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!!
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