I'm asking for not-faceted models guidance

Hello there.
I’m aware that it’s a broad matter that can hardly fit in a topic but I appreciate any help of any kind, be it related to math, design, programming etc.

I’m looking for a way to create and render continuous curves (splines) and surfaces not made up of segments/faces but rather parametric, CAD-like.
I don’t know how to approach this so I need some guidance.
I’m a OpenGL beginner but I know my way around here and there. I know of some glu NURBS functions but what I’m after is the curves / surfaces actually pass through the given points.
So since I don’t know of such a library, I thought I could do the whole thing myself. But please, don’t let me struggle with it if there’s a lib already.

I’d start from an interpolation function of G2 continuity (has 2nd derivative = 0(?)) like natural cubic spline. What interpolation functions does OpenGL have? I prefer the function isn’t in GLSL but if there’s one in there, I probably have to implement the logic in a shader.
But how am I going to render something that’s not comprised of faces?

I’m hoping for an already existing library, as I said.

Please, a moderator move this in a more appropriate section, I misplaced the thread :doh: