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.