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Get 3D-printable Batman logo given cross section?

Cameron Walker

Posted 8 years ago

Hi, I am new to Mathematica. For a school project we have to do a model of a 3D shape with a known base and cross sections (i.e. squares, circles, etc...), find the volume of that shape via integration, and present the 3D model. Does anyone know how to get a diagram of this model on Mathematica, and how to use that model to get a 3D printable version of the shape? This is the plot for base I am working with: Plot[{ With[{ w=3Sqrt[1-(x/7)^2], l=(6/7)Sqrt[10]+(3+x)/2-(3/7)Sqrt[10]Sqrt[4-(x+1)^2], h=(1/2)(3(Abs[x-1/2]+Abs[x+1/2]+6)-11(Abs[x-3/4]+Abs[x+3/4])), r=(6/7)Sqrt[10]+(3-x)/2-(3/7)Sqrt[10]Sqrt[4-(x-1)^2]}, w+(l-w)UnitStep[x+3]+(h-l)UnitStep[x+1]+(r-h)UnitStep[x-1]+(w-r)UnitStep[x-3]], (1/2)(3Sqrt[1-(x/7)^2]+Sqrt[1-(Abs[Abs[x]-2]-1)^2]+Abs[x/2]-((3Sqrt[33]-7)/112)x^2-3)* ((x+4)/Abs[x+4]-(x-4)/Abs[x-4])-3*Sqrt[1-(x/7)^2]}, {x,-7,7}, AspectRatio->Automatic]

Hi, I am new to Mathematica. For a school project we have to do a model of a 3D shape with a known base and cross sections (i.e. squares, circles, etc...), find the volume of that shape via integration, and present the 3D model. Does anyone know how to get a diagram of this model on Mathematica, and how to use that model to get a 3D printable version of the shape? This is the plot for base I am working with:

enter image description here

Plot[{

    With[{
       w=3*Sqrt[1-(x/7)^2],
       l=(6/7)*Sqrt[10]+(3+x)/2-(3/7)*Sqrt[10]*Sqrt[4-(x+1)^2],
       h=(1/2)*(3*(Abs[x-1/2]+Abs[x+1/2]+6)-11*(Abs[x-3/4]+Abs[x+3/4])),
       r=(6/7)*Sqrt[10]+(3-x)/2-(3/7)*Sqrt[10]*Sqrt[4-(x-1)^2]},
       w+(l-w)*UnitStep[x+3]+(h-l)*UnitStep[x+1]+(r-h)*UnitStep[x-1]+(w-r)*UnitStep[x-3]],

    (1/2)*(3*Sqrt[1-(x/7)^2]+Sqrt[1-(Abs[Abs[x]-2]-1)^2]+Abs[x/2]-((3*Sqrt[33]-7)/112)*x^2-3)*
    ((x+4)/Abs[x+4]-(x-4)/Abs[x-4])-3*Sqrt[1-(x/7)^2]},

{x,-7,7}, AspectRatio->Automatic]

POSTED BY: Cameron Walker