I am not a math-guy, but I sure enjoyed viewing the animations on this page: Bézier curves. The External Links section seems to point to possible sources of algorithms, some of which might be in code-form. I don’t know if code is what you’re asking for, Guillaume, but that jsDraw2d library might be useful for design ideas, even though it’s not C/C++.
I suppose a C/C++ library that wraps OpenGL would be what you’re looking for, optimally. Given that drawing smooth curves is such a core problem, there must be a GPL’ed library out there already.
No problem. I found that article while researching for my own path-following music project.
I just remembered that the above article is about creating closed curves. You probably also want to be able to make open ended smooth Bezier curves. Here is the companion article that covers open curves: