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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

→ =

Niωrωhω

( )( ) ( ) cosss

h 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

T

Ν

CS348B Lecture 13 Pat Hanrahan, Spring 2004

Reflection from a Cylinder

T

Ν

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CS348B Lecture 13 Pat Hanrahan, Spring 2004

Reflection from a Cylinder

T

L

ˆˆ( )NR L

N

CS348B Lecture 13 Pat Hanrahan, Spring 2004

Reflection from a Cylinder

T

L

ˆˆ( )NR L

N

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CS348B Lecture 13 Pat Hanrahan, Spring 2004

Reflection from a Cylinder

T

L

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 ssE L E L E Lθ θ θ θ θ θ− = +

L

E

T

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