[script] FxGraph - 2D/3D Function plotter  1-20  21-40  41-60  61-78

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 From:  Max Smirnov (SMIRNOV)
6447.1 
Here is a script to plot the 2D graphs of functions on the fly.
You can use all functions and constants of the Javascript Math object:
code:
abs(x)     Returns the absolute value of x
acos(x)    Returns the arccosine of x, in radians
asin(x)    Returns the arcsine of x, in radians
atan(x)    Returns the arctangent of x as a numeric value between -PI/2 and PI/2 radians
ceil(x)    Returns x, rounded upwards to the nearest integer
cos(x)     Returns the cosine of x (x is in radians)
exp(x)     Returns the value of Ex
floor(x)   Returns x, rounded downwards to the nearest integer
log(x)     Returns the natural logarithm (base E) of x
pow(x,n)   Returns the value of x to the power of n
random()   Returns a random number between 0 and 1
round(x)   Rounds x to the nearest integer
sin(x)     Returns the sine of x (x is in radians)
sqrt(x)    Returns the square root of x
tan(x)     Returns the tangent of an angle

E          Returns Euler's number (approx. 2.718)
LN2        Returns the natural logarithm of 2 (approx. 0.693)
LN10       Returns the natural logarithm of 10 (approx. 2.302)
LOG2E      Returns the base-2 logarithm of E (approx. 1.442)
LOG10E     Returns the base-10 logarithm of E (approx. 0.434)
PI         Returns PI (approx. 3.14)
SQRT1_2    Returns the square root of 1/2 (approx. 0.707)
SQRT2      Returns the square root of 2 (approx. 1.414)


If you want to use degrees instead of radians - use square brackets. sin(x) <- x in radians, sin[x] - x in degrees.
You can use "rnd" command instead of random() function

Other settings:
minX, maxX - limits of the function. Don't forget, in MoI you can use math expression in the settings.
Example: y=sin(x), minX = 0, maxX = 2*pi <- you will get one full period of sine function
points - number of points. If 500 points is not enough, you can set any other value manually.

Update:

v.1.1
- Some optimizations
- [Added] Variables (a,b,c,d)

v.1.2
- [Fixed] Unexpected condition error (I hope so)
- [Added] Radial mode (if script detects "t" variable in the formula, it automatically switches to R(t) mode)
- [Added] Command line arguments
Usage: "_fxGraph fx;min;max;points;a;b;c;d"
Examples:
_fxGraph sin(x) -> f(x)=sin(x)
_fxGraph sqrt(x);0;25 -> f(x)=sqrt(x), min(x)=0, max(x)=25
_fxGraph pow(x,a);;;;3 -> f(x)=pow(x,a), a=3

v1.2c
-[Added] Copy settings to clipboard by clicking f(x)/R(t) symbol. You can use this string as command line argument.

v1.2d
- [Added] R(t)3D mode. Add ^ symbol at the beginning of a R(t) formula to draw 3D graph.

EDITED: 7 Sep 2014 by SMIRNOV


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 From:  Frenchy Pilou (PILOU)
6447.2 
Excellent!

Useful for math lovers! :)

Waiting the 3D! ;)

EDITED: 20 Jan 2014 by PILOU

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 From:  bemfarmer
6447.3 
Superb script MAX !
Just assigned it to my SHIFT+F shortcut.

This script replaces a bunch of one-shot scripts.
It can create an unbounded number of curves.
It uses the fast method of scripting mostly in .htm file.
Other math functions could be added. Maybe for a catenary? Have to investigate the math, it uses hyperbolic trig, or exponentials.

? If a version were created for a U parameter, nested with a V parameter, it might do 3d curves ?

Do not know if it would do integration or differentiation? i.e Euler spiral?

- Brian
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 From:  bemfarmer
6447.4 
exp(x) give an "unknown command" error.

Edit: pow(x,2) works. (n needs to be a number:-), (pow(x,n) is not a correct entry)

log(x) works for minX = 0

- Brian

EDITED: 20 Jan 2014 by BEMFARMER

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 From:  Max Smirnov (SMIRNOV)
6447.5 In reply to 6447.4 
Thank you! :)

Frenchy Pilou (PILOU)
>> Waiting the 3D!
Not now. It was in the beta version of this script, but I haven't finished it.

Brian
>> exp(x) give an "unknown command" error
fixed

>>pow(x,2) works
pow(2,x) and pow(x,x) also works perfectly

>> log(x) works for minX = 0
I set "x=minx+1/10e8" because of "Unexpected condition error" with y=1/x function. For example, y=x/0 correctly works (infinity message appears). I don't know why..

>>If a version were created for a U parameter, nested with a V parameter, it might do 3d curves ?
Yes, I think so.
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 From:  bemfarmer
6447.6 
Thankyou Max

Formula for a catenary: y = 2 * (exp(x/2) + exp(-x/2))/2

A more general formula is avalue * (exp(x/avlaue) + exp(-x/avalue))/2
But in this case, avalue is just a scaling factor, so by using Scaling in MoI, the avalue is changeable.
For example doing a Scaling of 4, on a pre-created catenary, changes the avalue=2 to avalue = 8.

It might be nice to have a few parameters like avalue, bvalue ... ?

I should have referred to using U and V as creating a series of 3d curves which might be loft-able to a surface or solid.

- Brian
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 From:  bemfarmer
6447.7 
Tried out version 1.1 a little. Looks good.

I suspect a version depending upon a rotational parameter t or theta,
with x = some function of t,
and y = some function of t,
would be possible?

- Brian
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 From:  Frenchy Pilou (PILOU)
6447.8 In reply to 6447.5 
<<< y=x/0 correctly works (infinity message appears)

Seems normal, no ? ;)
If the language has not an automatically barrier for impossible operation!
---
Pilou
Is beautiful that please without concept!
My Gallery
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 From:  Max Smirnov (SMIRNOV)
6447.9 In reply to 6447.7 
The script has been updated with a new R(t) function.
xy(t) is possible. I'll think about it.
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 From:  Frenchy Pilou (PILOU)
6447.10 
Tricky the fact to use variables!

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 From:  Michael Gibson
6447.11 In reply to 6447.9 
This is really cool Max, to have a more general purpose curve constructor that can be used for a lot of different possible formulas!

- Michael
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 From:  wastzzz
6447.12 
Epic, funny and useful! Thank you.
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 From:  Max Smirnov (SMIRNOV)
6447.13 
v1.2d
- [Added] R(t)3D mode. Add ^ symbol at the beginning of a R(t) formula to draw 3D graph.

^pow(t,a)/pow(10,2*a-2);-100;100;500;3
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 From:  Frenchy Pilou (PILOU)
6447.14 In reply to 6447.13 
Born of the 3D world! ;)

EDITED: 22 Jan 2014 by PILOU

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 From:  Max Smirnov (SMIRNOV)
6447.15 
This is my new script - FxGraph3D which allows drawing 3D parametric surfaces.
x = X(u,v), y = Y(u,v), z = Z(u,v), where u,v are the parametric domain parameters.




Here is some interesting parametric equations.
http://msenux.redwoods.edu/Math4Textbook/Plotting/ParametricSurfaces.pdf

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 From:  Michael Gibson
6447.16 In reply to 6447.15 
Very cool Max!

- Michael
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 From:  wastzzz
6447.17 In reply to 6447.15 
Thank you!
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 From:  Max Smirnov (SMIRNOV)
6447.18 
Version 1.0
Changes since 0.6:
[fixed] some bugs
[added] Command line parameters support. Click X(u,v), Y(u,v) or Z(u,v) label to copy values to the clipboard.

Examples:
_FxGraph3D (u);(v);rnd;-10;10;-10;10;10;15;;;;U
_FxGraph3D u*a+rnd-0.5;v*b+rnd-0.5;rnd*c-c/2;-10;10;-10;10;50;50;2;2;40;P
_FxGraph3D 2*(1-exp(u/(6*pi)))*cos(u)*cos(v/2)*cos(v/2);2*(-1+exp(u/(6*pi)))*sin(u)*cos(v/2)*cos(v/2);1-exp(u/(3*pi))-sin(v)+exp(u/(6*pi))*sin(v);0;20;0;6.283185307179586;50;50;;;;V
_FxGraph3D (2+v*sin(u))*sin(2*pi*v);v*cos(u);(2+v*sin(u))*cos(2*pi*v)+2*v-v;0;3.14;0;1.3;50;50;;;;V
_FxGraph3D sin(u);cos(u);u*u/300;0;60;0;1.3;100;0;;;;V

Michael, Thank you!

EDITED: 7 Sep 2014 by SMIRNOV


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 From:  jotero (TOROLF)
6447.19 
Hello all :)

It's nice and what do do with the curves?

X():cos(2*u)*cos(v) + 1.0 *cos(u)
Y():sin(v)
Z():-sin(2*u)*cos(v) + 1.0*sin(u)

[u]:0, 2*pi
[v]:0, 2*pi

And how do I get now to my mathematical NURBS model...?

http://imaginary.org/gallery/k3dsurf

Cu
Torolf
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 From:  Frenchy Pilou (PILOU)
6447.20 
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