I have several (3 or 4) large-sized spheres with known radii ${r_L}$ and known coordinates. The spheres might overlap. I then add a small sphere with known coordinates and known radius ${r_S}$.
Is it possible to tell, just from the coordinates and radii, whether this small sphere will be completely contained within the union of the large spheres?
The easy case is when the small sphere is fully contained within a single large sphere, which occurs when the distance between their centres is less than ${r_L} - {r_S}$. If the distance is slightly larger, then the small sphere will be partially occluded by the large sphere. The difficulty is determining whether the bit that peeks out will then be occluded by another large sphere.
A Monte-Carlo approach might be to sample points within ${r_S}$ of the small sphere, and test whether these points are within or without the larger spheres, but I'm hoping for an analytical or faster solution.
