Billboard Clouds

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(No Transcript)
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Billboard Clouds

• Xavier Décoret
• Frédo Durand
• Francois Sillion?
• Julie Dorsey
• MIT-CSAIL ?Artis (INRIA/CNRS/UJF/INPG) Yale
  university

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What this is not about!
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What this is about

• New representation
• Rectangles ? global shape
• Textures with a ? finer details (silhouette)
  appearance

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Mesh Simplification

• Clustering RB93,LT97
• Hierarchical Dynamic Simplification LE97

• Decimation of Triangle Meshes SZL92
• Re-tiling Tur92
• Progressive Meshes Hop96,PH97
• Quadric Error Metrics GH97
• Out of Core Simplification Lin00

• Voxel based reconstruction HHK95
• Multiresolution analysis EDD95
• Superfaces KT96, face cluster WGH00

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Mesh Simplification

• Constraints on models
• Error control
• Simplification envelopes CVM96
• Permission Grids ZG02
• Image driven LT00
• Handling of attributes (textures and colors)
• Integration to the metricGH98Hop99
• Re-generation CMRS98,COM98
• Extreme Simplification
• Silhouette Clipping SGG00

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Alternative Rendering

• Image-based rendering
• Lightfield,Lumigraph LH96,GGRC96
• Impostors Maciel95,Aliaga96,DSSD99
• Relief Textures OB00
• Point-based rendering
• Surfels PZBG00
• Pointshop 3D ZPKG02

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Classic billboards

• A modelling trick RH94

• Generalization to many planes / formalism
• Automatic construction

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Classic Billboards
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Classic Billboards
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Classic Billboards
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Principle

• Illustrated in 2D

polygonal model
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Principle
Simplification by planes
polygonal model
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Principle (1)

• Allow vertex displacement

P
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Principle (2)

• Project faces onto planes

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Principle (2)

• Project faces onto planes

Valid approximation by a plane
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Problem

• How many planes? Which planes?

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Overview

• Express as an optimization problem
• Represent the space of planes
• Measure a planes relevance
• Find a set of planes

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Optimization problem

• Define over the set of Billboard clouds
• An error function
• Vertex displacement
• A cost function
• Number of planes
• Error Based bound max error ? minimize cost

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Overview

• Express as an optimization problem
• Represent the space of planes
• Dual representation
• Discretization
• Measure a planes relevance
• Find a set of planes

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Dual representation

• Illustrated in 2D
• Hough transform Hough62

Dual of line point
Line
Origin
Primal space
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Dual of a point

• Set of lines going through the point

?
(xP,yP)
?
0
Origin
2p
0
Dual space
Primal space
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Dual of a point

• Set of lines going through the point

?
(xP,yP)
?
0
Origin
2p
0
Dual space
Primal space
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Dual of a point

• Set of lines going through the point

?
(xP,yP)
?
0
Origin
2p
0
Dual space
Primal space
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Dual of a point

• Set of lines going through the point

?
(xP,yP)
?
0
Origin
2p
0
Dual space
Primal space
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Dual of a point

• Set of lines going through the point

?
r xPcosq yP sinq
(xP,yP)
?
0
Origin
2p
0
Dual space
Primal space
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Dual of a point

• Set of lines going through the point

?
r xPcosq yP sinqr ? 0
(xP,yP)
?
0
Origin
2p
0
Dual space
Primal space
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Dual of a sphere

• Set of lines intersecting the sphere

?
R
P
?
0
Origin
2p
0
Dual space
Primal space
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Dual of a sphere

• Set of lines intersecting the sphere

?
R
Dual of center P
P
?
0
Origin
2p
0
Dual space
Primal space
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Dual of a sphere

• Set of lines intersecting the sphere

?
R
Dual of center P
P
?
0
Origin
2p
0
Dual space
Primal space
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Dual of a sphere

• Set of lines intersecting the sphere

?
Dual of sphere2R-thick slice
R
P
?
0
Origin
2p
0
Dual space
Primal space
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Dual of a face

• Planes intersecting all vertices spheres

?
?
0
Origin
2p
0
Dual space
Primal space
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Dual of a face

• Planes intersecting all vertices spheres

?
?
0
Origin
2p
0
Dual space
Primal space
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Dual of a face
?
?
0
2p
0

• How to work with this complex set of planes?

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Discretization
?
Bins
?
0
2p
0

• How to work with this complex set of planes?

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Discretization
?
?
0
2p
0

• How to work with this complex set of planes?

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Overview

• Express as an optimization problem
• Represent the space of planes
• Dual representation
• Discretization
• Measure a planes relevance
• Density function
• Find a set of planes

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Discretization
?
?
0
2p
0

• How to work with this complex set of planes?

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Discretization
?
?
0
2p
0
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Discretization
?
There is (at least) one plane valid for the face
?
0
2p
0

• Relevance of this plane?

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Relevance
?
Grey plane is a better approximation of face !
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0
2p
0
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Density function

• Compute in plane space (a float per bin)
• Represent the relevance of each plane
• Accumulate face contributions into the bins

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Density function
Faces
?
?
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Density function
Faces
Planes valid for face
?
?
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Density function
Faces
Planes valid for face
?
?
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Density function
Faces
Planes valid for face
?
?
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Density function
Faces
Planes valid for face
?
?
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Density function
Faces
Planes valid for face
?
?
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Density function
Faces
Planes valid for face
?
?
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Density function
Faces
Planes valid for face
Density

?
-
?
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Density function
Faces
Planes valid for face
?
?
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Density function
Faces
?
?
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Overview

• Express as an optimization problem
• Represent the space of planes
• Hough transform
• Discretization
• Measure a planes relevance
• Density function
• Find a set of planes
• Greedy selection of best plane

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Density function
Faces
?
?
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Density function
Faces
?
?
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Density function
Faces

• How to find this plane?

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Adaptive search
Faces

• How to find this plane?

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Algorithm
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The Full Monty (3D)
2D
3D
Triangles
Faces
Segments
Lines
Planes
Primal
?,f,?
Dual
?,?
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A Simple Example
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Texture optimization

• Working in dual space can group faces that are
  far away in primal space
• No need for connectivity
• - Can potentially waste texture space fill rate

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Texture optimization

• Working in dual space can group faces that are
  far away in primal space
• No need for connectivity
• - Can potentially waste texture space fill rate

Billboards
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Texture Optimization
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Texture Optimization
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Results (1)
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Results (2)
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Results (2)
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Results (2)
Billboard Cloud
Polygons
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Limitations

• Gaps
• If of planes is too small
• Project faces on multiple planes
• Texture memory
• Other methods need resampling as well
• Overhead transparent texels (30)
• Use texture packing

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Conclusions

• New representation
• Rectangles ? global shape
• Textures ? finer details (silhouette)
  appearance
• Arbitrary models
• Automatic construction
• Simple error criterion
• Extreme simplification

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Future work

• Texture compression
• Hardware compression
• Adaptive Texture Maps KrausErtl02
• Texture packing
• View-dependent billboard clouds
• Multi-meshed impostors DSSD99
• Stochastic density computation
• Application to collision detection
• e.g intersection of a ray texture lookup

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Acknowledgments

• INRIA
• NSF EIA-9802220
• NTT (partnership MIT9904-30)
• Addy Ngan, Ray Jones, Eric Chan
• people at MIT
• Reviewers