Very cool. I wonder if there could be an improvement in image quality if you added some form of lookahead, and chose the path that gives the best results. The branching factor would be horrendous, but I suspect that it could be pruned significantly using some A*-ish cost/ordering criterion.
You most definitely could! While experimenting with it it turned out however that the quality of the image is far more sensitive to the number of pins on the loom. And it is this that quickly escalates your branching factor.
Increasing the amount of pins thus resulted in a far better result for the same amount of computational power than the improved algorithm you propose.
True, but an increased number of pins is slower on the plotter and making the scaffolding is also harder. Plus it is easier to rewrap the loom better than to make a finer loom.
I suspect that a forward-look of 2 or 3 will give a noticeably better result, particularly if you combine it with the length-normalised score like was suggested by another commenter. Using a Dykstra algorithm and taking the first path that reaches length N should also keep the branching reasonable.
If you haven't seen it, there was something similar (algorithmically) for the FaceBull problem, which should still be kicking around online somewhere.
