Approximation of surface with conical patches

Hi all,

I am wondering where to start to approximate a given surface with conical patches.
The discussion began towards the bottom of the thread here:

Different from @DanielPiker’s response, however, I am not looking for planar quads where the 4 vertices lie on cones, but to use the actual conical surfaces as the patches to approximate. In addition, are there ways to optimize such that you minimize the amount of patches or even modifying the underlying surface so that itself becomes part of a cone or a combination of a few conical segments?

An example surface I’m interested in attached here, thank you.
srf.3dm (270.7 KB)