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!