algorithmic modeling for Rhino
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You could define a vector for each catenary? Two examples attached do so, the second one remaps the length values by vector length a bit so it's more even (if you look at a cross section through the centre you can see that the first option gives a strange kink).
Alternative option for the 3 point, although I don't think it's right option for this, would use a 3 point arc and scale the middle geometry. This is not to be confused with a catenary though.
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