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

TL;DR

This paper analyzes the resolution quality of planar straight-line drawings and morphs generated by Tutte, Floater, and Gotsman's algorithms, providing bounds and highlighting potential resolution issues during morphing.

Contribution

It establishes bounds on the resolution of drawings from Floater's algorithm and demonstrates possible exponential resolution loss in morphs.

Findings

Bounds on resolution for Floater's algorithm

Lower bounds on resolution of morphs

Potential exponential resolution loss during morphing

Abstract

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. In this paper, focusing on maximal plane graphs, we prove upper and lower 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 results 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.