cse 872 dr. charles b. owen advanced computer graphics1 bssrdf – bidirectional surface scattering...

CSE 872 Dr. Charles B. OwenAdvanced Computer Graphics1

BSSRDF

• BSSRDF– Bidirectional surface scattering reflectance distribution

function

• Radiance theory• BRDF


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


What is subsurface transport?

Skin

Flesh

Bone


Radiance Theory

• Outgoing radiance equation

),(),;,(),( 00 iiiiiooo xdxxSxdL

x0 – Surface point we are computing for0 – View direction for point x0

i(xi,i) – Incident flux on point xi from direction i

Flux = rate of energy per unit time.

If xi=x0, we get BRDF – Bidirectional reflectance distribution function (surface only!)

BSSRDF


Solving for radiance

A

iiiiiiiiooo xdAdnxLxxSxL

2

00 )())(,(),;,(),(

Okay, how do we solve for this, assuming we have an equation for S?

x0 – Surface point we are computing for0 – View direction for point x0

Li(xi,i) – Incident flux on point xi from direction i

Flux = rate of energy per unit time.


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”


The equation

),;,(),;,(),;,( 00)1(

0000

xxSxxSxxS iiiidii

That’s all there is to it, we can all go home now…


The equation

Diffusion term

Single scattering term

),;,(),;,(),;,( 00)1(

0000

xxSxxSxxS iiiidii


Diffusion approximation


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

r

d

r d

e

Dx

rtr

4)(

v

d

v d

e

Dx

vtr

4)(

D = Diffusion constant


Parameters for this

• Effective transport coefficient

• Absorption coefficient (material property)

• Reduced scattering coefficient (material property)

a

)'(2 asatr

's

r

d

r d

e

Dx

rtr

4)(


Big ugly equation

33 '1

'1

4

')(

vt

d

vtrv

rt

d

rtrdd

edd

d

edrR

vtrrtr

),()(),(1

),;,( 0

toiditooiid FxxRFxxS

Albedo

Fresnel transmittance


Single scattering


Single Scattering Term

Exercise for the viewer: Determine what S(1) is from the above equations.

Note the change of variable. (ouch)

)''( 0wwp i

Phase function – Distribution that describes the scattering

of light to a given angle.

tc Combined extinction coefficient – How much loss as we pass through the material.


Obtaining parameters


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?


Simple optimizations

• Falloff is exponential with distance for both terms– What does that give us?

• Is anything redundant happening here?


Caveat Emptor

• The dipole approximation assumes a flat surface• Assumes only one surface layer

Be these problems?

cse 872 dr. charles b. owen advanced computer graphics1 bssrdf – bidirectional surface scattering...

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