Precomputed Radiance Transfer Field for Rendering Interreflections in Dynamic Scenes

Precomputed Radiance Transfer Fieldfor Rendering Interreflections in Dynamic

Scenes

Precomputed Radiance Transfer Fieldfor Rendering Interreflections in Dynamic

Scenes

Minhao Pan, Rui Wang, Xinguo Liu, Qunsheng Peng and Hujun Bao

State Key Lab of CAD&CG, Zhejiang University, P.R. China

23/7/2007

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

Related worksRelated works

Traditional global illumination methodsBased on ray-trace or radiosityRealistic but slow

Precomputed light transportStatic scene —— PRT[Sloan, 2002]Shadow in dynamic Scene

——[Zhou, 2005]Interreflections in dynamic scene

——[Iwasaki, 2007]



Radiance Transfer FieldRadiance Transfer Field



Radiance Transfer FieldInterreflection Transfer Function (ITF)


( ) ( ) ( , )( )q p p pI L s f s s n ds q

p





Environment Lightingq

p1p

2p

1

( )m

p j jj

L l y

( ) ( ) ( , )( )q p p pI L s f s s n ds

1

( )n

iq p

iiI T l

11

nip p

iilT

21

nip p

iilT

...

1

( ) ( )n

iq q i

i

I M l

[Sloan, 2002]





q

ITF( ) ijqq M

( )iqM Environment Lighting

1

( )m

p j jj

L l y

[Sloan, 2002]

( ) ( ) ( , )( )q p p pI L s f s s n ds

( ) ( )ij iq q iM M y d

1

( )n

iq p i

i

I T l

11

nip p i

i

T l

21

nip p i

i

T l

...

1

( ) ( )n

iq q i

i

I M l





q

p

1p

2p

Local lighting

( ) ( ) ( , )( )q p p pI L s f s s n ds

1

( )n

iq p

iilI T

11

nip p

iilT

21

nip p

iilT

...



Radiance Transfer FieldProxy-based incidient light approximation






,1

m

p p k kk

L w L

1X

2X

kX

mX

mL 1L

2L

kL

p

The incident light to p





1X

2X

kX

mX

p

q

p

( ) ( ) ( , )( )q p p pI L s f s s n ds Local lighting





1X

1Lp

q

p


1p

2p1 1 1 ,, ,

1

niX p X p X

iilT w

1 11 1 1, ,1

,

niX p p X p

iX ilT w

2 11 1 2, ,1

,

niX p p X p

iX ilT w

...

1 , ( )X qI

1 11

, ,( )n

i

iX q X iM l





p

q

p


1p

2p

2X2L

2 2, ,1

niX p X p i

i

T lw

2 1 2 1, ,1

niX p p X p

iiT w l

2 2 2 2, ,1

niX p p X p

iiT w l

...

2 , ( )X qI

2 ,1

( )iX i

n

qi

M l





1X

2X

kX

mX

mL 1L

2L

kL

pp

q

p


( )qI 2 , ( )X qI

1 , ( )X qI ...

,1 1

( )k k

m ni iX q X

k i

M l

2 2

1, ,( )i

X qi

X i

n

M l

1 11

, ,( )n

i

iX q X iM l

...

, , ( )k k

ij iX q X q iM M y d

1 2 ,, ,,...} { }ITF( ) { ,k

ijX q

ijX

ijX q qMq M M



Radiance Transfer FieldRadiance Transfer Field

21 , , ,..., }{ ijX q

ijX q MM



PrecomputationPrecomputation

Compute radiance transfer on each vertexCompute radiance transfer on samples in

fieldCompress the radiance transfer field



PrecomputationCompute radiance transfer on vertices

PrecomputationCompute radiance transfer on vertices

1X

2X

kX

mX



PrecomputationCompute radiance transfer on samples in field

PrecomputationCompute radiance transfer on samples in field

q ( )iqM



PrecomputationCompressionPrecomputationCompression

The raw RTF data is quite large 4th-order SH, 8 - 24 proxies, 16 concentric

spheres with 1536(6×16×16) directions.

——192 ∼ 576MBCPCA (Clustered Principle Component Analysis)

The compression ratio is about 40-50:1



A two-level scheme

Bouncing Step accumulate interreflections between objects

RenderingOverviewRenderingOverview



A two-level scheme

Bouncing Step accumulate interreflections between objects

Shading Stepcompute the final shadings on vertices.

RenderingOverviewRenderingOverview



RenderingBouncing StepRenderingBouncing Step

Iterative bouncing strategyIn one iteration:

For proxy q in bunny1. compute the interreflections

from proxy qk

2. sum all interreflections from other proxies

,( ) TripleProduct( , , )k k

ijk q bird q qL q q L V M

kq

q

( ) ( )kk

L q L q q



RenderingShading StepRenderingShading Step

One pass.For each vertex:

1. compute the illumination from proxy qk

2. sum all illumination from proxies

3. standard PRT process

kq

,( ) TripleProduct( , , )k k

ijk q bird q pL q p L V M

p

( )p kk

L L q p

TripleProduct( , , )p p selfI L V f



RenderingCaching strategiesRenderingCaching strategies

Caching RTF samplesStore incident light at

samples.

Caching RTF eigensBy using CPCA, we can store the product of eigens and the incident light of proxies.

——hit rate > 95% and reduce the cost > 90%



ResultsComparisonResultsComparison

Our approach Reference



ResultsResults

A PC with Intel Core 2 Duo 1.8GHz, 2G RAM and a nVidia 7800 graphics card.

Objects VertsRTF size

FPS

Cornell-box

7 22K 44.1MB 8-12

Cornell-box dynamic

8 40K 50.0MB 10-16

Table 4 40K 32.8MB 8-10

Brick game

10 86K 63.5MB 5-8

http://cornell.02.wmv/

http://cornell.02.wmv/



Conclusion and future workConclusion and future work

Contributions:1. Radiance transfer field2. A proxy-based approximation method for precomputed RTF3. An efficient interreflection rendering algorithm using precomputed RTF

There are also some limitations.1. only handle low-frequency interreflections and illumination.2. only limited to rigid objects.

Thank you!Thank you!

Precomputed Radiance Transfer Field for Rendering Interreflections in Dynamic Scenes

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