This document presents an approach for interactively rendering complex 3D treemaps with over 600,000 items. It generates geometry for treemap items using a GPU-based approach, representing each item as an attributed point cloud. This enables efficient rendering while using less memory than CPU-based approaches. The method culls invisible geometry, applies thematic mappings, and uses post-processing for styling. It outperforms existing techniques in rendering speed and memory usage. Future work could improve readability, apply new visualization techniques, and generalize the approach.

1. Interactive Rendering
of Complex 3D-Treemaps
Matthias Trapp, Sebastian Schmechel, Jürgen Döllner
Hasso-Plattner-Institute, University of Potsdam, Germany

2. Agenda
I. Motivation
II. Conceptual Overview
III. Implementation Details
IV. Results & Discussion
V. Future Work & Conclusions
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3. SECTION I
Motivation

4. 3D Treemap Example
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5. Related Work
 2D Treemaps [Shneiderman ’92, Bederson ’02]:
 Common technique for space restricted hierarchy
visualization
 Various layouting algorithms available
 3D Treemap / StepTree [Bladh, 2004]
 Can be used to map additional attributes of the data items
 Significantly better performance in interpreting the
hierarchical structure
 Preserve performance in interpretational/navigational
tasks
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6. Image-Synthesis of a 3D Treemap
Computation of 2D Treemap Layout
Mapping of Thematic Data to Treemap Items
Generation of 3D Rendering Primitives
Rendering/Rasterization of 3D Rendering Primitives
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7. 3D Treemap >600k Items
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8. 3D Treemap Item
Additional dimension =
additional complexity
 Observation: 3D treemap = 2.5D virtual
environment
 3-5 times more geometry required than 2D case
 Attributes for thematic mappings vary per item
 Number of items determines update performance
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9. Challenges for Complex 3D Treemaps
3D Treemap ~ geometrical complex
representation:
 High memory footprint in VRAM
 High run-time complexity for item updates
 High run-time complexity for layout
Efficient rendering depends on/is determined by:
 Rendering run-time complexity
 Update run-time complexity
 Client/Server memory consumption/space
complexity
 Goal: Reduction ofComplex 3D Treemaps :: Matthias Trapp complexity
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10. SECTION II
Conceptual Overview

11. Treemap Item :: Parameterization
 Goals:
1. Provide a small-as-possible memory footprint on client
2. Support fast client-server updates
 Layout-dependent attributes:
 2D item position & size (X, Y, W, H)
 Mapping-dependent attributes:
 Item color & item identity (R, G, B, ID)
 Item depth & Z-position (D, Z)
 Hierarchy Level (L)
 Binary flags, e.g., isLeaf, isVisible, isSelected,… (F)
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12. Treemap Item :: Buffer Mapping
Assumption:
mapping and layout are often modified separately
 Two separate buffers: layout and mapping buffer
 Can be updated separately and saves bandwidth
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13. Approach :: Overview
Three-stage deferred rendering process:
1. Generate and render attributed point cloud
2. Generate primitives & rasterize to G-Buffer (1 pass)
3. Apply post-processing techniques (1 pass)
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14. Approach :: Attributed Point Cloud
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15. Approach :: Generated Primitives
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16. Approach :: Thematic Mapping
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17. Approach :: Post Processing
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18. Approach :: Summary
 Fully GPU accelerated shape generation
 Render attributed point cloud and generate triangles
 Enables a compact representation of treemaps
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19. SECTION III
Implementation Details

20. Primitive Template
 Optimal GPU representation: 8 vertices + 12 indices
 Format: triangle-strip without swaps
 Omit bottom face of treemap item
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21. Emitter Function
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22. Culling Strategies
 Backface Culling:
 Goal: omit rasterization of back-facing primitives
 Performed using fixed-function pipeline feature
 Overhead if performed in geometry shader
 View-frustum Culling:
 Goal: omit shape generation for items outside the frustum
 Performed per-item in vertex shader
 Size Culling:
 Goal: omit rasterization of small treemap items
 Performed per-item in vertex shader
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23. Size–Culling using a Screen-Space Metric
a max p0 x ,, p7 x min p0 x ,, p7 x b max p0 y ,, p7 y min p0 y ,, p7 y
true a b
passSizeCulling
false otherwise
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24. Culling Implementation
bool passCulling(const in mat4 mvp, const in vec4 vertex, const in vec4 dimensions,
const in bool applyViewFrustumCulling, const in bool applySizeCulling)
{ float cPMaxX=-10000.0;float cPMinX=10000.0;float cPMaxY=-10000.0;float cPMinY=10000.0;
bool passCulling = true;
if(useViewFrustumCulling)
{ // 1. Do conservative culling and test only center of item
vec4 V = mvp * vertex;
passCulling=((-V.w<V.x)&&(V.x<V.w))&&((-V.w<V.y)&&(V.y<V.w))&&((-V.w<V.z)&&(V.z<V.w));
if(!passCulling)
{ // 2. Perform precise culling if item center is not in frustum
vec4 AABB[8];
for (int i = 0; i < 8; i++){
AABB[i] = mvp * (vertex + VERTEX[i] * dimensions);
vec4 p = AABB[i] / AABB[i].w;
p.xy = (p.xy + 1.0) * (viewport.zw * 0.5) + viewport.xy;
cPMaxX = max(cPMaxX, p.x); cPMinX = min(cPMinX, p.x);
cPMaxY = max(cPMaxY, p.y); cPMinY = min(cPMinY, p.y);
} //endfor
// 2. Perform precise culling if item center is not in frustum
int bounds[6] = int[6](0,0,0,0,0,0);
for(int i = 0; i < 8; i++){
if(AABB[i].x>AABB[i].w) bounds[0]++; if(AABB[i].x<-AABB[i].w) bounds[1]++;
if(AABB[i].y>AABB[i].w) bounds[2]++; if(AABB[i].y<-AABB[i].w) bounds[3]++;
if(AABB[i].z>AABB[i].w) bounds[4]++; if(AABB[i].z<-AABB[i].w) bounds[5]++;
}//endfor
for(int i = 0; i < 6; i++) if(bounds[i]==8) passCulling = false;
}//endif }//endif
// 3. Apply size culling if enable to every visible item
if(passCulling && applyViewFrustumCulling && useSizeCulling)
passCulling = ((abs(cPMaxX)-abs(cPMinX))*(abs(cPMaxY)-abs(cPMinY)))
> float(pixelSizeThreshold);
return passCulling;
}
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25. Deferred Stylization :: Overview
 Performed in post-processing: low per-fragment cost
 Can be customized to user demands/rendering
speed
 Rendering overhead: ca. 1-3 ms @ 720p
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26. Deferred Stylization :: Variances
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27. SECTION IV
Results & Discussion

28. Comparison of Approaches
Difference: Geometry generation on CPU vs. GPU
Utilized stage/approach has impact on:
 Bandwidth required (CPU  GPU)
 Main (CPU) and video (GPU) memory footprints
 Number of draw calls issued
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29. Existing Approaches
Vertex Buffer Objects (VBO):
 Generate geometry for each treemap item
client-side (CPU) and push to server (GPU)
 Index variant has low memory footprint and
leverage post-transform cache (~32 vertices)
 CPU bound for frequent treemap updates
Geometry Instancing (Pseudo, UBO, TBO)
Encoding of per-instance-data (PID) is bottleneck:
 Pseudo-Instancing: encode PID in shader constant
registers
 Uniform-Buffer Instancing: encode PID to L1-Cache
(~64K)
 Texture-Buffer Instancing:3Dencode PID to texture
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30. Rendering Performance
GPU: NVIDIA GTX 460 / CPU: Intel Xeon 2,79GHz
250
200
150
milliseconds
100
50
0
Pseudo UBO TBO Indexed Non-Indexed Intermediate
Shape Generation
Instancing Instancing Instancing VBO VBO Mode
13.884 0.38 1.68 1.47 1.49 0.63 1.37 5.12
98.858 1.75 6.28 4.01 4.01 3.42 8.67 35.45
365.645 6.15 27.49 15.91 14.93 12.57 32.35 133.05
614.920 14.76 60.88 31.12 31.51 28.46 54.71 220.01
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31. Memory Footprint :: Metric
 #Bytes for n treemap items with a attributes
 compression ratios for VRAM consumption:
 1:2.5 over indexed vertex representations
 1:3.75 over non-index vertex representations
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32. Memory Footprint :: Results
1E+09
10000000
10000000
1000000
100000
byte
10000
1000
100
10
1
CPU GPU CPU GPU CPU GPU CPU GPU
13.884 98.858 365.645 614.920
Shape Generation 444288 444368 3163456 3163536 11700640 11700640 19677440 19677520
Pseudo Instancing 444368 444368 3163536 3163536 11700640 11700640 19677520 19677520
UBO Instancing 444368 444368 3163536 3163536 11700640 11700640 19677520 19677520
TBO Instancing 444368 444368 3163536 3163536 11700640 11700640 19677520 19677520
Indexed VBO 1999296 1555008 14235552 11072096 52652880 40952240 88548480 68871040
Non-Indexed VBO 15439008 14994720 109930096 106766640 406597240 394896600 683791040 664113600
Intermediate Mode 444288 0 3163456 0 11700640 0 19677440 0
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33. Discussion
 Outperforms all existing rendering techniques:
 Pseudo & UBO Instancing are CPU bound
 TBO instancing is bound by L2-Cache performance
 VBOs probably transform bound
 Indexed VBO leverage post-transform cache
 Generation and instancing have similar memory footprint
 All approaches are not fill-limited
 Theoretical limits of the presented approach:
 ~2.5 million 3D treemap items at ~20 frames-per-second
 Equals 1 pixel-per-item at full HD resolution (1920x1080)
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34. SECTION V
Future Work & Conclusions

35. Future Work :: Reduce Overdraw
high overdraw low overdraw
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36. Future Work :: Reduce Overdraw
Independent Representation Interdependent Representation
A B
L2
Item Origin
L1
L0
Unnecessary Item Overdraw L ~ Hierachy Level of Item
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37. Future Work :: Improve Readability
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38. Future Work :: Concept Transfer
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39. Future Work :: Summary
Foundation for advanced visualization techniques:
 Animated transition between 3D treemap states
 Application of interactive focus+context lenses
 Multi-perspective views of 3D treemaps
Generalize approach for other treemap types:
 3D Voronoi treemaps
 Classical 2D (Voronoi) treemaps
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40. Conclusions
 Rendering technique for complex 3D treemaps
 Outperforms existing approaches w.r.t.:
 Rendering speed
 Memory requirements (client & server)
 Building block for GPU framework for 3D treemaps
 Stylization possibilities are limited (e.g.
,transparency)
 Potentials for future work
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41. Questions & Comments
Contact:
www.4dndvis.de
 Matthias Trapp
matthias.trapp@hpi.uni-potsdam.de
 Sebastian Schmechel
sebastian.schmechel@hpi.uni-potsdam.de
 Jürgen Döllner
juergen.doellner@hpi.uni-potsdam.de
Publications:
http://www.hpi.uni-potsdam.de/doellner/4dndvis/publikationen.html
This work was funded by the Federal Ministry of Education and Research
(BMBF), Germany within the InnoProfile Transfer research group "4DnD-Vis".
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