microfacet model and material appearancesungeui/gcg/student_presentations/... · siggraph 2016 [2]...
TRANSCRIPT
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Microfacet Model and
Material Appearance
19.05.14
Student Presentation
20193163 Hakyeong Kim
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Review
• Light Transport for Participating Media (Joowon Lim)
– Point based light global illumination
– Higher-Dimensional photon samples for volumetric light transport
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Microfacet theory
Surface light transport framework
• Assumption: Surface is made up of tiny flat microfacets
• Surface normal 𝝎𝒈 is average of microfacet normals 𝝎𝒎
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𝝎𝒈𝝎𝒎
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Microfacet theory
Surface light transport framework
• Assumption: Surface is made up of tiny flat microfacets
• Surface normal 𝝎𝒈 is average of microfacet normals 𝝎𝒎
• Described by normal distribution function NDF 𝑫(𝝎𝒎)
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𝜔𝑚
𝑫(𝝎𝒎)
![Page 5: Microfacet Model and Material Appearancesungeui/GCG/Student_Presentations/... · SIGGRAPH 2016 [2] A Two-Scale Microfacet Reflectance Model Combining Reflection and Diffraction Nicolas](https://reader036.vdocuments.site/reader036/viewer/2022071000/5fbc86ce93f25735ea42c0e4/html5/thumbnails/5.jpg)
Microfacet theory
Surface light transport framework
• Assumption: Surface is made up of tiny flat microfacets
• Surface normal 𝝎𝒈 is average of microfacet normals 𝝎𝒎
• Described by normal distribution function NDF 𝑫(𝝎𝒎)
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![Page 6: Microfacet Model and Material Appearancesungeui/GCG/Student_Presentations/... · SIGGRAPH 2016 [2] A Two-Scale Microfacet Reflectance Model Combining Reflection and Diffraction Nicolas](https://reader036.vdocuments.site/reader036/viewer/2022071000/5fbc86ce93f25735ea42c0e4/html5/thumbnails/6.jpg)
Papers
[1] Multiple Scattering Microfacet BSDFs
with the Smith ModelEric Heitz, Johannes Hanika, Eugene d’Eon
SIGGRAPH 2016
[2] A Two-Scale Microfacet Reflectance Model
Combining Reflection and DiffractionNicolas Holzschuch, Romain Pacanowski, SIGGRAPH 2017
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Papers
[1] Multiple Scattering Microfacet BSDFs
with the Smith ModelEric Heitz, Johannes Hanika, Eugene d’Eon
SIGGRAPH 2016
[2] A Two-Scale Microfacet Reflectance Model
Combining Reflection and DiffractionNicolas Holzschuch, Romain Pacanowski, SIGGRAPH 2017
7
Microfacet model
• The Smith Model
• Cook-Torrance Model
Volumetric Scattering
Microflake theory+
Single-Scattering BSDF/
Unphysical Multiple-Scattering
Multiple-Scattering BSDF
=
![Page 8: Microfacet Model and Material Appearancesungeui/GCG/Student_Presentations/... · SIGGRAPH 2016 [2] A Two-Scale Microfacet Reflectance Model Combining Reflection and Diffraction Nicolas](https://reader036.vdocuments.site/reader036/viewer/2022071000/5fbc86ce93f25735ea42c0e4/html5/thumbnails/8.jpg)
Papers
[2] A Two-Scale Microfacet Reflectance Model
Combining Reflection and DiffractionNicolas Holzschuch, Romain Pacanowski, SIGGRAPH 2017
8
Microfacet model
• The Smith Model
• Cook-Torrance Model
Diffraction model
Harvey-Shack Theory+
New Reflectance model
that both considers
Reflection and Diffraction=
![Page 9: Microfacet Model and Material Appearancesungeui/GCG/Student_Presentations/... · SIGGRAPH 2016 [2] A Two-Scale Microfacet Reflectance Model Combining Reflection and Diffraction Nicolas](https://reader036.vdocuments.site/reader036/viewer/2022071000/5fbc86ce93f25735ea42c0e4/html5/thumbnails/9.jpg)
MULTIPLE SCATTERING MICROFACET BSDFS
WITH THE SMITH MODELERIC HEITZ, JOHANNES HANIKA, EUGENE D’EON
SIGGRAPH 2016
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Overview
1. Background
• Smith Model
• Microflake Theory
2. Model
• Define medium
• Track intersection (Extinction coefficient & free-path distribution)
• Track light scatter (Phase function)
• Simulate random walk
• Define multiple-scattering BSDF (Expectation of random walk)
3. Evaluation
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Smith Model
Statistical model of random microsurface described by
Distributions of Heights and Distributions of Normals
Main Assumption : 𝑃1 (ℎ) and 𝐷(𝜔𝑚) is independent
⟹ Final reflectance is independent of height distribution
𝑷𝟏 (𝒉) : Uniform, Gaussain
𝑫(𝝎𝒎) : Anisotropic Beckmann distribution, GGX distribution
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𝜔𝑚 = 𝑥𝑚, 𝑦𝑚 , 𝑧𝑚
ℎ
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Smith Model
Classic Single-Scattering BSDF(Bidirectional Scattering Distribution Function)
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( , , )
( , )( , ) ( , , ) , ( )i m o
ii m
G
i o m i m o o m m mGf f D d
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Smith Model
Classic Single-Scattering BSDF(Bidirectional Scattering Distribution Function)
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( , , )
( , )( , ) ( , , ) , ( )i m o
ii m
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i o m i m o o m m mGf f D d
Micro-BRDF
𝒇𝒎 of each materials :
• Rough dielectric
• Rough conductor 𝑓𝑟𝑑𝑖𝑒𝑙 + 0
• Rough diffuse𝑎
𝜋𝜔𝑜, 𝜔𝑚
BRDF(Reflection) BTDF(Transmission)
![Page 14: Microfacet Model and Material Appearancesungeui/GCG/Student_Presentations/... · SIGGRAPH 2016 [2] A Two-Scale Microfacet Reflectance Model Combining Reflection and Diffraction Nicolas](https://reader036.vdocuments.site/reader036/viewer/2022071000/5fbc86ce93f25735ea42c0e4/html5/thumbnails/14.jpg)
Smith Model
Classic Single-Scattering BSDF(Bidirectional Scattering Distribution Function)
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( , , )
( , )( , ) ( , , ) , ( )i m o
ii m
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i o m i m o o m m mGf f D d
Masking-shadowing function
Visible Normal Distribution
Masking function
Visibility to viewer
Shadowing function
Visibility to light
Multiple Scattering
Only allows single scattering
Masking-shadowing function Visible Normal Distribution
1 ( ) , ( )( )
cosi
dist
i i m m
m
i
G DD
1cos ( , ) ,i i m i m m mG D d
Smith-like masking function Microflake theory
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Microflake theory
[Jakob et al. 2010]
• Framework that describes volumetric scattering
• Use oriented non-spherical particals defined by distribution of normals
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Microflake theory
Light Transport in Volume : Anisotropic Radiative Transfer Equation
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( ) ( ) ( ) ( ) ( ) ( ) ( )i i t i i s i p i o o o iL L f L d Q
Directional derivative of radiance
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Microflake theory
Light Transport in Volume : Anisotropic Radiative Transfer Equation
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( ) ( ) ( ) ( ) ( ) ( ) ( )i i t i i s i p i o o o iL L f L d Q
Directional derivative of radiance
( ) ( )
( ) ( )
: volume density
: direction independent albedo
: microflake projected area
( ) , ( )
t i i
s i i
i i m m mD d
Attenuation
coefficientScattering
coefficient
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Microflake theory
Light Transport in Volume : Anisotropic Radiative Transfer Equation
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( ) ( ) ( ) ( ) ( ) ( ) ( )i i t i i s i p i o o o iL L f L d Q
Directional derivative of radiance
Phase Function
1
, ,( )
p i o
m i o i m m m
i
f
p D d
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Microflake theory
Light Transport in Volume : Anisotropic Radiative Transfer Equation
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( ) ( ) ( ) ( ) ( ) ( ) ( )i i t i i s i p i o o o iL L f L d Q
Directional derivative of radiance
Phase Function
1
, ,( )
p i o
m i o i m m m
i
f
p D d
“Smith-like” masking function
1cos ( , ) ,i i m i m m mG D d
Without shadowing function Multiple Scattering
Recall Smith model
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Multiple Scattering BSDF Model
1) Build medium
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Multiple Scattering BSDF Model
1) Build medium
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1|Smith
h h P hh P h h h
C h
1
1
SmithP h
hC h
( ) , ( )microflake
r r m m mD d
( ) , ( ) ( ) cosSmith
r r m m m r rD d
( ) ( )microflake microflake microflake
t r r ( ) ( )Smith Smith Smith
t r r
Volume density
Projected area
Extinction coefficient
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Multiple Scattering BSDF Model
1) Build medium
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Multiple Scattering BSDF
2) Track intersection
• Microsurface intersection Probability
• Free-Path Distribution
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𝜏′ 𝜏′ + 𝑑𝜏′
1
0
( ) ( )1 1
1 1
1
, ,
exp , cot
( ) ( )
( cot ) ( )
r r
dist
r r
Smith
t r r r
r r r
G h
dh d
C h C h
C h C h
Probability that there is no intersection in [0, 𝜏]
1
, 1 1
0 if 0
1 , , if 0
1 if r r
dist
h r r rC h G h
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Multiple Scattering BSDF
2) Track intersection
• Free Path Sampling1
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Multiple Scattering BSDF
3) Track light scatter
• Phase Function
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, , , ,ii o m m i o i m m mp f D d
, ( ) , ( )( )
( ), ( )i
i m m i m m
m Smith
ii m m m
D DD
D d
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Multiple Scattering BSDF
4) Simulate random walk
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Track intersection
Track light scatter
![Page 27: Microfacet Model and Material Appearancesungeui/GCG/Student_Presentations/... · SIGGRAPH 2016 [2] A Two-Scale Microfacet Reflectance Model Combining Reflection and Diffraction Nicolas](https://reader036.vdocuments.site/reader036/viewer/2022071000/5fbc86ce93f25735ea42c0e4/html5/thumbnails/27.jpg)
Multiple Scattering BSDF
5) Define multiple scattering BSDF
: Expectation of random walk
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Random walk
Sequence of N heights, directions and energy throughput 𝜔1, ℎ1, 𝑒1 , … , 𝜔𝑁, ℎ𝑁, 𝑒𝑁 ,
Distribution
• Contribution of 𝑟𝑡ℎ bounce in direction 𝜔𝑂
• Total scattered energy by random walk
• Mutiple Scattering BRDF
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( ) , ( , )dist
r o r r o o rE e p G h
1,...,
1
( ) ( )N
N o r o
r
E E
1
1,...,
1
( , ) cos ( )
, ( , )
i o o N o
Ndist
r r o o r
r
f E
e p G h
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Multiple Scattering BSDF
Result
- Practical rendering
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A TWO-SCALE MICROFACET REFLECTANCE MODEL
COMBINING REFLECTION AND DIFFRACTIONNICOLAS HOLZSCHUCH, ROMAIN PACANOWSKI
SIGGRAPH 2017
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Papers
[2] A Two-Scale Microfacet Reflectance Model
Combining Reflection and DiffractionNicolas Holzschuch, Romain Pacanowski, SIGGRAPH 2017
30
Microfacet model
• The Smith Model
• Cook-Torrance Model
Diffraction model
Harvey-Shack Theory+
New Reflectance model
that both considers
Reflection and Diffraction=
![Page 31: Microfacet Model and Material Appearancesungeui/GCG/Student_Presentations/... · SIGGRAPH 2016 [2] A Two-Scale Microfacet Reflectance Model Combining Reflection and Diffraction Nicolas](https://reader036.vdocuments.site/reader036/viewer/2022071000/5fbc86ce93f25735ea42c0e4/html5/thumbnails/31.jpg)
Overview
1. Background
• Cook-Torrance Model
• Modified Harvey-Shack Theory
2. Model
• Two-scale BRDF model
• NDF
3. Evaluation
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Cook-Torrance Model
Main Assumption:
1. Microfacet is larger than light wavelength Geometric optic applies
2. Each microfacet act as specular mirror
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𝜔𝑚 𝑜
𝑖
( ( ), )( , ) ( , )
cosF
o
refl i oi o F i o
( , )F i o
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Cook-Torrance Model
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𝑫(𝝎𝒎)
( ( ), )( , ) ( , )
cosF
o
refl i oi o F i o
Main Assumption:
1. Microfacet is larger than light wavelength Geometric optic applies
2. Each microfacet act as specular mirror
( , )4cos cos
Cook Torrance i o
i o
DFG
𝜔𝑚 𝑜
𝑖
( , )F i o
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Cook-Torrance Model
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𝑫(𝝎𝒎)
( ( ), )( , ) ( , )
cosF
o
refl i oi o F i o
Main Assumption:
1. Microfacet is larger than light wavelength Geometric optic applies
2. Each microfacet act as specular mirror
( , )4cos cos
Cook Torrance i o
i o
DFG
𝜔𝑚 𝑜
𝑖
( , )F i o𝑭(𝜼, 𝜽𝒅) : Fresnel term• Defines material color
• Only wavelength determinant
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Harvey-Shack theory
• Based on optical path length (OPD) difference
• Phase difference:
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(cos cos ) ( , )i oOPD h x y
(2 / )(cos cos ) ( , )i o h x y 1
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Harvey-Shack theory
• Based on optical path length (OPD) difference
• Phase difference:
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(cos cos ) ( , )i oOPD h x y
(2 / )(cos cos ) ( , )i o h x y
( ( ), )( , ) ( , ) (1 ) ( , ) ( )
cos
i odiff i o i o i o HS
o
reflAF A Q S f
Specular lobe Scattered lobe
Average
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Harvey-Shack theory
• Based on optical path length (OPD) difference
• Phase difference:
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(cos cos ) ( , )i oOPD h x y
(2 / )(cos cos ) ( , )i o h x y
( ( ), )( , ) ( , ) (1 ) ( , ) ( )
cos
i odiff i o i o i o HS
o
reflAF A Q S f
AverageMirror reflection direction
2
02 cos cossi
A e
𝝈𝒔: Surface roughness
= Variance of height distribution
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Two-Scale BRDF model
• Surface detail
– Micro-geometry : larger than light wavelength
– Nano-geometry : similar to light wavelength
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Two-Scale BRDF model
• Generic BRDF in original microfacet framework
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( , ) ( , , ) , ( , ) ( )i m o mi o s i m o o m i o m m
i n o n
f G D d
1
•
•
2
•
•
3
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Two-Scale BRDF model
• Generic BRDF in original microfacet framework
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( , ) ( , ) ( ( ), )F i o F i o refl i o
Recall) Cook- Torrance model if microfacet reflectance is Dirac,
( , ) ( , , ) , ( , ) ( )i m o mi o s i m o o m i o m m
i n o n
f G D d
1
•
•
2
•
•
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Two-Scale BRDF model
• Generic BRDF in original microfacet framework
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( , , ) ( , ) ( ( ), ) (1 ) ( , ) ( )s i o m i o i o i o HSf AF refl A Q S f
Diffraction model
( , ) ( , , ) , ( , ) ( )i m o mi o s i m o o m i o m m
i n o n
f G D d
1
•
•
2
•
•
3
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Two-Scale BRDF model
• Generic BRDF in original microfacet framework
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( , , ) ( , ) ( ( ), ) (1 ) ( , ) ( )s i o m i o i o i o HSf AF refl A Q S f
Standard Cook-Torrance Lobe
Diffraction model
Cook Torrance Diffraction Lobe
( , ) ( )i o spec d Cook Torrance Cook TorranceDiffractionA
( , ) ( , , ) , ( , ) ( )i m o mi o s i m o o m i o m m
i n o n
f G D d
1
•
•
2
•
•
3
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Two-Scale BRDF model
• Generic BRDF in original microfacet framework
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( , ) ( , , ) , ( , ) ( )i m o mi o s i m o o m i o m m
i n o n
f G D d
( , , ) ( , ) ( ( ), ) (1 ) ( , ) ( )s i o m i o i o i o HSf AF refl A Q S f
Diffraction model
4cos cosi o
DFG
2
2 reli m o m
e
( , ) ( )i o spec d Cook Torrance Cook TorranceDiffractionA
Approximation
Spherical convolution between
𝑫 and 𝑺𝑯𝑺
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Two-Scale BRDF model
• Generic BRDF in original microfacet framework
( , ) ( , , ) , ( , ) ( )i m o mi o s i m o o m i o m m
i n o n
f G D d
• NDF 𝑫(𝝎𝒎): Exponential power distribution
• Shadow function 𝑮 𝜽𝒉 : 𝟏
𝟏+𝚲(𝜷+𝒕𝒂𝒏𝜽), computed by Smith’s method
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Two-Scale BRDF model
• Result
– Validation with measured materials(MERL database)
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Two-Scale BRDF model
• Result
– Validation with measured materials(Good performance)
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Two-Scale BRDF model
• Result
– Validation with measured materials (materials with larger RMSE)
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THANK YOU
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Quiz
1. What is responsible for material appearance both in classical
microfacet and microflake theory?
① Height distribution function
② Normal distribution function
③ Extinction coefficient
④ Phase function
2. Which one is not microfacet model?
① Smith Model
② Cook-Torrance model
③ Harvey-Shack model
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ADDITIONAL SLIDES
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Microfacet Theory
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The Smith Model Single Scattering BSDF
Distribution of heights
Distribution of normals
Smith masking function
Masking-shadowing function
Distribution of visible normals
• Probability that 𝜔𝑛 is in 𝜔ℎ - X
•
• Projected surface area of the microfacets
above area is equal to dA
𝜔𝑛
𝑑𝜔ℎ
1( ) hD h n h d
hdA n h dA
h hdA D h d A
1
( 1) ( )h hn h dA D h n h dA
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Microfacet Theory
52
The Smith Model Single Scattering BSDF
Distribution of heights
Distribution of normals
Smith masking function
Masking-shadowing function
Distribution of visible normals
1 1 1( , , ) ( , ) ( , )local dist
i m i m iG h G G h
𝜔𝑛
𝜔𝑖
Visibility of a point on microsurface
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Microfacet Theory
53
The Smith Model Single Scattering BSDF
Distribution of heights
Distribution of normals
Smith masking function
Masking-shadowing function
Distribution of visible normals
1 1 1( , , ) ( , ) ( , )local dist
i m i m iG h G G h
𝜔𝑛
𝜔𝑖
1 ( , ) ( )local
i m i mG
Non-backfacing
Visibility of a point on microsurface
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Microfacet Theory
54
The Smith Model Single Scattering BSDF
Distribution of heights
Distribution of normals
Smith masking function
Masking-shadowing function
Distribution of visible normals
1 1 1( , , ) ( , ) ( , )local dist
i m i m iG h G G h
𝜔𝑛
𝜔𝑖 ( )1
1 ( , ) ( ) idist
iG h C h
Probability that ray does not
intersect microsurface
Smith lambda function
CDF of heights
Visibility of a point on microsurface
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Microfacet Theory
55
The Smith Model Single Scattering BSDF
Distribution of heights
Distribution of normals
Smith masking function
Masking-shadowing function
Distribution of visible normals
1
1 1
1( ) ( , ) ( )
1 ( )
dist dist
i i
i
G G h P h dh
Masking function averaged over all heights
1 1 1( , ) ( , ) ( )local dist
i m i m iG G G
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Microfacet Theory
56
The Smith Model Single Scattering BSDF
Distribution of heights
Distribution of normals
Smith masking function
Masking-shadowing function
Distribution of visible normals
22 1 1( , , ) ( , ) ( , ) ( , )local local dist
i m o i m o i oG G G h G
Visible to both ingoing and
outgoing direction
Height-correlated distant
masking-shadowing function
1
2 1 1( , ) ( , ) ( , ) ( )
1
1 ( ) ( )
(1 ( ),1 ( ))
dist dist dist
i o i o
i o
i o
G G h G h P h dh
B
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Microfacet Theory
57
The Smith Model Single Scattering BSDF
Distribution of heights
Distribution of normals
Smith masking function
Masking-shadowing function
Distribution of visible normals
DVNF of Smith model
1 ( ) , ( ) , ( )( )
cos cos (1 ( ))i
dist
i i m m i m m
m
i i i
G D DD
1cos ( , ) ,i i m i m m mG D d
Normalization [1]
Visible microsurface
= Projected area of geometric surface
[1] Understanding the Masking-Shadowing Function in Microfacet-Based BRDFs, Eric Heitz, 2014
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Microfacet Theory
58
The Smith Model Single Scattering BSDF
Distribution of heights 𝑃1(ℎ)
Distribution of normal 𝐷(𝜔𝑚)
Smith masking function 𝐺1(𝜔𝑖 , 𝜔𝑜)
Masking-shadowing function 𝐺2(𝜔𝑖 , 𝜔𝑜, 𝜔𝑚)
Distribution of visible normals 𝐷𝜔𝑖(𝜔𝑚)
2
1
( , , )
( , )
( , )
( , , ) , ( )i m o
ii m
i o
G
m i m o o m m mG
f
f D d
Single-Scattering BSDF of Generic Rough Materials
Given visible for 𝜔𝑖, visible for 𝜔𝑜
Micro-BRDF
Derivable: Rough dielectric, rough conductor, rough diffuse