curves – points to B-splines to right segments?

I would like to create a smooth path between points in 3D, and I think this is usually done by B-splines, although it's not really a requirement.

The input is a set of points (about 10 to 20 of them) and the output must be another set of points, including a configurable number, basically describing a point-to-point path for easy interpolation to run, as well as guidance information. for the character who is on this path (although this can be deduced from the path itself).

This seems like a common problem, but I do not know what to look for?

No avoidance of obstacles, etc. it's not necessary.