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nextstep Site Admin
Joined: 06 Jan 2007 Posts: 539
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Posted: Sun Feb 11, 2007 7:09 am Post subject: Bretzel (Implicit) |
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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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_________________ Cheers,
Abderrahman |
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inode
Joined: 27 Jan 2007 Posts: 127 Location: Austria
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Posted: Sun Feb 18, 2007 9:12 am Post subject: |
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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] |
http://commons.wikimedia.org/wiki/Image:Bretzel5.png
Gerd
Last edited by inode on Fri Feb 23, 2007 11:33 am; edited 5 times in total |
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nextstep Site Admin
Joined: 06 Jan 2007 Posts: 539
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Posted: Sun Feb 18, 2007 4:32 pm Post subject: |
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inode wrote: |
Do you know Bretzel5 too?
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Hi all,
Thanks inode for the simpler equation and for the link. Also, I didn't know the Bretzel5... is really great _________________ Cheers,
Abderrahman |
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jotero
Joined: 27 Jan 2007 Posts: 153 Location: Germany Hannover
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Posted: Mon Feb 19, 2007 6:44 am Post subject: |
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hello all
link of Mike Williams http://www.econym.demon.co.uk/isotut/xref.htm
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 _________________ Kontakte |
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inode
Joined: 27 Jan 2007 Posts: 127 Location: Austria
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Posted: Thu Feb 22, 2007 11:02 am Post subject: |
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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 |
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inode
Joined: 27 Jan 2007 Posts: 127 Location: Austria
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Posted: Sat May 12, 2007 9:42 am Post subject: |
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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
Joined: 27 Jan 2007 Posts: 153 Location: Germany Hannover
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Posted: Sat May 12, 2007 9:58 am Post subject: |
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very nice Gerd _________________ Kontakte |
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