Planar drawings of graphs tend to be favored over non-planar drawings. Testing planarity and creating a planar layout of a planar graph can be done in linear time. However, creating readable drawings of nearly planar graphs remains a challenge. We therefore seek to answer which edges of nearly planar graphs create clutter in their drawings generated by mainstream graph drawing algorithms. We present a heuristic to identify problematic edges in nearly planar graphs and adjust their weights in order to produce higher quality layouts with spring-based drawing algorithms. Our experiments show that our heuristic produces significantly higher quality drawings for augmented grid graphs, augmented triangulations, and deep triangulations.

翻译：平面图绘制通常优于非平面图绘制。测试平面性并为平面图创建平面布局可以在线性时间内完成。然而，为近平面图创建可读性强的布局仍是一个挑战。因此，我们试图回答近平面图中哪些边会使其主流图绘制算法生成的布局产生杂乱。我们提出了一种启发式方法，用于识别近平面图中的问题边，并调整其权重，以便基于弹簧的绘制算法能生成更高质量的布局。实验表明，对于增广网格图、增广三角剖分和深三角剖分，我们的启发式方法能显著提升布局质量。