Quote - for parabolas the general form of the equation y = ax^2 + bx + c can be solved for 3 points and a matrix used to solve for a,b,c.  with those you can solve for the vertex, or just use a  range of x  in the equation for the start and end points of the chain.   

For the hyperbolic cosine I have no idea, but I would expect it to be similar. 

Umm.  :unsure:  Okay.  :lol:

My apologies, but I think your math skills are so far beyond mine that I'm not quite sure what you've just said.    Can you provide a URL which could explain more fully, or a search term I could use to use Google to locate such a URL?

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Cage can be an opinionated jerk who posts without thinking.  He apologizes for this.  He's honestly not trying to be a turkeyhead.

Cage had some freebies, compatible with Poser 11 and below.  His Python scripts were saved at archive.org, along with the rest of the Morphography site, where they were hosted.