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1 Preprocessing of Large databasesV for Interactive visualisation Xavier Décoret iMAGIS-GRAVIR / IMAG i MAGIS est un projet commun CNRS - INPG - INRIA - UJF

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2 Summary Context Visibility computation –Previous work –Contributions Level of details –Previous Work –Billboard clouds Conclusion

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3 Summary Context Visibility computation –Previous work –Contributions Level of details –Previous Work –Billboard clouds Conclusion

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4 Context Virtual environments –Video game, virual tourism, simulations User walk freely through the modl The computer is in charge of generating images of what user « sees » Frequent refresh (25 / sec)

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5 Feeling of immersion Complex environments –Large spatial extent –Highly detailed Realistic effects –Shadows –Ligthing effets (reflection) –Appearance High computation time

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6 User actions User actions Context Rendering System Rendering System Database images Model complexityBounded computation time Preprocess to speed-up Reusing results Optimizing representations

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7 Hidden Faces Removal Vertex projections Face rasterisation View frustum

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8 Image Vertex projections Face rasterisation Hidden Faces Removal

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9 Image Pixel Vertex projections Face rasterisation Hidden Faces Removal

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10 Image Vertex projections Face rasterisation Hidden Faces Removal

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11 Image Vertex projections Face rasterisation Hidden Faces Removal

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12 Image Vertex projections Face rasterisation Hidden Faces Removal

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13 Image Vertex projections Face rasterisation Hidden Faces Removal

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14 Image Pixel = Color Depth depth Vertex projections Face rasterisation Hidden Faces Removal

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15 Image depth > depth Vertex projections Face rasterisation Z-buffer [Cat74] Hidden Faces Removal

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16 Consequences Complex 3D model ) lot of calculations Redundancy in computations Unadapted computations

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17 Consequences Image Complex 3D model ) lot of calculations Redundancy in computations Unadapted computations

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18 Consequences Image Complex 3D model ) lot of calculations Redundancy in computations Unadapted computations

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19 Consequences Image Complex 3D model ) lot of calculations Redundancy in computations Unadapted computations

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20 Consequences Image Complex 3D model ) lot of calculations Redundancy in computations Unadapted computations

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21 Consequences Image Complex 3D model ) lot of calculations Redundancy in computations Unadapted computations

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22 Consequences Image Complex 3D model ) lot of calculations Redundancy in computations Unadapted computations

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23 Consequences Image Complex 3D model ) lot of calculations Redundancy in computations Unadapted computations

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24 Consequences Image Complex 3D model ) lot of calculations Redundancy in computations Unadapted computations

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25 Possible solutions Visibility computations –Finding what is hidden –Prevent unecessary rasterization Level of Details –Several level of modelisation –Using the level fitted to objects distance Alternative rendering

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26 Summary Context Visibility computation –Previous work –Contributions Level of details –Previous Work –Billboard clouds Conclusion

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27 Visibility computation Reject as soon as possible what will not contribute to an image Two approaches –Online ) for current view point –Offline ) for a region of space Difficulty: umbrae and penumbrae fusion

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28 Umbrae fusion Viewpoint Shadow volume Buildings (top view)

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29 Shadow volume Viewpoint Buildings (top view) Umbrae fusion

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30 Shadow volume Viewpoint Buildings (top view) Umbrae fusion

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31 Viewpoint Buildings (top view) Umbrae fusion

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32 Penumbrae fusion Viewcell Buildings (topview)

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33 Penumbrae fusion Viewcell Buildings (topview)

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34 Visibility Lot of previous work [Dur99] Classification [SPS74] Image SpaceObject Space Hierarchical Frustum Culling [GBW90] Shaft culling [HW91] Shadow volumes [CT97] Bloqueurs convexes [CZ98] Convex Vertical Prisms [DM01] Volumetric visibility [SDSD00] Portals [ST91] Hierarchical Z-buffer [GKM93] Hierarchical Occlusion Map [ZMH97] 2D1/2 Occlusion maps [WS99] Extended projections [DDTP00] Line Space subdivision [BWW01] Portals [LG95]

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35 Complexe problem No exact solution ) being conservative Umbrae fusion more or less done Object space ) extended visibility Image space ) fusion (implicit) Combining approaches

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36 Summary Context Visibility computation –Previous work –Contributions Level of details –Previous Work –Billboard clouds Conclusion

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37 Difficulty Visibility from-point easy –Z-buffer Visibility from region difficult Reducing to a from-point problem

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38 Blocker shrinking Proposed by [WWS00] Viewcell Object Blockers

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39 Object Shrunk blockers Center of viewcell Proposed by [WWS00] Blocker shrinking

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40 O Proposed by [WWS00] Blocker shrinking

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41 O { P such as B r (P) O } r-shrinking Proposed by [WWS00] Blocker shrinking

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42 O V M Generalisation to convex viewcells Shrinking of occludees V Proposed by [WWS00] Blocker shrinking

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43 Occluder/occludees shrinking Viwcell Object Blockers

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44 Shrunk blockers Center of viewcell Shrunk object Image taken fom viewcells center with shrunk objects Same treatment to occluders/occludees One pass algorithm Occluder/occludees shrinking

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45 Formalisation (1) Dilatation (Minkowski sum) Set of points O Set of vectors X O © XO © X { P+x, P 2 O and x 2 X }

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46 Formalisation (2) Erosion Set of points O Set of vectors X O ª XO ª X { P such as 8 x 2 X, P+x 2 O }

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47 Theorem If a ray (VM) is blocked by O ª X with X convex, then: Any ray (VM) is blocked by O with: V 2 {V} © X and M 2 {M} © X V M V M O ª XO ª X O

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48 Approximative erosion Exact erosion is hard to compute We can have approximations M E R C R E D I 1 6 O C T O B R E 2 0 0 2 1 2 3 4 5 6 7 8 9 1010 1 1212............

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49 Difficulty M E R C R E D I 1 6 O C T O B R E 2 0 0 2 1 2 3 4 5 6 7 8 9 1010 1 1212............ O ª XO ª X Erosion by X O ª XO ª X Internal erosion ½ O ª XO ª X External erosion ½ Exact erosion is hard to compute We can have approximations

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50 Mise en oeuvre Building an occlusion map with internal erosions Testing external erosions against the map Objects+erosions

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51 Mise en oeuvre Building an occlusion map with internal erosions Testing external erosions against the map

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52 Modification de lalgorithme Carte docclusion Building an occlusion map with internal erosions Testing external erosions against the map

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53 Modification de lalgorithme Carte docclusion Building an occlusion map with internal erosions Testing external erosions against the map

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54 Modification de lalgorithme Carte docclusion Building an occlusion map with internal erosions Testing external erosions against the map

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55 Modification de lalgorithme Carte docclusion Building an occlusion map with internal erosions Testing external erosions against the map

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56 Modification de lalgorithme Carte docclusion Visibles Building an occlusion map with internal erosions Testing external erosions against the map

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57 Modification de lalgorithme Carte docclusion Visibles Building an occlusion map with internal erosions Testing external erosions against the map

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58 Modification de lalgorithme Carte docclusion Visibles Building an occlusion map with internal erosions Testing external erosions against the map

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59 Modification de lalgorithme Carte docclusion Visibles Building an occlusion map with internal erosions Testing external erosions against the map

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60 Modification de lalgorithme Carte docclusion Visibles Hidden Building an occlusion map with internal erosions Testing external erosions against the map

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61 Pros & cons Two pass of rendernig (map + test) Tests can be done par graphic card Linear complexity Linear memory cost Objects 2 pass Approximative erosion Exact erosion 1 pass Visibility pre-computation

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62 Approximative erosion Voxelisation of object –Volumetric information [SDDS00] –Suitable representation [DM01] Erosion on voxels –Simple –Robust and fast

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63 Voxelisation

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64 Voxelisation

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65 Voxelisation

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66 Erosion of voxels by a cube = © = ©©

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67 O ª ( X © Y ) = ( O ª X ) ª Y = ª ª ª ª Erosion of voxels by a cube

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68 Erosion 1D Of half a voxel Direction of erosion Topological change

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69 Erosion 1D Of half a voxel Direction of erosion Of less than a half Topological change Topology preserved

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70 = ª ª ª ª Aligned axis Erosion of voxels by a cube

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71 Erosion of voxels by X convex Cellule X voxels If X ½ Y then O ª Y ½ O ª X ª Internal erosion ) ª External erosion )

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72 Demo Erosion of voxels Visibility pre-computation

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73 Conclusion Formalism and new theorem –Érosion of occluders and occludees Per object voxelisation –Optimized orientation –Do no discretize empty spaces Working in image space –Implicit fusion of umbrae –Acceleration Hardware : graphic cards Software : combining with other visibility algorithm

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74 Ext step… We know what is visible How to display it?

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75 Summary Context Visibility computation –Previous work –Contributions Level of details –Previous Work –Billboard clouds Conclusion

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76 Level of details Mesh simplification Clusterisation [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] Re-tiling [Tur92] Voxel based reconstruction [HHK+95] Multiresolution analysis [EDD+95] Superfaces [KT96], face cluster [WGH00]

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77 Limitations Constraints on models Erreur contrôle –Simplification enveloppes [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 –Sillouhette Clipping [SGG+00]

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78 Alternative rendering Image based rendering –Lightfield,Lumigraph [LH96,GGRC96] –Imposteurs [DSSD99] –Relief Textures [OB00] Point based rendering –Surfels [PZBG00] –Pointshop 3D [ZPKG02]

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79 Summary Context Visibility computation –Previous work –Contributions Level of details –Previous Work –Billboard clouds Conclusion

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80 Billboards cloud New representation Used for extreme simplification

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81 Billboard Classical solution [RH94] Generalising to many planes Automating synthesis

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82 Overview Approaching shape by a set of plane Projecting model on those planes ) textures Textures interleaving replace the object

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83 Principle polygonal 3D model

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84 Principle Simplification by planes

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85 Principle Moving vertices Maximum allowed displacement for P P

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86 Principle Projecting polygons on planes Polygon Valide plane

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87 Principle How many planes? Which planes?

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88 Overview It is an optimisation problem Measuring plane interest Traversing the space of planes Finding a set of planes

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89 Overview It is an optimisation problem –Greedy algorithm Measuring plane interest Traversing the space of planes Finding a set of planes

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90 Optimisation We define over the set of Billboards clouds: –An error function –A cost function Two goals –Budget-based cost fixed minimising error –Error-based max error fixed minimising cost

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91 Optimisation We define over the set of Billboards clouds: –An error function –A cost function Two goals –Budget-based cost fixed minimising error –Error-based max error fixed minimising cost

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92 Optimisation Cost function –Number of planes Error function –Vertex displacement In object space In image space

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93 Overview It is an optimisation problem –Greedy algorithm Measuring plane interest –Defining a density function Traversing the space of planes Finding a set of planes

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94 Replaces a lot of faces Fonction de densité Important plane = low cost Density function over The space of planes density = measure of the amount of faces that a plane can replace

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95 Validité Faces for which a plane is valid –Enforces the error bound Density = number of valid faces Allowed displacement Density de 3

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96 Validité Allowed displacement Density of 3 Faces for which a plane is valid –Enforces the error bound Density = number of valid faces

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97 Contribution Ponderation by projected area –Favor large faces –Favor planes parallel to faces

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98 Overview It is an optimisation problem –Greedy algorithm Measuring plane interest –Defining a density function Traversing the space of planes –discretisation Finding a set of planes

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99 Discretisation Discretisation of plane space Hough transform ρ φ θ (θ,φ)(θ,φ) O ρ primaldual H

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100 Dual space planes through a point ) a sheet φ θ ρ

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101 Plans through a sphere ) a slice φ θ ρ Dual space

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102 Plans through a sphere ) a slice Planes through 3 spheres ) intersection of 3 slices φ θ ρ Uniform discretisation Dual space

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103 Cumulated density

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104 Overview It is an optimisation problem –Greedy algorithm Measuring plane interest –Defining a density function Traversing the space of planes –discretisation Finding a set of planes –Refinement

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105 Greedy iteration Faces Plane space Planes valid for the face Discretisation

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106 Faces Plane space Planes valid for the face DiscretisationDensity + - Greedy iteration

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107 Faces Planes valid for the face Density + - Plane space Discretisation Greedy iteration

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108 Faces Planes valid for the face Density + - Plane space Discretisation Greedy iteration

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109 Faces Planes valid for the face Density + - Plane space Discretisation Greedy iteration

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110 Faces Planes valid for the face Density + - Plane space Discretisation Greedy iteration

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111 Faces Planes valid for the face Density + - Plane space Discretisation Greedy iteration

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112 Faces Planes valid for the face Density + - Plane space Discretisation Greedy iteration

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113 Faces Planes valid for the face Density + - Plane space Discretisation Greedy iteration

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114 Faces Planes valid for the face Density + - Plane space Discretisation Greedy iteration

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115 Cell of highest density Faces for which cell is valid Greedy iteration

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116 High density There is probably a plan valid for all the faces How to find such a plane? Greedy iteration

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117 We test central plane We subdivide Local density recomputation Greedy iteration

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118 Texture synthesis To each plane is associated a set of faces Orthogonal projection on plane Minimal bounding rectangle (CGAL) Orthogonal rendering ) texture

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119 Results Movies ExamplesShadows

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120 View-dependent extension Changing the error function –Reprojection error P-P- M P+P+ viewcell V T θ

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121 View-dependent extension Textures rendered from viewcells center Automatic selection of resolution Saving the projection matrix

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122 Results Close zoom View from the cell Billboards cloudpolygonal model

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123 Middle Range Results zoom View from the cell Billboards cloudpolygonal model

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124 Far Results zoom View from the cell Billboards cloudpolygonal model

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125 Conclusion New representation Automatic construction Arbitrary models Simple error criteria / no parameter Extreme simplification

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126 Extensions Optimising texture usage –Integration to the cost function –Texture compression Re-lighting –Normal maps –Pixel shading Transition Moving objects

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127 Summary Context Visibility computation –Previous work –Contributions Level of details –Previous Work –Billboard clouds Conclusion

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128 Conclusion New tools for the studied proble, Visibility computation –Theoretical results –Practical algorithm easy to implement Level of details –New representation / Algorithm for construction –Extreme simplification / handling of attributes Integration

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129 Questions

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Division ÷ 1 1 ÷ 1 = 1 2 ÷ 1 = 2 3 ÷ 1 = 3 4 ÷ 1 = 4 5 ÷ 1 = 5 6 ÷ 1 = 6 7 ÷ 1 = 7 8 ÷ 1 = 8 9 ÷ 1 = 9 10 ÷ 1 = 10 11 ÷ 1 = 11 12 ÷ 1 = 12 ÷ 2 2 ÷ 2 =

Division ÷ 1 1 ÷ 1 = 1 2 ÷ 1 = 2 3 ÷ 1 = 3 4 ÷ 1 = 4 5 ÷ 1 = 5 6 ÷ 1 = 6 7 ÷ 1 = 7 8 ÷ 1 = 8 9 ÷ 1 = 9 10 ÷ 1 = 10 11 ÷ 1 = 11 12 ÷ 1 = 12 ÷ 2 2 ÷ 2 =

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