Advise on Curving Planar Curves

Hello people,

I have a surface result of a revolve.

But I need to generate specific isocurves, matching this picture.

As you can see, the section curves curve as they move in the x axis.

Right now I have something like this:

I have figured out the order of how these lines connect, but I have no idea how I can curve them so they match the reality.

Any ideas would be really appreciated. Thanks in advance.