A Practical Model for Subsurface Light Transport Henrik Wann Jensen Stephen R. Marschner Marc Levoy Pat Hanrahan 這篇paper介紹了一個半透明物質的subsurface light transport的model

Outlines Diffusion Theory Measuring the BSSRDF Rendering the BSSRDF Results 1.介紹diffusion theory:用來predict散射性高物體的光學性質。本篇使用diffusion theory+single scattering。 2.Measuring:實際測量一些material的散射性質(BSSRDF的parameter) 3.Rendering:要render translucent material 的要點 4.一些結果的圖

Diffusion Theory BRDF:BSSRDF的特例，假設光從同一點進出。 extinct,

phase function mean cosine g:

first-order scattering of Lri： 同老師上課所講。 無限小的光射進homogeneous medium Q(x,w):像volumetric source

Equation (1) scalar irradiance： vector irradiance： Light source：

Diffusion Approximation The light distribution in highly scattering media tends to become isotropic. -----Equation (2) 第一式combine radiative transport equation得第二式

Substituting equation2 into equation1 classic diffusion equation： isotropic , infinite medium r : x跟光源的距離

Boundary condition： ---equation (3) 不太懂 net inward diffuse flux = 0 at each point on the surface

Diffuse Fresnel reflectance Fr：Fresnel formula 兩個介面折射率不同 new boundary condition：

跟equation 3很像，只是多了一個D

diffuse BSSRDF Rd Rd is equal to the radiant exitance divided by the incident flux 沒有Analytical solutioin subsurface reflection,which is often modeled as a semi-finite plane parallel medium.

The dipole method represent incident source distribution

(4) (5)

Single Scattering Term 沿著s把入射的radiance積起來

----flat surface

The BSSRDF Model

Measuring the BSSRDF

Rendering using the BSSRDF Efficient integration of the BSSRDF including importance sampling Single scattering evaluation for arbitrary geometry Diffusion approximation for arbitrary geometry Texture (spatial variation on the object surface).

Integrating the BSSRDF stochastically sampling the location of both endpoints of the shadow ray We sample the two terms of BSSRDF separately Monte carlo density：

Single scattering evaluation for arbitrary geometry pick a random distance

Results