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How would I convert spline factor into a gaussian curve using math?

I am able to do it with a float curve but would like to make it parametric.

example with float curve:

EDIT: figured out how to implement 𝑦=−𝑥^2+𝑥 as nodes to get an arc. Still not sure how to flatten out the curve at the ends.

enter image description here

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It's just the slightly tedious business of converting the formula into Math nodes.

Here the curve is expressed in terms of μ, the mean, and σ, the standard deviation:

enter image description here

Here, (object-space) Y is set by the function, and the Spline Parameter maps X, but you could group it up and use it to set any other attribute..

enter image description here

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    $\begingroup$ Robin!!! You did write text in images! You must not do that. Quellenform just got a ruffle because of that (because he is "new" here). But i am sure you won't get a ruffle of that moderator because he ruffles only new guys....+1 great answer as usual ;) $\endgroup$
    – Chris
    Jul 21, 2022 at 5:27
  • $\begingroup$ @Chris :D I'm no good at mathjax, so I just grabbed the .SVG from Wikipedia and plonked it in the .blend file. It's not really part of the answer, so I just might get away with it....,🙏 $\endgroup$
    – Robin Betts ♦
    Jul 21, 2022 at 6:53
  • $\begingroup$ Sorry, wrote plus 1 but didn’t do it - just did it now🤦🏻‍♂️ $\endgroup$
    – Chris
    Jul 21, 2022 at 6:56
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    $\begingroup$ Thanks Robin! this works great, I can see now that I was way off. Definitely adding the node group as a present. $\endgroup$
    – special_frog
    Jul 21, 2022 at 8:07
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    $\begingroup$ @Chris i.stack.imgur.com/3bXvV.jpg $\endgroup$
    – quellenform ♦
    Jul 21, 2022 at 8:40

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