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inode
Joined: 27 Jan 2007
Posts: 127
Location: Austria
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 Posted: Sun Apr 14, 2013 10:02 am Post subject: Helix torus variants |
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Here some variants of a helix torus...
| Code: | Name: PG_HelixTorusQ6x17
/* Isosurface: PG_HelixTorusQ6x17 4/2013
*/
F(): 0.00001 * (sqrt((sqrt(x^2+y^2)-4)^2+z^2)-2)^8 + (x^2+y^2)
* (atan2(sqrt((sqrt(x^2+z^2)-3)^2+z^2) * sin(6*atan2(z,sqrt(x^2+y^2)-3)-17*atan2(y,x)) ,sqrt((sqrt(x^2+z^2)-3)^2+z^2) * cos(6*atan2(z,sqrt(x^2+y^2)-3)-17*atan2(y,x))
) / 23)^8 -0.00000001
[x]: -6.5 , 6.5
[y]: -6.5 , 6.5
[z]: -2.5 , 2.5
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| Code: | Name: PG_HelixTorus9x1
/* Isosurface: PG_HelixTorus9x1 4/2013
*/
F(): (sqrt((sqrt(x^2+y^2)-4)^2+z^2)-2)^2 + (x^2+y^2)
* (atan2(sqrt((sqrt(x^2+z^2)-3)^2+z^2) * sin(9*atan2(z,sqrt(x^2+y^2)-3)-1*atan2(y,x))
,sqrt((sqrt(x^2+z^2)-3)^2+z^2) * cos(9*atan2(z,sqrt(x^2+y^2)-3)-1*atan2(y,x))
) / 16)^2 -0.1
[x]: -6.5 , 6.5
[y]: -6.5 , 6.5
[z]: -2.5 , 2.5
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Last edited by inode on Thu Aug 01, 2013 3:28 pm; edited 4 times in total |
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abdelhamid belaid
Joined: 13 Aug 2009
Posts: 170
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| Posted: Sun Apr 14, 2013 6:39 pm Post subject: |
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Nice, Gerd, thanks for sharing and I'm waiting for more, also thank you very much, ufoace 
I would like to add, a simplified general formula for the HelixTorus1xn is:
| Code: |
(sqrt((sqrt(x^2+y^2)-R1)^2+z^2)-R2)^2 + (x^2+y^2)
* (atan2( sin(atan2(z,sqrt(x^2+y^2)-R1)- n*atan2(y,x))
cos(atan2(z,sqrt(x^2+y^2)-R1)- n*atan2(y,x))
) / n)^2 - R3^2 =0
[x]: -(R1+R2+R3) , R1+R2+R3
[y]: -(R1+R2+R3) , R1+R2+R3
[z]: -(R2+R3) , R2+R3 |
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inode
Joined: 27 Jan 2007
Posts: 127
Location: Austria
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| Posted: Thu Aug 01, 2013 3:24 pm Post subject: A 'higher' helix torus... |
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Another variant of a helix torus which is higher and thicker to the middle...
| Code: | Name: PG_HelixTorus11x3
F(): (sqrt((sqrt(x^2+y^2)-5)^2 +(0.5*z)^2)-3)^2 + (x^2+y^2)
* (atan2(sqrt((sqrt(x^2+(0.5*z)^2)-4)^2+(0.5*z)^2) * sin(11*atan2(z,sqrt(x^2+y^2)-4)-3*atan2(y,x))
,sqrt((sqrt(x^2+(0.5*z)^2)-4)^2+(0.5*z)^2) * cos(11*atan2(z,sqrt(x^2+y^2)-4)-3*atan2(y,x))
) / 16)^2 -0.1
[x]: -8.3 , 8.3
[y]: -8.3 , 8.3
[z]: -6.7 , 6.7
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abdelhamid belaid
Joined: 13 Aug 2009
Posts: 170
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| Posted: Thu Aug 01, 2013 4:34 pm Post subject: |
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very very beautiful, Gerd 
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