Thanks, vade! And thank you again, Chris! This is very educational. Just to clarify, I'm not rushing to push out a new version now, right before the show -- the exponential scaling will have to do and there's plenty of controls for Wiley to play with. ;)
cheers, dan On Mar 19, 2010, at 4:41 PM, Christopher Wright wrote: >> Chris Wright also threw in the sigmoid function >> (http://en.wikipedia.org/wiki/Sigmoid_function) -- thank you, Chris(x2). >> The difficulty is in fitting the curve to the desired range -- any tips, >> mathemagicians? > > Going with the sigmoid, you have an equation like this: > > y = 1 / (1 + e^-x) > > We can generalize this a bit more, and turn it into this: > > y = r / (1 + e^(-(x - o) * s)) > > Where r is the "range" (0 to r), s is the "scale" (or "sharpness"?) (higher > numbers make the change from 0 to r occur more rapidly, default is 1), and o > is the "offset", where the transition takes place (normally 0). > > Varying r, s, and o will give you a sigmoid mapped however you'd like. (and > varying e will make you impossibly powerful ;) > > The other equations (sin being another good easy one) have similar > scale/offset changes to tweak them as necessary. > > (disclaimer: i'm not a real mathemagician, and was also educated by the US > education system ;) > > Chris On Mar 19, 2010, at 4:46 PM, vade wrote: > 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 >>>>>> _______________________________________________ >>>>>> Do not post admin requests to the list. They will be ignored. >>>>>> Quartzcomposer-dev mailing list ([email protected]) >>>>>> Help/Unsubscribe/Update your Subscription: >>>>>> http://lists.apple.com/mailman/options/quartzcomposer-dev/dan%40danwinckler.com >>>>>> >>>>>> This email sent to [email protected] >>>>> >>>>> _______________________________________________ >>>>> Do not post admin requests to the list. They will be ignored. >>>>> Quartzcomposer-dev mailing list ([email protected]) >>>>> Help/Unsubscribe/Update your Subscription: >>>>> http://lists.apple.com/mailman/options/quartzcomposer-dev/psonice%40gmail.com >>>>> >>>>> This email sent to [email protected] >>>> >>>> _______________________________________________ >>>> Do not post admin requests to the list. They will be ignored. >>>> Quartzcomposer-dev mailing list ([email protected]) >>>> Help/Unsubscribe/Update your Subscription: >>>> http://lists.apple.com/mailman/options/quartzcomposer-dev/tkoelling%40apple.com >>>> >>>> This email sent to [email protected] >>> >> >> _______________________________________________ >> Do not post admin requests to the list. They will be ignored. >> Quartzcomposer-dev mailing list ([email protected]) >> Help/Unsubscribe/Update your Subscription: >> http://lists.apple.com/mailman/options/quartzcomposer-dev/doktorp%40mac.com >> >> This email sent to [email protected] > > _______________________________________________ > Do not post admin requests to the list. They will be ignored. > Quartzcomposer-dev mailing list ([email protected]) > Help/Unsubscribe/Update your Subscription: > http://lists.apple.com/mailman/options/quartzcomposer-dev/dan%40danwinckler.com > > This email sent to [email protected] _______________________________________________ Do not post admin requests to the list. They will be ignored. Quartzcomposer-dev mailing list ([email protected]) Help/Unsubscribe/Update your Subscription: http://lists.apple.com/mailman/options/quartzcomposer-dev/archive%40mail-archive.com This email sent to [email protected]
