I'm making my own blimp out of emergency blankets (Mylar), and I want it to have a NACA0025 airfoil shape. I'm new to Mathematica, but I still managed to create the shape I wanted with RevolutionPlot3D. But now I'm stuck: how can I unfold the mesh so that I can print the UV map, and therefore be able to cut it out of Mylar sheets?

Here is my code so far:

c = 1;
f[x_] := 
  (1.25 (0.2969 (x/c)^(1/2) - 0.1260 (x/c) - 0.3516 (x/c)^2 + 
   0.2843 (x/c)^3 - 0.1036 (x/c)^4))

petal = 
  RevolutionPlot3D[f[x], {x, 0, c}, {θ, 0, Pi/3}, 
    RevolutionAxis -> {1, 0, 0}, 
    Mesh -> All, 
    PlotRange -> All, 
    AspectRatio -> Automatic]
  • 2
    $\begingroup$ You probably want to add the option PlotPoints->40 to smooth the mesh out a bit. A UV map can have areas that are stretched a lot in the 3D model which would exceed the elastic limit of the material and tear it. Producing an ideal UV map which minimizes this stress is a tricky optimization problem. With that in mind, perhaps it's easier to handle this in blender, MeshLab, or another tool that can produce UV maps. You can export the mesh as a Wavefront .OBJ using Export["mesh.obj",petal] $\endgroup$ – flinty Jun 30 '20 at 15:02

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