Make a curved surface from a network of curves

Hello, i cant figure out how to make a surface like the one on the picture. If i use rebuild and then move points, it dosnt relate to the shape af the curve anymore.

Thank you so much!

From your sketch it looks like it should be done with four surfaces, something like an extruded arc copied/rotated four times and trimmed.
Check the example joined.
example.3dm (833.9 KB)