Bretzel (Implicit)

 
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nextstep
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Joined: 06 Jan 2007
Posts: 538

PostPosted: Sun Feb 11, 2007 7:09 am    Post subject: Bretzel (Implicit) Reply with quote

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
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inode



Joined: 27 Jan 2007
Posts: 127
Location: Austria

PostPosted: Sun Feb 18, 2007 9:12 am    Post subject: Reply with quote

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

Cool 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

Surprised 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]   

http://commons.wikimedia.org/wiki/Image:Bretzel5.png

Wink Gerd


Last edited by inode on Fri Feb 23, 2007 11:33 am; edited 5 times in total
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nextstep
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Joined: 06 Jan 2007
Posts: 538

PostPosted: Sun Feb 18, 2007 4:32 pm    Post subject: Reply with quote

inode wrote:

Surprised 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 Very Happy
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Abderrahman
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jotero



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

PostPosted: Mon Feb 19, 2007 6:44 am    Post subject: Reply with quote

hello all Smile

link of Mike Williams http://www.econym.demon.co.uk/isotut/xref.htm Wink

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

PostPosted: Thu Feb 22, 2007 11:02 am    Post subject: Reply with quote

hello all Smile

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"

Wink Gerd


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



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PostPosted: Sat May 12, 2007 9:42 am    Post subject: Reply with quote

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
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jotero



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Posts: 153
Location: Germany Hannover

PostPosted: Sat May 12, 2007 9:58 am    Post subject: Reply with quote

very nice Gerd Smile
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