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CS348B Lecture 17 Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing Torrance-Sparrow Model Today Multiple importance sampling Anisotropic reflection models

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Page 1: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

CS348B Lecture 17 Pat Hanrahan, Spring 2005

Reflection Models

Previous lecture

Phong model

Microfacet models

Gaussian height field on surface

Self-shadowing

Torrance-Sparrow Model

Today

Multiple importance sampling

Anisotropic reflection models

Page 2: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

Multiple Importance Sampling

Page 3: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

CS348B Lecture 17 Pat Hanrahan, Spring 2005

Multiple Importance Sampling

Reflection of a circular light source by a rough surface

Radius

Sh

inin

ess

Sampling the light source Sampling the BRDF

( ) ( )f x g x dx

Page 4: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

CS348B Lecture 17 Pat Hanrahan, Spring 2005

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 x

f XY

p X

1, 1

1,1,

1 1,

~ ( )

( )

( )

i

ii

i

X p x

f XY

p X

1 1, 2 2,i i iY wY w Y

1 1 2 21 2

( )( ) ( ) ( ) ( ) ( ) ( )

( ) ( )i

i

p xw x p x w x p x w x p x

p x p x

Page 5: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

CS348B Lecture 17 Pat Hanrahan, Spring 2005

Multiple Importance Sampling

Source: Veach and Guibas

Page 6: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

Anisotropic Reflection Model

Page 7: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

CS348B Lecture 17 Pat Hanrahan, Spring 2005

Anisotropic Reflection

Page 8: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

CS348B Lecture 17 Pat Hanrahan, Spring 2005

Quarterhorse

Page 9: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

CS348B Lecture 17 Pat Hanrahan, Spring 2005

Reflection from a Cylinder

T

Page 10: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

CS348B Lecture 17 Pat Hanrahan, Spring 2005

Reflection from a Cylinder

T

Page 11: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

CS348B Lecture 17 Pat Hanrahan, Spring 2005

Reflection from a Cylinder

T

L

ˆˆ( )

NR L

N

Page 12: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

CS348B Lecture 17 Pat Hanrahan, Spring 2005

Reflection from a Cylinder

T

L

ˆˆ( )

NR L

N

Page 13: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

CS348B Lecture 17 Pat Hanrahan, Spring 2005

Reflection from a Cylinder

T

L

ˆˆ( )

NR L

Page 14: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

CS348B Lecture 17 Pat Hanrahan, Spring 2005

Anisotropic Reflection

Page 15: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

CS348B Lecture 17 Pat Hanrahan, Spring 2005

Shape of Anisotropic Highlights

From Lu, Koenderink, Kappers

Fibers tangent to the plane defined by the halfway vector reflect light

Page 16: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

CS348B Lecture 17 Pat Hanrahan, Spring 2005

Shape of Anisotropic Highlights

From Lu, Koenderink, Kappers

Page 17: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

CS348B Lecture 17 Pat Hanrahan, Spring 2005

Kajiya-Kay Model

Diffuse

Specular

2ˆ ˆsin 1L T L

cos cos cos sin sinss

E L E L E L

L

E

T

ˆˆ( )

NR L

Page 18: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

CS348B Lecture 17 Pat Hanrahan, Spring 2005

Herbert

Page 19: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

CS348B Lecture 17 Pat Hanrahan, Spring 2005

Fiber Model

Page 20: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

CS348B Lecture 17 Pat Hanrahan, Spring 2005

Fiber Model

Page 21: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

CS348B Lecture 17 Pat Hanrahan, Spring 2005

Fiber Model

Page 22: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

CS348B Lecture 17 Pat Hanrahan, Spring 2005

Caustics

Page 23: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

CS348B Lecture 17 Pat Hanrahan, Spring 2005

Hair Appearance

Page 24: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

CS348B Lecture 17 Pat Hanrahan, Spring 2005

Hair Appearance

Page 25: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing
Page 26: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

CS348B Lecture 17 Pat Hanrahan, Spring 2005

Page 27: CS348B Lecture 17Pat Hanrahan, Spring 2005 Reflection Models Previous lecture Phong model Microfacet models Gaussian height field on surface Self-shadowing

CS348B Lecture 17 Pat Hanrahan, Spring 2005


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