An efficient algorithm for touring a sequence of given convex polygons in the plane

Given a sequence of ordered convex polygons in which the adjacent polygons may intersect with each other, but the nonadjacent polygons do not intersect, a start point s, and an end point t in the plane, our goal is to obtain a shortest path that starts from s, visits each given polygon in order, and ends at t finally. We converted the touring polygons problem into the problem of computing the shortest path of visiting the disjoint line segments by analyzing the geometrical features of the given convex polygons, and preprocessing the intersection points of the jointed polygons, and using a forward partition process combined with a backward search process for finding the access edge of each convex polygon. Thus, we proposed an 0(max{n, klog⁁2k}) algorithm for solving the original problem, where n is the total number of vertices of the given polygons and k is the total number of polygons.