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An interesting question, since you could record the positions of the whales, but that alone doesn't fully determine the curve. I guess you'd have to also record the distances along the spline between those pinned points.

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I think the pins aren’t ‘pinning’ specific points on the wood strips to specific locations, but just prevent the strip of wood from becoming a straight-lined strip of wood. The tendency of the strip of wood to straighten itself would provide enough force to make the wood slide along the pins to find the minimum energy solution.

(Edit: https://en.wikipedia.org/wiki/Flat_spline seems to confirm that)

Both types are used - pinning and sliding. See figure 3.19 in https://www.levien.com/phd/thesis.pdf

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