论文标题
在飞机上发现大约凸起的绳索
Finding Approximately Convex Ropes in the Plane
论文作者
论文摘要
凸绳问题是要在顶点A开始逆时针或顺时针凸绳绳索，并在简单多边形P的顶点B处结束，其中A是P和B凸面的顶点，从Infinity可以看到P和B的凸壳。提到的凸绳是连接A和B的最短路径，该路径未进入P的内部。在本文中，该问题被重建为在简单多边形中找到如此短的路径之一，并通过多次拍摄的方法解决。然后，我们表明，如果该方法的共线条件在所有射击点都保持，那么这些射击点会形成最短的路径。否则，通过该方法的更新获得的路径序列会收敛到最短路径。该算法在C ++中实现，用于数值实验。
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.
