2. Billboard Clouds Xavier Décoret† Frédo Durand† Francois Sillion
Julie Dorsey‡
†MIT-CSAIL Artis (INRIA/CNRS/UJF/INPG) ‡ Yale university

3. What this is not about!

4. What this is about New representation: Rectangles  global shape
Textures with a  finer details (silhouette) + appearance
Take more to explain what it is
Explain why we use the term “cloud”
Geometry is captured with plane AND textures

5. 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]
Comprehensive
Voxel based reconstruction [HHK+95]
Multiresolution analysis [EDD+95]
Superfaces [KT96], face cluster [WGH00]

6. 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 metric[GH98][Hop99]
Re-generation [CMRS98,COM98]
Extreme Simplification
Silhouette Clipping [SGG+00]
Go faster + images (oversimplified)
“Error that you incur”

7. Alternative Rendering
Image-based rendering
Lightfield,Lumigraph [LH96,GGRC96]
Impostors [Maciel95,Aliaga96,DSSD99]
Relief Textures [OB00]
Point-based rendering
Surfels [PZBG00]
Pointshop 3D [ZPKG02]

8. Classic billboards A modelling “trick” [RH94]
Generalization to many planes / formalism
Automatic construction

9. Classic Billboards
Pause
For a very non convex model

10. Classic Billboards

11. Classic Billboards
Hide the gaps under the carpet

12. Principle
Illustrated in 2D
polygonal model

13. Simplification by planes
Principle
Simplification by planes
polygonal model

14. Principle (1)
Allow vertex displacement
Maximum displacement P

15. Valid approximation by a plane
Principle (2)
Project faces onto planes
Valid approximation by a plane
Face

16. Valid approximation by a plane
Principle (2)
Project faces onto planes
Valid approximation by a plane

17. Problem
How many planes? Which planes?

18. Overview Express as an optimization problem
Represent the space of planes
Measure a plane’s relevance
Find a set of planes

19. 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

20. Overview Express as an optimization problem
Represent the space of planes
Dual representation
Discretization
Measure a plane’s relevance
Find a set of planes

21. Dual representation Dual space  Primal space Illustrated in 2D
Hough transform [Hough62]
Dual space   2p
Dual of line =
point 
Line   
Origin
Primal space

22. Dual of a point Primal space Dual space
Set of lines going through the point 
(xP,yP) 
Origin 2p
Primal space
Dual space

23. Dual of a point Primal space Dual space
Set of lines going through the point 
(xP,yP) 
Origin 2p
Primal space
Dual space

24. Dual of a point Primal space Dual space
Set of lines going through the point 
(xP,yP) 
Origin 2p
Primal space
Dual space

25. Dual of a point Primal space Dual space
Set of lines going through the point 
(xP,yP) 
Origin 2p
Primal space
Dual space

26. Dual of a point Primal space Dual space
Set of lines going through the point 
r = xPcosq +yP sinq
(xP,yP) 
Origin 2p
Primal space
Dual space

27. Dual of a point Primal space Dual space
Set of lines going through the point 
r = xPcosq +yP sinq r  0
(xP,yP) 
Origin 2p
Primal space
Dual space

28. Dual of a sphere Primal space Dual space
Set of lines intersecting the sphere  R P 
Origin 2p
Primal space
Dual space

29. Dual of a sphere Primal space Dual space
Set of lines intersecting the sphere  R
Dual of center P P 
Origin 2p
Primal space
Dual space

30. Dual of a sphere Primal space Dual space
Set of lines intersecting the sphere  R 2R
Dual of center P P 
Origin 2p
Primal space
Dual space

31. Dual of sphere = 2R-thick slice
Dual of a sphere
Set of lines intersecting the sphere 
Dual of sphere = 2R-thick slice R P 
Origin 2p
Primal space
Dual space

32. Dual of a face Primal space Dual space
Planes intersecting all vertices’ spheres  R P’ R P 
Origin 2p
Primal space
Dual space

33. Dual of a face Primal space Dual space
Planes intersecting all vertices’ spheres  R P’ R P
Don’t’ mention dual space when you say planes 
Origin 2p
Primal space
Dual space

34. Dual of a face How to work with this complex set of planes?  R P’ R P 2p
How to work with this complex set of planes?

35. Discretization How to work with this complex set of planes?  Bins R 2p
How to work with this complex set of planes?

36. Discretization How to work with this complex set of planes?  R P’ R P 2p
How to work with this complex set of planes?

37. Overview Express as an optimization problem
Represent the space of planes
Dual representation
Discretization
Measure a plane’s relevance
Density function
Find a set of planes

38. Discretization How to work with this complex set of planes?  R P’ R P 2p
How to work with this complex set of planes?

39. Discretization R P P’ R P P’ R P P’ R P P’ R P P’ R P P’  R P P’  2p

40. There is (at least) one plane valid for the face
Discretization 
A tagged bin indicates that:
There is (at least) one plane valid for the face  2p
Relevance of this plane?

41. Use projected area of face (on central plane)
Relevance 
Grey plane is a better approximation of face !
Use projected area of face (on central plane) 
Density function 2p

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

43. Density function + - Faces   Density Planes valid for face
Vary -> vari  

44. Density function
Faces
Planes valid for face
Density + -  

45. Density function
Faces
Planes valid for face
Density + -  

46. Density function
Faces
Planes valid for face
Density + -  

47. Density function
Faces
Planes valid for face
Density + -  

48. Density function
Faces
Planes valid for face
Density + -  

49. Density function
Faces
Planes valid for face
Density + -  

50. Density function
Faces
Planes valid for face
Density +  - 

51. Density function
Faces
Planes valid for face
Density + -  

52. Density function
Faces
Density + -  

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

54. Density function
Faces
Bin with highest
density  

55. Density function Faces Faces for which bin is valid Bin with highest 

56. Density function How to find this plane?  Faces High density
There is probably a plane valid for
all the faces 
How to find this plane?

57. Adaptive search How to find this plane?  Faces Test central plane
High density
There is probably a plane valid for
all the faces 
Subdivide
Local density
recomputation
How to find this plane?

58. Algorithm Details more the Build Billboard construction Adaptive
“For example using OpenGL”

59. 2D 3D The Full Monty (3D) Faces Segments Triangles Primal Lines Planes
Dual
,
,f,
Density function  r
Dual space
Primal space  f
Origin
q,f

60. A Simple Example
Talk all the time

61. 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
Billboard
Wasted space
(transparent)

62. 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

63. Texture Optimization

64. Texture Optimization
Connected component

65. Results (1) Shadows = trick And no self shadowing Synchronize
We are using a cloud of # billboards
Mention the gaps now
Realistic
Emphasize we show full screen

66. Results (2)

67. Results (2)

68. Results (2)
Billboard Cloud
Polygons

69. Limitations Gaps Texture memory 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

70. Conclusions New representation Arbitrary models Automatic construction
Rectangles  global shape
Textures  finer details (silhouette) + appearance
Arbitrary models
Automatic construction
Simple error criterion
Extreme simplification

71. Future work Texture compression View-dependent billboard clouds
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

72. Acknowledgments INRIA NSF EIA-9802220 NTT (partnership MIT9904-30)
Addy Ngan, Ray Jones, Eric Chan
people at MIT
Reviewers
Thank you