Elastica curves have only three parameters, compared with four for cubic Béziers, Spiro curves, and the new hyperbezier. The easiest way to understand that limitation is to consider the parallel curve of an Euler spiral. That has a built-in asymmetry, one end has higher tension than the other. But the math for elastica locks in odd symmetry around the inflection point.
I think hyperbezier would be a natural fit for boat hulls, but it's not a mathematically precise approximation to elastica either. I'd say to carefully evaluate it, and I'd very much like to hear how that goes.
ETA: "parallel curve of elastica" is an intriguing curve family to consider for this application, as it has the correct number of parameters and ticks a lot of the other boxes. However, the math for this is hard mode.
For reference, drawing lines for a wooden boat is still made with actual wood splines on the drafting table, held in place by heavy "ducks" or "whales". Here's what is looks like:
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Elastica curves have only three parameters, compared with four for cubic Béziers, Spiro curves, and the new hyperbezier. The easiest way to understand that limitation is to consider the parallel curve of an Euler spiral. That has a built-in asymmetry, one end has higher tension than the other. But the math for elastica locks in odd symmetry around the inflection point.
I think hyperbezier would be a natural fit for boat hulls, but it's not a mathematically precise approximation to elastica either. I'd say to carefully evaluate it, and I'd very much like to hear how that goes.
ETA: "parallel curve of elastica" is an intriguing curve family to consider for this application, as it has the correct number of parameters and ticks a lot of the other boxes. However, the math for this is hard mode.
Thanks for your reply.
For reference, drawing lines for a wooden boat is still made with actual wood splines on the drafting table, held in place by heavy "ducks" or "whales". Here's what is looks like:
https://dataphys.org/list/physical-splines/
https://www.core77.com/posts/55368/when-splines-were-physica...
That's especially true when taking the paper plans and drawing them (lofting) at scale 1:1 on the shop floor.