ways to smooth faceted lines

Divide%20surface_cull%20list.gh

Curved%20Surface_HL.3dm

Hello,

I am trying to create a definition with which I can get a result shown in the attached image. I have a basic definition that looks somewhat close to the desired result but still the lines are too faceted especially when it hits the center bottom of the cone. Anyone with better approaches to creating such lines, please share your wisdom. Your help is greatly appreciated.