That's not quite what I meant when I said cubic are generally 3D. I'm saying that flat-span cubic Beziers are a tiny subset of possible general-span cubic Bezie

That's not quite what I meant when I said cubic are generally 3D. I'm saying that flat-span cubic Beziers are a tiny subset of possible general-span cubic Beziers. The degrees of freedom pertain to the _embedding dimensions_ (could be ten dimensions for instance, which gives each of the control points 10 DoF), but the _span_ of them can be no more than two (for quadratic) or three (for cubic), because there are only ever that many vectors involved respectively. The linked video is in fact one of the sources I had in mind when referring to "lerps of lerps" style of description, just stretched to half an hour with some auxiliary elaboration on what lerps-of-lerps means. Of course they are all still useful tidbits, but it is still fundamentally the same approach of defining an elephant as the sum of its legs and trunks, albeit with more details about said body parts, but still not saying what the thing _is_ from a more cohesive standpoint. By no means am I asserting "my way is the only way", rather the intent is to point out that the candidate explanations should offer something more than just disembodied _description_ of parts