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nextstep

Joined: 06 Jan 2007
Posts: 539

Posted: Sun Feb 11, 2007 7:09 am    Post subject: Bretzel (Implicit)

Hi all,
 Quote: F(): ((x^2*(1-x^2)-y^2)^2+0.5*z^2-0.025*(1+(x^2+y^2+z^2))) [x]:-1.5, 1.5 [y]:-1, 1 [z]:-0.4, 0.4

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Abderrahman
inode

Joined: 27 Jan 2007
Posts: 127
Location: Austria

Posted: Sun Feb 18, 2007 9:12 am    Post subject:

Hi Taha
 Code: F(x,y,z,t) := ((x^2*(1-x^2)-y^2)^2+0.5*z^2-0.025*(1+(x^2+y^2+z^2)))  x [ -1.5, 1.5];  y [ -1.0, 1.0];  z [ -0.4, 0.4];

I know this isometric surface under the name Bretzel2 !
http://commons.wikimedia.org/wiki/Image:Bretzel2.png

A simpler formula for Bretzel2 is:
 Code: F(x,y,z,t) := (x^2*(1-x^2)-y^2)^2+z^2-0.03  x [ -1.1, 1.1];  y [ -0.7, 0.7];  z [ -0.2, 0.2];

http://www.mathcurve.com/surfaces/tore/tn.shtml

Do you know Bretzel5 too?
 Code: F(x,y,z,t) := ((x^2+y^2/4-1) * (x^2/4+y^2-1))^2 + z^2 - 0.1  x [ -2.2, 2.2]  y [ -2.2, 2.2]  z [-0.33, 0.33]

Last edited by inode on Fri Feb 23, 2007 11:33 am; edited 5 times in total
nextstep

Joined: 06 Jan 2007
Posts: 539

Posted: Sun Feb 18, 2007 4:32 pm    Post subject:

 inode wrote: Do you know Bretzel5 too?

Hi all,
Thanks inode for the simpler equation and for the link. Also, I didn't know the Bretzel5... is really great
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Abderrahman
jotero

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

Posted: Mon Feb 19, 2007 6:44 am    Post subject:

hello all

DecoCube:
 Code: F():((x^2+y^2-0.8^2)^2+(z^2-1)^2) * ((y^2+z^2-0.8^2)^2+(x^2-1)^2) * ((z^2+x^2-0.8^2)^2+(y^2-1)^2) -0.02 [x]:-1.2,  1.2 [y]:-1.2,  1.2 [z]:-1.2,  1.2

ciao
torolf
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inode

Joined: 27 Jan 2007
Posts: 127
Location: Austria

Posted: Thu Feb 22, 2007 11:02 am    Post subject:

hello all

DecoCube looks like 3 thin torus are melt together.

Another variation with rounded rectangle frames you'll get with
DecoCube4:
 Code: F(x,y,z,t) := ((x^4+y^4-1)^2+(z^4-1)^2) * ((y^4+z^4-1)^2+(x^4-1)^2) * ((z^4+x^4-1)^2+(y^4-1)^2) -0.06 [x]:-1.2,  1.2 [y]:-1.2,  1.2 [z]:-1.2,  1.2

"DecoCube4"

Gerd

Last edited by inode on Sat May 12, 2007 10:24 am; edited 2 times in total
inode

Joined: 27 Jan 2007
Posts: 127
Location: Austria

Posted: Sat May 12, 2007 9:42 am    Post subject:

hello

A nice Bretzel variation ... BretzelQ4

 Code: # Isosurface formula: BretzelQ4 (x*x*(1.21-x*x)^2*(3.8-x*x)^3-10*y*y)^2/10+60*z*z-2 [x]: -2.4 , 2.7 [y]: -2.4 , 2.7 [z]: -2.4 , 2.7

"BretzelQ4"

Last edited by inode on Sat May 12, 2007 10:23 am; edited 1 time in total
jotero

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

 Posted: Sat May 12, 2007 9:58 am    Post subject: very nice Gerd _________________Kontakte
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