Surface unrolling

The modelling of the kite's cells as described here is slighty wrong, because the surface is considered flat from the leading edge to the trailing edge. In real world, the cell bulge because of the internal pressure. Here's a few pictures to illustrate this :

On the above picture, you can see a 'simple' modelling of the upper skin of a cell. For simplification, the two profiles are of the same length, and the canopy is flat.

On the pictures below, I've kept the same profiles and profile's positions, but I've (roughly) simulated the cell bulge. Notice that the leading edge and trailing edge don't bulge, because that's exactly what we want to obtain with skin tensionning. In that order : front view, side view and perspective view :

Now, here are the corresponding unrolled surfaces :

I let you guess wich one match the bulging cell... There's some work left before beeing able to sew something like this. Notice the trapezoid shape of the unrolled trailing edge (up) : it's exactly what we are doing with skin tensionning and pinches ! For the leading edge, it's not so obvious.

For information, it took me four hours to manually unroll this single (and symetrical) cell (50 small surfaces). Who wants to try for a whole kite ?