# Unfold/develop a RevolutionPlot3D mesh onto a 2D plane?

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]

• 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] – flinty Jun 30 '20 at 15:02