1. BSSRDF: Bidirectional Surface Scattering Reflectance Distribution Functions Jared M. Dunne C95 Adv. Graphics Feb. 7, 2002 Based on: "A Practical Model for Subsurface Light Transport" Henrik Wann Jensen, Steve Marschner, Marc Levoy and Pat Hanrahan

2. What is BSSRDF? Bidirectional surface scattering reflectance distribution function In other words… An equation that determines how incident light reflects and scatters from a surface Also, simulates how light reflects off of and throughout a surface

3. Example: Skin

4. BRDF Bidirectional reflectance distribution function Simplification of BSSRDF Assumes that light entering a material leaves it at the same point Usually tries to approximate surface scattering in some way

5. BSSRDF v. BRDF BSSRDF allows simulation of light transport Light can enter a material at one point and be reflected at another point. BSSRDF  Translucence, Color Bleeding BRDF  Opague, Hard-looking… But… BSSRDF is EXPENSIVE

6. BSSRDF v. BRDF BRDF BSSRDF

7. BRDFBSSRDF Example

8. The Theory Outgoing radiance at point x 0 is computed by integrating incident radiance at points x i over the surrounding area and incoming directions w i.

9. Hendrik Wann Jensen et al Basic Idea: Break into two parts Diffuse = the radiance at a given point due to light transport within the media, via an approximation of the scatting Single Scattering = the first order scattering from a surface… BRDF reflection + light refracted through the material

10. Diffuse vs. Single Scatter

11. The Diffusion Approximation In highly scattering media (like milk), light scatters many times (often several hundred) Causes a lot more calculations, more expensive (if you use full BSSRDF)

12. Diff. Approx. (cont.) = S d It is observed that in such materials the scattering becomes isotropic (in all directions) even with a highly focused light distribution. So the following two-term approximation is used: radiant fluence vector irradiance

13. Single Scattering Term = S (1) The light which refracts directly through or reflects off of the material Directional component of incident light Jensen (et al) extend a BRDF model (Hanrahan and Krueger) to achieve this scatter

14. Putting the two together… So Jensen’s model of BSSRDF becomes: Or: BSSRDF = Diffuse Approximation + Single Scatter Term

15. Light propagation  a = Absorption Coefficient  s = Scattering Coefficient  t = Extinction Coefficient =  a +  s These are used in the volume rendering equation, which describes how light moves through a medium

16. Getting the Coefficients

17. Got Milk?

18. Marble bust 1.3 Million Triangles BRDF: 2 minutes BSSRDF: <5 minutes Monte Carlo: 1250 minutes

19. Stanford Bunny

20. Future Plans of Hendrik Wann Jensen In an interview of Jensen by CGarchitect.com: “I would like to combine the BSSRDF with photon mapping, and also work on making these algorithms generally available and easy to use for complex models.”

21. FinalRender First Render Engine to support BSSRDF More Info: http://trinity3d.com http://trinity3d.com/productinfo/FinalRende r/finalrender.shtml