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nextstep Site Admin
Joined: 06 Jan 2007 Posts: 539

Posted: Sat Jul 07, 2007 8:24 pm Post subject: Dynamic System Simulation 


Hi all,
This thread is to show some use of K3DSurf to make some Dynamic System Simulation.
The morph effect allong with the parameter "t" can be used to make complex animations with deformable objects. Here is a simple example of a drop falling on a planar surface:
Quote:  Name: drop
/*
Simulation of a Drop falling a planar surface
*/
F(): (z+1) * ((z+1.4)*(x*x + y*y) + (zt*t*3 +1)*(zt*t*3+1)1)
[x]: 2 , 2
[y]: 2 , 2
[z]: 1.2 , 3
; 
More examples will come soon _________________ Cheers,
Abderrahman 

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François LE COAT
Joined: 03 Feb 2007 Posts: 27 Location: France

Posted: Sun Jul 08, 2007 7:33 am Post subject: Re: Dynamic System Simulation 


nextstep wrote:  Hi all,
This thread is to show some use of K3DSurf to make some Dynamic System Simulation.
The morph effect allong with the parameter "t" can be used to make complex animations with deformable objects. Here is a simple example of a drop falling on a planar surface:
Quote:  Name: drop
/*
Simulation of a Drop falling a planar surface
*/
F(): (z+1) * ((z+1.4)*(x*x + y*y) + (zt*t*3 +1)*(zt*t*3+1)1)
[x]: 2 , 2
[y]: 2 , 2
[z]: 1.2 , 3
; 
More examples will come soon 
That looks nice
Did you already looked at http://eureka.atari.org/vrml/vogue.mov ?
It is defined with http://eureka.atari.org/vrml/vagues.pov ... The effects are quite similar, and this POVRay script is exported from my Eureka 2.12 software.
It's a nice work ! _________________  archimedium
http://eureka.atari.org/ 

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jotero
Joined: 27 Jan 2007 Posts: 153 Location: Germany Hannover

Posted: Sun Jul 08, 2007 8:19 am Post subject: Re: Dynamic System Simulation 


nextstep wrote:  Hi all,
This thread is to show some use of K3DSurf to make some Dynamic System Simulation.
The morph effect allong with the parameter "t" can be used to make complex animations with deformable objects. Here is a simple example of a drop falling on a planar surface:
Quote:  Name: drop
/*
Simulation of a Drop falling a planar surface
*/
F(): (z+1) * ((z+1.4)*(x*x + y*y) + (zt*t*3 +1)*(zt*t*3+1)1)
[x]: 2 , 2
[y]: 2 , 2
[z]: 1.2 , 3
; 
More examples will come soon 
very nice taha
Code:  Name: drop_1
/*
Simulation of a Drop falling a planar surface
*/
F(): cos(x) + cos(y) + (z+1) * ((z+1.4)*(x*x + y*y) + (zt*t*13 +1)*(zt*t*26+1)13)
[x]: 4 , 4
[y]: 4 , 4
[z]: 2 , 8.5
; 
ciao
torolf _________________ Kontakte 

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François LE COAT
Joined: 03 Feb 2007 Posts: 27 Location: France

Posted: Sun Jul 08, 2007 9:04 am Post subject: Re: Dynamic System Simulation 


I forgot ...
Code:  X():u
Y():5*(1cos(sqrt(u*u+v*v)t*2*pi))/sqrt(u*u+v*v)
Z():v
[u]:10, 10
[v]:10, 10 
That's supposed to be the fall of a drop.
Code:  X():u*2/3
Y():(sin(2*pi*(u*v*2.2t))+sin(2*pi*t))/8
Z():v
[u]:1, 1
[v]:0, 1 
And a flag flying in the wind.
Cheers. _________________  archimedium
http://eureka.atari.org/ 

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nextstep Site Admin
Joined: 06 Jan 2007 Posts: 539

Posted: Sun Jul 08, 2007 4:23 pm Post subject: Re: Dynamic System Simulation 


Hi all,
Thanks François and I'm glad you like it . Your example is simply beautiful and the use of parametric forme make it very nice. Eureka seems to have a powerful povscript export tool but I can't use it since I have only a PC. There is likely a way to make very interessant animation by using the morph effect and I'll try to put some of them here as soon as possible. _________________ Cheers,
Abderrahman 

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nextstep Site Admin
Joined: 06 Jan 2007 Posts: 539

Posted: Sun Jul 08, 2007 4:33 pm Post subject: Re: Dynamic System Simulation 


Hi all,
jotero wrote:  Name: drop_1
/*
Simulation of a Drop falling a planar surface
*/
F(): cos(x) + cos(y) + (z+1) * ((z+1.4)*(x*x + y*y) + (zt*t*13 +1)*(zt*t*26+1)13)
[x]: 4 , 4
[y]: 4 , 4
[z]: 2 , 8.5
; 
Thanks jotero and the use of "cos(x) + cos(y)" at the begining is a clever thing : That make the intersection of the drop with the plan very smooth . _________________ Cheers,
Abderrahman 

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nextstep Site Admin
Joined: 06 Jan 2007 Posts: 539

Posted: Sun Jul 08, 2007 9:21 pm Post subject: 


Hi all,
I had the idea of using François's surface and jotero's way of elliminating the intersections artefacts and here is the result :
Code:  Name: drop_2
/*
Example of the Morph effect
*/
F(): (z6*(1cos(sqrt(x^2+y^2) t*2*pi))/sqrt(x^2+y^2+4)) *
(2*(x^2 + y^2)+(z  40*t^2+1)^2 10) 1000
[x]: 20 , 20
[y]: 20 , 20
[z]: 1 , 50
; 
Enjoy _________________ Cheers,
Abderrahman 

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nextstep Site Admin
Joined: 06 Jan 2007 Posts: 539

Posted: Fri Sep 07, 2007 4:49 am Post subject: 


Hi all,
A new pendulumlike system. Right now, It's only the part on it's center
Quote:  Name: Pendulum
/*
pendulum :
*/
F(): if( sqrt( (x)^2 +(y)^2 +(z)^2) < 5 ,min((x)^2 + (y(z4)*cos(pi*t))^2  .1 ,(2*x)^2 + (y+4.5*cos(pi*t))^2 +(z+4.5*sin(pi*t))^2 4) ,(2*x)^2 + (y+4.5*cos(pi*t))^2 +(z+4.5*sin(pi*t))^2 4 )
[x]: 1 , 1
[y]: 7 , 7
[z]: 6.5 , 5
; 
_________________ Cheers,
Abderrahman 

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François LE COAT
Joined: 03 Feb 2007 Posts: 27 Location: France

Posted: Sun Sep 16, 2007 3:41 pm Post subject: Re: Dynamic System Simulation 


Quote: 
Thanks François and I'm glad you like it . Your example is simply beautiful and the use of parametric form make it very nice. Eureka seems to have a powerful povscript export tool but I can't use it since I have only a PC. There is likely a way to make very interesting animation by using the morph effect and I'll try to put some of them here as soon as possible. 
Just that Eureka 2.12 software can be used on a PC machine thanks to the ATARI Virtual Machine called ARAnyM http://aranym.org/ from which I maintain a Mini Pack http://eureka.atari.org/MacAranym.zip that can be launched hosted with GNU/Linux and Mac OS X at the moment.
So you may be able to see what Eureka 2.12 is able to generate. It already integrates a lot of very nice mathematical shapes coming from K3DSurf, besides many other mathematical formulas in 2D (plane) 3D (space) and 4D (timespace) coordinates.
You may enjoy it, if the ATARI (virtual) machine is not too strange using
Regards, _________________  archimedium
http://eureka.atari.org/ 

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nextstep Site Admin
Joined: 06 Jan 2007 Posts: 539

Posted: Sat Jun 14, 2014 4:57 pm Post subject: 


Hi,
Here is an adaptation to MathMod of the falling drop example.
Click the "Morph" button to see the morph effect. enjoy
Quote: 
{
"Iso3D": {
"Component": [
"fallingdrop"
],
"Fxyz": [
"((z6*(1cos(sqrt(x^2+y^2)t*2*pi))/sqrt(x^2+y^2+4))*(2*(x^2+y^2)+(z40*sin(t*pi)+1)^210)1000)"
],
"Name": [
"FallingDrop"
],
"Xmax": [
"20"
],
"Xmin": [
"20"
],
"Ymax": [
"20"
],
"Ymin": [
"20"
],
"Zmax": [
"50"
],
"Zmin": [
"1"
]
}
}

fallingdrop by taha_ab, on Flickr _________________ Cheers,
Abderrahman 

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