Bezier curves were invented to design physical objects (cars), but they were an idealized and simplified solution to enable CAD at the time computer were much less powerful. Ideally, CAD should put elastica curves as the first choice - but they are difficult to compute as they can diverge drastically when control points get too close, and there is sometimes more than one solution for a set of constraints.
Spiro curves were supposed to solve it but I am surprised to read here that even spiro fails to approximate elastica. Have you mapped where the limitations are?
For information, I am drawing boat hulls, and elastica would model the natural bend of wood/plywood/metal much better than bezier... Amateur naval designers really lack good tools to bridge the gap between ideal hydrodynamic forms and ease of construction, and there are still a lot of tiny but annoying adjustments when one planks the first hull.
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:
Comments
Bezier curves were invented to design physical objects (cars), but they were an idealized and simplified solution to enable CAD at the time computer were much less powerful. Ideally, CAD should put elastica curves as the first choice - but they are difficult to compute as they can diverge drastically when control points get too close, and there is sometimes more than one solution for a set of constraints.
Spiro curves were supposed to solve it but I am surprised to read here that even spiro fails to approximate elastica. Have you mapped where the limitations are?
For information, I am drawing boat hulls, and elastica would model the natural bend of wood/plywood/metal much better than bezier... Amateur naval designers really lack good tools to bridge the gap between ideal hydrodynamic forms and ease of construction, and there are still a lot of tiny but annoying adjustments when one planks the first hull.
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.