Outside and inside views of a pneumatic cover for a swimming pool. You can see the cylindrical central section and the corners with a symmetrical pattern.
Air supported or pneumatic structures have been popular at certain times (especially in the second half of the 20th century) in the design of economic covers: warehouses, sports fields, swimming pools, etc.
Their patterning, when the plant is rectangular (most of the time), is reduced to solving the corner, in fact, half of the corner. By symmetry, we get the other half and, through the symmetry of the whole, we get also the other end of the cover.
The central section between corner to corner is a perfect cylinder, of which development is completely flat and therefore does not present any difficulty in patterning.
If you need to perform the calculation of the set, the cover needs to be mounted in order to see its behavior against wind or snow loads. In fact most of these covers do not support much snow and their behavior is based on melting accumulated snow through the interior heat. And we see that this is a solution with high risk since any failure in the heating can cause the collapse of the roof in case of heavy snow fall.