Graham’s convex hull algorithm outperforms the others on those distributions where most of the points are on or near the boundary of the hull (Allison and Noga, 1984). To use this algorithm for finding an orthogonal convex hull of a finite planar point set, we introduce the concept of extreme points of a connected orthogonal convex hull of the set, and show that these points belong to the set. Then we prove that the connected orthogonal convex hull of a finite set of points is an orthogonal ($x,y$)-polygon where its convex vertices are its connected orthogonal convex hull’s extreme points. As a result, an efficient algorithm, based on the idea of Graham’s convex hull algorithm, for finding the connected orthogonal convex hull of a finite planar point set is presented. We also show that the lower bound of computational complexity of such algorithms is $O\left(n\log n\right)$. Some numerical results for finding the connected orthogonal convex hulls of random sets are given.

格雷厄姆的凸包算法在大多数点都位于或靠近包壳边界的那些分布上都优于其他算法（Allison和Noga，1984年）。为了使用该算法查找有限平面点集的正交凸包，我们引入了集合的相连正交凸包的极点的概念，并证明这些点属于该集。然后我们证明有限点集的连通正交凸包是正交（$X，ÿ$）-多边形，其中其凸顶点是其相连的正交凸壳的极限点。结果，提出了一种基于格雷厄姆凸壳算法思想的有效算法，用于寻找有限平面点集的连通正交凸壳。我们还表明，此类算法的计算复杂度下限为$Ø（ñ\mathrm{日志}ñ）$。给出了寻找随机集合的连通正交凸包的一些数值结果。