On the Number of Lines Tangent to Four Convex Polyhedra
Résumé
We prove that, under a certain general position assumption, the number of lines tangent to four bounded disjoint convex polyhedra in \Real3 with a total of n edges is O(n2). Under the same assumption, we show that a set of k bounded disjoint convex polyhedra has at most O(n2k2) lines, possibly occluded, that are tangent to four of these polyhedra.