Disclaimer, late in the night and math do not mix well. Its been a while since I looked at splines, but (if I recall correctly) the points list of points do no

Disclaimer, late in the night and math do not mix well. Its been a while since I looked at splines, but (if I recall correctly) the points list of points do not fully define the curve (even for quadratic splines). One common approach to uniquely define a spline is to add the additional requirement that the derivative of the curve be 0 at the endpoints. If you define it in such a way that the derivative of the end point is the same as that point on the original curve, then I think you will get a curve with the property you are looking for. However, I cannot think of a natural way of defining such a curve that does not amount to remembering the original curve. I suppose, depending on your use-case, when you move the point, you can compute the new derivative then forget about the old curve entirely; but I still don't see the advantage over remembering the old curve.