Unless your telescopic tubes are spring-loaded or something, you’ll need a lot of ropes! The transition of your mesh from flat to the desired surface is one where the mesh needs to grow radially outwards, so you’d need some kind of force in that direction (outwards for every tube).
Can you try to sketch what you think the endpoint would be? I can’t imagine a system of a few ropes being able to transform your flat mesh to the one you want. You’d be better off either with spring loaded tubes or maybe something like an inflatable bag beneath the mesh which when inflated would grow into the desired shape?
If you were to genuinely build this structure in real life I’d suggest having telescopic tubes which will lock when extended to the correct length (kinda like tent poles for large tents/gazebos). You’d then start in the middle and extend each one individually by hand. As the tubes lock into place the structure will slowly take shape. Not a fancy computational method but would be buildable like this! The last pavilion design I worked on was designed and fabricated using GH, but in the end the erection/installation was done the old fashioned by-hand way.