Ordered stabbing of pairwise disjoint convex sets in linear time

Abstract Given an ordered family of n pairwise disjoint convex simple objects in the plane, we give an O( n ) time algorithm for finding the directed line transversals of the family that intersect the objects in order. Objects are simple if they have a constant size storage description, and if the intersections and common tangents between any two objects can be found in constant time. Our O( n ) time algorithm contrasts with an Ω( n log n ) lower bound for finding a line transversal of a family of n convex simple objects in the plane.