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3 rd International Radiance Workshop 11 - 12 October 2004, Fribourg, Switzerland. Radiance Caching for Efficient Global Illumination Computation. J. Křivánek P. Gautron S. Pattanaik K. Bouatouch. High Quality GI. The Day After Tomorrow, © 2004 20th Century Fox.

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radiance caching for efficient global illumination computation

3rd International Radiance Workshop

11 - 12 October 2004, Fribourg, Switzerland

Radiance Caching for Efficient Global Illumination Computation

J. Křivánek P. Gautron

S. Pattanaik K. Bouatouch

Radiance Workshop 2004 – Fribourg, Switzerland

high quality gi
High Quality GI

The Day After Tomorrow, © 2004 20th Century Fox

Shrek 2, © 2004 PDI/DreamWorks

Radiance Workshop 2004 – Fribourg, Switzerland

global illumination how
Global Illumination… How?

Li(P, ωi)

=

Lo(P, ωo)

* BRDF(ωo, ωi) *cos(θ)dωi

Radiance Workshop 2004 – Fribourg, Switzerland

monte carlo
Monte Carlo

Li(P, ωi)

=

Lo(P, ωo)

* BRDF(ωo, ωi) *cos(θ)dωi

No analytical solution

Shooting

Gathering

Radiance Workshop 2004 – Fribourg, Switzerland

shooting
Shooting

Radiance Workshop 2004 – Fribourg, Switzerland

shooting6
Shooting

Radiance Workshop 2004 – Fribourg, Switzerland

shooting7
Shooting

Final gathering: costly

Photon map only for indirect diffuse

Distribution ray tracing for non diffuse: noisy

Radiance Workshop 2004 – Fribourg, Switzerland

gathering
Gathering

Radiance Workshop 2004 – Fribourg, Switzerland

gathering9
Gathering

Support for glossy GI

Random sampling: noisy

High quality: many rays

Radiance Workshop 2004 – Fribourg, Switzerland

irradiance caching
Irradiance Caching

Sparse computation of indirect diffuse lighting

Radiance Workshop 2004 – Fribourg, Switzerland

irradiance caching11
Irradiance Caching

Sparse computation of indirect diffuse lighting

Radiance Workshop 2004 – Fribourg, Switzerland

irradiance caching12
Irradiance Caching

Sparse computation of indirect diffuse lighting

Interpolation

Radiance Workshop 2004 – Fribourg, Switzerland

gradients
Gradients

Why?

Without gradients

With gradients

Images from "Irradiance Gradients", Gregory J. Ward, Paul S. Heckbert

Eurographics Workshop on Rendering 1992

Radiance Workshop 2004 – Fribourg, Switzerland

gradients14
Gradients

ni

n

E = Ei

+ …

Radiance Workshop 2004 – Fribourg, Switzerland

rotational gradient
Rotational gradient

ni

n

ni

n

+ (ni x n)

Ei

r

θ

E = Ei

E = Ei

+ …

Radiance Workshop 2004 – Fribourg, Switzerland

translational gradient
Translational gradient

ni

n

D

+ (ni x n)

E = Ei

+ D

Ei

Ei

r

t

Radiance Workshop 2004 – Fribourg, Switzerland

non diffuse surfaces
Non diffuse surfaces

Irradiance values: indirect diffuse

Indirect glossy: distribution ray tracing

High quality: many rays

Radiance Workshop 2004 – Fribourg, Switzerland

contributions
Contributions

Extension to indirect glossy lighting

BDRF-based selection of record points

Low frequency: records

High frequency: distribution ray tracing

Novel translational gradient

Radiance Workshop 2004 – Fribourg, Switzerland

outline
Outline

Introduction

IC for glossy surfaces

Hemispherical data representation

Radiance gradients

Outgoing radiance computation

Results

Conclusion

Radiance Workshop 2004 – Fribourg, Switzerland

outline20
Outline

Introduction

IC for glossy surfaces

Hemispherical data representation

Radiance gradients

Outgoing radiance computation

Results

Conclusion

Radiance Workshop 2004 – Fribourg, Switzerland

caching on glossy surfaces
Caching on glossy surfaces

Need hemispherical data representation

Radiance Workshop 2004 – Fribourg, Switzerland

caching on glossy surfaces22
Caching on glossy surfaces

ni

n

?

Need new gradients

Radiance Workshop 2004 – Fribourg, Switzerland

outline23
Outline

Introduction

IC for glossy surfaces

Hemispherical data representation

Radiance gradients

Outgoing radiance computation

Results

Conclusion

Radiance Workshop 2004 – Fribourg, Switzerland

hemispherical functions
Hemispherical Functions

Original Function

Piecewise linear approximation

Need a more compact and smooth

representation

Fast computation of integrals

Better fitting

Radiance Workshop 2004 – Fribourg, Switzerland

orthogonal polynomials
Orthogonal Polynomials

fi

bi(x)

f(x) =

fi = f(x)bi(x)dx

fi

gi

gi

bi(x)

g(x) =

f(x)g(x)dx =

Radiance Workshop 2004 – Fribourg, Switzerland

application to gi
Application to GI

Incident Radiance

BRDF

 dot product

Radiance Workshop 2004 – Fribourg, Switzerland

spherical harmonics
Spherical Harmonics

(0,0)

(1,-1)

(1,0)

(1,1)

(2,-2)

(2,-1)

(2,0)

(2,1)

(2,2)

Radiance Workshop 2004 – Fribourg, Switzerland

hemispherical harmonics
Hemispherical Harmonics

(0,0)

(1,-1)

(1,0)

(1,1)

(2,-2)

(2,-1)

(2,0)

(2,1)

(2,2)

A Novel Hemispherical Basis for Accurate and Efficient Rendering

P. Gautron, J. Křivànek, S. Pattanaik, K. Bouatouch, EGSR 04

Radiance Workshop 2004 – Fribourg, Switzerland

why hemi spherical harmonics
Why (Hemi)Spherical harmonics?

Ease of use

Rotation support

Radiance Workshop 2004 – Fribourg, Switzerland

representation limitations
Representation Limitations

Bandlimited: "ringing" artifacts

Limit to low-frequency BRDFs

Radiance Workshop 2004 – Fribourg, Switzerland

adaptive brdf representation
Adaptive BRDF Representation

Why?

High frequency

Low frequency

"(H)SH-Friendly"

Ward BRDF with same parameters

Radiance Workshop 2004 – Fribourg, Switzerland

adaptive brdf representation32
Adaptive BRDF Representation

How?

BRDF = 4D Function

Parabolic Parameterization

Radiance Workshop 2004 – Fribourg, Switzerland

incoming radiance
Incoming Radiance

λlm (P) = Li(P, ωi)Blm(ωi) d ωi

Same principle as Irradiance Caching

Radiance Workshop 2004 – Fribourg, Switzerland

incoming radiance34
Incoming Radiance

λlm (P) = Li(P, ωi)Blm(ωi) d ωi

(H)SH

Same principle as Irradiance Caching

Radiance Workshop 2004 – Fribourg, Switzerland

outline35
Outline

Introduction

IC for glossy surfaces

Hemispherical data representation

Radiance gradients

Outgoing radiance computation

Results

Conclusion

Radiance Workshop 2004 – Fribourg, Switzerland

radiance gradients
Radiance Gradients

ni

n

(H)SH

Radiance Workshop 2004 – Fribourg, Switzerland

rotational gradient37
Rotational gradient

ni

n

ni

n

θ

= R

(H)SH

(H)SH

Rotation Matrix

Radiance Workshop 2004 – Fribourg, Switzerland

translational gradient38
Translational gradient

ni

n

(H)SH

D

0

,

,

=

(H)SH

(H)SH

(H)SH

∂ x

∂ y

Goal

Radiance Workshop 2004 – Fribourg, Switzerland

translational gradient39
Translational Gradient

Numerical Method

p

Radiance Workshop 2004 – Fribourg, Switzerland

translational gradient40
Translational Gradient

p'

Δx

Numerical Method

p

Radiance Workshop 2004 – Fribourg, Switzerland

translational gradient41
Translational Gradient

*Li( )*Blm( )

λlm=

Ωk

*Li( )*Blm( )

λlm=

θk, Φk

θk, Φk

*Li( )*Blm( )

λ'lm=

N

N

Σ

Σ

Ω'k

*Li( )*Blm( )

λ'lm=

θk, Φk

θ'k, Φ'k

k=1

k=1

∂ λlm

λ'lm-λlm

p'

p

Δx

=

∂ x

Δx

Numerical Method

Radiance Workshop 2004 – Fribourg, Switzerland

translational gradient42
Translational Gradient

∂ Blm(θk, Φk)

∂ x

N

N

Σ

Σ

k=1

k=1

Ωk

*Li( )*Blm( )

λlm =

∂λlm =

∂ Ωk

θk, Φk

θk, Φk

Blm(θk, Φk)

0

,

,

∂ x

=

∂ x

∂ x

∂ y

+Ωk

Analytical Method

Li(θk, Φk)*

Radiance Workshop 2004 – Fribourg, Switzerland

outline43
Outline

Introduction

IC for glossy surfaces

Hemispherical data representation

Radiance gradients

Outgoing radiance computation

Results

Conclusion

Radiance Workshop 2004 – Fribourg, Switzerland

outgoing radiance
Outgoing Radiance

ni

n

dx

dy

+

+

(H)SH

(H)SH

(H)SH

∂ x

∂ y

(H)SH

Ri

=

Radiance Workshop 2004 – Fribourg, Switzerland

outgoing radiance45
Outgoing Radiance

ni

n

i S

i S

Σ

Σ

∂ Λi

∂ Λi

Λ(P)

Ri

Λi

dx

dy

=

wi(P)

+

+

∂ x

∂ y

wi(P)

Radiance Workshop 2004 – Fribourg, Switzerland

outgoing radiance46
Outgoing Radiance

Incident Radiance

BRDF

 dot product

Radiance Workshop 2004 – Fribourg, Switzerland

outline47
Outline

Introduction

IC for glossy surfaces

Hemispherical data representation

Radiance gradients

Outgoing radiance computation

Results

Conclusion

Radiance Workshop 2004 – Fribourg, Switzerland

stills comparison
Stills comparison

Monte Carlo Path Tracing

Radiance Caching

Rendering time: 155s

P4 2.2GHz, 512MB RAM

Radiance Workshop 2004 – Fribourg, Switzerland

stills comparison49
Stills comparison

Monte Carlo

Path Tracing

Radiance

Caching

Radiance Workshop 2004 – Fribourg, Switzerland

video cornell box
Video: Cornell Box

Radiance Workshop 2004 – Fribourg, Switzerland

video flamingo
Video: Flamingo

Radiance Workshop 2004 – Fribourg, Switzerland

outline52
Outline

Introduction

IC for glossy surfaces

Hemispherical data representation

Radiance gradients

Outgoing radiance computation

Results

Conclusion

Radiance Workshop 2004 – Fribourg, Switzerland

conclusion
Conclusion

Quality improvement

Efficiency improvement

Independent from distribution

Independent from basis functions

Extension of irradiance caching to radiance caching

Definition of new translational gradient

Radiance Workshop 2004 – Fribourg, Switzerland

future work
Future Work

"All-frequency" hemispherical representation

Hardware support

Radiance Workshop 2004 – Fribourg, Switzerland

any questions
Any Questions ?

Rendered using Radiance Caching

Radiance Workshop 2004 – Fribourg, Switzerland