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nextstep
Site Admin
Joined: 06 Jan 2007
Posts: 539
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 Posted: Wed Jan 10, 2007 6:04 am Post subject: How to make Isosurfaces with "tickness" ? |
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Hi all,
The ultimate formulas for tickness is :
G[x, y, z] = F[x, y, z] * F[x - (T/R)*dF()/dx, y - (T/R)*dF()/dy, z - (T/R)*df()/dz]
Where : dF()/dx == partial derivative of F() to the variable x.
R = sqrt[(dF()/dx)^2 + (dF()/dy)^2 + (dF()/dz)^2]
T = Tickness value
Applied to Schwartz-P :
F():(cos(x) + cos(y) + cos(z))*((cos(x + sin(x)/2.3) + cos(y + sin(y)/2.3) + cos(z + sin(z)/2.3)))
[x, y, z]: -7, 7
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tomot
Joined: 21 Jul 2007
Posts: 23
Location: Vancouver
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| Posted: Fri Jul 27, 2007 4:02 pm Post subject: |
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nextstep:
does one need to use a program such as Mathmatica or Maple
to do the calculus that produce thickness for other surfaces?
if the answer is No to the above question;
How do I implement the code for your "Ultimate thickness formula"
into a the .k3ds file
Please explain a little bit more about the process.
thanks! |
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nextstep
Site Admin
Joined: 06 Jan 2007
Posts: 539
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| Posted: Sun Jul 29, 2007 1:04 am Post subject: |
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Hi,
| Code: | does one need to use a program such as Mathematica or Maple
to do the calculus that produce thickness for other surfaces? |
If you want to make tick surfaces, you can use some 3D program (AFAIK Hexagon can do it) : This is how most 3D artists are generating them. Using my formula can be hard especially if you're not familiar with this kind of exercises  . Also, there is no way to implement it in a .k3ds file because K3DSurf can't generate the appropriate formulas for your surface.
In short, i suggest you to look for informations on which 3D program (like Hexagon, Maya...) that have implemented this kind of feature. Hope it's clear enought...
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inode
Joined: 27 Jan 2007
Posts: 127
Location: Austria
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| Posted: Sun Nov 04, 2007 11:39 am Post subject: Another simple way to make a surface thick |
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In some cases it's very easy to created a thick surface by squaring those part of the formular which is describing the main surface.
For example the formula of a hyperboloid is:
x*x - y*y + z
Squaring it and subtract it from a "thickness value" will give the desired formula:
4 -(x*x - y*y + z)^2
Gerd
example 2:
Sphere: 1-(x^2+y^2+z^2)
Hollow Sphere: 0.05-(1-(x^2+y^2+z^2))^2
example 3:
Rounded Cube: 1-(x^22 + y^22 + z^22)
Hollow Rounded Cube: 0.8-(1-(x^22 + y^22 + z^22))^2 |
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Schmiegel
Joined: 28 Nov 2009
Posts: 26
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| Posted: Mon Nov 30, 2009 10:03 pm Post subject: |
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Thanks for allowing me to participate in this forum 
I was digging out this old thread because it deals best with the problem I'm having.
I would like to do 3d renders of isosurfaces. Following the above instructions I succeed to create an object having thickness - however if I try this for infinite surfaces (my favourite is the gyroid) I end up with an open object resulting from K3D clipping a limited cube out of infinity (see also image at top).
So I cannot intersect etc the resulting object in 3D apps.
Now, the thread is old - is hopefully somebody aware of a freeware app or method that currently can do the job of adding a third dimension to 2D isosurfaces - or can close the 'open' faces of an clipped object.
P.S.: I have seen the hint for Hexagon but i'm just a 3d playchild so it is a bit expensive ... |
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nextstep
Site Admin
Joined: 06 Jan 2007
Posts: 539
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| Posted: Mon Nov 30, 2009 11:16 pm Post subject: |
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Hi all,
Welcome Schmiegel in the forum 
There is a way to make a closed and tick isosurface: in K3DSurf, the example "CloseIso" shows how to do it for a simple surface and the example "CloseIso_2" shows how to do it for a tick isosurface.
From K3DSurf:
CloseIso
| Quote: | /*
To make a closed Isosurface, you can use the "if" instruction like in this example with Schwartz :
if(
(x^10 + y^10 +z^10 < 200000), // We use a Cube as a condition
-(cos(x) + cos(y) + cos(z) ) , // Schwartz
(x^10 + y^10 +z^10 - 200000 ) // Cube
*/
if((x^10 + y^10 +z^10 < 200000),
-(cos(x) + cos(y) + cos(z) ) ,
(x^10 + y^10 +z^10 - 200000)) |
CloseIso_2
| Quote: |
/*
And now, to make a tick and closed Schwartz Isosurface, we use the two formulas described above :
*/
if((x^10 + y^10 +z^10 < 3*(3.5^10)),
(cos(x) + cos(y) + cos(z))*((cos(x + sin(x)/(2*sqrt(sin(x)^2 + sin(y)^2 + sin(z)^2))) +cos(y + sin(y)/(2*sqrt(sin(x)^2 + sin(y)^2 + sin(z)^2))) +cos(z + sin(z)/(2*sqrt(sin(x)^2 + sin(y)^2 + sin(z)^2))))) ,
(x^10 + y^10 +z^10 - 3*(3.5^10)))
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No need for a budget software to do this
Hope this can help.
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Abderrahman |
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Schmiegel
Joined: 28 Nov 2009
Posts: 26
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| Posted: Tue Dec 01, 2009 10:49 pm Post subject: |
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Merci beaucoup Taha!
This was the information I was looking for. And it worked for me. As I am an optimist I made that:
http://www.flickr.com/groups/1304045@N23/pool/
I hope it fills soon with some art. I have added there my first result - going in a totally different direction as expected but that's typical for play children
Thanks again! |
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sudhirsinghgill
Joined: 31 Jul 2012
Posts: 1
Location: India
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| Posted: Wed Aug 01, 2012 8:33 am Post subject: Thickening surface |
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Friends 
I have easy method to thicken the surface. First of all special thanks to admin to approve my request to join you guys. I also tried the method of using function to thicken the surface and somewhat successful. I tried many software for that most of them are not easy and failure.
Now I uses Blender to thicken the surface. I import the OBJ exported from the K3DSurf and then use Solidify Modifier with thickness. This works perfectly and then I export it as STL/OBJ.
Regards,
Sudhir Gill
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nextstep
Site Admin
Joined: 06 Jan 2007
Posts: 539
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| Posted: Wed Oct 08, 2014 1:21 am Post subject: |
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Hi all,
For the Gyroid, the formula for thickness T = 1:
| Quote: |
{
"Iso3D": {
"Name": [
"Gyroid"
],
"Component": [
"Gyroid"
],
"Fxyz": [
"(cos(x)*sin(y)+cos(y)*sin(z)+cos(z)*sin(x))*(cos(x-(-sin(x)*sin(y)+cos(x)*cos(z))/sqrt((-sin(x)*sin(y)+cos(x)*cos(z))^2+(-sin(y)*sin(z)+cos(y)*cos(x))^2+(-sin(z)*sin(x)+cos(z)*cos(y))^2))*sin(y-(-sin(y)*sin(z)+cos(y)*cos(x))/sqrt((-sin(x)*sin(y)+cos(x)*cos(z))^2+(-sin(y)*sin(z)+cos(y)*cos(x))^2+(-sin(z)*sin(x)+cos(z)*cos(y))^2))+cos(y-(-sin(y)*sin(z)+cos(y)*cos(x))/sqrt((-sin(x)*sin(y)+cos(x)*cos(z))^2+(-sin(y)*sin(z)+cos(y)*cos(x))^2+(-sin(z)*sin(x)+cos(z)*cos(y))^2))*sin(z-(-sin(z)*sin(x)+cos(z)*cos(y))/sqrt((-sin(x)*sin(y)+cos(x)*cos(z))^2+(-sin(y)*sin(z)+cos(y)*cos(x))^2+(-sin(z)*sin(x)+cos(z)*cos(y))^2))+cos(z-(-sin(z)*sin(x)+cos(z)*cos(y))/sqrt((-sin(x)*sin(y)+cos(x)*cos(z))^2+(-sin(y)*sin(z)+cos(y)*cos(x))^2+(-sin(z)*sin(x)+cos(z)*cos(y))^2))*sin(x-(-sin(x)*sin(y)+cos(x)*cos(z))/sqrt((-sin(x)*sin(y)+cos(x)*cos(z))^2+(-sin(y)*sin(z)+cos(y)*cos(x))^2+(-sin(z)*sin(x)+cos(z)*cos(y))^2)))"
],
"Xmax": [
"10"
],
"Xmin": [
"-10"
],
"Ymax": [
"10"
],
"Ymin": [
"-10"
],
"Zmax": [
"10"
],
"Zmin": [
"-10"
]
}
}
|
 TickGyroid by taha_ab, on Flickr
I didn't try to make the formula more compact but I'm open to all your suggestions
In the near future, MathMod's scripting language will support a better formulation for this kind of equations.
For your information:
F(x,y,z) = (cos(x)*sin(y)+cos(y)*sin(z)+cos(z)*sin(x))
dF/dx = (-sin(z)*sin(x) + cos(z)*cos(y))
dF/dy = (-sin(y)*sin(z) + cos(y)*cos(x))
dF/dz = (-sin(z)*sin(x) + cos(z)*cos(y))
R = sqrt[(dF()/dx)^2 + (dF()/dy)^2 + (dF()/dz)^2]
T = Tickness value = 1
Also you can play with the formula by making it a "closed" isosurface
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Abderrahman |
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nextstep
Site Admin
Joined: 06 Jan 2007
Posts: 539
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| Posted: Wed Oct 08, 2014 10:04 am Post subject: |
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Hi all,
when extracting the Gyroid equation from the above implicit surface, you will have a triply periodique latice equation (F[x - (T/R)*dF()/dx, y - (T/R)*dF()/dy, z - (T/R)*df()/dz] )
You can play with the this equation by given T some values between {-1, 1}
This another example is made with two triply periodic latice, for (T =1 , T=G=-1) and (T =.2 , T=G=-.2)
Now, the big question, what will happen if you make T = T(x,y,z) ? That should be a good way to make quite complicated pattern on a surface
| Quote: | {
"Iso3D": {
"Name": [
"Gyroid"
],
"Component": [
"Gyroid"
],
"Const": [
"T = 1",
"G = -1"
],
"Cnd": [
" (sqrt(x^2 + y ^2 + z ^2)) < 8"
],
"Fxyz": [
"((cos(x-(-sin(x)*sin(y)+cos(x)*cos(z))*T/sqrt((-sin(x)*sin(y)+cos(x)*cos(z))^2+(-sin(y)*sin(z)+cos(y)*cos(x))^2+(-sin(z)*sin(x)+cos(z)*cos(y))^2))*sin(y-(-sin(y)*sin(z)+cos(y)*cos(x))*T/sqrt((-sin(x)*sin(y)+cos(x)*cos(z))^2+(-sin(y)*sin(z)+cos(y)*cos(x))^2+(-sin(z)*sin(x)+cos(z)*cos(y))^2))+cos(y-(-sin(y)*sin(z)+cos(y)*cos(x))*T/sqrt((-sin(x)*sin(y)+cos(x)*cos(z))^2+(-sin(y)*sin(z)+cos(y)*cos(x))^2+(-sin(z)*sin(x)+cos(z)*cos(y))^2))*sin(z-(-sin(z)*sin(x)+cos(z)*cos(y))*T/sqrt((-sin(x)*sin(y)+cos(x)*cos(z))^2+(-sin(y)*sin(z)+cos(y)*cos(x))^2+(-sin(z)*sin(x)+cos(z)*cos(y))^2))+cos(z-(-sin(z)*sin(x)+cos(z)*cos(y))*T/sqrt((-sin(x)*sin(y)+cos(x)*cos(z))^2+(-sin(y)*sin(z)+cos(y)*cos(x))^2+(-sin(z)*sin(x)+cos(z)*cos(y))^2))*sin(x-(-sin(x)*sin(y)+cos(x)*cos(z))*T/sqrt((-sin(x)*sin(y)+cos(x)*cos(z))^2+(-sin(y)*sin(z)+cos(y)*cos(x))^2+(-sin(z)*sin(x)+cos(z)*cos(y))^2)))) *
( (cos(x-(-sin(x)*sin(y)+cos(x)*cos(z))*G/sqrt((-sin(x)*sin(y)+cos(x)*cos(z))^2+(-sin(y)*sin(z)+cos(y)*cos(x))^2+(-sin(z)*sin(x)+cos(z)*cos(y))^2))*sin(y-(-sin(y)*sin(z)+cos(y)*cos(x))*G/sqrt((-sin(x)*sin(y)+cos(x)*cos(z))^2+(-sin(y)*sin(z)+cos(y)*cos(x))^2+(-sin(z)*sin(x)+cos(z)*cos(y))^2))+cos(y-(-sin(y)*sin(z)+cos(y)*cos(x))*G/sqrt((-sin(x)*sin(y)+cos(x)*cos(z))^2+(-sin(y)*sin(z)+cos(y)*cos(x))^2+(-sin(z)*sin(x)+cos(z)*cos(y))^2))*sin(z-(-sin(z)*sin(x)+cos(z)*cos(y))*G/sqrt((-sin(x)*sin(y)+cos(x)*cos(z))^2+(-sin(y)*sin(z)+cos(y)*cos(x))^2+(-sin(z)*sin(x)+cos(z)*cos(y))^2))+cos(z-(-sin(z)*sin(x)+cos(z)*cos(y))*G/sqrt((-sin(x)*sin(y)+cos(x)*cos(z))^2+(-sin(y)*sin(z)+cos(y)*cos(x))^2+(-sin(z)*sin(x)+cos(z)*cos(y))^2))*sin(x-(-sin(x)*sin(y)+cos(x)*cos(z))*G/sqrt((-sin(x)*sin(y)+cos(x)*cos(z))^2+(-sin(y)*sin(z)+cos(y)*cos(x))^2+(-sin(z)*sin(x)+cos(z)*cos(y))^2))) )
"
],
"Xmax": [
"10"
],
"Xmin": [
"-10"
],
"Ymax": [
"10"
],
"Ymin": [
"-10"
],
"Zmax": [
"10"
],
"Zmin": [
"-10"
]
}
}
|
 PeriodiqueLatice1 by taha_ab, on Flickr
 PeriodiqueLatice by taha_ab, on Flickr
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Abderrahman |
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nextstep
Site Admin
Joined: 06 Jan 2007
Posts: 539
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| Posted: Fri Oct 10, 2014 2:20 am Post subject: |
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Hi,
A more compact version of the last script:
| Quote: | {
"Iso3D": {
"Cnd": [
" (sqrt(x^2 + y ^2 + z ^2)) < 8"
],
"Component": [
"GyroidLatice"
],
"Const": [
"T = 1",
"G = -1"
],
"Funct": [
"R=sqrt( (-sin(x)*sin(y)+cos(x)*cos(z))^2+(-sin(y)*sin(z)+cos(y)*cos(x))^2+(-sin(z)*sin(x)+cos(z)*cos(y))^2 )",
"df=(-sin(x)*sin(y)+cos(x)*cos(z))",
"Gyroid=(cos(x) * sin(y) + cos(y) * sin(z) + cos(z) * sin(x))"
],
"Fxyz": [
"Gyroid(x-df(x,y,z,t)*T/R(x,y,z,t), y - df(y,z,x,t)*T/R(x,y,z,t), z - df(z,x,y,t)*T/R(x,y,z,t) ,t)* Gyroid(x-df(x,y,z,t)*G/R(x,y,z,t), y - df(y,z,x,t)*G/R(x,y,z,t), z - df(z,x,y,t)*G/R(x,y,z,t) ,t)"
],
"Name": [
"GyroidLatice"
],
"Xmax": [
"8"
],
"Xmin": [
"-8"
],
"Ymax": [
"8"
],
"Ymin": [
"-8"
],
"Zmax": [
"8"
],
"Zmin": [
"-8"
]
}
}
|
_________________
Cheers,
Abderrahman |
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nextstep
Site Admin
Joined: 06 Jan 2007
Posts: 539
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| Posted: Fri Oct 10, 2014 3:56 am Post subject: |
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Hi,
With the Diamond implicit surface, I get something a little bit different:
| Quote: |
{
"Iso3D": {
"Name": [
"DiamondLatice"
],
"Component": [
"DiamondLatice"
],
"Cnd": [
" (sqrt(x^2 + y ^2 + z ^2)) < 8"
],
"Const": [
"T = 1",
"G = -1"
],
"Funct": [
"df=(cos(x)*sin(y)*sin(z) + cos(x)*cos(y)*cos(z) - sin(x)*sin(y)*cos(z) - sin(x)*cos(y)*sin(z))",
"R=sqrt( df(x,y,z,t)^2 + df(y,z,x,t)^2 + df(z,y,x,t)^2)",
"Diamond=(sin(x)*sin(y)*sin(z) + sin(x)*cos(y)*cos(z) + cos(x)*sin(y)*cos(z) + cos(x)*cos(y)*sin(z))"
],
"Fxyz": [
"Diamond(x-df(x,y,z,t)*T/R(x,y,z,t), y - df(y,z,x,t)*T/R(x,y,z,t), z - df(z,x,y,t)*T/R(x,y,z,t) ,t)*
Diamond(x-df(x,y,z,t)*G/R(x,y,z,t), y - df(y,z,x,t)*G/R(x,y,z,t), z - df(z,x,y,t)*G/R(x,y,z,t) ,t)"
],
"Xmax": [
"8"
],
"Xmin": [
"-8"
],
"Ymax": [
"8"
],
"Ymin": [
"-8"
],
"Zmax": [
"8"
],
"Zmin": [
"-8"
]
}
}
|
 DiamondLatice by taha_ab, on Flickr
If the first script doesn't work, try this one:
| Quote: | {
"Iso3D": {
"Cnd": [
" (sqrt(x^2 + y ^2 + z ^2)) < 8"
],
"Component": [
"DiamondLatice"
],
"Const": [
"T = 1",
"G = -1"
],
"Funct": [
"df=(cos(x)*sin(y)*sin(z) + cos(x)*cos(y)*cos(z) - sin(x)*sin(y)*cos(z) - sin(x)*cos(y)*sin(z))",
"R=sqrt(( cos(x)*sin(y)*sin(z) + cos(x)*cos(y)*cos(z) - sin(x)*sin(y)*cos(z) - sin(x)*cos(y)*sin(z))^2 + ( cos(y)*sin(z)*sin(x) + cos(y)*cos(z)*cos(x) - sin(y)*sin(z)*cos(x) - sin(y)*cos(z)*sin(x))^2 + ( cos(z)*sin(x)*sin(y) + cos(z)*cos(x)*cos(y) - sin(z)*sin(x)*cos(y) - sin(z)*cos(x)*sin(y))^2)",
"Diamond=(sin(x)*sin(y)*sin(z) + sin(x)*cos(y)*cos(z) + cos(x)*sin(y)*cos(z) + cos(x)*cos(y)*sin(z))"
],
"Fxyz": [
"Diamond(x-df(x,y,z,t)*T/R(x,y,z,t), y - df(y,z,x,t)*T/R(x,y,z,t), z - df(z,x,y,t)*T/R(x,y,z,t) ,t)* Diamond(x-df(x,y,z,t)*G/R(x,y,z,t), y - df(y,z,x,t)*G/R(x,y,z,t), z - df(z,x,y,t)*G/R(x,y,z,t) ,t)"
],
"Name": [
"DiamondLatice"
],
"Xmax": [
"8"
],
"Xmin": [
"-8"
],
"Ymax": [
"8"
],
"Ymin": [
"-8"
],
"Zmax": [
"8"
],
"Zmin": [
"-8"
]
}
}
|
_________________
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Abderrahman |
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nextstep
Site Admin
Joined: 06 Jan 2007
Posts: 539
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| Posted: Sat Oct 11, 2014 10:58 pm Post subject: Linoid Latice |
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Hi all,
This is what you get when given the Linoid some thickness:
| Quote: | {
"Iso3D": {
"Name": [
"LinoidLatice"
],
"Cnd": [
" (sqrt(x^2 + y ^2 + z ^2)) < 3"
],
"Component": [
"LinoidLatice"
],
"Const": [
"T = .05",
"G = -.05"
],
"Funct": [
"df=((1/2)*(2*cos(2*x)*cos(y)*sin(z) + sin(2*y)*cos(z)*cos(x) - sin(2*z)*sin(x)*sin(y)) -(1/2)*(-2*sin(2*x)*cos(2*y) - 2*cos(2*z)*sin(2*x)))",
"R=sqrt( df(x,y,z,t)^2 + df(y,z,x,t)^2 + df(z,y,x,t)^2)",
"Linoid=((1/2)*(sin(2*x)*cos(y)*sin(z) + sin(2*y)*cos(z)*sin(x)+ sin(2*z)*cos(x)*sin(y)) -(1/2)*(cos(2*x)*cos(2*y)+cos(2*y)*cos(2*z)+cos(2*z)*cos(2*x))+0.15)"
],
"Fxyz": [
"Linoid(x-df(x,y,z,t)*T/R(x,y,z,t), y - df(y,z,x,t)*T/R(x,y,z,t), z - df(z,x,y,t)*T/R(x,y,z,t) ,t)* Linoid(x-df(x,y,z,t)*G/R(x,y,z,t), y - df(y,z,x,t)*G/R(x,y,z,t), z - df(z,x,y,t)*G/R(x,y,z,t) ,t)"
],
"Xmax": [
"3"
],
"Xmin": [
"-3"
],
"Ymax": [
"3"
],
"Ymin": [
"-3"
],
"Zmax": [
"3"
],
"Zmin": [
"-3"
]
}
} |
 LinoidLatice by taha_ab, on Flickr
_________________
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Abderrahman |
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nextstep
Site Admin
Joined: 06 Jan 2007
Posts: 539
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| Posted: Sun Oct 12, 2014 3:10 am Post subject: |
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|
Hi,
For the Neovius implicit surface, you get this:
| Quote: |
{
"Iso3D": {
"Cnd": [
" (sqrt(x^2 + y ^2 + z ^2)) < 9"
],
"Component": [
"NeoviusLatice"
],
"Const": [
"T = .1",
"G = -.1"
],
"Funct": [
"df=(-3*sin(x) -4*sin(x)*cos(y)*cos(z))",
"R=sqrt( df(x,y,z,t)^2 + df(y,z,x,t)^2 + df(z,y,x,t)^2)",
"Neovius=(3*(cos(x)+cos(y)+cos(z))+4*cos(x)*cos(y)*cos(z))"
],
"Fxyz": [
"Neovius(x-df(x,y,z,t)*T/R(x,y,z,t), y - df(y,z,x,t)*T/R(x,y,z,t), z - df(z,x,y,t)*T/R(x,y,z,t) ,t)* Neovius(x-df(x,y,z,t)*G/R(x,y,z,t), y - df(y,z,x,t)*G/R(x,y,z,t), z - df(z,x,y,t)*G/R(x,y,z,t) ,t)"
],
"Name": [
"NeoviusLatice"
],
"Xmax": [
"9"
],
"Xmin": [
"-9"
],
"Ymax": [
"9"
],
"Ymin": [
"-9"
],
"Zmax": [
"9"
],
"Zmin": [
"-9"
]
}
}
|
 NeoviusLatice by taha_ab, on Flickr
_________________
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Abderrahman |
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nextstep
Site Admin
Joined: 06 Jan 2007
Posts: 539
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| Posted: Sun Oct 12, 2014 8:46 am Post subject: |
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Hi,
For the Schwarz P surface, we get this:
| Quote: | {
"Iso3D": {
"Name": [
"SchwarzSkelet"
],
"Cnd": [
" (sqrt(x^2 + y ^2 + z ^2)) < 9"
],
"Component": [
"SchwarzPSkelet"
],
"Const": [
"T = .9",
"G = -.9"
],
"Funct": [
"df=(-sin(x))",
"R=sqrt( df(x,y,z,t)^2 + df(y,z,x,t)^2 + df(z,y,x,t)^2)",
"SchwarzP=(cos(x) + cos(y) + cos(z))"
],
"Fxyz": [
"SchwarzP(x-df(x,y,z,t)*T/R(x,y,z,t), y - df(y,z,x,t)*T/R(x,y,z,t), z - df(z,x,y,t)*T/R(x,y,z,t) ,t)* SchwarzP(x-df(x,y,z,t)*G/R(x,y,z,t), y - df(y,z,x,t)*G/R(x,y,z,t), z - df(z,x,y,t)*G/R(x,y,z,t) ,t)"
],
"Xmax": [
"9"
],
"Xmin": [
"-9"
],
"Ymax": [
"9"
],
"Ymin": [
"-9"
],
"Zmax": [
"9"
],
"Zmin": [
"-9"
]
}
}
|
 SchwarzP by taha_ab, on Flickr
For MathMod's old version you should use this script:
| Code: | {
"Iso3D": {
"Name": [
"SchwarzSkelet"
],
"Cnd": [
" (sqrt(x^2 + y ^2 + z ^2)) < 9"
],
"Component": [
"SchwarzPSkelet"
],
"Const": [
"T = .9",
"G = -.9"
],
"Funct": [
"df1=(-sin(x))",
"df2=(-sin(y))",
"df3=(-sin(z))",
"R=sqrt( df1(x,y,z,t)^2 + df2(x,y,z,t)^2 + df3(x,y,z,t)^2)",
"SchwarzP=(cos(x) + cos(y) + cos(z))"
],
"Fxyz": [
"SchwarzP(x-df1(x,y,z,t)*T/R(x,y,z,t), y - df2(x,y,z,t)*T/R(x,y,z,t), z - df3(x,y,z,t)*T/R(x,y,z,t) ,t)* SchwarzP(x-df1(x,y,z,t)*G/R(x,y,z,t), y - df2(x,y,z,t)*G/R(x,y,z,t), z - df3(x,y,z,t)*G/R(x,y,z,t) ,t)"
],
"Xmax": [
"9"
],
"Xmin": [
"-9"
],
"Ymax": [
"9"
],
"Ymin": [
"-9"
],
"Zmax": [
"9"
],
"Zmin": [
"-9"
]
}
} |
_________________
Cheers,
Abderrahman |
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