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]

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

Radiance Transfer FieldRadiance Transfer Field

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

Radiance Transfer FieldRadiance Transfer Field

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

Radiance Transfer FieldInterreflection Transfer Function (ITF)

Radiance Transfer FieldInterreflection Transfer Function (ITF)

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

p

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

Radiance Transfer FieldInterreflection Transfer Function (ITF)

Radiance Transfer FieldInterreflection Transfer Function (ITF)

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]

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

Radiance Transfer FieldInterreflection Transfer Function (ITF)

Radiance Transfer FieldInterreflection Transfer Function (ITF)

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

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

Radiance Transfer FieldInterreflection Transfer Function (ITF)

Radiance Transfer FieldInterreflection Transfer Function (ITF)

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

...

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

Radiance Transfer FieldProxy-based incidient light approximation

Radiance Transfer FieldProxy-based incidient light approximation

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

Radiance Transfer FieldProxy-based incidient light approximation

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

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

Radiance Transfer FieldProxy-based incidient light approximation

Radiance Transfer FieldProxy-based incidient light approximation

1X

2X

kX

mX

p

q

p

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

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

Radiance Transfer FieldProxy-based incidient light approximation

Radiance Transfer FieldProxy-based incidient light approximation

1X

1Lp

q

p

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

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

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

Radiance Transfer FieldProxy-based incidient light approximation

Radiance Transfer FieldProxy-based incidient light approximation

p

q

p

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

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

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

Radiance Transfer FieldProxy-based incidient light approximation

Radiance Transfer FieldProxy-based incidient light approximation

1X

2X

kX

mX

mL 1L

2L

kL

pp

q

p

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

( )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

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

Radiance Transfer FieldRadiance Transfer Field

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

ijX q MM

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

PrecomputationPrecomputation

Compute radiance transfer on each vertexCompute radiance transfer on samples in

fieldCompress the radiance transfer field

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

PrecomputationCompute radiance transfer on vertices

PrecomputationCompute radiance transfer on vertices

1X

2X

kX

mX

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

PrecomputationCompute radiance transfer on samples in field

PrecomputationCompute radiance transfer on samples in field

q ( )iqM

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

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

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

A two-level scheme

Bouncing Step accumulate interreflections between objects

RenderingOverviewRenderingOverview

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

A two-level scheme

Bouncing Step accumulate interreflections between objects

Shading Stepcompute the final shadings on vertices.

RenderingOverviewRenderingOverview

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

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

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

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

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

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%

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

ResultsComparisonResultsComparison

Our approach Reference

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

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

State Key Lab of CAD&CG,Zhejiang University

Precomputed Radiance Transfer Field

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!