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.

翻译：在两条正方形高速公路H的情况下,我们考虑时间轴船体问题。 在这个问题中,高速公路的行驶速度比高速公路的行驶速度快,而P点定点的时轴船体是P的关闭,以包括最短的时道。在本文中,我们提供了用两条正方形高速公路建造时间轴船体的算法。我们达到了在L1测距中任意高速速度的O(nlog n)时间的最佳结果。对于L2测距,以无限的高速速度,我们也达到了O(nlog n)时间的目标。