多边形的顶点限制外部简化
Shortcut Hulls: Vertex-restricted Outer Simplifications of Polygons
摘要：
设$P$是一个无交叉多边形，$\mathcal C$是一组捷径，其中每个捷径是连接$P$的两个顶点的有向直线段。$P$的快捷外壳是另一个包含$P$的无交叉多边形，其定向边界由来自$\mathcal C$的元素组成。船体发现他们的应用在地理相关的问题，如简化等高线。我们的目标是一个快捷的船体，线性平衡的封闭面积和周长。如果捷径外壳中不允许有洞，则该问题可以通过最短路径直接解决。对于更具有挑战性的情况下，捷径船体可能包含孔，我们提出了一个多项式时间算法，该算法是基于计算的约束，加权三角形的输入多边形的外部。我们使用这个问题作为研究进一步变体的起点，例如，限制了边缘或弯曲的数量。我们证明，快捷外壳可以用于绘制点集的粗糙程度，以及为多边形的图式化。
英文摘要：
Let $P$ be a crossing-free 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 crossing-free polygon that encloses $P$ and whose oriented boundary is composed of elements from $\mathcal C$. Shortcut hulls find their application in geo-related problems such as the simplification of contour lines. We aim at a shortcut hull that linearly balances the enclosed area and perimeter. If no holes in the shortcut hull are allowed, the problem admits a straight-forward solution via shortest paths. For the more challenging case that 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 drawing the rough extent of point sets as well as for the schematization of polygons.
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