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*<http://www.brainyquote.com/quotes/quotes/a/antoinedes131176.html> > * * > > 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 < <http://qc.student.au> > qc.student.au@ <http://gmail.com>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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