Microfacet Model - Computer graphicsPage 1 CS348B Lecture 13 Pat Hanrahan, Spring 2004 Reflection...
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CS348B Lecture 13 Pat Hanrahan, Spring 2004
Reflection Models
Last lecture
Phong model
Microfacet models
Gaussian height field on surface
Self-shadowing
Today
Torrance-Sparrow model
Anisotropic reflection models
Multiple importance sampling
Microfacet Model
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CS348B Lecture 13 Pat Hanrahan, Spring 2004
Torrance-Sparrow Model
( )( )4cos cos
hr i r
i r
Df ωω ωθ θ
→ =
N̂iωrωhω
( )( ) ( ) cos ssh hD Dω α α ω= = = •N
iθ rθ
α
CS348B Lecture 13 Pat Hanrahan, Spring 2004
Torrance-Sparrow Theory
( )( ) ( ) ( ) ( )4 cos cos
r i r
i i r
i r
fF S S D
ω ωθ θ θ α
θ θ
→′
=
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CS348B Lecture 13 Pat Hanrahan, Spring 2004
Torrance-Sparrow Comparison
Aluminum
CS348B Lecture 13 Pat Hanrahan, Spring 2004
Torrance-Sparrow Comparison
Magnesium Oxide
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CS348B Lecture 13 Pat Hanrahan, Spring 2004
“Diffuse” Reflection
ExperimentalPressed magnesium oxide powder used as an example of a diffuse reflectorReflection greater at high angles of incidence
TheoreticalBouguer - Microfacet distribution
No microfacet distribution can reflect rays equally in all directions
Multiple surface or subsurface reflections
Paint manufactures attempt to create ideal diffuse
Anisotropic Reflection Model
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CS348B Lecture 13 Pat Hanrahan, Spring 2004
Anisotropic Reflection
CS348B Lecture 13 Pat Hanrahan, Spring 2004
Quarterhorse
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CS348B Lecture 13 Pat Hanrahan, Spring 2004
Reflection from a Cylinder
T̂
Ν̂
CS348B Lecture 13 Pat Hanrahan, Spring 2004
Reflection from a Cylinder
T̂
Ν̂
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CS348B Lecture 13 Pat Hanrahan, Spring 2004
Reflection from a Cylinder
T̂
L̂
ˆˆ( )NR L
N̂
CS348B Lecture 13 Pat Hanrahan, Spring 2004
Reflection from a Cylinder
T̂
L̂
ˆˆ( )NR L
N̂
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CS348B Lecture 13 Pat Hanrahan, Spring 2004
Reflection from a Cylinder
T̂
L̂
ˆˆ( )NR L
CS348B Lecture 13 Pat Hanrahan, Spring 2004
Shape of Anisotropic Highlights
From Lu, Koenderink, Kappers
Fibers tangent to the plane defined by the halfway vector reflect light
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CS348B Lecture 13 Pat Hanrahan, Spring 2004
Shape of Anisotropic Highlights
From Lu, Koenderink, Kappers
CS348B Lecture 13 Pat Hanrahan, Spring 2004
Anisotropic Reflection
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CS348B Lecture 13 Pat Hanrahan, Spring 2004
Kajiya-Kay Model
Diffuse
Specular
( )2ˆ ˆsin 1Lθ = − •T L
( ) ( )cos cos cos sin sin ss E L E L E Lθ θ θ θ θ θ− = +
L̂
Ê
T̂
ˆˆ( )NR L
CS348B Lecture 13 Pat Hanrahan, Spring 2004
Herbert
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CS348B Lecture 13 Pat Hanrahan, Spring 2004
Fiber Model
CS348B Lecture 13 Pat Hanrahan, Spring 2004
Fiber Model
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CS348B Lecture 13 Pat Hanrahan, Spring 2004
Fiber Model
CS348B Lecture 13 Pat Hanrahan, Spring 2004
Caustics
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CS348B Lecture 13 Pat Hanrahan, Spring 2004
Hair Appearance
CS348B Lecture 13 Pat Hanrahan, Spring 2004
Hair Appearance
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CS348B Lecture 13 Pat Hanrahan, Spring 2004
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CS348B Lecture 13 Pat Hanrahan, Spring 2004
Multiple Importance Sampling
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CS348B Lecture 13 Pat Hanrahan, Spring 2004
Multiple Importance Sampling
Reflection of a circular light source by a rough surface
Radius
Shin
ines
s
Sampling the light source Sampling the BRDF( ) ( )f x g x dx∫
CS348B Lecture 13 Pat Hanrahan, Spring 2004
Multiple Importance Sampling
Two sampling techniques
Form weighted combination of samples
The balance heuristic
2, 2
2,2,
2 2,
~ ( )( )( )
i
ii
i
X p xf X
Yp X
=
1, 1
1,1,
1 1,
~ ( )( )( )
i
ii
i
X p xf X
Yp X
=
1 1, 2 2,i i iY w Y w Y= +
1 1 2 21 2
( )( ) ( ) ( ) ( ) ( ) ( )( ) ( )
ii
p xw x p x w x p x w x p xp x p x
= ⇒ = ++
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CS348B Lecture 13 Pat Hanrahan, Spring 2004
Multiple Importance Sampling
Source: Veach and Guibas
