Say I want to find a B/U-Spline that exactly interpolates some points. How would one go about doing that? Note that in this question, when I say B-Spline I don’t mean the canonical B-Splines, but rather B-Splines made via the U-Spline algorithm. My guesses:

- Bezier Projection magic
- Create an interpolatory spline (such as Lagrange spline) and then convert either to a B-Spline or first a Bezier spline then to a B-Spline

For example, say I want a B-Spline to *exactly* pass through these points:

```
x, y
0., 0.
0.349, 0.342
0.698, 0.643
1.047, 0.866
1.396, 0.985
1.745, 0.985
```

I would assume you could fit B-Splines of uniform degree up to N-1, as well as mixed degree B-Splines? What about smoothnesses?

Inspiration for this question comes from this publicly available document.