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MathMod — Twisted Three Toroids
#mathmod #mathematics
Published: 2015-10-15 00:34:25 +0000 UTC; Views: 279; Favourites: 0; Downloads: 0
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Description
Following Carl Sequin way of cutting the Torus in interlocked smaller torus, I made a script that do just that
Here are some first results for the Torus cutting to 6 and 3 interlocked parts.
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Update:
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Here is it, the script to generate the "Inka Sun" and Carl Sequin cutted Toroids models.
By default, the attached model will cut the Torus to three Toroids.
You can set the number of Toroids with the parameter N (there is virtually no limit except the resolution of your model).
1) To generate the "Inka Sun", replace :
"Tickness1=if( t = 1, if ( (abs(sin((N/2)*u-v)))>.38,-.45,0),if ( (abs(sin((N/2)*u-v)))<.38,-.45,0))",
byÂ
"Tickness1= if(if(t=1,(abs(sin((N/2)*(u*(sin(v))-u))))<.4,(abs(sin((N/2)*(u*(sin(v))-u))))>.38),-.45,0)"
2) For the fourth model (see last attached image), replace by:
"Tickness1= if(if(t=1,(abs(sin((N/2)*(u*abs(sin(v))-u))))<.4,(abs(sin((N/2)*(u*abs(sin(v))-u))))>.38),-.45,0)"
Enjoy!
MathMod script:
{
"Param3D": {
"Description ": ["(Inka Sun) and Carl SequinToroids models by Abderrahman Taha 15/10/2015"],
"Name": ["Inka Sun"],
"Component": ["Inka Sun1",
"Inka Sun2"],
"Const": ["cu=0.001",
"cv=0.001",
"N=3"],
"Funct": ["TicknessInkaSun= if(if(t=1,(abs(sin((N/2)*(u*(sin(v))-u))))<.4,(abs(sin((N/2)*(u*(sin(v))-u))))>.38),-.45,0)",
"TicknessSave= if(if(t=1,(abs(sin((N/2)*(u*abs(sin(v))-u))))<.4,(abs(sin((N/2)*(u*abs(sin(v))-u))))>.38),-.45,0)",
"Tickness1=if( t = 1, if ( (abs(sin((N/2)*u-v)))>.38,-.45,0),if ( (abs(sin((N/2)*u-v)))<.38,-.45,0))",
"Fx= (1+0.5*cos(u))*cos(v)",
"Fy=0.5*sin(u)",
"Fz= (1+0.5*cos(u))*sin(v)",
"DFxu= ((Fx(u,v,t)-Fx(u+cu,v,t))/cu)",
"DFxv= ((Fx(u,v,t)-Fx(u,v+cv,t))/cv)",
"DFyu= ((Fy(u,v,t)-Fy(u+cu,v,t))/cu)",
"DFyv= ((Fy(u,v,t)-Fy(u,v+cv,t))/cv)",
"DFzu= ((Fz(u,v,t)-Fz(u+cu,v,t))/cu)",
"DFzv= ((Fz(u,v,t)-Fz(u,v+cv,t))/cv)",
"n1= (DFyu(u,v,t)*DFzv(u,v,t)-DFzu(u,v,t)*DFyv(u,v,t))",
"n2= (DFzu(u,v,t)*DFxv(u,v,t)-DFxu(u,v,t)*DFzv(u,v,t))",
"n3= (DFxu(u,v,t)*DFyv(u,v,t)-DFyu(u,v,t)*DFxv(u,v,t))",
"R=sqrt(n1(u,v,t)^2+n2(u,v,t)^2+n3(u,v,t)^2)",
"Gx=Fx(u,v,t)+Tickness1(u,v,t)*n1(u,v,t)/R(u,v,t)",
"Gy=Fy(u,v,t)+Tickness1(u,v,t)*n2(u,v,t)/R(u,v,t)",
"Gz=Fz(u,v,t)+Tickness1(u,v,t)*n3(u,v,t)/R(u,v,t)"],
"Fx": ["Gx(u,v,1)",
"Gx(u,v,0)"],
"Fy": ["Gy(u,v,1)",
"Gy(u,v,0)"],
"Fz": ["Gz(u,v,1)",
"Gz(u,v,0)"],
"Umax": ["2*pi",
"2*pi"],
"Umin": ["0",
"0"],
"Vmax": ["2*pi",
"2*pi"],
"Vmin": ["0",
"0"]
}
}
Carl Sequin video: www.youtube.com/watch?v=3_VydF…
