incremental grid-like layout using soft and hard ...skieffer.info/talks/gd13slides.pdfincremental...

Incremental Grid-Like Layout Using Soft and Hard Constraints

or...Grids for Dunnart

Steve Kieffer, Tim Dwyer, Kim Marriott, Michael WybrowMonash University

Graph Drawing 2013, Bordeaux, 23-25 Sep

Wednesday, 25 September 13

Grids for Dunnart?


Grids StressMinimization

Can Dunnart have grids?

+ =

Why? How?

grid-snapforce

withconstraints

withforces

axis-aligned edges

⇓

Problems Problems ProblemsWednesday, 25 September 13

Why use a grid?

•People like grid layouts?

•Grids promote:

•Alignment

•Nonoverlap

•Distribution


Nodes are either aligned

or not aligned

never almost aligned

Alignment


Nonoverlap

If grid is coarse enough, promotes nonoverlap of nodes.


Distribution

Nodes are distributed

or not

and there is a“global quasi-distribution”

L 2L


Objection: Dunnart already provides for alignment,nonoverlap, and distribution, using constraints.

Reply: We want a more flexible apparatus, whichis more like “snap-to-grid” when used interactively.




+ =

Why? How?

grid-snapforce

withconstraints

withforces

axis-aligned edges

⇓


How are grids used in VGEs?

• “snap-to-grid” tool

• “snap lines” tool

• align, and distribute, but not globally


Most obvious approach:add a “snap force”


snap force:


Problem: snap force and basic stress compete

So you can untangle OR land on grid, but not both.


Solution?

Selectively deactivate grid-snap forcein response to user dragging.

Can make it local?




+ =

Why? How?

grid-snapforce

withconstraints

withforces

axis-aligned edges

⇓


Stress MinimizationPick an ideal distance L between neighbouring nodes.


≈2L

≈3L≈L

Stress MinimizationPick an ideal distance L between neighbouring nodes.Then nodes separated by n links should be placedat a distance of about nL.


≈2L

≈3L≈L

Stress MinimizationPick an ideal distance L between neighbouring nodes.Then nodes separated by n links should be placedat a distance of about nL.

Deviation is measuredby the stress function:


Stress MinimizationSo when stress is minimized, neighbours are nearby

(under ideal conditions).

High stress Low stress


Putting it together

Low stress (neighbours nearby)Grid placement

Preferred placement pattern

⇒Wednesday, 25 September 13

One Consequence:

Preferred placementpattern

⇒Axis-aligned edges(where possible)

Note: this abandons global quasi-distribution.




+ =

Why? How?

grid-snapforce

withconstraints

withforces

axis-aligned edges

⇓


Adaptive Constrained Alignment (ACA)

Idea: - make edges H- and V-aligned - don’t create node-edge overlaps - preserve FD shape if possible - make long H- and V- chains instead of bends



Greedy algorithm: Choose “best” edge, and axis-align it. Stop when any further alignment would create an overlap.where “best” = closest to axis-aligned already (preserve FD shape) - but - postpone alignments that create bends until no others remain



Problem: As alignment constraints are added, node-edge overlaps can be created and enforced if orthogonal ordering of nodes changes.



Solution: Apply a separation constraint along with each alignment constraint, in order to preserve orthogonal ordering.


Problem

Constraints make graph too rigid.


Idea: Want to use Lagrange multipliers (LM) to automatically remove ACA’s constraints when the

“tension” on them becomes great enough.

Problem: How to compute the right thresholdfor the LMs?

Is it a function of the number of nodes?

The number of edges?

The number of constraints currently in force?

Not just the number of these things, but their configuration?




+ =

Why? How?

grid-snapforce

withconstraints

withforces

axis-aligned edges

⇓


Node Snap (NS)

Idea: Allow the user to align edges interactively, by making neighbouring nodes snap into alignment with one another.

Node snap force:


Idea: Make potential energy wells positioned relativeto nodes; let them move when nodes move?

Problem: Can we recover global quasi-distribution?




+ =

Why? How?

grid-snapforce

withconstraints

withforces

axis-aligned edges

⇓


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