One thing to consider is that a model train track segment does not necessarily represent a single vector. If you have a curved piece, you can make it model a left turn or a right turn depending on how you attach it to the end of an existing track. This means that the set of all the track pieces cannot be mapped 1…1 to a set of vectors.
Easily handled with Indistinguishible’s notation. If the left turning orientation is represented by (r,d) where r and d are complex numbers, then orientating the track to turn right will be represented by (r[sup][/sup],d[sup][/sup]) where r[sup]*[/sup] denotes the conjugate of r.