标题： 一种用于精确且看似简单的隐喻地图的算法 显示英文标题

标题： An algorithm for accurate and simple-looking metaphorical maps

摘要： "隐喻地图"或"接触表示"是基于地理地图隐喻的顶点加权图的视觉表示。 顶点由国家表示，权重由国家的面积表示，边由它们之间的接触/边界表示。 权重映射到面积的准确性以及表示国家的多边形的简单性是隐喻地图的两个经典优化目标。 Mchedlidze和Schnorr [用于动态顶点加权图的隐喻地图，EuroVis 2022]提出了一种基于力的算法，该算法创建的隐喻地图在这两个优化目标之间取得平衡。 他们的地图看起来视觉上很简单，但地图的准确性远非最优——与所需相比，国家的面积可以变化高达30%。 在本文中，我们提供了对[用于动态顶点加权图的隐喻地图，EuroVis 2022]中算法的多方面扩展。 更具体地说： 1. 为了提高准确性：我们引入了区域刚度的概念，并建议一种根据地图区域当前压力变化刚度的技术。 2. 为了保持简单性：我们根据对应点是否出现在狭窄通道上，向每个多边形点施加的压力力引入一个权重系数。 3. 为了提高通用性：与[用于动态顶点加权图的隐喻地图，EuroVis 2022]不同，我们涵盖了非三角化的图。 这是通过在多个区域相交的地方生成点或在隐喻地图中引入孔来实现的。 我们进行了扩展的实验评估，结果表明，我们的算法能够在稍微牺牲一些简单性的前提下构建出几乎完美的面积准确性的隐喻地图。 显示英文摘要

摘要： "Metaphorical maps" or "contact representations" are visual representations of vertex-weighted graphs that rely on the geographic map metaphor. The vertices are represented by countries, the weights by the areas of the countries, and the edges by contacts/ boundaries among them. The accuracy with which the weights are mapped to areas and the simplicity of the polygons representing the countries are the two classical optimization goals for metaphorical maps. Mchedlidze and Schnorr [Metaphoric Maps for Dynamic Vertex-weighted Graphs, EuroVis 2022] presented a force-based algorithm that creates metaphorical maps that balance between these two optimization goals. Their maps look visually simple, but the accuracy of the maps is far from optimal - the countries' areas can vary up to 30% compared to required. In this paper, we provide a multi-fold extension of the algorithm in [Metaphoric Maps for Dynamic Vertex-weighted Graphs, EuroVis 2022]. More specifically: 1. Towards improving accuracy: We introduce the notion of region stiffness and suggest a technique for varying the stiffness based on the current pressure of map regions. 2. Towards maintaining simplicity: We introduce a weight coefficient to the pressure force exerted on each polygon point based on whether the corresponding point appears along a narrow passage. 3. Towards generality: We cover, in contrast to [Metaphoric Maps for Dynamic Vertex-weighted Graphs, EuroVis 2022], non-triangulated graphs. This is done by either generating points where more than three regions meet or by introducing holes in the metaphorical map. We perform an extended experimental evaluation that, among other results, reveals that our algorithm is able to construct metaphorical maps with nearly perfect area accuracy with a little sacrifice in their simplicity.