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MathMod — Pseudo Hopf Tori
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Published: 2015-10-11 09:37:21 +0000 UTC; Views: 491; Favourites: 3; Downloads: 1
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Description
Pseudo Hopf Tori (parametric model)There are some similarities between this model and the "Hopf Tori" mathematical model
Would love to make some holes in the original model...
The attached script let you define the number of spirals with the parameter N (N=3 in the attached script)
Enjoy!
MathMod script:
{
"Param3D": {
"Description ": ["Pseudo Hopf Tori by Abderrahman Taha 10/10/2015"],
"Name": ["Pseudo Hopf Tori"],
"Component": ["PseudoHopfTori"],
"Const": ["cu=0.0000000001",
"cv=0.0000000001",
"N=3"],
"Funct": ["Thickness = (abs(sin(15*u)*cos(15*v)))^7 + .4*((sin(2*N*u)))",
"Fx=-cos(u+v)/(sqrt(2.)+cos(v-u))",
"Fy=sin(v-u)/(sqrt(2)+cos(v-u))",
"Fz=sin(u+v)/(sqrt(2.)+cos(v-u))",
"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)+Tickness(u,v,t)*n1(u,v,t)/R(u,v,t)",
"Gy=Fy(u,v,t)+Tickness(u,v,t)*n2(u,v,t)/R(u,v,t)",
"Gz=Fz(u,v,t)+Tickness(u,v,t)*n3(u,v,t)/R(u,v,t)"],
"Fx": ["Gx(u,v,t)"],
"Fy": ["Gy(u,v,t)"],
"Fz": ["Gz(u,v,t)"],
"Umax": ["pi"],
"Umin": ["0"],
"Vmax": ["2*pi"],
"Vmin": ["0"]
}
}
