karl krach

ok, this is embarassing but...: i regularly keep bumping into the problem that i need to scale one number to another using some function - of which i usually have some sort of visual idea but unfortunately no mathematical understanding whatsoever - eg. in the moment i would need to have something like [scale] but which works with a bell-shape sort of curve.

now, i know this can all be done with basic math knowledge and [expr] but since it takes me days to figure this out each time: is there some sort of visual cheat sheet for super-dummies somewhere? like some document showing (visually) a range of graphs with the according expressions (in the format [expr] understands) and maybe a simple explanation (like: "if you want this curve to be less steep, decrease this number")?

hi,
ok, this is embarassing but...: i regularly keep bumping into the problem that i need to scale one number to another using some function - of which i usually have some sort of visual idea but unfortunately no mathematical understanding whatsoever - eg. in the moment i would need to have something like [scale] but which works with a bell-shape sort of curve.
now, i know this can all be done with basic math knowledge and [expr] but since it takes me days to figure this out each time: is there some sort of visual cheat sheet for super-dummies somewhere? like some document showing (visually) a range of graphs with the according expressions (in the format [expr] understands) and maybe a simple explanation (like: "if you want this curve to be less steep, decrease this number")?
that would be sooooo helpful...
k


expr-graph-examples

u could build the chart yourself using lcd.

u might want to start with my old style abstractions found at 

https://cycling74.com/forums/re-mapping-a-range-of-numbers-add-your-tricks-here/

there is a little helpfile coming with it where you see in the input and output just as simple slider objects. mabye even better than a 2d-graph for most situations?

u might want to start with my old style abstractions found at https://cycling74.com/forums/re-mapping-a-range-of-numbers-add-your-tricks-here/

there is a little helpfile coming with it where you see in the input and output just as simple slider objects. mabye even better than a 2d-graph for most situations?


oh btw, multislider belongs to thze objects whose default settings between v7 and earlier are not compatible. complints should go directly to support@ ... sorry guys ;)

Also, go check in the help patcher of [scale], "advanced tab" offers a similar example with [itable]

What bugs me though, is why the multi slider "graph" changes if you change sample size, when using [scale]s exponent function. shouldn't it stay the same? Or am I not imaging things right?

edit: what you also want to check is "function graphs" (google it) and Max tutorial #22 "Designing equations"

edit: i keep editing stuff in my patcher. You can enable a "curve" in the function to get S curves or custom scaling

btw, the only way to find functions from given curves would be to test all known functions against it.

http://www.wolframalpha.com/input/?i=analyze%20image%20http%3A%2F%2Fdemonstrations.wolfram.com%2FParametricTrace%2FpreloadGraphic.jpg&lk=2

but it will help you find the function for a bell curve:

http://www.wolframalpha.com/input/?i=bell+curve

well, if you can read this stuff. i cant. :)

[exp(-(($f1-0.5)/0.125)*(($f1-0.5)/0.125))]

you can adapt it to other ranges by multiplying the 4 constants.

or do it like i do it in my abstractions: first scale to 0.-1., then apply the curve, then scale again to whatever you wish.

What I do is use a bezier function.For display, I build the curve with an uzi between start and end points,because I wanted a display in 30x50-pixel thumbnail which I couldn't create otherwise,. I have to say, it is not easy to program in Max. You will find my first implementation in Godel 2b on my website.

http://www.yofiel.com/software/cycling-74-patches/godel-2-beta

What I do is use a bezier function.For display, I build the curve with an uzi between start and end points,because I wanted a display in 30x50-pixel thumbnail which I couldn't create otherwise,. I have to say, it is not easy to program in Max.   You will find my first implementation in Godel 2b on my website.

http://www.yofiel.com/software/cycling-74-patches/godel-2-beta


thank you all so much for your help! combining all these tips and ressources i guess i do get quite close to my "graphs cheat-sheet for superdummies"... nice!

one last question (which is only vaguely related but as i seem to have gathered all the math pros already): how would i rearrange this function so it calculates α (α = ... ... ...) instead of G?

(using: G=Field of view, d=Distance, α=Angle of view)

and how would i format this so [expr] would understand it?

oh, wow!
thank you all so much for your help! combining all these tips and ressources i guess i do get quite close to my "graphs cheat-sheet for superdummies"... nice!

one last question (which is only vaguely related but as i seem to have gathered all the math pros already): how would i rearrange this function so it calculates α (α = ... ... ...) instead of G?
G = 2 × d × tan(α / 2)
(using: G=Field of view, d=Distance, α=Angle of view)
and how would i format this so [expr] would understand it?


wolfram alpha had replaced mathematica for me since it allows you to ask it things like this:

http://www.wolframalpha.com/input/?i=G+%3D+2+%C3%97+d+%C3%97+tan%28%CE%B1+%2F+2%29+%CE%B1%3D%3F

i am not sure how to write the "-1" (inverse tangent) in expr, and i know what the the "n" in "pi*n" means and where it comes from either.

most interesting! i didn't know wolfram alpha could do this...

regarding the inverse tangent, this seems to be "atan", regarding the "n"... no idea.

apart from the "n" i think this should be something like [expr exp(2*(atan($f1/(2*$f2))+3.1416))]. am i correct?

most interesting! i didn't know wolfram alpha could do this...
regarding the inverse tangent, this seems to be "atan", regarding the "n"... no idea.
apart from the "n" i think this should be something like [expr exp(2*(atan($f1/(2*$f2))+3.1416))]. am i correct?
but what is this mysterious "n"?


We know that tan(x) = tan(x + π) = tan(x + nπ), with n any integer.

So Wolfram gives you the complete set of possible values for α.

You will implement this with n=0, i.e. you will ignore the "+ n π".

tan(-1) is atan
We know that tan(x) = tan(x + π) = tan(x + nπ), with n any integer.
So Wolfram gives you the complete set of possible values for α.
You will implement this with n=0, i.e. you will ignore the "+ n π".


perfect, works like a charm!
thanks again!!!
k


expr graph examples?