Here is a simple little script, which creates a physics mathematics based Mylar Balloon.

The "oval" Mylar Balloon starts off as two circular disks of Mylar, fused together at their perimeters, which is then inflated.

Wrinkles or crimps or crinkles or creases are not included.

The (Mylar) Balloon script is a 2d curve generator, which creates a curve in one quadrant of the xz plane.

Mirror and Revolve to complete the balloon, are left up to the user. (Or Revolve and Mirror)

Mylar is a Dupont trademark.

A general link is:

http://en.wikipedia.org/wiki/Mylar_balloon_(geometry) add on the trailing )

Pretty pictures:

http://obzor.bio21.bas.bg/conference/Conference_files/sa14/Pulov%202014.pdf
There are several similar papers that can be downloaded from the internet:

The most detailed is viewable on jstor. (Sign up and use one of three "shelves".):

Mladenov I. and Oprea J., The Mylar Balloon Revisited. November 2003.

The script uses Carlson symmetric form elliptic integrals, and the Jacobi functions.

Additional papers, remarks and information are in the htm file.

The default modulus of .707106... (sqrt(2) /2) is correct for the mylar balloon.

Other values of the modulus between 0 and 1, exclusive, make a different 2d curve.

- Brian

Corrected script is in _Balloon2.zip, Oct31, 2014