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MathMod [2015-09-19 18:23:48 +0000 UTC]

My first Decorative Vase...hope you like it!
Because of their Symmetrical figures and shapes, Pottery and Vases Scuptures are well suited for the mathematical modeling.
MathMod script:

{
"Iso3D": {
"Description": ["Vases-1.0 by Abderrahman Taha 19/09/2015"],
"Name": ["Vases_1"],
"Component": ["Vase1",
"Vase2",
"Vase3",
"Vase4",
"Vase5",
"Vase6"],
"Const": ["cx=0.0000000000001",
"cy=0.0000000000001",
"cz=0.0000000000001",
"Tickness2= (.25)",
"Tickness4= (.2)",
"Tickness5= (.2)",
"Tickness6= (1.2)",
"Tickness7= (1.2)"],
"Funct": ["Torussqrt(x*x+y*y)-3)^2+z*z-1",
"Bottom= (x*x + y*y + z*z - 1)",
"CarvinCondition=sin(atan2(sqrt(x*x+y*y),(-z+cx)))>1/1.1",
"IsoExterior=x*x/3.+y*y/3.-abs(1.5*sin(2*z/pi+.3)+1.8)",
"DFx2= ((IsoExterior(x,y,z,t)-IsoExterior(x+cx,y,z,t))/cx)",
"DFy2= ((IsoExterior(x,y,z,t)-IsoExterior(x,y+cy,z,t))/cy)",
"DFz2= ((IsoExterior(x,y,z,t)-IsoExterior(x,y,z+cz,t))/cz)",
"Rapport2= (sqrt(DFx2(x,y,z,t)*DFx2(x,y,z,t)+DFy2(x,y,z,t)*DFy2(x,y,z,t)+DFz2(x,y,z,t)*DFz2(x,y,z,t)))",
"Iso2= (IsoExterior(x+t*DFx2(x,y,z,t)*Tickness2/Rapport2(x,y,z,t),y+t*DFy2(x,y,z,t)*Tickness2/Rapport2(x,y,z,t),z+t*DFz2(x,y,z,t)*Tickness2/Rapport2(x,y,z,t),t))",
"TickIsoExterior= (Iso2(x,y,z,1)*Iso2(x,y,z,-1))",
"Iso=cos(x)*sin(y)+cos(y)*sin(z)+cos(z)*sin(x)",
"DFx= ((Iso(x,y,z,t)-Iso(x+cx,y,z,t))/cx)",
"DFy= ((Iso(x,y,z,t)-Iso(x,y+cy,z,t))/cy)",
"DFz= ((Iso(x,y,z,t)-Iso(x,y,z+cz,t))/cz)",
"Rapport= (sqrt(DFx(x,y,z,t)*DFx(x,y,z,t)+DFy(x,y,z,t)*DFy(x,y,z,t)+DFz(x,y,z,t)*DFz(x,y,z,t)))",
"Iso4= (Iso(x+t*DFx(x,y,z,t)*Tickness4/Rapport(x,y,z,t),y+t*DFy(x,y,z,t)*Tickness4/Rapport(x,y,z,t),z+t*DFz(x,y,z,t)*Tickness4/Rapport(x,y,z,t),t))",
"TickIso2= (Iso4(x,y,z,-1)*Iso4(x,y,z,1))",
"isoTransform_2=if(CarvinCondition(x,y,z,t)=0,TickIsoExterior(x,y,z,t),1)",
"isoTransform_3=if(CarvinCondition(x,y,z,t)&TickIsoExterior(x,y,z,t)<0,TickIso2(5*x,5*y,5*z,t),1)",
"Iso6= (Iso(x+t*DFx(x,y,z,t)*Tickness6/Rapport(x,y,z,t),y+t*DFy(x,y,z,t)*Tickness6/Rapport(x,y,z,t),z+t*DFz(x,y,z,t)*Tickness6/Rapport(x,y,z,t),t))",
"isoTransform_4=if(CarvinCondition(x,y,z,t)&TickIsoExterior(x,y,z,t)<0,Iso6(x*5,y*5,z*5,-1),1)",
"isoTransform_5=if(CarvinCondition(x,y,z,t)&TickIsoExterior(x,y,z,t)<0,-Iso6(x*5,y*5,z*5,1),1)"],
"Fxyz": ["isoTransform_2(x,y,-z,t)",
"isoTransform_3(x,y,-z,t)",
"isoTransform_4(x,y,-z,t)",
"isoTransform_5(x,y,-z,t)",
"Torus(1.7*x,1.7*y,2.2*(z+cos(pi/4*sqrt(x*x+y*y)))-10.6,t)",
"Bottom(x/2.4,y/2.4,2*(z+5.1),t)"],
"Xmax": ["5",
"3.5",
"3.5",
"3.5",
"3",
"3"],
"Xmin": ["-5",
"-3.5",
"-3.5",
"-3.5",
"-3",
"-3"],
"Ymax": ["5",
"3.5",
"3.5",
"3.5",
"3",
"3"],
"Ymin": ["-5",
"-3.5",
"-3.5",
"-3.5",
"-3",
"-3"],
"Zmax": ["4.5",
"2",
"2",
"2",
"7",
"-2"],
"Zmin": ["-5",
"-2",
"-2",
"-2",
"0",
"-7"]
}
}

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