1. 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

2. 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

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

4. phase function
mean cosine g:

5. 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

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

7. 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

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

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

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

11. 跟equation 3很像，只是多了一個D

12. 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.

13. The dipole method
represent incident source distribution

14. (4)
(5)

15. Single Scattering Term
沿著s把入射的radiance積起來

16. ----flat surface

17. The BSSRDF Model

18. Measuring the BSSRDF

19. 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).

20. 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：

21. Single scattering evaluation for arbitrary geometry
pick a random distance

22. Results