ke chen charly collin ajit hakke-patil sumanta pattanaik
DESCRIPTION
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]. - PowerPoint PPT PresentationTRANSCRIPT
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:
),,(),,(),,(
SLd
dL
[Chandrasekhar 1960]
Ambartsumian’s integral equation),()(),( 010 ii pAR
'''0
1
02 ),(),()( dRpA i
''0
'1
03 ),(),()( dRpA i
'''''''1
0
1
0
''04 ),(),(),()( dRpdRA i
Iteratively solving each ),( 0 iR
Subsurface BRDFs are directionally dependent
Titanium dioxide Aluminium oxide
Invariant imbedding
''0
'1
0
),(),(2
dRp m
im
i
)1)(,()1(),( 00
0modi
im
im
ified RR
),(4 0
0i
m
i
p
'''0
1
00
),(),(2
dRp i
mm
'''''''1
0
1
0
''0 ),(),(),( dRpdR i
mmm
(2)
(4)
(3)
(5)
(1)
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?