accurate translucent material rendering under spherical gaussian lights
DESCRIPTION
Pacific Graphics 2012. PG 2012. Accurate Translucent Material Rendering under Spherical Gaussian Lights. Ling-Qi Yan 1 , Yahan Zhou 2 , Kun Xu 1 , Rui Wang 2. 1 Tsinghua University 2 University of Massachusetts. Pacific Graphics 2012. Introduction. Motivation Natural illumination - PowerPoint PPT PresentationTRANSCRIPT
PG 2011
Pacific Graphics 2011
The
19th
Pac
ific
Conf
eren
ce o
n Co
mpu
ter G
raph
ics
and
Appl
icati
ons
(Pac
ific
Gra
phic
s 20
11) w
ill b
e he
ld o
n Se
ptem
ber 2
1 to
23,
201
1 in
Kao
hsiu
ng, T
aiw
an. Accurate Translucent
Material Rendering under Spherical Gaussian LightsLing-Qi Yan1, Yahan Zhou2, Kun Xu1, Rui Wang2
1 Tsinghua University2 University of Massachusetts
PG 2012
Pacific Graphics 2012
Pacific Graphics 2011
2 | Kaohsiung, Taiwan
• Motivation• Natural illumination• Accurate rendering
• Goal• Analytic solution
• Challenge• Light integration complexity
Introduction
Accurate Translucent Material Rendering under Spherical Gaussian Lights
Pacific Graphics 2012
Pacific Graphics 2011
3 | Kaohsiung, Taiwan
• Translucent Material Rendering
• BSSRDF representation
• Multiple Scattering & Single Scattering
Background
Accurate Translucent Material Rendering under Spherical Gaussian Lights
BRDF BSSRDF
Pacific Graphics 2012
Pacific Graphics 2011
4 | Kaohsiung, Taiwan
• Environment Lighting
• Natural illumination
• Light modeling methods
• Spherical Harmonics
• Wavelets
• SRBFs
Background
Accurate Translucent Material Rendering under Spherical Gaussian Lights
Pacific Graphics 2012
Spherical HarmonicsWaveletsSRBFs
Pacific Graphics 2011
5 | Kaohsiung, Taiwan
• SRBF (Spherical Radial Basis Function)
• Typically Spherical Gaussian (SG)
• Useful Properties
• Closed under multiplication
• Has analytic solution under spherical integration
• Widely used in rendering• Environment lighting [Tsai and Shih 2006]• Light Transport [Green 2007]• BRDF [Wang 2009]
Background
Accurate Translucent Material Rendering under Spherical Gaussian Lights
Pacific Graphics 2012
Pacific Graphics 2011
6 | Kaohsiung, Taiwan
• Motivation• Natural illumination• Accurate rendering
• Goal• Analytic solution
• Challenge• Light integration complexity
Introduction
Accurate Translucent Material Rendering under Spherical Gaussian Lights
Pacific Graphics 2012
Use SG lights!
Pacific Graphics 2011
7 | Kaohsiung, Taiwan
Related Works
Accurate Translucent Material Rendering under Spherical Gaussian Lights
Jensen et al. 2001 d’Eon et al. 2011
• Translucent Material Rendering
Pacific Graphics 2012
• Limitations:
• Vertical scattering path
[d’Eon et al, 2011] ground truth
𝐼𝑛𝑐𝑖𝑒𝑛𝑡 : 45 °
𝐼𝑛𝑐𝑖𝑒𝑛𝑡 : 80 °
Pacific Graphics 2011
8 | Kaohsiung, Taiwan
• Motivation• Natural illumination• Accurate rendering
• Goal• Analytic solution
• Challenge• Light integration complexity
Introduction
Accurate Translucent Material Rendering under Spherical Gaussian Lights
Pacific Graphics 2012
Use SG lights
Account for oblique scattering path
Pacific Graphics 2011
9 | Kaohsiung, Taiwan
Related Works
Accurate Translucent Material Rendering under Spherical Gaussian Lights
Jensen et al. 2001 d’Eon et al. 2011
• Translucent Material Rendering
Pacific Graphics 2012
• Limitations:
• Vertical scattering path
• Unable to handle area lights
(require sampling)
Pacific Graphics 2011
10 | Kaohsiung, Taiwan
Related Works
Accurate Translucent Material Rendering under Spherical Gaussian Lights
• Translucent Rendering under Environment
Lighting
• Wang et al. 2005
• Xu et al. 2007
• ……
Based on pre-computation!
Pacific Graphics 2012
Pacific Graphics 2011
11 | Kaohsiung, Taiwan
• Motivation• Natural illumination• Accurate rendering
• Goal• Analytic solution
• Challenge• Light integration complexity
Introduction
Accurate Translucent Material Rendering under Spherical Gaussian Lights
Pacific Graphics 2012
Use SG lights
Account for oblique scattering path
No extra numerical integration or scene-dependent precomputation
Pacific Graphics 2011
12 | Kaohsiung, Taiwan
• Main Contribution
• An extended BSSRDF model
• under Spherical Gaussian light
• account for oblique scattering path
• include multiple and single
scattering
Overview
Accurate Translucent Material Rendering under Spherical Gaussian Lights
Pacific Graphics 2012
Pacific Graphics 2011
13 | Kaohsiung, Taiwan
Approximating Multiple Scattering
Accurate Translucent Material Rendering under Spherical Gaussian Lights
𝐿𝐷 (𝑥𝑜 ,𝑜 )=∫Ω
𝐺 ( 𝑖; 𝑖 𝑗 ,𝜆 𝑗 )(𝐹∫0
∞
𝑄 (𝑠 ) 𝑅 (𝑑 )𝑑𝑠)𝑑𝑖
• Multiple Scattering
𝑥𝑜
𝐿𝐷 (𝑥𝑜 ,𝑜 )=∫Ω
𝐺 ( 𝑖′ ; 𝑖 𝑗 ′ ,𝜆 𝑗 ′ )(𝐹∫0
∞
𝑄 (𝑠 )𝑅 (𝑑 )𝑑𝑠)𝑑𝑖 ′
Pacific Graphics 2012
𝑖 𝑗𝜆 𝑗
𝑖 𝑗 ′𝜆 𝑗 ′
𝑖𝑖𝑖
𝑖𝑖
𝑖 ′𝑖 ′ 𝑖 ′ 𝑖 ′
𝑖 ′
𝑜
𝑠 𝑑𝑥𝑖
Pacific Graphics 2011
14 | Kaohsiung, Taiwan
Approximating Multiple Scattering
Accurate Translucent Material Rendering under Spherical Gaussian Lights
𝐿𝐷 (𝑥𝑜 ,𝑜 )=∫Ω
𝐺 ( 𝑖′ ; 𝑖 𝑗 ′ ,𝜆 𝑗 ′ )(𝐹∫0
∞
𝑄 (𝑠 )𝑅 (𝑑 )𝑑𝑠)𝑑𝑖 ′
• Define as a combination of fluence term and flux term [d’Eon et al. 2011]
• Multiple Scattering
Pacific Graphics 2012
Pacific Graphics 2011
15 | Kaohsiung, Taiwan
Approximating Multiple Scattering
Accurate Translucent Material Rendering under Spherical Gaussian Lights
𝐿𝐷 (𝑥𝑜 ,𝑜 )=∫Ω
𝐺 ( 𝑖′ ; 𝑖 𝑗 ′ ,𝜆 𝑗 ′ )(𝐹∫0
∞
𝑄 (𝑠 ) (𝐶𝜙 𝜙 (𝑑 )+𝐶𝐸(−𝐷 (𝑛⋅𝛻𝜙 ) (𝑑)))𝑑𝑠)𝑑𝑖 ′
• Define as a combination of fluence term and flux term [d’Eon et al. 2011]
• Multiple Scattering
𝐿𝐷 (𝑥𝑜 ,𝑜 )=∫Ω
𝐺 ( 𝑖′ ; 𝑖 𝑗 ′ ,𝜆 𝑗 ′ )(𝐹∫0
∞
𝑄 (𝑠 )𝑅 (𝑑 )𝑑𝑠)𝑑𝑖 ′
Pacific Graphics 2012
Pacific Graphics 2011
16 | Kaohsiung, Taiwan
• Diffusion Function
Approximating Multiple Scattering
Accurate Translucent Material Rendering under Spherical Gaussian Lights
𝜙 (𝑑 )= 14𝜋𝐷
⋅ 𝑒− √𝜎 𝑎/𝐷𝑑
𝑑
𝑑
𝜙(𝑑)𝑥𝑜𝑥𝑖 𝑟
𝑠 𝑑
𝑖 ′
𝑖2
𝑑=√𝑠2+𝑟2−2 𝑠𝑟 (𝑖′ ⋅𝑖2)
Pacific Graphics 2012
Pacific Graphics 2011
17 | Kaohsiung, Taiwan
𝐿𝐷 (𝑥𝑜 ,𝑜 )=𝐹 𝐶𝜙𝐿𝜙+𝐹𝐷𝐶𝐸𝐿𝐸
• Multiple Scattering
Approximating Multiple Scattering
Accurate Translucent Material Rendering under Spherical Gaussian Lights
𝐿𝜙=∫Ω∫
0
∞
𝐺 (𝑖′ ; 𝑖 𝑗′ ,𝜆 𝑗′ )𝑄 (𝑠 )𝜙 (𝑑 )𝑑𝑠𝑑𝑖 ′
𝐿𝐸=∫Ω∫0
∞
𝐺 ( 𝑖′ ;𝑖 𝑗′ ,𝜆 𝑗′ )𝑄 (𝑠)(−𝑛⋅𝛻𝜙) (𝑑 )𝑑𝑠𝑑𝑖 ′
• Fluence Integral
• Flux Integral
Pacific Graphics 2012
Pacific Graphics 2011
18 | Kaohsiung, TaiwanAccurate Translucent Material Rendering under Spherical Gaussian Lights
𝐿𝜙=∫Ω∫
0
∞
𝐺 (𝑖′ ; 𝑖 𝑗′ ,𝜆 𝑗′ )𝑄 (𝑠 )𝜙 (𝑑 )𝑑𝑠𝑑𝑖 ′
• Fluence Integral
Approximating Multiple Scattering
¿∫0
∞
𝑄 (𝑠 )(∫Ω 𝐺 (𝑖′ ; 𝑖 𝑗′ ,𝜆 𝑗′ ) ⋅ 𝜙 (𝑑) 𝑑𝑖 ′)𝑑𝑠
• Change integral order so that• Inner integral: Spherical• Outer integral: Linear
Pacific Graphics 2012
Pacific Graphics 2011
19 | Kaohsiung, TaiwanAccurate Translucent Material Rendering under Spherical Gaussian Lights
𝐿𝜙=∫Ω∫
0
∞
𝐺 (𝑖′ ; 𝑖 𝑗′ ,𝜆 𝑗′ )𝑄 (𝑠 )𝜙 (𝑑 )𝑑𝑠𝑑𝑖 ′
• Fluence Integral
Approximating Multiple Scattering
¿∫0
∞
𝑄 (𝑠 )(∫Ω 𝐺 (𝑖′ ; 𝑖 𝑗′ ,𝜆 𝑗′ ) ⋅ 𝜙 (𝑑) 𝑑𝑖 ′)𝑑𝑠
• Our key insight• Can be represented by spherical
functions?• YES
Pacific Graphics 2012
Pacific Graphics 2011
20 | Kaohsiung, Taiwan
• Diffusion Function
Approximating Multiple Scattering
Accurate Translucent Material Rendering under Spherical Gaussian Lights
𝜙 (𝑑 )= 14𝜋𝐷
⋅ 𝑒− √𝜎 𝑎/𝐷𝑑
𝑑
• Approximate withsum of Gaussians
𝜙 (𝑑 )≈∑𝑘
𝑎𝑘𝑔 (𝑑 ;0 ,𝜆𝑘 )𝑑
𝜙(𝑑)
Pacific Graphics 2012
Pacific Graphics 2011
21 | Kaohsiung, TaiwanAccurate Translucent Material Rendering under Spherical Gaussian Lights
• Fluence Integral
Approximating Multiple Scattering
𝐿𝜙=∫0
∞
𝑄 (𝑠 )(∫Ω 𝐺 ( 𝑖′ ; 𝑖 𝑗′ ,𝜆 𝑗′ ) ⋅𝑒𝜆𝑘𝑑
2
𝑑𝑖 ′)𝑑𝑠𝑑=√𝑠2+𝑟2−2 𝑠𝑟 (𝑖′ ⋅𝑖2)
¿∫0
∞
𝑄 (𝑠 )𝑒−𝜆𝑘 (𝑠−𝑟 )2(∫Ω 𝐺 (𝑖′ ; 𝑖 𝑗′ ,𝜆 𝑗′ )⋅𝑒2𝑠𝑟 𝜆𝑘(𝑖
′⋅ 𝑖2−1 )𝑑𝑖 ′)𝑑𝑠Linear Integration Part Spherical Integration Part
¿∫0
∞
𝑄 (𝑠 )𝑒−𝜆𝑘 (𝑠−𝑟 )2(∫Ω 𝐺 (𝑖′ ; 𝑖 𝑗′ ,𝜆 𝑗′ )⋅𝐺(𝑖′ ; 𝑖2 ,2𝑠𝑟 𝜆𝑘)𝑑𝑖 ′)𝑑𝑠
Product-integral of two SGs!
Pacific Graphics 2012
Pacific Graphics 2011
22 | Kaohsiung, TaiwanAccurate Translucent Material Rendering under Spherical Gaussian Lights
𝐿𝜙≈∫0
∞
𝑄 (𝑠 )𝑒−𝜆𝑘 (𝑠−𝑟 )2𝑁 𝑑𝑠
• Fluence Integral
Approximating Multiple Scattering
• inner integral
Pacific Graphics 2012
where
• Variable:
• Parameters:
Pacific Graphics 2011
23 | Kaohsiung, TaiwanAccurate Translucent Material Rendering under Spherical Gaussian Lights
𝐿𝜙≈∫0
∞
𝑄 (𝑠 )𝑒−𝜆𝑘 (𝑠−𝑟 )2𝑁 𝑑𝑠
• Fluence Integral
Approximating Multiple Scattering
• inner integral
Pre-fit into a 2D table of and
Now has analytical solution!
𝑠
𝑁
Pacific Graphics 2012
Pacific Graphics 2011
24 | Kaohsiung, Taiwan
• directional derivative
Accurate Translucent Material Rendering under Spherical Gaussian Lights
𝐿𝐸=∫Ω∫0
∞
𝐺 ( 𝑖′ ;𝑖 𝑗′ ,𝜆 𝑗′ )𝑄 (𝑠)(−𝑛⋅𝛻𝜙) (𝑑 )𝑑𝑠𝑑𝑖
• Flux Integral
Approximating Multiple Scattering
Additional term!
Pacific Graphics 2012
Pacific Graphics 2011
25 | Kaohsiung, Taiwan
• inner integral
Accurate Translucent Material Rendering under Spherical Gaussian Lights
𝐿𝐸=2𝜆𝑘∫0
∞
𝑄 (𝑠)𝑒−𝜆𝑘 (𝑠 −𝑟 )2 𝑀𝑑𝑠
• Flux Integral
Approximating Multiple Scattering
Exponential attenuation!
Pre-fit into a 2D table
Now has analytical solution!
𝐿𝐸=∫Ω∫0
∞
𝐺 ( 𝑖′ ;𝑖 𝑗′ ,𝜆 𝑗′ )𝑄 (𝑠)(−𝑛⋅𝛻𝜙) (𝑑 )𝑑𝑠𝑑𝑖
𝑠
𝑀 𝑖
Pacific Graphics 2012
Pacific Graphics 2011
26 | Kaohsiung, Taiwan
The outer integral: Sample along the refracted outgoing directionThe inner integral: To be analytically approximated!
• Single Scattering
Approximating Single Scattering
Accurate Translucent Material Rendering under Spherical Gaussian Lights
𝐿(1) (𝑥𝑜 ,𝑜 )=𝜎𝑠∫0
∞
𝐹 𝑡𝐸(𝑠 ′)∫Ω
𝑝𝐺 (𝑖′ ; 𝑖 𝑗′ ,𝜆 𝑗′ )𝐸 (𝑠)𝑉 (𝑖 ′)𝑑𝑖 ′ 𝑑𝑠 ′
Fresnel transmittance termAttenuation term
𝐽 (𝑠 ′)=∫Ω
𝑝 (𝑖′ ,𝑜 ′)𝐺 (𝑖 ′ ; 𝑖 𝑗′ ,𝜆 𝑗′ )𝐸 (𝑠)𝑉 (𝑖 ′)𝑑𝑖 ′
Pacific Graphics 2012
𝑥𝑜
𝑜
𝑠 ′
scattering point
Pacific Graphics 2011
27 | Kaohsiung, Taiwan
• Single Scattering
Approximating Single Scattering
Accurate Translucent Material Rendering under Spherical Gaussian Lights
𝐽 (𝑠 ′)=∫Ω
𝑝 (𝑖′ ,𝑜 ′)𝐺 (𝑖 ′ ; 𝑖 𝑗′ ,𝜆 𝑗′ )𝐸 (𝑠)𝑉 (𝑖 ′)𝑑𝑖 ′
Phase functionRefracted SG lightAttenuation termVisibility term
Use soft shadow technique to approximate!
𝐽 (𝑠 ′ )=𝐸⋅𝑉∫Ω
𝑝 (𝑖′ ,𝑜 ′)𝐺 (𝑖′ ; 𝑖 𝑗′ ,𝜆 𝑗′ )𝑑𝑖 ′
Pacific Graphics 2012
𝑥𝑜Use SG center to approximate!
Pacific Graphics 2011
28 | Kaohsiung, Taiwan
• Single Scattering
Approximating Single Scattering
Accurate Translucent Material Rendering under Spherical Gaussian Lights
𝐽 (𝑠 ′ )=𝐸⋅𝑉∫Ω
𝑝 (𝑖′ ,𝑜 ′)𝐺 (𝑖′ ; 𝑖 𝑗′ ,𝜆 𝑗′ )𝑑𝑖 ′
• For Eddington phase function
Pacific Graphics 2012
𝐽 (𝑠 ′ )=𝐸⋅𝑉 (∫Ω 𝐺 (𝑖′ ; 𝑖 𝑗′ ,𝜆 𝑗′ )𝑑𝑖 ′+3𝑔∫
Ω
(𝑖′ ⋅𝑜′)𝐺 ( 𝑖′ ;𝑖 𝑗′ ,𝜆 𝑗′ )𝑑𝑖 ′ )
Both are analytical!
Pacific Graphics 2011
29 | Kaohsiung, Taiwan
Results
Accurate Translucent Material Rendering under Spherical Gaussian Lights
Pacific Graphics 2012
Pacific Graphics 2011
30 | Kaohsiung, Taiwan
Conclusion
Accurate Translucent Material Rendering under Spherical Gaussian Lights
• An extended BSSRDF model
• under Spherical Gaussian light
• accounts for oblique scattering path
• including multiple and single scattering
Pacific Graphics 2012
Pacific Graphics 2011
31 | Kaohsiung, Taiwan
• Heterogeneous translucent materials
• Participating media
• ……
Future Works
Accurate Translucent Material Rendering under Spherical Gaussian Lights
Pacific Graphics 2012
Pacific Graphics 2011
32 | Kaohsiung, Taiwan
Thank you!Any questions?
The End
Accurate Translucent Material Rendering under Spherical Gaussian Lights
Pacific Graphics 2012