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CSE 872 Dr. Charles B. OwenAdvanced Computer Graphics1
BSSRDF
• BSSRDF– Bidirectional surface scattering reflectance distribution
function
• Radiance theory• BRDF
CSE 872 Dr. Charles B. OwenAdvanced 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
CSE 872 Dr. Charles B. OwenAdvanced Computer Graphics3
What is subsurface transport?
Skin
Flesh
Bone
CSE 872 Dr. Charles B. OwenAdvanced Computer Graphics4
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
CSE 872 Dr. Charles B. OwenAdvanced Computer Graphics5
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.
CSE 872 Dr. Charles B. OwenAdvanced 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”
CSE 872 Dr. Charles B. OwenAdvanced Computer Graphics7
The equation
),;,(),;,(),;,( 00)1(
0000
xxSxxSxxS iiiidii
That’s all there is to it, we can all go home now…
CSE 872 Dr. Charles B. OwenAdvanced Computer Graphics8
The equation
Diffusion term
Single scattering term
),;,(),;,(),;,( 00)1(
0000
xxSxxSxxS iiiidii
CSE 872 Dr. Charles B. OwenAdvanced Computer Graphics9
Diffusion approximation
CSE 872 Dr. Charles B. OwenAdvanced 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
r
d
r d
e
Dx
rtr
4)(
v
d
v d
e
Dx
vtr
4)(
D = Diffusion constant
CSE 872 Dr. Charles B. OwenAdvanced Computer Graphics11
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)(
CSE 872 Dr. Charles B. OwenAdvanced Computer Graphics12
Big ugly equation
33 '1
'1
4
')(
vt
d
vtrv
rt
d
rtrdd
edd
d
edrR
vtrrtr
),()(),(1
),;,( 0
toiditooiid FxxRFxxS
Albedo
Fresnel transmittance
CSE 872 Dr. Charles B. OwenAdvanced Computer Graphics13
Single scattering
CSE 872 Dr. Charles B. OwenAdvanced Computer Graphics14
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.
CSE 872 Dr. Charles B. OwenAdvanced Computer Graphics15
Obtaining parameters
CSE 872 Dr. Charles B. OwenAdvanced 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?
CSE 872 Dr. Charles B. OwenAdvanced Computer Graphics17
Simple optimizations
• Falloff is exponential with distance for both terms– What does that give us?
• Is anything redundant happening here?
CSE 872 Dr. Charles B. OwenAdvanced Computer Graphics18
Caveat Emptor
• The dipole approximation assumes a flat surface• Assumes only one surface layer
Be these problems?