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. 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/qc.student.au%40gmail.com > > This email sent to qc.student...@gmail.com > > > >
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