The smooth(...) vex function - what's the maths behind it?

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Joined: 9月 2011
I need to be able to calculate where the midpoint of a smooth function will land for a given power. Or rather, the reverse - what power/rolloff to put in if I want the midpoint to land in a certain place.

I'm mucking about with CHOPs, generating my own channel data with Channel Wrangles and VEX. Lots of fun. I'm using the smooth() function to ease between values. It looks a bit like the smooth(start, end, amount, xxx) function works a bit like easep(xxx) function in the Animation Editor, with the power/rolloff parameter moving the transition forwards or backwards in time - values over 1 seem to be... uhh ... reciprocalated and inverted. Or something.

Ultimately I'd just like to work out how to "invert" the function, so if I want the midpoint of the smooth transition to land, say, exactly a quarter of the way through the transition, or exactly 2/3 of the way through, what power/rolloff I would need to use.

Any thoughts/pointers appreciated. Thanks
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