We prove that the set of directions of lines intersecting three disjoint
balls in R3 in a given order is a strictly convex subset of S2. We then
generalize this result to n disjoint balls in Rd. As a consequence, we can
improve upon several old and new results on line transversals to disjoint balls
in arbitrary dimension, such as bounds on the number of connected components
and Helly-type theorems.Comment: 21 pages, includes figure