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MathMod — Alien
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Published: 2015-10-10 05:59:32 +0000 UTC; Views: 242; Favourites: 1; Downloads: 0
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Description
Alien (parametric model)This model is to show a useful technique when you need to "cut" your mathematical model to see inside it. To do this, you can reduce the definition domain of u and v parameters or use the "CND" property defined in MathMod but in this case I simply changed the function definitions in the "Shells" script from:
"Fx": ["Gx(u,v,t)"],
"Fy": ["Gy(u,v,t)"],
"Fz": ["Gz(u,v,t)"]
to :
"Fx": [ "Gx(u*cos(v),v*sin(u),t)" ],
"Fy": [ "Gy(u*cos(v),v*sin(u),t)" ],
"Fz": [ "Gz(u*cos(v),v*sin(u),t)"]
MathMod script:
{
"Param3D": {
"Description ": ["Alien by Abderrahman Taha 10/10/2015"],
"Name": ["Alien"],
"Component": ["Alien"],
"Const": ["cu=0.0000000000001",
"cv=0.0000000000001"],
"Funct": ["Fx=-cos(u) *(3 *cos(v) - cos(3 *v))",
"Fy= 3 *sin(v) - sin(3 * v)",
"Fz= sin(u) *(3 *cos(v) - cos(3 * 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)",
"Tickness= (.4*abs(cos(11*(u))^2 - sin(13*(v))^5 ))^3",
"Gx=Fx(u,v,t)+Tickness(u,v,t)*n1(u,v,t)/(R(u,v,t)+.0001)",
"Gy=Fy(u,v,t)+Tickness(u,v,t)*n2(u,v,t)/(R(u,v,t)+.0001)",
"Gz=Fz(u,v,t)+Tickness(u,v,t)*n3(u,v,t)/(R(u,v,t)+.0001)"],
"Fx": ["Gx(u*cos(v),v*sin(u),t)"],
"Fy": ["Gy(u*cos(v),v*sin(u),t)"],
"Fz": ["Gz(u*cos(v),v*sin(u),t)"],
"Umax": ["2*pi"],
"Umin": ["0"],
"Vmax": [" pi/2"],
"Vmin": ["-pi/2"]
}
}
