Edge bundling methods can be considered as a simple optimization of physical objects consisting of linear members (think of e.g. tree structures or network structures), with respect to the quantity of material used. Bundling together members of such a structure decreases their overall length and subsequently the overall mass, considering that close-together parallel members may be represented by a single profile. In this sense, arrangements produced by bundling may sometimes approach minimum Steiner trees of a given set of points.

This could specifically benefit the design of structures that do not bear significant loads but are required to reach large spans, e.g. lighting fixtures.

Edge Bundling methods can be based on the action of forces between linear members, as shown in (1). This renders them interesting in yet another way: Their result can be physically modeled by using flexible linear members of the right length and constraints between them. The result of such an effort may be seen in the photos that follow.

These models were realized using flexible cylindrical plastic elements (the ones used for architectural model-making) and cyanacrylate adhesive. There are 7 nodes and about 20 edges connecting the nodes. The form of the object was quite easy to achieve using temporary fasteners in order to simulate the attractive forces between the links. The flexibility and linear stiffness of the plastic elements did the rest of the job by itself.

Further studies on such bundling methods will be performed.

A form-finding applet, eerkit, that demonstrates force-directed bundling is also available.

References

(1) Holten, D., van Wijk, J., Force-Directed Edge Bundling for Graph Visualization