Radiance Workshop 2004 – Fribourg, Switzerland 1

Radiance Caching for Efficient Global Illumination Computation

J. Křivánek P. Gautron

S. Pattanaik K. Bouatouch

3rd International Radiance Workshop

11 - 12 October 2004, Fribourg, Switzerland

Radiance Workshop 2004 – Fribourg, Switzerland 2

High Quality GI

The Day After Tomorrow, © 2004 20th Century Fox

Shrek 2, © 2004 PDI/DreamWorks

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Global Illumination… How?

Lo(P, ωo) ∫ Li(P, ωi)= * BRDF(ωo, ωi) *cos(θ)dωi

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Monte Carlo

Shooting Gathering

Lo(P, ωo) ∫ Li(P, ωi)= * BRDF(ωo, ωi) *cos(θ)dωi

No analytical solution

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Shooting

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Shooting

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Shooting

Final gathering: costly

Photon map only for indirect diffuse

Distribution ray tracing for non diffuse: noisy

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Gathering

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Gathering

Random sampling: noisy

High quality: many rays

Support for glossy GI

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Irradiance Caching

Sparse computation of indirect diffuse lighting

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Irradiance CachingSparse computation of indirect diffuse lighting

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Irradiance Caching

Interpolation

Sparse computation of indirect diffuse lighting

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GradientsWhy?

Without gradients With gradients

Images from "Irradiance Gradients", Gregory J. Ward, Paul S. HeckbertEurographics Workshop on Rendering 1992

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Gradients

ni

n

E = Ei + …

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Rotational gradient

ni

n

ni

n

θ

E = Ei + (ni x n)r Ei

E = Ei + …

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Translational gradient

ni

n

D

E = Ei + (ni x n)r Ei

+ Dt Ei

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Non diffuse surfaces

Indirect glossy: distribution ray tracing

High quality: many rays

Irradiance values: indirect diffuse

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Contributions

BDRF-based selection of record points

Novel translational gradient

Extension to indirect glossy lighting

Low frequency: records

High frequency: distribution ray tracing

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Outline

Introduction

IC for glossy surfaces

Hemispherical data representation

Radiance gradients

Outgoing radiance computation

Results

Conclusion

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Outline

Introduction

IC for glossy surfaces

Hemispherical data representation

Radiance gradients

Outgoing radiance computation

Results

Conclusion

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Caching on glossy surfaces

Need hemispherical data representation

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Caching on glossy surfaces

ni

n

?

Need new gradients

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Outline

Introduction

IC for glossy surfaces

Hemispherical data representation

Radiance gradients

Outgoing radiance computation

Results

Conclusion

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Hemispherical Functions

Original Function Piecewise linear approximation

Need a more compact and smoothrepresentation

Better fitting Fast computation of integrals

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Orthogonal Polynomials

fi = f(x)bi(x)dx f(x) = fi bi(x)

g(x) = gi bi(x) f(x)g(x)dx = fi gi

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Application to GI

Incident Radiance BRDF

dot product

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Spherical Harmonics

(0,0)

(1,-1)

(2,-2) (2,-1) (2,0) (2,1) (2,2)

(1,0) (1,1)

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Hemispherical Harmonics

(0,0)

(1,-1)

(2,-2) (2,-1) (2,0) (2,1) (2,2)

(1,0) (1,1)

A Novel Hemispherical Basis for Accurate and Efficient RenderingP. Gautron, J. Křivànek, S. Pattanaik, K. Bouatouch, EGSR 04

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Why (Hemi)Spherical harmonics?

Ease of use

Rotation support

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Representation Limitations

Bandlimited: "ringing" artifacts

Limit to low-frequency BRDFs

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Adaptive BRDF Representation

Low frequency"(H)SH-Friendly"

High frequency

Why?

Ward BRDF with same parameters

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Adaptive BRDF RepresentationHow?

BRDF = 4D FunctionParabolic Parameterization

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Incoming Radiance

λlm (P) = Li(P, ωi)Bl

m(ωi) d ωi∫

Same principle as Irradiance Caching

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Incoming Radiance

λlm (P) = Li(P, ωi)Bl

m(ωi) d ωi∫

Same principle as Irradiance Caching

(H)SH

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Outline

Introduction

IC for glossy surfaces

Hemispherical data representation

Radiance gradients

Outgoing radiance computation

Results

Conclusion

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Radiance Gradients

ni

n

(H)SH

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Rotational gradient

ni

n

Rotation Matrix

(H)SH

(H)SH= R

ni

n

θ

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Translational gradient

D

ni

n

(H)SH

Goal

(H)SH =∂ (H)SH

∂ x, ∂ (H)SH

∂ y, 0

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Translational GradientNumerical Method

p

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Translational GradientNumerical Method

p Δx p'

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Translational GradientNumerical Method

p Δx p'

∂ λlm

∂ x =λ'lm - λl

m

Δx

λlm = *Li( )*Bl

m( )

λ'lm = *Li( )*Blm( )

*Li( )*Blm( )θk, ΦkΩkΣ

k=1

N

λlm =

λ'lm = *Li( )*Blm( )Ω'kΣ

k=1

N

θk, Φk

θk, Φk θ'k, Φ'k

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Translational GradientAnalytical Method

*Li ( )*Blm( )θk, ΦkΩkΣ

k=1

N

λlm = θk, Φk

=∂∂ x

, ∂∂ y

, 0

Σk=1

N

∂ λlm =

∂ xLi (θk, Φk)*

+Ωk ∂ x

∂ Blm(θk, Φk)

∂ Ωk

∂ xBl

m(θk, Φk)

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Outline

Introduction

IC for glossy surfaces

Hemispherical data representation

Radiance gradients

Outgoing radiance computation

Results

Conclusion

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Outgoing Radiance

ni

n

(H)SH (H

)SHRi= dx+ ∂

∂ x(H)SH

+∂∂ y

(H)SH

dy

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Outgoing Radiance

ni

n

=Λ(P)

Ridx+

∂ Λi

∂ xΣi S

Λi dy∂ Λi

∂ y+ wi(P)

Σi S

wi(P)

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Outgoing Radiance

Incident Radiance BRDF

dot product

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Outline

Introduction

IC for glossy surfaces

Hemispherical data representation

Radiance gradients

Outgoing radiance computation

Results

Conclusion

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Stills comparison

P4 2.2GHz, 512MB RAM

Monte Carlo Path Tracing Radiance Caching

Rendering time: 155s

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Stills comparison

Monte Carlo Path Tracing

Radiance Caching

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Video: Cornell Box

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Video: Flamingo

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Outline

Introduction

IC for glossy surfaces

Hemispherical data representation

Radiance gradients

Outgoing radiance computation

Results

Conclusion

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Conclusion

Extension of irradiance caching to radiance caching

Definition of new translational gradient

Quality improvement

Efficiency improvement

Independent from distribution

Independent from basis functions

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Future Work

"All-frequency" hemispherical representation

Hardware support

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Any Questions ?

Rendered using Radiance Caching