I’m not sure I understand the question being asked in the original post at the start of this thread.
Is the aim to create a non inflated shape that takes on a specific pre-determined form when inflated?
This is actually a rather complex and non-linear problem.
First of all, many shapes are impossible to form as inflatables (for instance a bowl, or anything with parts which are concave but with positive Gaussian curvature), unless you add some other internal connections. So taking a shape and deflating it will not generally give you something that inflates to the original shape.
Also you need to consider the elasticity of the material. If you start with your target shape as the rest state of the membrane, when you apply the pressure it will expand until the tension balances the pressure, enlarging and changing the shape in the process. Therefore the challenge can be seen as finding the right levels of pre-tension across the mesh so that the pressure is already exactly balanced by the membrane tension when in the target shape.
There’s a nice paper on this problem of inverse design of inflatables here:
For smoothly curved shapes with everywhere inwards pointing mean curvature vectors and fairly non-stretchy material though, simpler approaches might work. Even just setting a constant pre-tension across the whole mesh, and adjusting it until the shape stays approximately the same when pressurized might get you close enough for practical purposes.
I think this is what Pneuhaus did for these projects, and I believe they used Kangaroo for some of the design process.