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Radiosity for Point-Sampled Geometry. Yoshinori Dobashi. Tsuyoshi Yamamoto. ( Hokkaido University ). Tomoyuki Nishita. ( The University of Tokyo ). Overview. Introduction Background and Motivation Previous Work Radiosity Method Proposed Method Basic Idea - PowerPoint PPT Presentation
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Hokkaido University
Radiosity forRadiosity forPoint-Sampled GeometryPoint-Sampled Geometry
Tsuyoshi YamamotoTsuyoshi Yamamoto
Tomoyuki NishitaTomoyuki Nishita((The University of TokyoThe University of Tokyo))
Yoshinori DobashiYoshinori Dobashi
((Hokkaido UniversityHokkaido University))
Hokkaido University
OverviewOverview
• Introduction• Background and Motivation• Previous Work
• Radiosity Method• Proposed Method
• Basic Idea• Computation of Effective Area• Construction of Hierarchy• Radiosity Calculation• Adaptive Addition of Surfels
• Examples• Conclusions and Future Work
• Introduction• Background and Motivation• Previous Work
• Radiosity Method• Proposed Method
• Basic Idea• Computation of Effective Area• Construction of Hierarchy• Radiosity Calculation• Adaptive Addition of Surfels
• Examples• Conclusions and Future Work
Hokkaido University
OverviewOverview
• Introduction• Background and Motivation• Previous Work
• Radiosity Method• Proposed Method
• Basic Idea• Computation of Effective Area• Construction of Hierarchy• Radiosity Calculation• Adaptive Addition of Surfels
• Examples• Conclusions and Future Work
• Introduction• Background and Motivation• Previous Work
• Radiosity Method• Proposed Method
• Basic Idea• Computation of Effective Area• Construction of Hierarchy• Radiosity Calculation• Adaptive Addition of Surfels
• Examples• Conclusions and Future Work
Hokkaido University
Background and MotivationBackground and Motivation• Point-sampled Geometry• Point-sampled Geometry
- Points sampled on surfaces of an object- Points sampled on surfaces of an object
PointsPointsObjectObject PolygonsPolygons
- No information on connectivity- No information on connectivity
- Used for objects with complex shapes- Used for objects with complex shapes
- Many researches on point-sampled geometry- Many researches on point-sampled geometry
Hokkaido University
- Points as display primitive [Levoy85]- Points as display primitive [Levoy85]
- Ray tracing [Shaufler00]- Ray tracing [Shaufler00]
- Surfel [Pfister00], Q-splat [Rusinkiewica00]- Surfel [Pfister00], Q-splat [Rusinkiewica00]
- Point sample rendering [Grossman98]- Point sample rendering [Grossman98]
- Surface splatting [Zwicker01]- Surface splatting [Zwicker01]
- Hardware-acceleration [Ren02]- Hardware-acceleration [Ren02]
• Previous methods for displaying point- sampled geometry• Previous methods for displaying point- sampled geometry
• No method for radiosity (Finite element approach)• No method for radiosity (Finite element approach)
Background and MotivationBackground and Motivation
- Points as display primitive [Levoy85]- Points as display primitive [Levoy85]
- Ray tracing [Shaufler00]- Ray tracing [Shaufler00]
- Surfel [Pfister00], Q-splat [Rusinkiewica00]- Surfel [Pfister00], Q-splat [Rusinkiewica00]
- Point sample rendering [Grossman98]- Point sample rendering [Grossman98]
- Surface splatting [Zwicker01]- Surface splatting [Zwicker01]
- Hardware-acceleration [Ren02]- Hardware-acceleration [Ren02]
(Monte-Carlo approach)(Monte-Carlo approach)
Hokkaido University
- Radiosity method for point-sampled
geometry
• Goal of this research• Goal of this research
- Diffuse surfaces
• Condition• Condition
Background and MotivationBackground and Motivation
Hokkaido University
OverviewOverview
• Introduction• Background and Motivation• Previous Work
• Radiosity Method• Proposed Method
• Basic Idea• Computation of Effective Area• Construction of Hierarchy• Radiosity Calculation• Adaptive Addition of Surfels
• Examples• Conclusions and Future Work
• Introduction• Background and Motivation• Previous Work
• Radiosity Method• Proposed Method
• Basic Idea• Computation of Effective Area• Construction of Hierarchy• Radiosity Calculation• Adaptive Addition of Surfels
• Examples• Conclusions and Future Work
Hokkaido University
Radiosity MethodRadiosity Method
light
directindirect
Hokkaido University
• Energy transfer between patches
Bi: radiosity
Fij: form factor
j: diffuse reflectance
Vij: visibility
light
patch i
patch j
• A linear system
n
ijjjijjii BFEB
,1
j iA A
jiijij
ji
iij dAdAV
rAF 2
coscos1
Radiosity MethodRadiosity Method
j
i
rij
Aj
Ai
Hokkaido University
• Energy transfer between patches
Bi: radiosity
Fij: form factor
j: diffuse reflectance
Vij: visibility
light
patch i
patch j
• A linear system
n
ijjjijjii BFEB
,1
Radiosity MethodRadiosity Method
j iA A
jiijij
ji
iij dAdAV
rAF 2
coscos1
j
i
rij
Aj
Ai
Hokkaido University
n
ijjjijjii BFEB
,1
• Energy transfer between patches
Bi: radiosity
Fij: form factor
j: diffuse reflectance
Vij: visibility
light
patch i
patch j
• A linear system
Radiosity MethodRadiosity Method
j
i
rij
Aj
Ai
jij
jiij A
rF
2
coscos
ijV
Hokkaido University
OverviewOverview
• Introduction• Background and Motivation• Previous Work
• Radiosity Method• Proposed Method
• Computation of Effective Area• Construction of Hierarchy• Radiosity Calculation• Adaptive Addition of Surfels
• Examples• Conclusions and Future Work
• Introduction• Background and Motivation• Previous Work
• Radiosity Method• Proposed Method
• Computation of Effective Area• Construction of Hierarchy• Radiosity Calculation• Adaptive Addition of Surfels
• Examples• Conclusions and Future Work
Hokkaido University
Basic IdeaBasic Idea
original surface
point xi
Ri
normal ni
max. distance
between points in
small neighborhood
• Use of surfels to represent object• Use of surfels to represent object [Pfister00][Pfister00]
tangent disk
Hokkaido University
Basic IdeaBasic Idea
1. Computation of effective area1. Computation of effective area
2. Construction of hierarchy2. Construction of hierarchy
3. Computation of interreflection3. Computation of interreflection
4. Creation of final images4. Creation of final images
Hokkaido University
Basic IdeaBasic Idea
1. Computation of effective area1. Computation of effective area
- Form factor:- Form factor: jij
jiij A
rF
2
coscos
(area)(area)
Area of tangent diskArea of tangent disk Effective areaEffective area
Overestimationdue to overlapOverestimationdue to overlap
Considering overlapConsidering overlap
Hokkaido University
Basic IdeaBasic Idea
2. Construction of hierarchy2. Construction of hierarchy
- Large number of surfels- Large number of surfels
- Increase in computation time- Increase in computation time
- Efficient computation using hierarchy- Efficient computation using hierarchy
Grouping neighborsGrouping neighbors
Hokkaido University
Basic IdeaBasic Idea
3. Computation of interreflection3. Computation of interreflection
- Hierarchical radiosity with global refinement- Hierarchical radiosity with global refinement[Stamminger00]
- Adaptive addition of surfels- Adaptive addition of surfels
4. Creation of final images4. Creation of final images- Hardware accelerated surface splatting- Hardware accelerated surface splatting [Ren02]
- Original points may not be sufficient- Original points may not be sufficient
Hokkaido University
Basic IdeaBasic Idea
1. Computation of effective area1. Computation of effective area
2. Construction of hierarchy2. Construction of hierarchy
3. Computation of interreflection3. Computation of interreflection
4. Creation of final images4. Creation of final images
Hokkaido University
Basic IdeaBasic Idea
1. Computation of effective area1. Computation of effective area
2. Construction of hierarchy2. Construction of hierarchy
3. Computation of interreflection3. Computation of interreflection
4. Creation of final images4. Creation of final images
Hokkaido University
Basic IdeaBasic Idea
1. Computation of effective area1. Computation of effective area
2. Construction of hierarchy2. Construction of hierarchy
3. Computation of interreflection3. Computation of interreflection
4. Creation of final images4. Creation of final images
Hokkaido University
Effective Area ComputationEffective Area Computation• Definition: effective area of surfel i • Definition: effective area of surfel i
y
A(y)
i: Influence functioni: Influence function
A: Differential areaA: Differential area
ri• Condition of i :• Condition of i :
- Decreasing with distance- Decreasing with distance
yy dArS iii )()( yy dArS iii )()(
Use of exponential func.Use of exponential func.
Hokkaido University
A(y)
Effective Area ComputationEffective Area Computation• Definition: effective area of surfel i • Definition: effective area of surfel i
yy dArS iii )()( yy dArS iii )()(
i: Influence functioni: Influence function
A: Differential areaA: Differential area
- Decreasing with distance- Decreasing with distance
- Taking into account overlap- Taking into account overlap
ri• Condition of i :• Condition of i :y
Use of exponential func.Use of exponential func.
Hokkaido University
Effective Area ComputationEffective Area Computation
A
• Simple case:• Simple case: Same normal vectors (coplanar disks)
i
iii
i dArS yy)()(Sum of effective areas:Sum of effective areas:
yy dAStotal )(
Total area:Total area:
== ++
==
0.1)()()( 21 yyy m
y
Hokkaido University
Effective Area ComputationEffective Area Computation• Simple case:• Simple case: Same normal vectors (coplanar disks)
(2) Taking into account overlap(2) Taking into account overlap
(1) Decreasing with distance (exp func.)(1) Decreasing with distance (exp func.)
0.1)()()( 21 yyy m
)exp()(,)(/)( iii
iii rrwrwrw )exp()(,)(/)( iii
iii rrwrwrw • We use following influence function• We use following influence function
for cond. (1)for cond. (1)for cond. (1)for cond. (1) for cond. (2)for cond. (2)for cond. (2)for cond. (2)
Hokkaido University
• General case• General case
Effective Area ComputationEffective Area Computation
yy dArS iii )()( yy dArS iii )()( - Effective area:
Ai
- Problem: how to compute A- Problem: how to compute A
Aj
- Use of weighted average of Ai and Aj- Use of weighted average of Ai and Aj
(Aj = Ai/cos )(Aj = Ai/cos )
ri
rjdisk j disk i
Hokkaido University
• General case• General case
Effective Area ComputationEffective Area Computation
• Effective area for general case• Effective area for general case
m
j j
m
j jj
iirw
ArwAdArS
1
1
)(
)(,)( y
m
j j
m
j jj
iirw
ArwAdArS
1
1
)(
)(,)( y for details,
see paper
• Use of graphics hardware• Use of graphics hardware
yy dArS iii )()( yy dArS iii )()( - Effective area:
- Problem: how to compute A- Problem: how to compute A
- Use of weighted average of Ai and Aj- Use of weighted average of Ai and Aj
Hokkaido University
Effective Area ComputationEffective Area Computation• Use of hardware-accelerated surface splatting• Use of hardware-accelerated surface splatting
virtual camera
m
j j
m
j jj
iirw
ArwAdArS
1
1
)(
)(,)( y
[Ren02][Ren02]
virtual screen
m: number of neighboring surfels
Hokkaido University
m: number of neighboring surfels
virtual screen
Effective Area ComputationEffective Area Computation• Use of hardware-accelerated surface splatting• Use of hardware-accelerated surface splatting
m
j j
m
j jj
iirw
ArwAdArS
1
1
)(
)(,)( y
[Ren02][Ren02]
R: w(r)A
: w(r)additive blending
virtual camera
Hokkaido University
Effective Area ComputationEffective Area Computation• Use of hardware-accelerated surface splatting• Use of hardware-accelerated surface splatting
m
j j
m
j jj
iirw
ArwAdArS
1
1
)(
)(,)( y
[Ren02][Ren02]
R
m
j jj Arw1
)(
m
j jrw1 )(
m: number of neighboring surfels
Hokkaido University
Effective Area ComputationEffective Area Computation• Use of hardware-accelerated surface splatting• Use of hardware-accelerated surface splatting
[Ren02][Ren02]
R
m
j jj Arw1
)(
m
j jrw1 )(÷
A
=
m
j j
m
j jj
iirw
ArwAdArS
1
1
)(
)(,)( y
. . . . .
m: number of neighboring surfels
Hokkaido University
Basic IdeaBasic Idea
1. Computation of effective area1. Computation of effective area
2. Construction of hierarchy2. Construction of hierarchy
3. Computation of interreflection3. Computation of interreflection
4. Creation of final images4. Creation of final images
Hokkaido University
Computation of InterreflectionComputation of Interreflection• Hierarchical radiosity with global refinement• Hierarchical radiosity with global refinement
- Algorithm- Algorithm[Stamminger00]
1. Compute intereflection1. Compute intereflection
2. Evaluate errors2. Evaluate errors
3. Replace surfels with their children3. Replace surfels with their children
4. If error > , go to step 14. If error > , go to step 1(: user-specified threshold)(: user-specified threshold)
• Original points may not be sufficientOriginal points may not be sufficient• Original points may not be sufficientOriginal points may not be sufficient
• Addition of new surfelsAddition of new surfels• Addition of new surfelsAddition of new surfels
Hokkaido University
Adaptive Addition of SurfelsAdaptive Addition of Surfels
Hokkaido University
Adaptive Addition of SurfelsAdaptive Addition of Surfels
• Two conditions• Two conditions
shadow boundary
Hokkaido University
Adaptive Addition of SurfelsAdaptive Addition of Surfels
(1) Place surfels according to intensity gradient
• Two conditions• Two conditions
shadow boundary
Hokkaido University
Adaptive Addition of SurfelsAdaptive Addition of Surfels
• Two conditions• Two conditions
(1) Place surfels according to intensity gradient
(2) Place surfels as uniformly as possible
shadow boundary
Hokkaido University
• Local coordinate based on intensity gradient• Local coordinate based on intensity gradient
Adaptive Addition of SurfelsAdaptive Addition of Surfels
- Compute error vector- Compute error vector
j ij
ijijij d
xx
xxe
)(
Hokkaido University
• Local coordinate based on intensity gradient• Local coordinate based on intensity gradient
Adaptive Addition of SurfelsAdaptive Addition of Surfels
- Compute error vector- Compute error vector
j ij
ijijij d
xx
xxe
)(
- Define local coordinate- Define local coordinate
- Add four surfels at:- Add four surfels at:(-cRi , cRi , 0.0), (-cRi , cRi , 0.0),
(cRi , -cRi , 0.0), (-cRi , -cRi , 0.0)
(-cRi , cRi , 0.0), (-cRi , cRi , 0.0),
(cRi , -cRi , 0.0), (-cRi , -cRi , 0.0)
Ri : radius of surfel iRi : radius of surfel i c : user-specified cnst.c : user-specified cnst.
Normal vetor, reflectance: interpolationNormal vetor, reflectance: interpolationEffective area: x0.25Effective area: x0.25Disk size: x0.5Disk size: x0.5
uu
vv ww
Hokkaido University
Adaptive Addition of SurfelsAdaptive Addition of Surfels
• Two conditions• Two conditions
(1) Place surfels according to intensity gradient
(2) Place surfels as uniformly as possible(2) Place surfels as uniformly as possible
Hokkaido University
• Use of point repulsion method• Use of point repulsion method
Adaptive Addition of SurfelsAdaptive Addition of Surfels
- Compute repulsive forces- Compute repulsive forces
[Turk92][Pauly03]
(Newly added surfels only)(Newly added surfels only)
- Move surfels- Move surfels
Hokkaido University
OverviewOverview
• Introduction• Background and Motivation• Previous Methods
• Radiosity Method• Proposed Method
• Basic Idea• Computing Representative Area• Construction of Hierarchy• Computing Interreflection using Progressive Radiosity• Adaptive addition of surfels
• Examples• Conclusions and Future Work
• Introduction• Background and Motivation• Previous Methods
• Radiosity Method• Proposed Method
• Basic Idea• Computing Representative Area• Construction of Hierarchy• Computing Interreflection using Progressive Radiosity• Adaptive addition of surfels
• Examples• Conclusions and Future Work
Hokkaido University
Experimental ResultsExperimental Results
• Three spheres in a simple room• Three spheres in a simple room
3.5m x 3.5m, 400 surfels
0.2m0.4m
0.8m
642 surfels
- Sum of effective areas:- Sum of effective areas:
- True value:- True value:
8.23 m2 8.23 m2
8.04 m2 8.04 m2
- Relative error:- Relative error:
2.63 % 2.63 %
Very accurateVery accurate
Hokkaido University
Experimental ResultsExperimental Results
• Three spheres in a simple room• Three spheres in a simple room
ResultResult(15,748 surfels)(15,748 surfels)
Distribution of surfelsDistribution of surfels
Computer: Pentium 4 (2.8GHz), GPU: nVidia Geforce4Computation time (radiosity): 38 sec.
Hokkaido University
Complex ResultsComplex Results
ResultResult
• Two bunnies in a simple room• Two bunnies in a simple room
Distribution of surfelsDistribution of surfels(72,068 surfels)(72,068 surfels)
Computer: Pentium 4 (2.8GHz), GPU: nVidia Geforce4Computation time (radiosity): 47 sec.
Hokkaido University
Complex ResultsComplex Results
• Gallery of statues• Gallery of statues
ResultResult Distribution of surfelsDistribution of surfels(315,686 surfels)(315,686 surfels)
Computer: Pentium 4 (2.8GHz), GPU: nVidia Geforce4Computation time (radiosity): 2,541 sec.
Hokkaido University
ConclusionsConclusions
• Interreflection of light for point- sampled geometry• Interreflection of light for point- sampled geometry
- Efficient computation of effective areas- Efficient computation of effective areas
- Adaptive addition of surfels- Adaptive addition of surfels
Future WorkFuture Work
• Specular reflection• Specular reflection