Packing a closed 3D surface with non-overlapping spheres starting with the largest possible one and then working the way down

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 non-overlapping 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.

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It can't be unique in general. For example, the original volume may have rotational symmetries, which the packed versions do not respect. For some packings, one may have a choice of where to put the currently-largest-fitting sphere, and this choice may rule out other choices that might have been valid. – Joel David Hamkins Feb 25 '13 at 2:34
I see. Thanks. I was thinking of a particular approach. Please opine if you think it is reasonable. Say, my surface shape is defined by polygons. I can find all the voronoi spheres (allowing overlaps) in it. Then I start with the largest voronoi sphere contained inside my surface, then pick the next largest non-overlapping voronoi sphere and so on working my way down. Wouldn't that be a reasonably robust approach - even if I can't prove it is THE best collection? Are there better alternative approaches to that? – Raghavan Feb 25 '13 at 3:05