Let's say, I have a closed 3D surface (say, the surface of a pebble). I want to pack it with spheres, but starting with the largest possible sphere, then the next largest possible nonoverlapping sphere and so on until I reach a specified lower limit on sphere size. Is there a unique solution? Is this a known, solved problem? Is there an obvious algorithmic approach to do this? Please advice. I am not in applied math or computational geometry, but love to wet my feet in these fine fields.

An analogous process to the one you describe is known as Apollonian sphere packing:


