The algorithm of Tutte for constructing convex planar straight-line drawings and the algorithm of Floater and Gotsman for constructing planar straight-line morphs are among the most popular graph drawing algorithms. Quite surprisingly, little is known about the resolution of the drawings produced by these algorithms. In this paper, focusing on maximal plane graphs, we prove tight bounds on the resolution of the planar straight-line drawings produced by Floater's algorithm, which is a broad generalization of Tutte's algorithm. Further, we use such a result in order to prove a lower bound on the resolution of the drawings of maximal plane graphs produced by Floater and Gotsman's morphing algorithm. Finally, we show that such a morphing algorithm might produce drawings with exponentially-small resolution, even when transforming drawings with polynomial resolution.

翻译：Tutte构造凸平面直线图的算法与Floater和Gotsman构造平面直线形变的算法是图绘制领域最流行的算法之一。令人惊讶的是，关于这些算法所产生图形的分辨率，目前所知甚少。本文聚焦于极大平面图，证明了Floater算法（作为Tutte算法的重要推广）所生成平面直线图的分辨率的紧界。进而，我们利用该结果证明了Floater和Gotsman形变算法所生成极大平面图的分辨率下界。最后，我们证明该形变算法在变换具有多项式分辨率的图形时，仍可能产生指数级小分辨率的图形。