Trees and Cushions
Jack van Wijk
Eindhoven University of Technology
Treemap Workshop, May 31, 2001
HCIL, University of Maryland
InfoVis at Eindhoven
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Started 1998
Focus:
• Trees and graphs
• Large data sets
• Use of computer graphics knowledge
(textures, geometry, shading) to generate
more effective visualizations
Trees (T) and Cushions (C)
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T+C: Cushion treemaps (InfoVis’99)
T+C: Squarified treemaps (Vissym’00)
C: Voronoi diagrams (Vissym’01)
C: Enridged contour maps (Vis’01)
T: Botanical vis (InfoVis’01)
What next?
Cushion Treemaps
Visualization of Hierarchical Information
Jarke J. van Wijk
Huub van de Wetering
Eindhoven University of Technology
IEEE InfoVis’99
Insight in structure of large trees
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Why is my disk full?
What is our product portfolio?
How is this university organized?
Fuzzy questions: Visualization needed
Treemap (Shneiderman, 1992)
A16
G2
E1
H4
B3
C3
C3
D10
F2
I4
E1
F2
G2
I4 H4
Alternating directions, area represents size
1400 files
3060 employees
How to emphasize structure?
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Color?
Linewidth?
Nesting?
Shading?
Use shaded geometric model!
Ridges for more insight
Binary tree
Ridges
Ridge + rotated ridge = cushion
z = ax2 + bx + cy2 + dy + e
+
=
Standard treemap
Cushion Treemap
H = 0.75
level
H = 0.50
level
Demo
www.win.tue.nl/sequoiaview
May 21 2001: 45,000 downloads
Squarified Treemaps
Mark Bruls
Kees Huizing
Jarke J. van Wijk
Eindhoven University of Technology
Vissym’00, Amsterdam
Thin rectangles
(small leaves high in hierarchy
e.g., .cshrc)
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hard to compare sizes
hard to point at
waste of pixels
inaccurate size
How to avoid thin rectangles?
drop the single direction layout
(emphasize structure by other means)
Squarification algorithm
1. Start placing recs in one row
2. stop when aspect ratio stops getting better
3. repeat with remaining area and recs
Recursive per level (just like standard treemap
algorithm)
6
6
Squarification algorithm
4
6
4
6
6
6
3
2
6
aspect ratio: 8/3
4/1
3/2
2
1
6
6
6
6
4
9/4
etc.
6
4
6
3
49/27
4 3 2
9/2
6
2 2 1
6
4
3
25/9
Result of squarification
directory
Squarified organization
Shaded frames for structure
Frames for structure
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no maze running for the viewer
depth in structure as frame height
“remote cousins” are visibly separated by
indent
Organization
Directory structure
Visualization of Generalized
Voronoi Diagrams
Alex Telea, Jarke van Wijk
Vissym’01, Ascona
Cushions
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Cushions help to understand hierarchical
spatial tesselations of the plane
How about cushions to visualize
Generalized Voronoi Diagrams?
Generalized Voronoi diagrams
N=1
N=2
Polygon = area where N seeds are closest
Cushions and bevels
Cushions, bevels, color
N= 3 Cushions, bevels, color
Generalized Voronoi Diagrams
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Many other types (different distance
measures)
Applications
Enridged Contour Maps
Van Wijk & Telea, Vis’01, San Diego
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Given: Height field f(x,y)
Required:
• Qualitative (where are the ridges) and
• Quantitative (how high is this peak) info
Standard visualizations
Enridged height field ...
height(f(x, y))
linear mapping
non-linear mapping
f(x, y)
Height field
Soft, convex ridges
Strong, convex ridges
Soft,concave ridges
Climate (January)
Color: Temperature; Height: Precipitation
Climate (July)
Color: Temperature; Height: Precipitation
Dense contours (equid. in space)
With ridges...
Hierarchical ridges
Back to Trees:
Botanical Visualization of
Huge Hierarchies
Ernst Kleiberg, Huub van de
Wetering, Jarke van Wijk
InfoVis’01, San Diego
Idea
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Botanical trees are easy to understand, yet
contain a lot of branches and leaves
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Can we use ideas from botanical modeling
for InfoVis?
Strand model (Holton, 1994)
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Mimics vascular system
Each leaf is connected to one strand
Branch = bundle of strands
Rules define when a branch is split
First try:
 Each directory is a branch
 Each file is a leaf
Naive result...
Three problems
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Continuing branches are hard to see
Long, thin branches emerge
Leaves are messy
Smoothed continuing branches
Contract long branches
Files: Phi-balls (Lintermann,99)
One big file
Many small files
Botanical modeling
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Compact, natural visualization
Phyllotaxis = magic!
Many treasures to be discovered
Usability?
Botanical treemaps?
My treemap to-do list
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Non-rectangular shapes/subdivisions
• circles, polygons?
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Multivariate data
• color, texture?
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Applications
• genealogy, data mining?
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Evaluation