a practical model for subsurface light transport
DESCRIPTION
A Practical Model for Subsurface Light Transport. Henrik Wann Jensen Stephen R. Marschner Marc Levoy Pat Hanrahan. Outlines. Diffusion Theory Measuring the BSSRDF Rendering the BSSRDF Results. Diffusion Theory. phase function. mean cosine g:. first-order scattering of L ri ：. - PowerPoint PPT PresentationTRANSCRIPT
A Practical Model for Subsurface Light Transport
Henrik Wann JensenStephen R. MarschnerMarc LevoyPat Hanrahan
Outlines
Diffusion Theory Measuring the BSSRDF Rendering the BSSRDF Results
Diffusion Theory
phase function
mean cosine g:
)(),( pp
dpg )()(4
),(),( iiis
iiiri xLesxL t
dxLpxQ ris ),(),(),( 4
first-order scattering of Lri ：
Equation (1))()()( 0 xQxxE a
dxLxE
dxLx
),()(
),()(
4
4scalar irradiance ：
vector irradiance ：
dxQxQ ),()( 40
Light source ：
41 ),()( dxQxQ
Diffusion Approximation The light distribution in highly scattering
media tends to become isotropic.
)(4
3)(
4
1),( xExxL
)()(3)( 1 xQxEx t
ast g )1(
-----Equation (2)
Substituting equation2 into equation1
)(3)()()( 102 xQDxQxxD a
t
D
3
1
classic diffusion equation ：
)(4)(
)(
xr
e
Dx
xrtr
tatr 3
Boundary condition ：
_2
0))()(,(
dxnxL ss
0)()(2)( ss xnDx
---equation (3)
Diffuse Fresnel reflectance
2 ))(,( dnnFF rdr
0636.0668.0710.0440.1
2drF
Fr ： Fresnel formula
dnxLFdnxL dr )(),()(),(2_2
new boundary condition ：
)]()(2)([)()(2)( ssdrss xnDxFxnDx
0)()(2)( ss xnADx
dr
dr
F
FA
1
1
0)()(2)( ss xnDx
diffuse BSSRDF Rd
Rd is equal to the radiant exitance divided by the incident flux
)(
))(()(
ii
sisd xd
xnDxxR
subsurface reflection,which is often modeled as a semi-finite plane parallel medium.
The dipole method
ADzz rv 4
)(4
)(v
d
r
d
d
e
d
e
Dx
vtrrtr
])1()1[(4
))(()(
33vt
d
vtrv
rt
d
rtr
i
sd
d
edz
d
ed
d
xnDrR
vtrrtr
(4)
),()(),(1
),;,( otoiditooiid FxxRFxxS
(5)
Single Scattering Term
)())(,(),;,(
),()()(),(
2
)1(
02 1)1(
iiiiiiA ooii
iiiis
oosooo
xdAdnxLxxS
dsdxLeFpxxL tc
ii
oi
itottc
itot
n
nG
xGx
FFF
)()(
),(),(
----flat surface
The BSSRDF Model
),;,(),;,(),;,( )1(ooiiooiidooii xxSxxSxxS
Measuring the BSSRDF
Rendering using the BSSRDF
• Efficient integration of the BSSRDF including importance sampling
• Single scattering evaluation for arbitrary geometry
• Diffusion approximation for arbitrary geometry
• Texture (spatial variation on the object surface).
Integrating the BSSRDF
stochastically sampling the location of both endpoints of the shadow ray
We sample the two terms of BSSRDF separately
dtr
tre density ：
Single scattering evaluation for arbitrary geometry
pick a random distance )()log( oto xs
Results
