Interpolation methods / Re-mapping with various curves (exponential / logarithmic, sinusoidal, etc) - add your tricks here...

hey, great idea! 🙌
here's another kind of circular for comparison, and then i had a weird obsession with sigmoid after taking a short course on neural networks so they're there as well(even though one doesn't map to the same normalized values it can be useful for infinitely large ranges like tanh), plus a bunch from here:
http://www.flong.com/texts/code/shapers_exp/
http://www.flong.com/texts/code/shapers_circ/

i'll probably finish up some more of the circ ones later along with these as well:
http://www.flong.com/texts/code/shapers_poly/
http://www.flong.com/texts/code/shapers_bez/
(unless someone else wants to have a go)

For everything here, they might need correct parameters entered before working correctly(just in case it needs mentioning).

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and then from here:
https://www.iquilezles.org/www/articles/functions/functions.htm
i've created them in audio versions because they're very interesting as envelopes:

but you can easily return them to event-mapping status by removing the tilde(~) from "gen~" and then cutting out the "+=" op along with everything above it(connecting "in 1" straight through to whatever the output of "+=" is connected to)...
(on the other hand, if you like the audio versions, i also recommend creating an inlet substituted for the 1 going into the input of "+=" as that can be thought of as a speed/length multiplier for the envelopes).

just to consolidate, too, there's also these threads somewhat related:
https://cycling74.com/forums/easing-and-tweening-how-to-make-a-tulip
https://cycling74.com/forums/sharing-is-caring-a-modest-set-of-gen-ified-easing-functions
https://cycling74.com/articles/content-you-need-the-ease-package

cheers🍻