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!!
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