Giuseppe Di Battista ; Fabrizio Frati - From Tutte to Floater and Gotsman: On the Resolution of Planar Straight-line Drawings and Morphs

dmtcs:12439 - Discrete Mathematics & Theoretical Computer Science, March 5, 2025, vol. 27:2 - https://doi.org/10.46298/dmtcs.12439
From Tutte to Floater and Gotsman: On the Resolution of Planar Straight-line Drawings and MorphsArticle

Authors: Giuseppe Di Battista ; Fabrizio Frati

    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.


    Volume: vol. 27:2
    Section: Combinatorics
    Published on: March 5, 2025
    Accepted on: February 20, 2025
    Submitted on: October 19, 2023
    Keywords: Computer Science - Computational Geometry,Computer Science - Discrete Mathematics,Computer Science - Data Structures and Algorithms

    Consultation statistics

    This page has been seen 73 times.
    This article's PDF has been downloaded 38 times.