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You should be able to describe (within any reasonable tolerance) the same curve with a bezier, however the control points will obviously be different.

Any imperfections in the physical spline, say a knot if it's wooden, would translate to a slight curvature difference.

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Sounds like the physical curves are a subset of bezier? So there might be some bezier curves that cannot be replicated physically

Not really, you can just add more and more control points to a Bézier and it will be possible to describe a curve to a greater accuracy.

However, in reality when using Bézier curves you want to really want to use the minimum number of control point neccesery to ensure a nice smooth curve.

> Not really, you can just add more and more control points to a Bézier and it will be possible to describe a curve to a greater accuracy.

The more control points you add to your curve the more computationally expensive it becomes, though.

This is just the law of spline demand.

Excellently integrated pun!

I mean vice versa. Can the physical thing do any CAD Bezier?

A Bézier curve can have a cusp, which you can’t do with a physical spine.

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