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MathMod — Twin Klein
#parametric #mathmod #mathematics
Published: 2017-04-30 00:03:09 +0000 UTC; Views: 676; Favourites: 2; Downloads: 3
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Description
Mathmod was used to generate this animation from a parametric definition, described in the attached script.This animation (and nine other slightly different) can be generated from the same script by giving the parameter M a value from 1 to 10.
MathMod script:
{
"Param3D": {
"Description ": ["Twin Klein by Abderrahman Taha 29/04/2017"],
"Name": ["Twin Klein"],
"Component": ["TwinKlein"],
"Const": ["cu=0.001",
"cv=0.001",
"N=5",
"M=3",
"A=3.5",
"B=2",
"C=3",
"D=3",
"MaxU=2*pi",
"MinU=0",
"MaxV=10*pi",
"MinV=0"],
"Funct": ["th=if(M=1, 0.3*((abs(sin(11*u)*cos(11*v)))^19+0.1*((sin(2*N*u)))),if(M=2, 0.9*sin((N*v)% pi/3), if(M=3, (0.4*abs(cos(7*(u))^2 - sin(9*(v))^5 ))^3,if(M=4, 0.4*sin(N*v-u)^100,if(M=5, 0.4*sin(N*v),if(M=6, 0.4*sin(2*N*v-u),if(M=7, 0.4*sin(N*v)^10,if(M=8, -0.3*cos((abs(cos(12*v)+cos(6*(v-u))*sin(12*u))/1.8)^5)*2*sin((abs(cos(7*v)+cos(7*(v-u))*sin(17*u))/1.9)^5.5),if(M=9, ((sin(15*u)*cos(15*u)))^4 + (sin(2*N*v)),if(M=10, ((sin(9*u)*cos(9*v)))^2 +0.5* (sin(2*N*u)), (0.4*abs(cos(7*(u))^2 - sin(9*(v))^5 ))^3))))))))))",
"Fx=if(v<2*pi, (A-(A-1)*cos(v))*cos(u),if(v < 3*pi, -B+(B+cos(u))*cos(v),-B+B*cos(v)-cos(u)))",
"Fy=if(v < 2*pi,(A-(A-1)*cos(v))*sin(u), sin(u))",
"Fz=if(v < pi, -C*sin(v), if(v < 2*pi, D*v-D*pi, if(v < 3*pi,((D-1)+cos(u))*sin(v)+D*pi,-D*v+D*4*pi)))",
"Fx=if(v<6*pi, Fx(u,v,t), -Fx(u,(v-6*pi)%(4*pi),t))",
"Fy=if(v<6*pi,Fy(u,v,t), Fy(u,(v-6*pi)%(4*pi),t))",
"Fz=if(v<6*pi,Fz(u,v,t), -Fz(u,(v-6*pi)%(4*pi),t)-19)",
"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))",
"Rapp=u/sqrt(u*u+v*v+t*t)",
"Fx=Fx(u,v,t)+if(v<6*pi,th(u,v-3*t,t),th(u,v+3*t,t))*Rapp(n1(u,v,t),n2(u,v,t),n3(u,v,t))",
"Fy=Fy(u,v,t)+if(v<6*pi,th(u,v-3*t,t),th(u,v+3*t,t))*Rapp(n2(u,v,t),n1(u,v,t),n3(u,v,t))",
"Fz=Fz(u,v,t)+if(v<6*pi,th(u,v-3*t,t),th(u,v+3*t,t))*Rapp(n3(u,v,t),n1(u,v,t),n2(u,v,t))"],
"Fx": ["Fx(u,v,t)"],
"Fy": ["Fy(u,v,t)"],
"Fz": ["Fz(u,v,t)"],
"Umax": ["MaxU"],
"Umin": ["MinU"],
"Vmax": ["MaxV"],
"Vmin": ["MinV"]
}
}
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Comments: 3
Wow, I thought the single kleinian bottle was awesome, but this is even better! Great work
👍: 0 ⏩: 1
