2D Vector Graphics From 3D Parametric Surfaces

I want to build a renderer that can display 3D BREP style models as 2D vector graphics.

I can kind of see how this would be done with flat faces, just project onto a different plane, but 3D surfaces? It’s not hard to imagine a situation where you could see both sides of a 3D surface at once, which means that you’d have to figure out how to draw geometry that might not explicitly exist in the face.

Such a renderer would be all math. I don’t think it would even utilize the GPU.

Is there a name for this kind of thing? I’ve been searching, but I’m not even really sure what I’m searching for.

Any tips or info would be greatly appreciated.

Thanks