Let P be a polygon and $\mathcal{C}$ a set of shortcuts, where each shortcut is a directed straight-line segment connecting two vertices of P. A shortcut hull of P is another polygon that encloses P and whose oriented boundary is composed of elements from $\mathcal{C}$. We require P and the output shortcut hull to be weakly simple polygons, which we define as a generalization of simple polygons. Shortcut hulls find their application in cartography, where a common task is to compute simplified representations of area features. We aim at a shortcut hull that has a small area and a small perimeter. Our optimization objective is to minimize a convex combination of these two criteria. If no holes in the shortcut hull are allowed, the problem admits a straight-forward solution via computation of shortest paths. For the more challenging case in which the shortcut hull may contain holes, we present a polynomial-time algorithm that is based on computing a constrained, weighted triangulation of the input polygon's exterior. We use this problem as a starting point for investigating further variants, e.g., restricting the number of edges or bends. We demonstrate that shortcut hulls can be used for the schematization of polygons.

令P为多边形且$\mathcal{C}$一组快捷方式，其中每个快捷方式都是连接P的两个顶点的有向直线段。P的快捷外壳是另一个包围P的多边形，其定向边界由来自的元素组成$\mathcal{C}$. 我们需要P输出快捷方式外壳是弱简单多边形，我们将其定义为简单多边形的泛化。Shortcut hulls 在制图学中得到应用，其中一项常见任务是计算区域特征的简化表示。我们的目标是具有小面积和小周长的捷径船体。我们的优化目标是最小化这两个标准的凸组合。如果快捷船体中不允许存在任何漏洞，则该问题允许通过计算最短路径的直接解决方案。对于快捷外壳可能包含孔的更具挑战性的情况，我们提出了一种多项式时间算法，该算法基于计算输入多边形外部的约束加权三角剖分。我们使用这个问题作为研究进一步变体的起点，例如，限制边缘或弯曲的数量。我们证明了快捷外壳可用于多边形的模式化。