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ufoace
Joined: 11 Mar 2013 Posts: 46
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inode
Joined: 27 Jan 2007 Posts: 127 Location: Austria
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Posted: Sun Apr 27, 2014 8:23 am Post subject: GridBall-Varations |
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Variations of an Algebraic Surface call 'GridBall', where you can change the integer value 'n'.
Will MathMod be able to create an animation e.g. with values 2,4,6,8,6,4 for 'n' ?
Code: | Name: PG_GridBallN6
/* Isosurface: PG_GridBallN6 4/2014 Gerd Platl */
F(): 0.0001 - ((x*x-y*y) * (y*y-z*z) * (z*z-x*x))^2 - 10*(x*x+y*y+z*z-1)^6
[x]: -1.11 , 1.11
[y]: -1.11 , 1.11
[z]: -1.11 , 1.11
;
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inode
Joined: 27 Jan 2007 Posts: 127 Location: Austria
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Posted: Sun Apr 27, 2014 8:41 am Post subject: Another variation... |
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This is - hard to believe - another variation of the Gridball.
Will MathMod be able to create an animation e.g. with values 2,4,6,8,6,4 for 'n' ?
Code: | Name: PG_RubberStar1
/* Isosurface: PG_RubberStar1 4/2014 Gerd Platl
a variant of PG_GridBallN6
*/
F(): 1 + 79*((x*x-y*y) * (y*y-z*z) * (z*z-x*x))^2 - (x*x+y*y+z*z-1)^6
[x]: -4 , 4
[y]: -4 , 4
[z]: -4 , 4
;
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nextstep Site Admin
Joined: 06 Jan 2007 Posts: 539
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Posted: Sun Apr 27, 2014 11:35 pm Post subject: |
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Hi,
This is a good starting script to animate your gridball. You can define some variables if you need more calculation speed. The problem with your examples is that "n" is an integer but "t" in MathMod scripts is not a discrete variable.
Quote: | {
"Iso3D": {
"Component": [ "GridBall" ],
"Fxyz": [ "0.0001-((x*x-y*y)*(y*y-z*z)*(z*z-x*x))^2-10*(x*x+y*y+z*z-1)^(23+int(20*sin(t*2*pi)))" ],
"Name": [ "GridBall" ],
"Xmax": [ "1.4" ],
"Xmin": [ "-1.4" ],
"Ymax": [ "1.4" ],
"Ymin": [ "-1.4" ],
"Zmax": [ "1.4" ],
"Zmin": [ "-1.4" ]
}
} |
_________________ Cheers,
Abderrahman |
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inode
Joined: 27 Jan 2007 Posts: 127 Location: Austria
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Posted: Fri May 16, 2014 9:25 am Post subject: PG_CagedStar1 = PG_GridBallN6 + PG_RubberStar1 |
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RubberStar meets GridBall - together in harmonie...
Code: | Name: PG_CagedStar1
/* Isosurface: PG_CagedStar1 5/2014 Gerd Platl
= PG_GridBallN6 + PG_RubberStar1
*/
F(): (4000 - ((x*x-y*y) * (y*y-z*z) * (z*z-x*x))^2 - 44*(x*x+y*y+z*z-16)^6)
* (1 + 89*((x*x-y*y) * (y*y-z*z) * (z*z-x*x))^2 - (x*x+y*y+z*z-1)^6 )
[x]: -5 , 5
[y]: -5 , 5
[z]: -5 , 5
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inode
Joined: 27 Jan 2007 Posts: 127 Location: Austria
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Posted: Fri May 16, 2014 12:41 pm Post subject: Witch of Maria Agnesi |
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Todays Google theme is the 296. birthday of Versiera der Maria Agnesi...
Code: | Name: PG_WitchOfAgnesi
X():tan(u)
Y():cos(u)^2*cos(v)
Z():cos(u)^2*sin(v)
[u]:-1.3, 1.3
[v]:0, 2*pi |
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inode
Joined: 27 Jan 2007 Posts: 127 Location: Austria
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Posted: Sat May 31, 2014 10:59 am Post subject: A new world record ? |
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Hi all
Oliver Labs constructed 2004 a surface of degree 7 (septic) with 99 singularities - that's world record.
The maximum number of singularities are 104.
See http://www.algebraicsurface.net/
and http://imaginary.org/gallery/oliver-labs (and press >) for the comprehensive formula.
Martin Heider has published his new septic with more than 99 singularities.
Take a look at http://www.spektrum.com/artikel/950384&_z=798888
Is that a new world record ???
Code: | Name: MH_Septik2
/* Isosurface: MH_Septik2
Septik mit 105 ??? Singularitäten, Martin Heider
http://www.spektrum.com/artikel/950384&_z=798888
*/
F(): (x*0.8358 -(z-0.5)*0.549)
* (x*cos( 2*pi/7)*0.8358 -y*sin( 2*pi/7)*0.8358 -(z-0.5)*0.549)
* (x*cos( 4*pi/7)*0.8358 -y*sin( 4*pi/7)*0.8358 -(z-0.5)*0.549)
* (x*cos( 6*pi/7)*0.8358 -y*sin( 6*pi/7)*0.8358 -(z-0.5)*0.549)
* (x*cos( 8*pi/7)*0.8358 -y*sin( 8*pi/7)*0.8358 -(z-0.5)*0.549)
* (x*cos(10*pi/7)*0.8358 -y*sin(10*pi/7)*0.8358 -(z-0.5)*0.549)
* (x*cos(12*pi/7)*0.8358 -y*sin(12*pi/7)*0.8358 -(z-0.5)*0.549)
- (x^2 +y^2 -4.731)^2
[x]: -4.5 , 4.5
[y]: -4.5 , 4.5
[z]: -4.5 , 8
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