess/p/6093982.html
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