Copy a planar surface on a curved surface

Hi,

I am looking for a way to “project” or “draw” a flat surface on a spherical or curved surface. My main goal is to maintain the original surface’s area, which means that the actual Project command does not work.

Furthermore, since my flat surface contains thousands of curves, projecting those curves and drawing a surface out of them might take up to days.

If my question is not clear, I can provide some .cub files for you to have a clearer view.

Regards,
Christos

It would be helpful to have a .cub file or journal file to see how you want to maintain the surface area on the curved surface.