From Tutte to Floater and Gotsman: On the Resolution of Planar Straight-line Drawings and Morphs

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.