Given an ordered family of n pairwise disjoint convex simple objects in the plane, the authors given 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. The present O(n) time algorithm contrasts with an ¦[(nlogn) lower bound for finding a line transversal of a family of n convex simple objects in the plane.
