The article really could use a picture. If I understand correctly you can get a parabolic shape if you have a stretchy film over ring and apply a pressure diffe

The article really could use a picture. If I understand correctly you can get a parabolic shape if you have a stretchy film over ring and apply a pressure differential. The spherical balloon functions as the support ring for an internal reflective third layer. If both halves of the balloon are inflated to equal pressure the reflective layer is flat, but by changing the pressure in both halves the layer takes on a parabolic shape.