The convex rope problem is to find a counterclockwise or clockwise convex rope starting at the vertex a and ending at the vertex b of a simple polygon P, where a is a vertex of the convex hull of P and b is visible from infinity. The convex rope mentioned is the shortest path joining a and b that does not enter the interior of P. In this paper, the problem is reconstructed as the one of finding such shortest path in a simple polygon and solved by the method of multiple shooting. We then show that if the collinear condition of the method holds at all shooting points, then these shooting points form the shortest path. Otherwise, the sequence of paths obtained by the update of the method converges to the shortest path. The algorithm is implemented in C++ for numerical experiments.

翻译：凸绳问题是指在简单多边形P中，寻找从顶点a到顶点b的逆时针或顺时针凸绳，其中a是P的凸包顶点，b从无穷远处可见。所述凸绳是连接a和b且不进入P内部的最短路径。本文将该问题重构为在简单多边形中寻找此类最短路径的问题，并采用多点打靶法进行求解。我们证明：若该方法在所有打靶点处满足共线条件，则这些打靶点构成最短路径；否则，通过该方法更新得到的路径序列收敛至最短路径。该算法以C++实现并进行了数值实验。