On the Number of Lines Tangent to Four Convex Polyhedra

• Version appeared in CCCG'02.

Abstract: We prove that, under a certain general position assumption, the number of lines tangent to four bounded disjoint convex polyhedra in R³ 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.

Related publications

• Transversals to line segments in R³, with Hazel Everett, Sylvain Lazard, Frank Sottile and Sue Whitesides. CCCG'03.
• On the number of lines tangent to arbitrary polytopes in R³, with O. Devillers, V. Dujmovic, H. Everett, M. Glisse, X. Goaoc, S. Lazard, H.-S. Na, and S. Whitesides. SoCG'04.
• On the number of lines tangent to four polyhedra, with Olivier Devillers, Sylvain Lazard, Frank Sottile, and Sue Whitesides. CCCG'04.