Dan, you can get close with a ease-in-ease-out function, aka easy-ease in AE.

Check out : http://abstrakt.vade.info/?p=132 the javascript in the Max/MSP 
patch potentially be of help, while it has some extra junk for Max/MSP, the 
basic math is in there, implemented in a similar way as to what you want.


On Mar 19, 2010, at 4:42 PM, Dan Winckler wrote:

> Thanks, Troy!  I don't need to draw the curve, actually -- I'm just using it 
> to scale incoming data.  Specifically, I'm taking an incoming float number 
> between 0. and 1.0 that is a linear scaling of pitch and reshaping it.  
> 
> If you're curious, yes, this is related to my previous post about 
> pitch-tracking.  Specifically, I'm doing the pitch-tracking in Max/MSP with 
> the fiddle~ object and sending the resulting pitch and amplitude, scaled, to 
> a QC comp that uses the pitch to control the hue of a gradient.  
> 
> Even more specifically, it's something I put together for Wiley Wiggins, who 
> is doing visuals with The Octopus Project in Hexadecagon, which is a free 
> show this evening in Austin, TX.  "Music for eight-channel sound and 
> eight-channel video performed live in the round.  Awesome!"  
> http://www.theoctopusproject.com/hxdx.html  Wish I could be there but, alas, 
> I'm in NYC.
> 
> cheers,
> dan
> 
> 
> 
> On Mar 19, 2010, at 4:27 PM, Troy Koelling wrote:
> 
>> If those circles are control points, I'd probably guess this is a cubic 
>> spline. CoreGraphics has the ability to draw that if you need to.
>> 
>> This is a pretty good rundown:
>> http://cocoawithlove.com/2008/07/coregraphics-curves-and-lines-sample.html
>> 
>> On Mar 19, 2010, at 1:15 PM, Chris Wood wrote:
>> 
>>> See also gaussian curve/bell curve/s-curve... Although of course that was a 
>>> straight spline curve in the first pic. Splines will give you what you 
>>> want, but maybe not in the most simple way. 
>>> 
>>> Chris
>>> 
>>> 
>>> On 19 Mar 2010, at 19:52, Dan Winckler wrote:
>>> 
>>>> Thanks, Tom and Jon!  I remembered Grapher earlier today and it was a big 
>>>> help, even though polynomial curves are not among its examples (sure beats 
>>>> my old TI-82).  Now to tweak the numbers until they give me the shape I 
>>>> need.  Additional help still welcome if offered.  :)
>>>> 
>>>> best,
>>>> dan
>>>> 
>>>> 
>>>> 
>>>> <Screen shot 2010-03-19 at 3.49.57 PM.png>
>>>> 
>>>> 
>>>> On Mar 19, 2010, at 3:40 PM, Jon Pugh wrote:
>>>> 
>>>>> At 3:14 PM -0400 3/19/10, Dan Winckler wrote:
>>>>>> What do you call a curve like the one in the attached image?  Rather, 
>>>>>> what's the mathematical term for the equation that produces such a 
>>>>>> double curve.  I am trying to scale an incoming float number (0.0  1.0) 
>>>>>> so that it changes more quickly in the middle of the range (~0.2 - 0.8) 
>>>>>> than at the top and bottom (~ 0.0 - 0.2, 0.8 - 1.0).  Right now I've got 
>>>>>> exponential scaling, which works for the bottom of the range but not the 
>>>>>> top.
>>>>> 
>>>>> This is a curve produced by a polynomial equation.  I recommend opening 
>>>>> the application Grapher, which came with your Mac, and entering this 
>>>>> equation: x = y^3+y^2+y
>>>>> 
>>>>> This will give you a curve approximating the one you've drawn.  Then you 
>>>>> can play with adding numbers before the various terms (i.e. 3y^3, etc) to 
>>>>> change the shape of the curve.
>>>>> 
>>>>> Good luck.
>>>>> 
>>>>> Jon
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