Author Message
nextstep

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) + (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
_________________
Cheers,
Abderrahman
François LE COAT

Joined: 03 Feb 2007
Posts: 28
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) + (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

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

It's a nice work !
_________________
-- archimedium
http://eureka.atari.org/
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) + (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

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

ciao
torolf
_________________
Kontakte
François LE COAT

Joined: 03 Feb 2007
Posts: 28
Location: France

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

 François LE COAT wrote: 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 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.
_________________
-- archimedium
http://eureka.atari.org/
nextstep

Joined: 06 Jan 2007
Posts: 539

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

 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 . 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
nextstep

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) + (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 : That make the intersection of the drop with the plan very smooth .
_________________
Cheers,
Abderrahman
nextstep

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(): (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
_________________
Cheers,
Abderrahman
nextstep

Joined: 06 Jan 2007
Posts: 539

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

Hi all,
A new pendulum-like 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-(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 ;

_________________
Cheers,
Abderrahman
François LE COAT

Joined: 03 Feb 2007
Posts: 28
Location: France

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

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 . 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 (time-space) coordinates.

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

Regards,
_________________
-- archimedium
http://eureka.atari.org/
nextstep

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": [ "-((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
_________________
Cheers,
Abderrahman
 Display posts from previous: All Posts1 Day7 Days2 Weeks1 Month3 Months6 Months1 Year Oldest FirstNewest First
 All times are GMT Page 1 of 1

 Jump to: Select a forum MathMod----------------MathMod Progress & featuresMathematical Models CollectionHow toBugsMathMod for WindowsMathMod for Linux/UnixMathMod For MACOSXMathMod TutorialsOther Mathematical ToolsOpen Discussion K3DSurf----------------K3DSurf Discuss/DiscussionsHow toK3DSurf math related questionsK3DSurf for WindowsK3DSurf for MacOSK3DSurf for LinuxOnline K3DSurf: J3DSurfNewsBugsOnline DocumentationAccount Activation Issue ?/ Problème d'activation de votre compte ?
You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot vote in polls in this forum