Line transversals of balls and smallest enclosing cylinders in three dimensions

We establish a near-cubic upper bound on the complexity of the space of lin e transversals of a collection of n balls in three dimensions, and show tha t the bound is almost tight, in the worst case. We apply this bound to obta in a near-cubic algorithm for computing a smallest infinite cylinder enclos ing a given set of points or balls in 3-space. We also present an approxima tion algorithm for computing a Smallest enclosing cylinder.