Global Illumination Adapted from Thomas Funkhouser Princeton - - PowerPoint PPT Presentation

Global Illumination

Adapted from… Thomas Funkhouser Princeton University C0S 526, Fall 2002 Additional material from…

H.W. Jensen, Realistic Image Synthesis Using Photon Mapping, A.K. Peters Ltd., 2001

Overview

• Global illumination
• Rendering equation
• Overview of solution methods

Direct Illumination

n

• '

x ω

• '

ω

• ω
• d

Light Camera

Ω

• Ω
• +

=

L

d n x L x f x L x L

i r e

• ω

ω ω ω ω ω ω

• )

)( , ' ( ) ' , , ' ( ) ' , ' ( ) ' , ' (

Direct Illumination

Philip Dutré

Global Illumination

n

• '

x ω

• '

ω

• ω
• d

Ω

• Ω
• +

= ω ω ω ω ω ω ω

• d

n x L x f x L x L

i r e

• )

)( , ' ( ) ' , , ' ( ) ' , ' ( ) ' , ' (

Surface Surface Light

Global Illumination

Jensen

Ray tracing

Henrik Wann Jensen

Global Illumination

Jensen

+ soft shadows

Henrik Wann Jensen

Global Illumination

Jensen

+ caustics

Henrik Wann Jensen

Global Illumination

Jensen

+ indirect diffuse illumination

Henrik Wann Jensen

Rendering Equation

n

• '

x ω

• '

ω

• ω
• d

Ω

• Ω
• +

= ω ω ω ω ω ω ω

• d

n x L x f x L x L

i r e

• )

)( , ' ( ) ' , , ' ( ) ' , ' ( ) ' , ' (

Surface Surface

Kajiya 1986

Rendering Equation (2)

n

• '

x x " x

i

Θ′

ω

• '

ω

• dA

' dA

• Θ
• →

→ → + → = →

S r e

dA x x G x x V x x L x x x f x x L x x L ) ' , ( ) ' , ( ) ' ( ) " ' ( ) " ' ( ) " ' (

2

' cos cos ) ' , ( x x x x G

• i

− Θ Θ′ =

Kajiya 1986

Solution Methods

• OpenGL
• Radiosity
• Ray tracing
• Distribution ray tracing
• Path tracing

Path Types

Path Types?

Henrik Wann Jensen

Path Types?

Paul Debevec

Path Types?

Henrik Wann Jensen

Path Types?

RenderPark

Path Type Notation

• Introduced by [Heckbert, 1990]
• Vertices of the light path can be:

L – a light source E – the eye S – a specular reflection D – a diffuse reflection

• Combinations of paths:

(k)+

• ne or more of k events

(k)* zero or more of k events (k)? zero or one k event (k|k’) a k or a k’ event

• Examples:

Radiosity: LD*E Ray Tracing: LD?S*E Path Tracing: L(D|S)*E Caustics: LS+DE

Path Types

• OpenGL

LDE

• Ray tracing

LD?S*E

• Radiosity

LD*E

• Path tracing

L(D|S)*E

John Hart

OpenGL

Assume direct illumination from point lights and ignore visibility Assume direct illumination from point lights and ignore visibility

• Ω
• +

= ω ω ω ω ω ω ω

• d

n x L x f x L x L

i r e

• )

)( , ' ( ) ' , , ' ( ) ' , ' ( ) ' , ' ( n

• '

x ω

• '

ω

• Light

Camera

Ω

• =
• +

=

nlights i i r e

• n

x L x f x L x L

1

) )( , ' ( ) ' , , ' ( ) ' , ' ( ) ' , ' (

• ω

ω ω ω ω ω

Ray Tracing

Assume specular reflection is only significant indirect illumination Assume specular reflection is only significant indirect illumination

n

• '

x ω

• '

ω

• Camera

Ω

Surface Light

specular n x L x f x L x L

nlights i i r e

• +
• +

=

• =1

) )( , ' ( ) ' , , ' ( ) ' , ' ( ) ' , ' (

• ω

ω ω ω ω ω

• Ω
• +

= ω ω ω ω ω ω ω

• d

n x L x f x L x L

i r e

• )

)( , ' ( ) ' , , ' ( ) ' , ' ( ) ' , ' (

Ray Tracing Algorithm

Radiosity

• →

→ → + → = →

S r e

dA x x G x x V x x L x x x f x x L x x L ) ' , ( ) ' , ( ) ' ( ) " ' ( ) " ' ( ) " ' (

• +

=

S d r e

dA x x G x x V x B x f x B x B ) ' , ( ) ' , ( ) ( ) ' ( ) ' ( ) ' (

,

• +

=

S d e

dA x x G x x V x B x x B x B ) ' , ( ) ' , ( ) ( ) ' ( ) ' ( ) ' ( π ρ

• =

+ =

N j ij j i i e i

F B B B

1 ,

ρ

i j A A i ij

dA dA x x G x x V A F

i j

= π ) ' , ( ) ' , ( 1

Assume everything is Lambertian Assume everything is Lambertian

n

• i

Θ′

j

dA

i

dA

• Θ

' x

x

where

Path Tracing

• Ω
• +

= ω ω ω ω ω ω ω

• d

n x L x f x L x L

i r e

• )

)( , ' ( ) ' , , ' ( ) ' , ' ( ) ' , ' (

Perform Neumann series expansion Perform Neumann series expansion

TL L L

e +

=

• Ω
• =

ω ω ω ω ω ω

• d

n x g x f g x T

r

) )( , ' ( ) ' , , ' ( ) ' , ' (

where

...

3 2

+ + + + =

e e e e

L T L T TL L L

• Convergent approximation
• Also suggested by [Kajiya, 1986]

Path Tracing

Le TLe T2Le T3Le Le +TLe Le +TLe+T2Le Le+…+T3Le Le

Philip Dutré

Path Tracing Algorithm

Distribution Ray Tracing

• Ω
• +

= ω ω ω ω ω ω ω

• d

n x L x f x L x L

i r e

• )

)( , ' ( ) ' , , ' ( ) ' , ' ( ) ' , ' ( n

• '

x

1

ω

• '

ω

• Ω

Estimate integral for each reflection by random sampling Estimate integral for each reflection by random sampling

2

ω

• 3

ω

• 4

ω

• 5

ω

• 6

ω

• Also:
• Depth of field
• Motion blur
• etc.

Distribution Ray Tracing

• Random direction

is computed as follows.

• Given two uniformly distributed random variables,

Monte Carlo Path Tracing

• Ω
• +

= ω ω ω ω ω ω ω

• d

n x L x f x L x L

i r e

• )

)( , ' ( ) ' , , ' ( ) ' , ' ( ) ' , ' (

Estimate integral for each pixel by random sampling Estimate integral for each pixel by random sampling Also:

• Depth of field
• Motion blur
• etc.

Ray Tracing vs. Path Tracing

Ray tracing Path tracing

Jim Kajiya

Bidirectional Path Tracing

• Role of source and receiver can be switched,

flux does not change

• Exploiting duality can increase convergence rate

Philip Dutré

Bidirectional Path Tracing

Philip Dutré

Tracing From Eye

Philip Dutré

Tracing from Lights

Philip Dutré

Bidirectional Path Tracing

Philip Dutré

Bidirectional Path Tracing Algorithm

Bidirectional Path Tracing

(RenderPark 98)

Philip Dutré

Summary

• Global illumination

Rendering equation

• Overview of solution methods

OpenGL Radiosity Ray tracing Distribution ray tracing Path tracing