Experimental Analysis of the Accessibility
of Drawings with Few Segments
Philipp Kindermann Wouter Meulemans André Schulz
Visual Complexity
Number of geometric objectsEdges: 21
Segments: 21
Why?
1. Aesthetic
2. Path Finding
1. Aesthetic
2. Path Finding
Two graph classes:
sparse graphs and trees
sparse graphs and trees
Sparse Graphs Algorithms
ForceDirected
[Fruchterman & Reingold '81]
Well separated vertices Adjacent vertices close
[Fruchterman & Reingold '81]
Well separated vertices Adjacent vertices close
ForceDirFewSeg
Like ForceDirected... But we can straighten paths
Like ForceDirected... But we can straighten paths
Tree Algorithms
Tidier
[Reingold & Tilford '81], [Walker II '90]
[Reingold & Tilford '81], [Walker II '90]
Quad
[Rusu et al. '08]
[Rusu et al. '08]
FewSeg
[Hültenschmidt et al. '17]
Parallel levels
Parent centered
Specified angular resolution
Evenly spread out children
Heavy path decomposition
Min. number of segments
Heuristic area reduction
Min. number of segments
Heuristic area reduction
Task: Aesthetics
Task: Path Finding
Task: Furthest Pair
Hypotheses
ForceDirected
ForceDirFewSeg
H1: Path Finding
ForceDirFewSeg > ForceDirected
ForceDirFewSeg > ForceDirected
H2: Aesthetics
ForceDirected > ForceDirFewSeg
ForceDirected > ForceDirFewSeg
H3: Furthest Pair
FewSeg > Tidier > Quad
FewSeg > Tidier > Quad
H4: Aesthetics
Math/CS:
Other:
Other:
Tidier > FewSeg > Quad
FewSeg > Tidier > Quad
FewSeg > Tidier > Quad
Tidier
Quad
FewSeg
Stimuli
| Sparse Graphs | Trees | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Layout | ForceDirected | ForceDirFewSeg | Tidier | Quad | FewSeg | |||||||
| Type | ROME | Random | Balanced | Deep | Wide | |||||||
| Size | 20 nodes | 40 nodes | 20 nodes | 40 nodes | ||||||||
| Task | Shortest Path | Aesthetics | Furthest Pair | Aesthetics | ||||||||
| Rep. | 2 Rep. | 4 Rep. | 2 Rep. | 4 Rep. | ||||||||
| Tasks | ||||||||||||
| Users | 42 | 21 | 21 | |||||||||
92 tasks in total: split into three groups
84 users: distribute evenly among groups
Results
H1: Path Finding
ForceDirFewSeg > ForceDirected
ForceDirFewSeg > ForceDirected
ForceDirFewSeg
ForceDirected
ForceDirected
Results
H2: Aesthetics
ForceDirected > ForceDirFewSeg
ForceDirected > ForceDirFewSeg
ForceDirFewSeg
ForceDirected
ForceDirected
Results
H3: Furthest Pair
FewSeg > Tidier > Quad
FewSeg > Tidier > Quad
FewSeg
Tidier
Quad
Tidier
Quad
| = : | p > 0.05 |
| ≤ : | p < 0.05 |
| < : | p < 0.01 |
| ≪ : | p < 0.001 |
Results
H4: Aesthetics
Math/CS:
Other:
Other:
Tidier > FewSeg > Quad
FewSeg > Tidier > Quad
FewSeg > Tidier > Quad
FewSeg
Tidier
Quad
Tidier
Quad
Follow-up study:
576 extra responses
576 extra responses
Conclusion
ForceDirected
ForceDirFewSeg
H1: Path Finding
ForceDirected > ForceDirFewSeg
(except random large)
ForceDirected > ForceDirFewSeg
(except random large)
H2: Aesthetics
ForceDirected ≥ ForceDirFewSeg
ForceDirected ≥ ForceDirFewSeg
H3: Furthest Pair
Tidier ≥ FewSeg > Quad
Tidier ≥ FewSeg > Quad
H4: Aesthetics
Math/CS:
Other:
Other:
Tidier > FewSeg > Quad
FewSeg > Tidier > Quad
FewSeg > Tidier > Quad
Tidier
Quad
FewSeg