Vertical Visibility Among Parallel Polygons in Three Dimensions

Abstract

Abstract. Let C = {C1, . . . , Cn} denote a collection of translates of a regular convex k-gon in the plane with the stacking order. The collection C forms a visibility clique if for every i < j the intersection Ci and Cj is not covered by the elements that are stacked between them, i.e., (Ci ∩ Cj) \ i<l<j C l = ∅. We show that if C forms a visibility clique its size is bounded from above by O(k 4 ) thereby improving the upper bound of 2 2 k from the aforementioned paper.We also obtain an upper bound of 2 2(k 2 )+2 on the size of a visibility clique for homothetes of a convex (not necessarily regular) k-gon.