Dynamic System Simulation

 
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nextstep
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Joined: 06 Jan 2007
Posts: 538

PostPosted: Sat Jul 07, 2007 8:24 pm    Post subject: Dynamic System Simulation Reply with quote

Hi all,
This thread is to show some use of K3DSurf to make some Dynamic System Simulation. Very Happy
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) + (z-t*t*3 +1)*(z-t*t*3+1)-1)
[x]: -2 , 2
[y]: -2 , 2
[z]: -1.2 , 3
;

More examples will come soon Razz
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François LE COAT



Joined: 03 Feb 2007
Posts: 27
Location: France

PostPosted: Sun Jul 08, 2007 7:33 am    Post subject: Re: Dynamic System Simulation Reply with quote

nextstep wrote:
Hi all,
This thread is to show some use of K3DSurf to make some Dynamic System Simulation. Very Happy
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) + (z-t*t*3 +1)*(z-t*t*3+1)-1)
[x]: -2 , 2
[y]: -2 , 2
[z]: -1.2 , 3
;

More examples will come soon Razz


That looks nice Laughing

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 POV-Ray script is exported from my Eureka 2.12 software.

It's a nice work !
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jotero



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

PostPosted: Sun Jul 08, 2007 8:19 am    Post subject: Re: Dynamic System Simulation Reply with quote

nextstep wrote:
Hi all,
This thread is to show some use of K3DSurf to make some Dynamic System Simulation. Very Happy
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) + (z-t*t*3 +1)*(z-t*t*3+1)-1)
[x]: -2 , 2
[y]: -2 , 2
[z]: -1.2 , 3
;

More examples will come soon Razz


very nice taha Very Happy

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) + (z-t*t*13 +1)*(z-t*t*26+1)-13)
[x]: -4 , 4
[y]: -4 , 4
[z]: -2 , 8.5
;


ciao
torolf
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François LE COAT



Joined: 03 Feb 2007
Posts: 27
Location: France

PostPosted: Sun Jul 08, 2007 9:04 am    Post subject: Re: Dynamic System Simulation Reply with quote

François LE COAT wrote:
That looks nice Laughing

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 POV-Ray script is exported from my Eureka 2.12 software.

It's a nice work !

I forgot ...
Code:
X():u
Y():5*(1-cos(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*2.2-t))+sin(2*pi*t))/8
Z():v
[u]:-1,  1
[v]:0,  1

And a flag flying in the wind.
Cheers.
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nextstep
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Joined: 06 Jan 2007
Posts: 538

PostPosted: Sun Jul 08, 2007 4:23 pm    Post subject: Re: Dynamic System Simulation Reply with quote

François LE COAT wrote:

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 POV-Ray script is exported from my Eureka 2.12 software.

Hi all,
Thanks François and I'm glad you like it Razz. Your example is simply beautiful and the use of parametric forme make it very nice. Eureka seems to have a powerful povscript export tool Shocked 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. Razz
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nextstep
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Posts: 538

PostPosted: Sun Jul 08, 2007 4:33 pm    Post subject: Re: Dynamic System Simulation Reply with quote

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) + (z-t*t*13 +1)*(z-t*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 Razz : That make the intersection of the drop with the plan very smooth Shocked .
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nextstep
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Posts: 538

PostPosted: Sun Jul 08, 2007 9:21 pm    Post subject: Reply with quote

Hi all, Very Happy
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(): (z-6*(1-cos(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 Razz
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nextstep
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Posts: 538

PostPosted: Fri Sep 07, 2007 4:49 am    Post subject: Reply with quote

Hi all,
A new pendulum-like system. Right now, It's only the part on it's center Razz
Quote:
Name: Pendulum
/*
pendulum :
*/
F(): if( sqrt( (x)^2 +(y)^2 +(z)^2) < 5 ,min((x)^2 + (y-(z-4)*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
;


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François LE COAT



Joined: 03 Feb 2007
Posts: 27
Location: France

PostPosted: Sun Sep 16, 2007 3:41 pm    Post subject: Re: Dynamic System Simulation Reply with quote

Quote:
Quote:

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 POV-Ray script is exported from my Eureka 2.12 software.

Thanks François and I'm glad you like it Razz. Your example is simply beautiful and the use of parametric form make it very nice. Eureka seems to have a powerful povscript export tool Shocked 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. Razz

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 (time-space) coordinates.

You may enjoy it, if the ATARI (virtual) machine is not too strange using Shocked

Regards,
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nextstep
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Posts: 538

PostPosted: Sat Jun 14, 2014 4:57 pm    Post subject: Reply with quote

Hi,
Here is an adaptation to MathMod of the falling drop example.
Click the "Morph" button to see the morph effect. enjoy Smile

Quote:

{
"Iso3D": {
"Component": [
"fallingdrop"
],
"Fxyz": [
"-((z-6*(1-cos(sqrt(x^2+y^2)-t*2*pi))/sqrt(x^2+y^2+4))*(2*(x^2+y^2)+(z-40*sin(t*pi)+1)^2-10)-1000)"
],
"Name": [
"FallingDrop"
],
"Xmax": [
"20"
],
"Xmin": [
"-20"
],
"Ymax": [
"20"
],
"Ymin": [
"-20"
],
"Zmax": [
"50"
],
"Zmin": [
"-1"
]
}
}

fallingdrop by taha_ab, on Flickr
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