Method for wrapping a 2D shape over a 3D sphere-like shape

I am trying to figure out a method by which I can design a 2D shape that could be bent/draped over a 3D surface. My end goal is to find the most efficient way to bend thin sheet metal over the round part of a semi-sphere. It would be highly beneficial to figure out a way to optimize the 2D shape that would need to be cut out so that I could cover the semi-sphere with only 1 cutout, and some overlapping between the petals would be desirable. A starting point I thought of was the interruped-sinusoidal map gores that are made to cover globes:

Does anyone have an idea of a starting point for creating the optimal 2D shape? The starting point would be the XYZ (at some small grid spacing) of the underlying shape's coordinates.

Thanks and have a great one.