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Data Visualization 2
Yasuhide Okamoto
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Digest
• Huge 3D data– Easy to obtain, Hard to visualize
Very Very huge!!
Good Sensors Huge 3D Data Too complex to process
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Solutions
Simplification using Quadric Error Metric
Progressive Meshes
Adaptive TetraPuzzles
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3D representation
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Why we use triangles?
• Planar• Convex• Simplest polygon
• Possible to represent accurate surfaces
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Rendering a triangle
1. Transformation of vertices
2. Rasterization
3. Texturing, Pixel shading
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Triangle is the only solution?
Triangles cannot be seen because they are too small…
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Another solution
• Everything is built up of atoms…
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Another solution
• Triangle -> Point
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Another solution
• Point based rendering
St. Matthew(127 millions triangles)
8 frame/sec 8 sec/frame
Points Triangles
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Merits of points
• Data simplicity– Triangles
• 3 vertices• 1 set of indices
– Points• 1 vertex• point size • (no connectivity)
(x0, y0, z0)
(x1, y1, z1) (x2, y2, z2)
(0, 1, 2)
(x0, y0, z0)
r
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Merits of points
• Processing cost– Triangles
• Projection of 3 vertices• Precise rasterization
– Points• Projection of 1 vertex• Simple rasterization
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Applications of point rendering
• Particle system
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Demerit of point rendering
• Rendering qualityPoints Triangles
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QSplat
• Point based rendering with LOD– Bounding sphere hierarchy
Szymon Rusinkiewicz, Marc LevoySIGGRAPH2000
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Data construction
• Input a triangle mesh• Place a sphere at each triangle, large enough
to touch neighbor spheres
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Creating a hierarchy
• Recursive splitting and merging
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Point tree
Leaf Node:Points in Original Resolution
Increase in data size…
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Hierarchical data compression
• Using relative values to the parent node• Quantization
Parent Node: Center (xp, yp, zp), Radius: rp
Child Node: Center (xp+kx*r, yp+ky*r, zp+kz*r), Radius: r*kr
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Node structure
Positionand
Radius
TreeStructure Normal
Width ofCone ofNormals
Color(Optional)
13 bits 3 bits 14 bits 2 bits 16 bits
6 bytes
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Position and radius
• Position and radius encoded relative to parent node
Positionand
Radius
TreeStructure Normal
Width ofCone ofNormals
Color(Optional)
13 bits 3 bits 14 bits 2 bits 16 bits
Center Offset
Radius Ratio
413notvalid,arenscombinatio7621only1313to
131asdrepresenteare),,,( rzyx
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Tree structure
• Number of children (0, 2, 3, or 4) – 2 bits• Presence of grandchildren – 1 bit
Positionand
Radius
TreeStructure Normal
Width ofCone ofNormals
Color(Optional)
13 bits 3 bits 14 bits 2 bits 16 bits
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Normal
• Normal quantized to gridon faces of a cube
Positionand
Radius
TreeStructure Normal
Width ofCone ofNormals
Color(Optional)
13 bits 3 bits 14 bits 2 bits 16 bits
52526
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Normal cone
• Normal cone: range of visible directions
Positionand
Radius
TreeStructure Normal
Width ofCone ofNormals
Color(Optional)
13 bits 3 bits 14 bits 2 bits 16 bits
1616,
169,
164,
161
• Quantizing cone’s width to
Visible Invisible
Visible
Invisible
Original Point (leaf node) Inner node’s point
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Color
• Per-vertex color is quantized 5-6-5 (R-G-B)
Positionand
Radius
TreeStructure Normal
Width ofCone ofNormals
Color(Optional)
13 bits 3 bits 14 bits 2 bits 16 bits
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Rendering algorithm
• Traverse hierarchy recursively
if (node not visible)Skip this subtree
else if (leaf node)Draw points
else if (size on screen < threshold)Draw points
elseTraverse children
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Data alignmentPosition
andRadius
TreeStructure Normal
Width ofCone ofNormals
Color(Optional)
13 bits 3 bits 14 bits 2 bits 16 bits
• Breadth-First Order=> Good for memory coherency
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Results of data construction
Model Input points Interior Nodes
Data construction
(min)
Output size(MB)
David’s head 2,000,651 974,114 0.7 18
David (2mm) 4,251,890 2,068,752 1.4 27
St. Matthew 127,072,827 50,285,122 59 761
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Comparing splat shapes
Same recursion level
Same rendering time
aliasing
Highest quality
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Comparing splat shapes
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Demonstration video
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Summary of QSplat
• Hierarchical representation using points
• High speed and high quality rendering for complex models
• Fast preprocessing• High compression rate
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Similar works
• Layered Point Clouds
QSplat --- Point based TreeTree Depth: log(n)
Layered Point Clouds --- Point Cloud based TreeTree Depth: log(n/k)
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Similar works
• Layered Point Clouds
![Page 35: Data Visualization 2 - 東京大学•Point based rendering with LOD –Bounding sphere hierarchy SzymonRusinkiewicz,Marc Levoy SIGGRAPH2000 Data construction •Input a triangle mesh](https://reader034.vdocuments.net/reader034/viewer/2022050608/5faee51bd6810c282b5498d1/html5/thumbnails/35.jpg)
Similar works
• POP– Hybrid method using Points and Polygons
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Similar works
• Combining Edges and Points
Edge & Point image Final image
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Far Voxels Enrico Gobbetti, Fabio MartonSIGGRAPH2005
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Tree structure
• Recursive Split• Make inner nodes in bottom up order
Leaf Node:Points or Triangles
in Original Resolution
Inner Node:•QSplat: A simplified point•LPC: A group of simplified points•TetraPuzzles: A group of
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Tree structure of Far Voxels
• View Dependent Voxels for inner nodes
View dependent voxel
Leaf Node:A group of Triangles
in Original Resolution
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Construction of tree structure
• Recursive split of bounding boxes along the longest axis
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Define inner nodes
• Bottom-up order construction• Assign a voxel grid from the bounding box
to each inner node
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Sampling
• Define “View-Dependent Voxel” for each grid
Sampling Fitting
Voxel Context Sampled Voxel VView Dependent Voxel
C(v) = (r, g, b)
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Sampling by ray casting
S
d
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Recursive sampling
S
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Simpler representation
• The representation of View-Dependent Voxelis still complex…
• Classify VDVs to simple Parametric Shaders– K1: Flat Shader– K2: Smooth Shader
V
C(v) = (r, g, b)
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Parametric shaders
• K1: Flat Shader– 1 Normal & 2 Colors
• K2: Smooth Shader– 1 Primary Normal & 6 Colors
K1 K1 K1
K1 K1
K1 K1 K1
K1
K2
K2
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Parametric shaders
Yellow :K1 (Flat Shader)Red :K2 (Smooth Shader)White :Leaf (Original Triangles)
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Rendering process
if (node not visible)Skip this subtree
else if (leaf node)Draw triangles
else if (size on screen < threshold)Draw VDVs or triangles
elseTraverse children
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Asynchronous I/O & renderingif (node not visible)
Skip this subtreeelse if (leaf node)
Draw triangleselse if (size on screen < threshold)
Draw VDVs or triangleselse if (children are not loaded on memory)
Draw VDVs or trianglesRegister children to Fetch Queue
elseTraverse children
Rendering Process
while (Nodes exist in Fetch Queue)Load Nodes on memory
I/O ProcessFetch Queue
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Demonstration movie
![Page 51: Data Visualization 2 - 東京大学•Point based rendering with LOD –Bounding sphere hierarchy SzymonRusinkiewicz,Marc Levoy SIGGRAPH2000 Data construction •Input a triangle mesh](https://reader034.vdocuments.net/reader034/viewer/2022050608/5faee51bd6810c282b5498d1/html5/thumbnails/51.jpg)
Results
ModelInput Data Output Data Frames/sec
Triangle DataSize
Construction time
Data Size Min Avg
St. Mathew 372M 14.5GB 14592 sec 10.6GB 9 45
Boeing 777 350M 13.7GB 16461 sec 14.9GB 8 44
Isosurface 472M 18.4GB 23751 sec 16.1GB 7 34
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Summary of Far Voxels
• Using Triangles and View-Dependent Voxels
• Simple sampling and classifications for VDV– Recursive sampling by ray casting– Classification to Flat & Smooth shaders
• Real-time rendering – Simple voxel shading – Asynchronous I/O processing
![Page 53: Data Visualization 2 - 東京大学•Point based rendering with LOD –Bounding sphere hierarchy SzymonRusinkiewicz,Marc Levoy SIGGRAPH2000 Data construction •Input a triangle mesh](https://reader034.vdocuments.net/reader034/viewer/2022050608/5faee51bd6810c282b5498d1/html5/thumbnails/53.jpg)
Summary
• Data visualization methods for huge 3D data– Triangle(Polygon) based methods
• Mesh Simplification• Progressive Meshes• Adaptive TetraPuzzles
– Point & Another Primitive based Rendering• QSplat• Far Voxels
![Page 54: Data Visualization 2 - 東京大学•Point based rendering with LOD –Bounding sphere hierarchy SzymonRusinkiewicz,Marc Levoy SIGGRAPH2000 Data construction •Input a triangle mesh](https://reader034.vdocuments.net/reader034/viewer/2022050608/5faee51bd6810c282b5498d1/html5/thumbnails/54.jpg)
Papers• “Surface Simplification Using Quadric Error Metrics”, Michael
Garland, Paul S. Heckbert, SIGGRAPH’97• “Progressive Meshes”, Hugues Hoppe, SIGGRAPH’96• “Adaptive TetraPuzzles – Efficient Out-of-Core Construction
and Visualization of Gigantic Polygonal Models”, Paolo Cignoniet al., SIGGRAPH2004
• “QSplat: A Multiresolution Point Rendering System for Large Meshes”, Szymon Rusinkiewicz, Marc Levoy, SIGGRAPH2000
• “Far Voxels – A Multiresolution Framework for Interactive Rendering of Huge Complex 3D Models on Commodity Graphics Platforms”, Enrico Gobbetti, Fabio Marton, SIGGRAPH2005
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Additional Papers
• “Layered Point Clouds”, Enrico Gobbetti, Fabio Marton, Eurographics Symposium on Point-Based Graphics 2004
• “POP: A Hybrid Point and Polygon Rendering System for Large Data”, Baoquan Chen, Minh Xuan Nguyen, Conference on Visualization 2001
• “Combining Edges and Points for Interactive High-Quality Rendering”, Kavita Bala et al., SIGGRAPH2003
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AnnouncementBefore12/17 Data Processing(1) (Prof. Oishi)1/7 Data Processing(2) (Prof. Oishi)1/14 Patch-based Object Recognition(1) (Prof. Kagesawa)1/21 Patch-based Object Recognition(2) (Prof. Kagesawa)
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