Mesh like spiderweb on not regular surface

[zimerman]

Hello,
I've got problem with making good and proper mesh on surface with shape like picture below.

I'd like to create mesh like spiderweb (and I can create it), but I need to reduce it by edges that I marked on the picture. I've tried Break Surface option, but it doesn't work. Could you help me and give some advice how can I do it in easiest way?

Thanks for help