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nextstep Site Admin
Joined: 06 Jan 2007 Posts: 539

Posted: Sun Nov 04, 2007 10:09 pm Post subject: 


Hi all,
That's a lovely new serie of mathematical objects .
How about making a .k3ds master file with your mathematical objetcs to be included in the K3DSurf package?
Thanks for sharing _________________ Cheers,
Abderrahman 

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inode
Joined: 27 Jan 2007 Posts: 127 Location: Austria

Posted: Sun Dec 09, 2007 10:27 am Post subject: Cuby Face 


Code:  Name: PG_CubyFace_1
/* Name: PG_CubyFace_1 11/2007 by Gerd */
F(): (x^22 +y^22 +z^22)+3*x^4*y^4*z^4
+2*x^2*y^4*z^25*(x^3 + y^3 + z^3 + 1) +4*(x + y + z + 1) + 2
[x]: 2 , 2
[y]: 2 , 2
[z]: 2 , 2
;

This face looks a little crackbrained!
Last edited by inode on Thu Jan 03, 2008 9:58 am; edited 1 time in total 

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windir
Joined: 20 Dec 2007 Posts: 2 Location: Hungary

Posted: Thu Dec 20, 2007 8:23 pm Post subject: 


hi all! I've got a mutant animal:)
Name: mutant
F(): (abs(x*y)z+abs(x*z)y+abs(z*y)xz^2x^2y^2(x*y*z)+1(x*y)^2)
*((x+0.3)^2+(y+0.1)^2+(z+0.4)^20.75)
*((x+0.1)^2+(y+0.3)^2+(z+0.4)^20.75)
*((x0.2)^2+(y0.2)^2+(z+1.3)^20.2)
[x]: 4 , 4
[y]: 4 , 4
[z]: 4 , 4
; 

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

Posted: Thu Dec 20, 2007 8:33 pm Post subject: 


hello all
WOW... interesting figure windir
ciao
torolf _________________ Kontakte 

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nextstep Site Admin
Joined: 06 Jan 2007 Posts: 539

Posted: Fri Dec 21, 2007 1:18 pm Post subject: 


Hi all,
Yes that's a very beautiful "Cartoon like" mathematical object
Also, your way of making it from simple math objects is quite clever : I think a little explanation should be great . Thanks for sharing _________________ Cheers,
Abderrahman 

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windir
Joined: 20 Dec 2007 Posts: 2 Location: Hungary

Posted: Fri Dec 21, 2007 6:45 pm Post subject: 


hi!
I'm just a maths fan ,not a mathematician:)
If I find an interesting shape(random), I try to form it to a more interesting object .
In this case:
from the very first form:
1. abs(x*y)z+abs(x*z)y+abs(z*y)x+z^2+x^2+y^2
2. abs(x*y)z+abs(x*z)y+abs(z*y)xz^2x^2y^2
3. abs(x*y)z+abs(x*z)y+abs(z*y)xz^2x^2y^2(x^2*y^2*z^2)
4. abs(x*y)z+abs(x*z)y+abs(z*y)xz^2x^2y^2(x*y*z)+1
5.abs(x*y)z+abs(x*z)y+abs(z*y)xz^2x^2y^2(x*y*z)+1(x^2*y^2*z^2)
it's getting more exciting:)
6.abs(x*y)z+abs(x*z)y+abs(z*y)xz^2x^2y^2(x*y*z)+1(x*y)^2
7.abs(x*y)z+abs(x*z)y+abs(z*y)xz^2x^2y^2(x*y*z)+1(x*y)^2+z
8.abs(x*y)z+abs(x*z)y+abs(z*y)xz^2x^2y^2(x*y)^2+2*x*y
I like this too:abs(x*y)z+abs(x*z)y+abs(z*y)xz^2x^2y^2(x*y*z)+1(x*y)^2+z+x*y+x+y
and the sixth combined with spheres is the elephanthamster mutant 

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nextstep Site Admin
Joined: 06 Jan 2007 Posts: 539

Posted: Sat Dec 22, 2007 10:31 am Post subject: 


Hi all,
Very interesting "face modeling" technique and primary shape
Formulas Number 7 and 8 are very interesting too ( Num 8 or "Big Nose" make me )
I think you've done a so good job with theses cartoonlike faces that the remaining of theres bodies will not be so difficult for you
PS: You can use this free service to post some screenshot (after 5 posts, sorry that's a web server limitation) and also you probably better create your own thread
_________________ Cheers,
Abderrahman 

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inode
Joined: 27 Jan 2007 Posts: 127 Location: Austria

Posted: Sat Dec 29, 2007 6:37 pm Post subject: 


Hi WinDir
You are playing around with nice looking formulas.
I was trying to simplify your "Mutant" figure given by
Quote:  Name: Mutant1
/* mutant from 12/2007 from windir */
F(): (abs(x*y)z+abs(x*z)y+abs(z*y)x
z^2x^2y^2(x*y*z)+1(x*y)^2)
*((x+0.3)^2+(y+0.1)^2+(z+0.4)^20.75)
*((x+0.1)^2+(y+0.3)^2+(z+0.4)^20.75)
*((x0.2)^2+(y0.2)^2+(z+1.3)^20.2)
[x]: 4 , 2
[y]: 4 , 2
[z]: 4 , 2
; 
and suprise ... it can be simplified to ...
Quote:  Name: Mutant2
/* simplified mutant 12/2007 from windir */
F(): 1+ abs(x*y)z +abs(x*z)y +abs(z*y)x z^2x^2y^2 (x*y*z)(x*y)^2
[x]: 4 , 2
[y]: 4 , 2
[z]: 4 , 2
; 
but the eyes disappears.
Here another variant ...
Quote:  Name: Mutant3
/* another mutant 12/2007 original from windir */
F(): 0.3+abs(3*x*y)z +abs(0.7*x*z)y +abs(0.7*z*y)x z^2x^2y^2 (0.8*x*y*z)(x*y)^2
[x]: 4 , 2
[y]: 4 , 2
[z]: 6 , 2
;



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inode
Joined: 27 Jan 2007 Posts: 127 Location: Austria

Posted: Sun Dec 30, 2007 1:59 pm Post subject: 


Hi all
Have used some time to collect my isosurface formulas.
You can now download the zipfile K3DSurf_PG_Surfaces.zip and load a surfacefile (*.k3ds) with all my surface formulas.
Press the [load] button to select a surface file and select a loaded surface definition.
(Download: K3DSurf_PG_Surfaces.zip ) sorry, geocities has closed his pages
PG_Basics.k3ds includes some basic examples.
PG_IsoSurfaces.k3ds includes my published isosurface examples.
Last edited by inode on Fri Jul 09, 2010 2:12 pm; edited 1 time in total 

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nextstep Site Admin
Joined: 06 Jan 2007 Posts: 539

Posted: Sun Dec 30, 2007 4:12 pm Post subject: 


Hi all,
Thank you Gerd for the great list, it should be easy for K3DSurf users to use them in an archive file
For Windir's formula, eyes disappeared because the last part of the formula is missing, which consists on three spheres (two for eyes and one for the mouth). Windir used those spheres to make three holes on your simplified formula. _________________ Cheers,
Abderrahman 

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inode
Joined: 27 Jan 2007 Posts: 127 Location: Austria

Posted: Wed Jan 02, 2008 3:08 pm Post subject: Icosahedron variants... 


Icosahedron variants...
Code:  Name: PG_Icosa_2
/* Isosurface: PG_Icosa_2 1/2008 Gerd Platl */
F(): 2(cos(x+(1+sqrt(5))/2*y)
+ cos(x(1+sqrt(5))/2*y)
+ cos(y+(1+sqrt(5))/2*z)
+ cos(y(1+sqrt(5))/2*z)
+ cos(z(1+sqrt(5))/2*x)
+ cos(z+(1+sqrt(5))/2*x))*16
/(x*x+y*y+z*z)+0.172*sqrt(x*x+y*y+z^2)
[x]: 5 , 5
[y]: 5 , 5
[z]: 5 , 5
Cnd: (sin(5*x)^2 + cos(5*y)^2 +cos(5*z)^2 > 1.3)
; 
Code:  Name: PG_Icosa_3
/* Isosurface: PG_Icosa_3 1/2008 Gerd Platl */
F(): 2(cos(x+(1+sqrt(5))/2*y)
+ cos(x(1+sqrt(5))/2*y)
+ cos(y+(1+sqrt(5))/2*z)
+ cos(y(1+sqrt(5))/2*z)
+ cos(z(1+sqrt(5))/2*x)
+ cos(z+(1+sqrt(5))/2*x))
*12/(x*x+y*y+z*z)
0.0028*(x*x+y*y+z*z)^2
[x]: 6 , 6
[y]: 6 , 6
[z]: 6 , 6
; 
Last edited by inode on Tue Feb 12, 2008 2:30 pm; edited 1 time in total 

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Phil999
Joined: 08 Feb 2007 Posts: 24

Posted: Sun Jan 13, 2008 12:49 am Post subject: 


thank you very much for the formulas. 

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inode
Joined: 27 Jan 2007 Posts: 127 Location: Austria

Posted: Tue Feb 12, 2008 2:39 pm Post subject: 


Code:  Name: PG_WireCube_2
/* Isosurface: PG_WireCube_2 2/2008 Gerd Platl */
F(): x^18+y^18+z^18  (x^16+y^16+z^160.06)
[x]: 1.1 , 1.1
[y]: 1.1 , 1.1
[z]: 1.1 , 1.1
; 
Code:  Name: PG_Tuetue_1
/* Isosurface: PG_Tuetue_1 2/2008 Gerd Platl */
F(): (sin(x*y) + sin(y*z) + sin(z*x))  0.07*(x^4+y^4+z^422)
[x]: 5 , 5
[y]: 5 , 5
[z]: 5 , 5
; 
Code:  Name: PG_Tuetue_2
/* Isosurface: PG_Tuetue_2 2/2008 Gerd Platl */
F(): (sin(x*y) + sin(y*z) + sin(z*x))  0.037*(x^4+y^4+z^431)
[x]: 4 , 4
[y]: 4 , 4
[z]: 4 , 4
; 
Code:  Name: PG_Tuetue_3
/* Isosurface: PG_Tuetue_3 2/2008 Gerd Platl */
F(): 1000000*(sin(x*y) + sin(y*z) + sin(z*x))  (x^12+y^12+z^12)*11+700000
[x]: 5 , 7
[y]: 5 , 7
[z]: 5 , 7
; 
Last edited by inode on Tue Aug 25, 2009 8:46 am; edited 3 times in total 

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inode
Joined: 27 Jan 2007 Posts: 127 Location: Austria

Posted: Fri Mar 21, 2008 3:57 pm Post subject: Happy Easter! 


Wish you Happy Easter!
http://images.bizhat.com/show.php?id=332933
http://www.flickr.com/photos/flisp3d/4170703509
Playing with the CND function and setting some colors ...
To produce your own easter eggs using this simple Isosurface...
Code:  Name: PG_EasterEgg_1
/* Isosurface: PG_EasterEgg_1 3/2008 Gerd Platl */
F(): (15(x^2 +y^2 +0.6*z^2)z*3)sin(2222*atan2(z, sqrt(x*x + y*y)))
[x]: 5 , 5
[y]: 5 , 5
[z]: 9 , 8
Cnd: sin(16*atan2(x,y)+2*sin(2*z))>0
;

Last edited by inode on Tue Aug 03, 2010 12:20 pm; edited 2 times in total 

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inode
Joined: 27 Jan 2007 Posts: 127 Location: Austria

Posted: Thu Nov 27, 2008 11:31 am Post subject: PG_RippleCube_2 11/2008 


Code:  Name: PG_RippleCube_2
/* Isosurface: PG_RippleCube_2 11/2008 Gerd Platl */
F(): ((2*x)^2*(2*y)^2*(2*z)^2*(x+y)^2*(z+y)^2*(x+z)^2*(xz)^2*(xy)^2*(2*y2*z)^2)
0.1*(0.5(1(x^22 + y^22 + z^22))^2)
[x]: 1.1 , 1.1
[y]: 1.1 , 1.1
[z]: 1.1 , 1.1
Cnd: sin(26*atan2(x,y))
+sin(26*atan2(y,z))
+sin(26*atan2(z,x))>0
;

Last edited by inode on Fri Jul 09, 2010 2:02 pm; edited 2 times in total 

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