title: Check if box is covered by spheres
body: <p>I have an axis alligned 3D box (cuboid), and a sphere at each of its vertices (each with different radius). How can I check if all points of the box are covered by any of the spheres?</p>
  
  <p>I need an algorithm that is rather fast, and not necessarily exact.
  False negatives -- that is saying that the box is not covered when in fact it is -- are not a big problem, but still I would like to minimise this kind of errors. False positives are unacceptable.</p>
  
  <p>Intended use is calculating volume of an object specified by a signed distance function. I'm recursively dividing space and if a given box is completely outside or inside of the object, I know I can stop recursion on this level. False negative would cause extra splitting of the box, but not an error in the result.</p>