interactive hair rendering and appearance editing under environment lighting
DESCRIPTION
Interactive Hair Rendering and Appearance Editing under Environment Lighting. Kun Xu 1 , Li- Qian Ma 1 , Bo Ren 1 , Rui Wang 2 , Shi-Min Hu 1 1 Tsinghua University 2 University of Massachusetts. Hair Appearance Editing under Environment Lighting. Motivation hair appearance editing - PowerPoint PPT PresentationTRANSCRIPT
Interactive Hair Rendering and Appearance Editing
under Environment Lighting
Kun Xu1, Li-Qian Ma1, Bo Ren1, Rui Wang2, Shi-Min Hu1
1Tsinghua University2University of Massachusetts
Hair Appearance Editing under Environment Lighting
• Motivation• hair appearance editing• Natural illumination
• Challenges• Light integration complexity
Related Works
• Hair scattering function/models
• Self Shadowing• deep shadow maps [Lokovic & Veach 2000]• opacity shadow maps [Kim & Neumann 2001]• density clustering [Mertens et al. 2004]• deep opacity maps [Yuksel & Keyser 2008]• occupancy maps [Sintorn & Assarson 2009]
[Kajiya & Kay 89] [Marschner 03] [Zinke & Webber 07] [Sadeghi 10] [d’Eon 11]
Related Works
• Multiple scattering• Photon Mapping [Moon & Marschner 2006]• Spherical Harmonics [Moon et al. 2008]• Dual Scattering [Zinke et al. 2008]
• Environment lighting [Ren 2010]• Model lighting using SRBFs• Precomputed light transport into
4D tables• Fix hair scattering properties
hair appearance editing under environment
lighting remains unsolved
Light Integration
𝐿 (𝜔𝑜 )=𝐷∫Ω
❑
𝐿 (𝜔𝑖 )𝑇 (𝜔𝑖 )𝑆(𝜔𝑖 ,𝜔𝑜)cos𝜃 𝑖 𝑑𝜔𝑖
Single scattering
• : environment lighting• : self shadowing• : hair scattering function
Light Integration
𝐿 (𝜔𝑜 )=𝐷∫Ω
❑
𝐿 (𝜔𝑖 )𝑇 (𝜔𝑖 )𝑆(𝜔𝑖 ,𝜔𝑜)cos𝜃 𝑖 𝑑𝜔𝑖
Single scattering
• Approximate by a set of SRBFs [Tsai and Shih 2006]
𝐿 (𝜔𝑜 )≈𝐷∫Ω
❑
(∑𝑗 𝑙 𝑗𝐺 𝑗 (𝜔𝑖 ))𝑇 (𝜔𝑖 )𝑆 (𝜔𝑖 ,𝜔𝑜)cos𝜃 𝑖𝑑𝜔𝑖𝐿 (𝜔𝑜 )≈𝐷∑𝑗𝑙 𝑗∫Ω
❑
𝐺 𝑗 (𝜔𝑖 )𝑇 (𝜔𝑖 )𝑆 (𝜔𝑖 ,𝜔𝑜 ) cos𝜃𝑖 𝑑𝜔 𝑖
Light Integration
Single scattering
• Approximate by a set of SRBFs [Tsai and Shih 2006]
• Move T out from the integral [Ren 2010]
𝐿 (𝜔𝑜 )≈𝐷∑𝑗𝑙 𝑗~𝑇∫
Ω
❑
𝐺 𝑗 (𝜔𝑖 )𝑆 (𝜔𝑖 ,𝜔𝑜 )cos𝜃 𝑖 𝑑𝜔𝑖𝐿 (𝜔𝑜 )≈𝐷∑𝑗𝑙 𝑗∫Ω
❑
𝐺 𝑗 (𝜔𝑖 )𝑇 (𝜔𝑖 )𝑆 (𝜔𝑖 ,𝜔𝑜 ) cos𝜃𝑖 𝑑𝜔 𝑖
Problem: evaluate scattering Integral
Single ScatteringIntegral
• Previous Approach [Ren 2010]• Precompute the integral into 4D table
• Our key insight • Is there an approximated analytic solution? • YES
• Decompose SRBF into products of circular Gaussians• Approximate scattering function by circular Gaussians
∫Ω
❑
𝐺 𝑗 (𝜔𝑖 )𝑆 (𝜔𝑖 ,𝜔𝑜 ) cos𝜃 𝑖𝑑𝜔𝑖
Circular Gaussian
• SRBF (Spherical Radial Basis Function)• Typically spherical Gaussian• Widely used in rendering
• Environment lighting [Tsai and Shih 2006]
• Light Transport [Green 2007]
• BRDF [Wang 2009]
• Circular Gaussian • 1D case of SRBF • Share all benefits of SRBFs
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Circular Gaussian
𝑔𝑐 (𝑥 ;𝑢 , 𝜆 )=𝑒2 [cos (𝑥−𝑢)−1]
𝜆2
bandwidthcenter
• Useful Properties• Local approximation by Gaussian
, error < 1.3%,
• Closed on product
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Circular Gaussian• SRBF Decomposition
1D Longitudinalcircular Gaussian
1D Azimuthalcircular Gaussian
= *
¿𝑔𝑐 (𝜃 𝑖 ;𝜃 𝑗 , 𝜆 𝑗 ) ⋅𝑔𝑐 (𝜙𝑖 ;𝜙 𝑗 ,𝜆 𝑗 /√cos𝜃𝑖𝑐𝑜𝑠𝜃 𝑗 )
2D SRBF
Scattering Function
• Sum of three modes: R, TT, TRT [Marschner03]
hair fiber longitudinal
angle
R mode: Reflection
(p=0)
TT Mode:Transmission-Transmission
(p=1)
TRT Mode:Transmission-Reflection-
Transmission (p=2)
tilted angle
Scattering Function
• Sum of three modes: R, TT, TRT [Marschner03]
hair fiber cross section azimuthal angle
R mode: Reflection
(p=0)
TT Mode:Transmission-Transmission
(p=1)
TRT Mode:Transmission-Reflection-
Transmission (p=2)
Scattering Function
• Definition [Marschner03]
Scattering Function
• Definition [Marschner03]
• Longitudinal function : normalized Gaussian
simulates specular reflection along longitudinal direction
Scattering Function
• Definition [Marschner03]
• Azimuthal function • Complex analytic functions• Different for each mode
– Fresnel reflection term– exponential attenuation term
Azimuthal Functions
• R mode
• Fresnel term (Schlick’s approximation)
• Approximated by polynomial of
Azimuthal Functions
• TT mode
• Simple shape: look like Gaussian• approximated by 1 circular Gaussian centered at
• Parameters fitted by preserving energy
𝜃𝑑=0 𝜃𝑑=𝜋6 𝜃𝑑=
𝜋3
TT mode approximation
• : coefficient • set as the peak value,
• : bandwidth• Preserving energy
𝑁 𝑇𝑇 (𝜙 )≈𝑏𝑇𝑇𝑔𝑐 (𝜙 ;𝜋 ,𝜆𝑇𝑇)
∫ 𝑁𝑇𝑇 (𝜙 )𝑑𝜙¿12 ∫ (1−F (𝜂 ,𝜃𝑑 , h ))2𝑇 (𝜎 𝑎
′ , h )𝑑 h• : fresnel reflection• : attenuation function
TT mode approximation
• : coefficient • set as the peak value,
• : bandwidth• Preserving energy
𝑁 𝑇𝑇 (𝜙 )≈𝑏𝑇𝑇𝑔𝑐 (𝜙 ;𝜋 ,𝜆𝑇𝑇)
∫ 𝑁𝑇𝑇 (𝜙 )𝑑𝜙¿12 ∫ (1−F (𝜂 ,𝜃𝑑 , h ))2𝑇 (𝜎 𝑎
′ , h )𝑑 h• : fresnel reflection• : attenuation function 4-th order Taylor expansion
¿12 ∫ (1−F (𝜂 ,𝜃𝑑 , h ))2( ∑
𝑘=0,2,4𝑎𝑘 (𝜃𝑑 ,𝜎𝑎 )h𝑘)𝑑 h¿
12 ∑𝑘=0,2,4
𝑎𝑘 (𝜃𝑑 ,𝜎𝑎 )∫ (1−F (𝜂 ,𝜃𝑑 , h ))2h𝑘 h𝑑
Precompute into 2D tables
Azimuthal Functions• TRT mode:
• Shape: sum of Circular Gaussians • : approximated by 3 circular Gaussians• approximated by 1 circular Gaussian
• Fitted by preserving energy similar as TT mode
𝜃𝑑=0 𝜃𝑑=𝜋6 𝜃𝑑=
𝜋3
Single ScatteringIntegral
• =: SRBF decomposition• : scattering func. def.
Circular Gaussian
Circular Gaussian Gaussian Cosine /
Circular Gaussian
Analytic Integral
Light Integration
Multiple scattering
𝐿 (𝜔𝑜 )≈𝐷∑𝑗𝑙 𝑗𝑇 𝑓∫
Ω
❑
ψ (⋅ )𝑆𝐷 (𝜔𝑖 ,𝜔𝑜 ) cos𝜃 𝑖 𝑑𝜔𝑖[Ren 2010]
• Spread function: • BCSDF: [Zinke 2010]
• Approximate scattering function similarly
Analytic Integral
Results
Results
Results
Performance
hair model #fibers #segments FPSanimation 10K 270K 8.3ponytail 6K 100K 8.9natural 10K 1.6M 4.8
• Testing Machine• Intel Core 2 Duo 3.00 GHz CPU, 6 GB RAM NVIDIA
GTX 580• 720 * 480 with 8x antialias
Conclusion
• 1D circular Gaussian• Accurate and compact for representing hair
scattering functions• Closed form integral with SRBF lights
• New effects • interactive hair appearance editing under
environment lighting • Rendering of spatially varying hair scattering
parameters under environment lighting
Future works
• View transparency effects [Sintorn and Assarsson 2009]
• Other hair scattering models• Artist friendly model [Sadeghi 2010]
• Energy conserving model [d’Eon 2011]
• Near-field light sources• Accelerate off-line hair rendering
Acknowledgement
• Anonymous Siggraph and Siggraph Asia reviewers • Ronald Fedkiw, Cem Yuksel, Arno Zinke, Steve
Marschner • Sharing their hair data
• Zhong Ren• Useful discussion
Thank you for your attention.
Circular Gaussian vs Gaussian• 1D Circular Gaussian
• Defined on unit circle :
• 1D Gaussian • Defined on x-axis
Single ScatteringIntegral
N 𝒕 (⋅ )=∫❑
❑
𝑁 𝑡 (𝜙𝑖−𝜙𝑜 )𝑔𝑐 (𝜙 𝑖 )𝑑𝜙 𝑖
• =: SRBF seperation• : scattering func. def.• Two dimensional integral over and
¿∑∫𝜃𝑖
❑
𝑔𝑐 (𝜃𝑖)𝑀 𝑡 (𝜃h )cos2𝜃𝑖
cos2𝜃𝑑N𝒕 (⋅ )𝑑𝜃𝑖 Outer integral
inner integral:
Inner Integral R Mode• Hair scattering function approx.
• polynomial of : • Inner integral
Precompute into 2D tables
Inner IntegralTT & TRT modes• Hair scattering function approx.
• sum of circular Gaussians : • Inner integral
Analytic Integral
N 𝒕 (⋅ )≈∑ 𝑏𝑘∫❑
❑
𝑔𝑐(𝜙 𝑖−𝜙𝑜 ;𝜙𝑘 ,𝜆𝑘)𝑔𝑐 (𝜙 𝑖 ;𝜙 𝑗 ,𝜆 𝑗 )𝑑𝜙𝑖
Outer Integral
Piecewise Linear approximation
Smooth FunctionGaussian
Analytic Integral
Summary ofSingle Scattering • Hair scattering function approximation
• R mode: polynomial of cosine • TT/TRT mode: circular Gaussian
• Inner integral• R mode: 2D tables • TT/TRT mode: 2D tables, analytic integral
• Outer integral• Piecewise linear approximation for smooth func.• Analytic integral.