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math behind scale?

May 17 2010 | 7:30 am

Can someone give me some details about the math behind the scale object?

May 17 2010 | 10:21 am

I don’t have access to the scale source code, but I can make a guess.

The linear part is easy:

– Subtract the low input value from the number, then divide the result by the difference between high input value and low input value. This gives you a number between 0 and 1.

– Then multiply this again with the difference between low output and high output value, and finally add the low output value.

As an expression, this would look like this:

expr "(($f1-$f2)/($f3-$f2)) * ($f5-$f4) + $f4"
$f1 being your number input, $f1 the low input value, $f2 the high input value, $f3 the low output value, $f4 the high output value.

This still ignores the exponential part, but I don’t think this should be too hard to figure out as well.


eh, I’m silly. Should have looked into the documentation of [scale] first where the formula is written down. So that’s what you should do as well!

May 17 2010 | 11:26 am

here’s the formula from the docs:

y = b*e^(-a*log(c)) * e^(x*log(c))

it says "a,b and c are the three typed-in arguments".
So c is the exponential factor and e is the base of the natural logarithm.
But what’s a and b ??

May 17 2010 | 8:22 pm

Woops, I didn’t now that the formula is inside the docs.

Thanks a lot guys!

Jun 28 2010 | 10:39 am

I think that what is written in the docs is for exponential mode calculations. I was interested as well to use a jit.expr expression that simulates the scale object.

I managed to do something similar to [scale 0 255 -1. 1.] with the following expresion

[expr (in[0]/255-0.5)*2]

but I don’t have a clue how to do [scale 0 255 1. -1.]

Does anyone know? I’m not good at maths either

Jun 30 2010 | 10:07 pm

Please, if anyone knows how to reverse a scale in jit.expr. I am trying to reverse a short matrix with 2d xy coordinates for a 640×480 pixels to have 3d xy coordinates which are -1. 1. for both x and y (with the center as 0.).

I did the first part for the x coordinate where 0 becomes -1. and 640 becomes 1. But for the y value, 0 is 1. and 480 is -1.

So I would need an expresion for jit.expr to turn a (-1. 1) matrix the other way around (1. -1.)

— Pasted Max Patch, click to expand. —
Jun 30 2010 | 10:34 pm

Could you just multiply by -1. after the scale?

[jit.op @op * @val -1.]

Jun 30 2010 | 11:04 pm

I guess it’s mid school mathematics! I’m loosing my mind!!

Thank you so much, Jesse!!

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Forums > MaxMSP