  We consider the time-convex hull problem in the presence of two orthogonal
highways H. In this problem, the travelling speed on the highway is faster than
off the highway, and the time-convex hull of a point set P is the closure of P
with respect to the inclusion of shortest time-paths. In this paper, we provide
the algorithm for constructing the time-convex hull with two orthogonal
highways. We reach the optimal result of O(n log n) time for arbitrary highway
speed in the L1-metric. For the L2-metric with infinite highway speed, we hit
the goal of O(n log n) time as well.
