New IsoSurfaces...
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nextstep
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Joined: 06 Jan 2007
Posts: 538

PostPosted: Sun Nov 04, 2007 10:09 pm    Post subject: Reply with quote

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



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Sun Dec 09, 2007 10:27 am    Post subject: Cuby Face Reply with quote

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^2-5*(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

PostPosted: Thu Dec 20, 2007 8:23 pm    Post subject: Reply with quote

hi all! I've got a mutant animal:)

Name: mutant
F(): (abs(x*y)-z+abs(x*z)-y+abs(z*y)-x-z^2-x^2-y^2-(x*y*z)+1-(x*y)^2)
*((x+0.3)^2+(y+0.1)^2+(z+0.4)^2-0.75)
*((x+0.1)^2+(y+0.3)^2+(z+0.4)^2-0.75)
*((x-0.2)^2+(y-0.2)^2+(z+1.3)^2-0.2)
[x]: -4 , 4
[y]: -4 , 4
[z]: -4 , 4
;
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jotero



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

PostPosted: Thu Dec 20, 2007 8:33 pm    Post subject: Reply with quote

hello all Smile

WOW... Shocked interesting figure windir Wink

ciao
torolf
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nextstep
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Joined: 06 Jan 2007
Posts: 538

PostPosted: Fri Dec 21, 2007 1:18 pm    Post subject: Reply with quote

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



Joined: 20 Dec 2007
Posts: 2
Location: Hungary

PostPosted: Fri Dec 21, 2007 6:45 pm    Post subject: Reply with quote

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)-x-z^2-x^2-y^2

3. abs(x*y)-z+abs(x*z)-y+abs(z*y)-x-z^2-x^2-y^2-(x^2*y^2*z^2)

4. abs(x*y)-z+abs(x*z)-y+abs(z*y)-x-z^2-x^2-y^2-(x*y*z)+1

5.abs(x*y)-z+abs(x*z)-y+abs(z*y)-x-z^2-x^2-y^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)-x-z^2-x^2-y^2-(x*y*z)+1-(x*y)^2

7.abs(x*y)-z+abs(x*z)-y+abs(z*y)-x-z^2-x^2-y^2-(x*y*z)+1-(x*y)^2+z

8.abs(x*y)-z+abs(x*z)-y+abs(z*y)-x-z^2-x^2-y^2-(x*y)^2+2*x*y

I like this too:abs(x*y)-z+abs(x*z)-y+abs(z*y)-x-z^2-x^2-y^2-(x*y*z)+1-(x*y)^2+z+x*y+x+y

and the sixth combined with spheres is the elephant-hamster mutant Very Happy
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nextstep
Site Admin


Joined: 06 Jan 2007
Posts: 538

PostPosted: Sat Dec 22, 2007 10:31 am    Post subject: Reply with quote

Hi all,
Very interesting "face modeling" technique and primary shape Razz
Formulas Number 7 and 8 are very interesting too ( Num 8 or "Big Nose" make me Very Happy )
I think you've done a so good job with theses cartoon-like faces that the remaining of theres bodies will not be so difficult for you Razz
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



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Abderrahman
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Sat Dec 29, 2007 6:37 pm    Post subject: Reply with quote

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^2-x^2-y^2-(x*y*z)+1-(x*y)^2)
*((x+0.3)^2+(y+0.1)^2+(z+0.4)^2-0.75)
*((x+0.1)^2+(y+0.3)^2+(z+0.4)^2-0.75)
*((x-0.2)^2+(y-0.2)^2+(z+1.3)^2-0.2)
[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^2-x^2-y^2 -(x*y*z)-(x*y)^2
[x]: -4 , 2
[y]: -4 , 2
[z]: -4 , 2
;

but the eyes disappears. Sad

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^2-x^2-y^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

PostPosted: Sun Dec 30, 2007 1:59 pm    Post subject: Reply with quote

Hi all

Have used some time to collect my isosurface formulas.
You can now download the zip-file K3DSurf_PG_Surfaces.zip and load a surface-file (*.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
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Joined: 06 Jan 2007
Posts: 538

PostPosted: Sun Dec 30, 2007 4:12 pm    Post subject: Reply with quote

Hi all,
Thank you Gerd for the great list, it should be easy for K3DSurf users to use them in an archive file Smile
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.
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Abderrahman
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Wed Jan 02, 2008 3:08 pm    Post subject: Icosahedron variants... Reply with quote

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

PostPosted: Sun Jan 13, 2008 12:49 am    Post subject: Reply with quote

thank you very much for the formulas.
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Tue Feb 12, 2008 2:39 pm    Post subject: Reply with quote


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^16-0.06)
[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^4-22)
[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^4-31)
[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

PostPosted: Fri Mar 21, 2008 3:57 pm    Post subject: Happy Easter! Reply with quote

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 ... Wink

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

PostPosted: Thu Nov 27, 2008 11:31 am    Post subject: PG_RippleCube_2 11/2008 Reply with quote



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*(x-z)^2*(x-y)^2*(2*y-2*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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