Cartograms depict geographic regions with areas proportional to quantitative data. However, when created using density-equalizing map projections, cartograms may exhibit invalid topologies if boundary polygons are drawn using only a finite set of vertices connected by straight lines. Here we introduce a method for topology-preserving line densification that guarantees that cartogram regions remain connected and non-overlapping when using density-equalizing map projections. By combining our densification technique with a flow-based cartogram generator, we present a robust framework for strictly topology-preserving cartogram construction. Quantitative evaluations demonstrate that the proposed algorithm produces cartograms with greater accuracy and speed than alternative methods while maintaining comparable shape fidelity.

翻译：变形地图通过将地理区域的面积与定量数据成比例来描绘地理信息。然而，当使用密度均衡地图投影创建变形地图时，如果边界多边形仅通过有限顶点集以直线连接绘制，则可能出现无效拓扑结构。本文提出一种保持拓扑结构的线加密方法，确保在使用密度均衡地图投影时变形地图区域保持连通且无重叠。通过将我们的加密技术与基于流的变形地图生成器相结合，我们提出了一个严格的保持拓扑结构的变形地图构建鲁棒框架。定量评估表明，所提算法在保持相当形状保真度的同时，能以更高的精度和速度生成变形地图，优于其他方法。