In addition to that a parallel curve is not necessarily in the same class as the original curve. For example the parallel curve of a cubic Bézier is itself not

In addition to that a parallel curve is not necessarily in the same class as the original curve. For example the parallel curve of a cubic Bézier is itself not expressible as a cubic Bézier. So, while the translation of a curve is pretty simple the parallel curve can get tricky to deal with analytically. A good source for this kind of stuff is also Knuth' work on Metafont, even if Metafont iself completely side-steps these issues by just painting many circles along the original curves to produce the parallel.