1. Simplified Representation of Vector Fields
Alexandru C. Telea
Jarke J. van Wijk
Eindhoven University of Technology
The Netherlands

2. Overview Why simple vector field representation?
Vector field visualization
Simplification
Setting the parameters
Applications
Ongoing research

3. Problems:
how to visualize large 2D/3D fields ?
how to convey information to non experts ?
how to easily produce visualizations ?

4. Goal:
We desire to obtain an image that:
is effective
is compact (simple)
offers local and global insight
is produced automatically

5. Show a vector field with a few arrows
Solution
Show a vector field with a few arrows
Method
But how?
dataset
visualization

6. 1 Existing Methods Icon-Based Methods
(hedgehogs, glyphs, flow icons) visual clutter for large datasets
undersampling may cause aliasing
arrows are easily interpreted by large public

7. 2 Existing Methods Texture-Based Methods (spot noise, LIC)
lack directional information
may produce noisy images for complex flows
give good global insight
easy to generate automatically

8. 3 Existing Methods Advection-Based Methods
(stream/streak lines, flow tubes, particles)
require strong user input for advection seed point placement
results highly dependent on seed point choice
give good local insight

9. 4 Existing Methods Feature Extraction / Tracking Methods
(vortex detection, selection expressions)
highly dependent on seed point choice
require user input on which feature to select /track (often in the form of many parameters)
too abstract for some users
reduces dataset to a compact representation

10. 5 Existing Methods Topological Analysis
(vortex / critical point analysis and detection)
critical points may be too abstract for some users
unstable for fields with many singularities
reduces dataset to a compact representation

11. 6 Existing Methods Multiresolution Techniques
(Fourier / wavelet analysis)
if uniform sampling is used, can not convey both global and local insight
mostly used for scalar fields
reduced dataset can be easily visualized by other methods

12. Generate vector field visualizations:
Our Goal
Generate vector field visualizations:
automatically
combine local and global insight
show directional information
convey a simple and intuitive perception of the vector field

13. A curved arrow is easily understood
perception
process
User sees
curved arrow
User perceives
vector field
An arrow carries a clear representation of the
direction and curvature of the vector field it suggests

14. Solution Simplify vector field in zones which are
representable by (curved) arrows
cluster
dataset
simplification
arrow icon

15. Algorithm: Initial dataset Cluster = Final root cluster Bottom-up
(16 cells,
16 clusters)
Cluster =
contiguous
set of cells
Final
root
cluster
Bottom-up
clustering

16. Create clusters of level 0 for all dataset cells
Algorithm:
Create clusters of level 0 for all dataset cells 1
Seek the two neighboring clusters that are most similar
Merge them into new cluster 2
Repeat step 2 until one cluster results. 3

17. Most Similar: error computation
Key operations
Most Similar: error computation
Merging of clusters A B C
Should A be merged
with B or with C ? A B AB ?
How to compute
AB’s vector ?

18. Similarity computation
Clusters are compared by:
the direction and length of their vectors
the origins of their vectors
Cluster shapes are not used

19. Similarity computation
Direction and length comparison (s)
elliptic
similarity
isocontours
Origin comparison (t) 2
2
((x-l) 2)(2-2) + 2 (x-l)2 + (x-l)
s =
(2-2)
xo2
yo2
t = d2 e2
similarity = As + (1-A)t

20. How are clusters merged ?
Cluster areas are added
Cluster vectors are averaged A B
A+B AB

21. How do we use clusters for visualization ?
Use cluster tree to visualize the desired simplification level:
select all clusters for desired level
visualize selected clusters e.g. by an icon

22. Visualization Options
plain arrows
curved arrows (obtained by streamline tracing through cluster centers)
arrows on a spot noise textured background

23. More 2D examples...

24. … and 3D examples

25. Clustering Parameters
Two user-controlled
parameters:
A: favor clustering along similar directions vs similar origins
B: favor clustering along or across the vector field’s direction

26. Clustering Parameters
clusters
across
streamlines
clusters
along
streamlines
uniform
sampling

27. Clustering Parameters
Effect of the elliptic similarity function shape
Uniform field
clustering across (B=0)
clusteting along (B=1)

28. Examples original dataset default settings favor direction
favor origin

29. Examples
original dataset
hedgehog
Toroidal field
(vector icons)

30. Examples
favor direction
favor origin
Toroidal field
(curved arrows)

31. Air convection (kitchen.vtk)
Examples
Air convection (kitchen.vtk)

32. Examples Air convection (kitchen.vtk) straight and curved arrows
transparent clusters
grid
shrunk clusters

33. Implementation The simplification toolkit is implemented
in VTK and integrated
in the interactive
dataflow system
VISSION

34. Possible Extensions ? Convenience Conceptual
heuristics for controlling the clustering parameters
accelerate cluster pair search
introduce perceptual criteria for simplification

35. The End