To clarify, I meant B-splines _lack local control_ like Catmull-Rom splines, not that the latter is an instance of the former. Though indeed, all cubic splines are just cubic polynomials.
I disagree with your characterization that the proposed solution lacks local control, because edits only affect the segments in question, just like with a classic bezier. From the point of view of curvature handles, the handles you don't touch don't change. (The splitting of a curvature bezier is imo the best illustration of this.)
Re: the meaning of the scalars, I imagine they are derived similarly as the perpendicular-distance diagram in the post. If you plug bezier formulas into curvature formulas, a lot of terms cancel out.
To clarify, I meant B-splines _lack local control_ like Catmull-Rom splines, not that the latter is an instance of the former. Though indeed, all cubic splines are just cubic polynomials.
I disagree with your characterization that the proposed solution lacks local control, because edits only affect the segments in question, just like with a classic bezier. From the point of view of curvature handles, the handles you don't touch don't change. (The splitting of a curvature bezier is imo the best illustration of this.)
Re: the meaning of the scalars, I imagine they are derived similarly as the perpendicular-distance diagram in the post. If you plug bezier formulas into curvature formulas, a lot of terms cancel out.