I'm in Dagstuhl this week for a workshop on Drawing Graphs and Maps with Curves. I gave a talk today surveying the use of curved edges in graph drawing, which may be older than you might think. For instance, did you know that arc diagrams, named from a 2002 paper by Wattenberg in information visualization, actually go back to two papers from the 1960s on crossing minimization? Here are my talk slides.


Great slides! Thanks for sharing!!
The power of using graph drawings is illustrated by the notion of wiring diagrams developed by Jacob Eli Goodman ( Goodman, Jacob E. (1980), "Proof of a conjecture of Burr, Grünbaum, and Sloane", Discrete Math. 32: 27–35.) and exploited by him and Richard Pollack, as well as many others in studying arrangements of lines and pseuduolines.
Yes, wiring diagrams are definitely a helpful way of visualizing arrangements. (I have a graph drawing paper I've been working on, not yet released, that involves them, and I know of another one by some other authors that does as well). So the "many others" will likely continue to grow.) They're usually drawn with polylines rather than curves, though, so they're not really a fit for my workshop talk.