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

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Bibliographic Details
Published in:Discrete Mathematics and Theoretical Computer Science Vol. 27:2; no. Combinatorics; pp. 1 - 31
Main Authors: Di Battista, Giuseppe, Frati, Fabrizio
Format: Journal Article
Language:English
Published: Nancy DMTCS 01.08.2025
Discrete Mathematics & Theoretical Computer Science
Subjects:
Algorithms
Computer science
computer science - computational geometry
computer science - data structures and algorithms
computer science - discrete mathematics
Graph theory
Graphs
Lower bounds
Mathematical research
Morphing
Polynomials
Italy
ISSN:1365-8050, 1462-7264, 1365-8050
Online Access:Get full text
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Summary: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. Comment: Appears in the Proceedings of the 29th International Symposium on Graph Drawing and Network Visualization (GD 2021) Appears in DMTCS
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ISSN:1365-8050
1462-7264
1365-8050
DOI:10.46298/dmtcs.12439