trying to find the ease in out function that matches this curve.
it's none of the usual suspects (smooth step or cubic (or any other simple polynomials), I can split it into to 2
bezier solutions but was wondering if there was anything else ?
looks like 2 curves to me? be interesting to know the maths behind making it.
Sigmoid-ish?
anyone interested the raw data is here it's quite noisey as it was converted from a bitmap
The Weibull failure curve gives a similar 'S' shaped curve.
y = 1 - e^(-(x/x0)^m))
You might need to offset your x values to get a decent fit, and might have to compute x>0 and x<0 separately.
[edit - I suspect this is also a sigmoidal curve. Must be cleverer...]
got a result that will do, a 2 bezier solution but the maths isn't pretty 🙂
series 2 is what my function generates and a graphical illustration...
the top is the original, and the bottom my "reverse engineered" variant
found the exact maths in the end turns out it's 2 "scaled" smoothstep functions back to back.
Ahh, so I wasn't miles off as a smoothstep is "sigmoid like" according to Wikipedia.
https://en.m.wikipedia.org/wiki/Smoothstep
That’s a pentic polynomial. X^5 will be the highest power. Beware of the function outside the bounds of interest for extrapolation. I’ve fitted a lot worse
be interesting to know the maths behind making it.
the solution i'm going with is....
where t >= 0 and t <= 1
fn hermite t a b = (3 * pow t a - 2 * pow t b) -- variation on smoothstep
fn ease_in_out t =
(
if t <= 0.5 then
0.5 * hermite (t * 2) 1.5 2.15
else
1 - 0.5 * hermite ((1 - t) * 2) 1.5 2.15
)
Unexpected maths content.
What language is all of the above written in? Is it English? 😉
Out of interest, what line of work needs to know this stuff?
This sort of thing scares me, we studied this sort of maths at uni to earn a degree in my (now) line of work.
These days though if I use any maths above high school level I tend to suspect I've done something wrong, I dread the day somebody expects me to understand any of the above 😬
Out of interest, what line of work needs to know this stuff?
graphics/computer games etc
graphics/computer games etc
Ah, that figures. I got a C at O-level maths (worked hard for that, got a U the first time around!). Computing was never a thing at my school (mid-80s). I feel a whole strata of computing society moved on without me realising. Is it just me...?