BSSRDF BSSRDF Bidirectional surface scattering reflectance distribution function

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

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 2 CSE 872 Dr. Charles B. Owen Advanced Computer Graphics

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

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

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

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” 6 CSE 872 Dr. Charles B. Owen Advanced Computer Graphics

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

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

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

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 10 CSE 872 Dr. Charles B. Owen Advanced Computer Graphics

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

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

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

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. 14 CSE 872 Dr. Charles B. Owen Advanced Computer Graphics

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

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? 16 CSE 872 Dr. Charles B. Owen Advanced Computer Graphics

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

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