Historic boat-building has little to do with nurbs or Bézier curves.

It is true that a boat is a curved shape (as were cars or aeroplanes before the mathematical models were devised) but the construction is quite different. To state the obvious, there are no control points. Instead you get some cross-sections for various different planes, then scale it up and manually try to achieve G2 continuity by comparing the points described in multiple places in the plan (ie in different cross sections from different but intersecting planes), adjusting them, and springing batons to create curved lines. You get different shapes depending on how thick/springy your baton is. Once more of the boat is built, the process continues with adjustments and baton-springing to try to ensure that curvature is continuous and it’s derivative is not too large.

But these plans would traditionally be produced by starting with a scale model for half the boat (often this model would be scaled up straight into the boat without plans in between). And traditional boat building (say 100 years ago) would often not be particularly true to the plans anyway, treating them much more as a guide (a case where this matters more is some of the traditional steel shipbuilding in Scotland where the yards were too small so boats were built in two halves then perfectly joined together at the end).

Now compare this to the OP which is about various mathematical models for curves and surfaces, and the comments above which talk about the history of those models. I think the automaker usage described above was about the problem of going from the computer-described curves to the real world and I guess CNC at the time couldn’t do it properly (you surely aren’t going to CNC-mill a car model out of a massive block of metal) hence transforming a computer description into something suitable for a physical model—fixed lengths of spring steel plus weights. Spring steel sounds a bit like springing batons but I think that is where the connection ends and I think this connection has little to do with the rest of this reply chain.

Though to be honest I’m not particularly sad that you posted it.

Traditional boat builders obviously did not employ piecewise-rational parametric curves with off-curve control points.

But they did use physical splines to draw smooth curves long before car/airplane designers.

Yes, and citroen used those same splines like boat builders, but they developed mathematical models based on those physical splines so that computers could draw and execute accurate physical items. That's what grandparent comment is about.

I didn't know that; that's a great video, thanks! I'm crazy jealous of his workshop.

The whole series is great and he releases videos every two weeks. The shop in that video he was able to use thanks to a nice couple who own it. He's since had to move the boat as a neighbor complained about him and he's in the Port Townsend shipyard.