Find the middle point of a grid of curves and create a secondary grid with the middle points.

Hello everyone, 

I'm new in grasshopper and Im trying to figure out the following issue:

I have at the moment a grid made of curves, now I need to find the intersection between this curves to have the individual segments. Afterwards I need to find the middle point of every individual segment and connect them. 

Please, any suggestion? I've been strugglinh with it and I can not fin the solution.

I attached the rhino file and grasshopper and a skecth of what im trying to do.

I would really appreciate your help!

THANKS in advance, 

Maria.