Transcript Rendering Translucent Materials Using Isotropic Phase

A Practical Model for Computing Subsurface BRDF of
Homogeneous Materials with A Thin Layer of Paint
Ke Chen
Charly Collin
Ajit Hakke-Patil
Sumanta Pattanaik
Overview
Introduction and motivation
BRDF = surface BRDF + subsurface BRDF
[Hanrahan and Krueger 1993]
Subsurface BRDFs are directionally
dependent
Shape does
not change
Shape changed
Previous Works and Limitations
• Kubelka-Munk [Kubelka 1954]
• Single scattering approximation [Blinn 1982],
[Farrell et al. 1992]
• Adding and doubling [de Haan 1987]
• Discrete Ordinate Methods[Chandrasekhar
1960]
Contributions
• Subsurface BRDF for semi-infinite
homogeneous materials
based on Ambartsumian’s integral equation [Chen et al. 2013]
• Adding a thin layer of paint
based on invariant imbedding method [Hansen and Travis
1974]
Radiative transfer
Plane-parallel radiative transfer equation:
dL ( , ,  )

  L( , ,  )  S ( , ,  )
d
[Chandrasekhar 1960]
Ambartsumian’s integral equation
R(0 ,i )  A1 ( ) p(0 ,i )
1
 A2 ( )  p(0 , ' ) R( ' ,i )d '
0
1
 A3 ( )  p( ' ,i ) R(0 , ' )d '
0
1
1
0
0
 A4 ( )  R(0 , ' )d '  p( ' , '' ) R( '' ,i )d ''
Iteratively solving each R(0 ,i )
Subsurface BRDFs are directionally
dependent
Titanium dioxide
Aluminium oxide
Invariant imbedding
m
Rmod
ified (0 ,i )  (1 

) R m (0 ,i )(1 
0
 m

p (0 ,i )
40i


2i


20

i
)
(1)
(2)
1
m
'
m
'
'
p
(

,

)
R
(

,

)
d

i
0

(3)
0
1
m
'
m
'
'
p
(

,

)
R
(

,

)
d

0
i

(4)
0
1
1
   R m (0 , ' )d '  p m ( ' , '' ) R m ( '' ,i )d ''
0
0
(5)
Results
Conclusions
• Subsurface BRDFs are directionally dependent
• Using Ambartsumian’s integral equation and invariant
imbedding to compute the subsurface BRDF is fast.
• Accurate
Future work
• Polarization
• Multiple layered materials
Thank You
Questions?