1. CSE 872 Dr. Charles B. Owen Advanced Computer Graphics1 BSSRDF – Bidirectional surface scattering reflectance distribution function Radiance theory BRDF

2. CSE 872 Dr. Charles B. Owen Advanced Computer Graphics2 Subsurface scattering Lighting approximations based on only surface reflection fails for: – Translucent materials – Marble, cloth, paper, skin, milk, cheese, bread, meat, fruits, plants, fish, water, snow, etc. – Heck, darn near everything

3. CSE 872 Dr. Charles B. Owen Advanced Computer Graphics3 What is subsurface transport? Skin Flesh Bone

4. CSE 872 Dr. Charles B. Owen Advanced Computer Graphics4 Radiance Theory Outgoing radiance equation x 0 – Surface point we are computing for  0 – View direction for point x 0  i (x i,  i ) – Incident flux on point x i from direction  i Flux = rate of energy per unit time. If x i =x 0, we get BRDF – Bidirectional reflectance distribution function (surface only!) BSSRDF

5. CSE 872 Dr. Charles B. Owen Advanced Computer Graphics5 Solving for radiance Okay, how do we solve for this, assuming we have an equation for S? x 0 – Surface point we are computing for  0 – View direction for point x 0 L i (x i,  i ) – Incident flux on point x i from direction  i Flux = rate of energy per unit time.

6. CSE 872 Dr. Charles B. Owen Advanced Computer Graphics6 Simplifying assumption We’ll only model first order events – Single reflections – We’ll cheat and add a “term” to simulate all other events “Each scattering event blurs the light distribution, and as a result the light distribution tends toward uniformity as the number of scattering events increases”

7. CSE 872 Dr. Charles B. Owen Advanced Computer Graphics7 The equation That’s all there is to it, we can all go home now…

8. CSE 872 Dr. Charles B. Owen Advanced Computer Graphics8 The equation Diffusion term Single scattering term

9. CSE 872 Dr. Charles B. Owen Advanced Computer Graphics9 Diffusion approximation

10. CSE 872 Dr. Charles B. Owen Advanced Computer Graphics10 Strange new worlds Light hitting a surface and diffusing below the surface is simulated with two light sources – A positive (real) light source below the surface – A negative (virtual) light source above the surface D = Diffusion constant

11. CSE 872 Dr. Charles B. Owen Advanced Computer Graphics11 Parameters for this Effective transport coefficient Absorption coefficient (material property) Reduced scattering coefficient (material property)

12. CSE 872 Dr. Charles B. Owen Advanced Computer Graphics12 Big ugly equation Albedo Fresnel transmittance

13. CSE 872 Dr. Charles B. Owen Advanced Computer Graphics13 Single scattering

14. CSE 872 Dr. Charles B. Owen Advanced Computer Graphics14 Single Scattering Term Exercise for the viewer: Determine what S (1) is from the above equations. Note the change of variable. (ouch) Phase function – Distribution that describes the scattering of light to a given angle. Combined extinction coefficient – How much loss as we pass through the material.

15. CSE 872 Dr. Charles B. Owen Advanced Computer Graphics15 Obtaining parameters

16. CSE 872 Dr. Charles B. Owen Advanced Computer Graphics16 Doing this in a Monte Carlo ray tracer For each ray – Integrate over random points around the ray intersection to compute diffusion term – Integrate over random distances into the material to compute the single scattering term How do we get the areas?

17. CSE 872 Dr. Charles B. Owen Advanced Computer Graphics17 Simple optimizations Falloff is exponential with distance for both terms – What does that give us? Is anything redundant happening here?

18. CSE 872 Dr. Charles B. Owen Advanced Computer Graphics18 Caveat Emptor The dipole approximation assumes a flat surface Assumes only one surface layer Be these problems?