A simulated abacus in QC with no plugins please :) Chris
On 5 Jan 2011, at 14:57, George Toledo <gtole...@gmail.com> wrote: > Alastair, can you demonstrate interpolation with an abacus for us? :) > > Best, > gt > > On Wed, Jan 5, 2011 at 9:49 AM, Alastair Leith <qc.student...@gmail.com> > wrote: > Well when I learnt maths it's was the PDP8 and Apple ][ era and everything > was hand-written. The dots I saw (probably from my dad's maths which takes > them back another 40 years again) and wrote were all on the baseline and > small as in "." But yes with object.property all the rage these days it > probably would do to use a•x (even if it looks a little odd to me). > > > On 05/01/2011, at 7:24 PM, Joshua wrote: > >> I sometimes use the key command option-8 to create a black dot • as it's >> centered and doesn't get confused with anything. That's how they taught us >> back in school. >> >> Best, >> Joshua TS >> >> Sent from my iPhone >> >> On Jan 4, 2011, at 9:18 PM, Alastair Leith <qc.student...@gmail.com> wrote: >> >>> You're welcome Oscar. >>> >>> In response to an off-list email I wrote this, (doesn't hurt to share it). >>> Sentence in blue is a correction to first post: >>> >>> . = * >>> >>> Mathematicians use it in hand-written equations as a quick sign for >>> 'product' or multiplication. >>> >>> I tried * (and 'x' would be downright confusing) but it looked messy so I >>> went with '.' — except where there were numbers involved and then it could >>> be confused for a decimal point. eg 5.x or y.5 Of course you could just >>> write y=ax+c but in code that makes ax look like one variable not two. >>> >>> I should have written at the end of that post, all version 'In-Out', 'In' >>> and 'Out' will require two equations to get the easing in and out, except >>> maybe for sinusoidal 'In-Out' in some cases since it already has a curve >>> that is characteristic of ease-in ease-out if you use the correct half >>> phase of the curve. >>> >>> Alastair Leith >>> >>> The machine does not isolate man from the great problems of nature but >>> plunges him more deeply into them. >>> Antoine de Saint-Exupery >>> >>> On 04/01/2011, at 11:55 PM, Oscar 'offonoll' wrote: >>> >>>> Interesting! thank you so much!!!! >>>> >>>> On Tue, Jan 4, 2011 at 12:54, Alastair Leith <qc.student...@gmail.com> >>>> wrote: >>>> Each Interpolation has it's own equation (linear, quadratic in, sinusiodal >>>> in-out, etc etc) >>>> >>>> For linear, the general equation (using x and y since they're familiar) is: >>>> >>>> y= a.x + c >>>> >>>> For your range mapping [0,1] —> [-1,1], simultaneous equations can quickly >>>> tell us the values of a and c: >>>> When x=0, y=-1 ∴ c= -1 ie, y= a.x -1 >>>> For x=1, y=1 so substituting into y= a.x -1, >>>> 1 = a*1 -1 >>>> ⇔ a=2 >>>> >>>> So your equation for linear mapping of [0,1] —> [-1,1] >>>> is y = 2.x -1, >>>> >>>> Test our formula for x=0.5, >>>> y = 2*0.5 -1 >>>> = 0 ✔ It checks out ok! >>>> >>>> Other general equations to use: >>>> >>>> y = a(x+b)² +c [Quadratic] or >>>> y = a.x² +b.x + c or >>>> y = (x+a)(x+b) + c (Fixed the Typo present in the >>>> version I sent you earlier Oscar) >>>> y = a.sin(x+b) +c [Sinusoidal] >>>> y = cb(x+a) + d [Exponential] or >>>> y = a.exp(x+b) + c >>>> y = a.x³ + b.x² + c.x +d [cubic] >>>> >>>> Solving some of these equations can be a bit more involved but mostly not >>>> to difficult by substituting in your range limits and mid-point or >>>> whatever. These should work for In-Out. In cases of just In or just Out >>>> you'll need two equations. One being say quadratic the other linear. Then >>>> switch from one equation to the other depending if x is < or ≥ the >>>> crossover point. I find Apples Grapher app (Utilities Folder) helps to >>>> visualise these equations. Many resources via wikipedia too. >>>> >>>> Hope that helps >>>> Alastair >>>> >>>> >>>> On 04/01/2011, at 9:03 PM, Oscar 'offonoll' wrote: >>>> >>>>> Hello and happy new year! >>>>> I am wondering what is the Interpolation mathematical equation. as I >>>>> normaly use it to transform a range of 0-1 (position) to my personal >>>>> range such as -1 to 1. >>>>> thank you!! >>>>> _______________________________________________ >>>>> Do not post admin requests to the list. 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They will be ignored. > Quartzcomposer-dev mailing list (Quartzcomposer-dev@lists.apple.com) > Help/Unsubscribe/Update your Subscription: > http://lists.apple.com/mailman/options/quartzcomposer-dev/gtoledo3%40gmail.com > > This email sent to gtole...@gmail.com > > > > -- > George Toledo > gtole...@gmail.com > www.georgetoledo.com > > The information contained in this E-mail and any attachments may be > confidential. > If you have received this E-mail in error, please notify us immediately by > telephone or return E-mail. > You should not use or disclose the contents of this E-mail or any of the > attachments for any purpose or to any persons. > > _______________________________________________ > Do not post admin requests to the list. 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