I am interested in building a program to accomodate the following workflow:
A user begins with an arbitrary vector/CAD shape, which they wish to transfer onto paper without using a printer (there are both realistic and novelty reasons why this problem is interesting to me). The program will accept this file and create a list of instructions to draft the shape using ruler, square, compass, and standard curve forms. I am not currently concerned with the details of this program (file formats, types of vector curve [spline, bezier, etc], output formatting, etc) but with the core geometric description problem. I think it is fairly straightforward to accomplish this with straight lines, angles, and offsets.
However, I am not sure how to approach the problem of curve fitting. Ideally, the user would be able to have curves in the cad file fit (probably approximated) so that they may draft them using standard French curve forms, including:
Assume that these curves are made to standard shapes and sizes and are modeled with dimensional accuracy. Furthermore, they are ruled at specific points and a user can place them on the paper diagram at specific positions and angles (relative to the other elements in the diagram that have already been drafted).
What would be the first steps towards solving this problem? Are there existant computational geometry methods for approximating curves with (segments and combinations of) standard forms? What literature would I want to read? I apologize for the somewhat open-ended nature of this question, but it's difficult for me to determine where to begin.
If it's helpful, the CAD patterns are probably such that the curves can, in fact, be very closely approximated with just one or two of these shapes - the primary use would be for fashion pattern drafting, and these French curves are specifically designed for creating the geometry of flat patterns that fit a human body.