research-article

Morphing orthogonal planar graph drawings

Authors:

Michael SpriggsAuthors Info & Claims

ACM Transactions on Algorithms (TALG), Volume 9, Issue 4

Article No.: 29, Pages 1 - 24

https://doi.org/10.1145/2500118

Published: 03 October 2013 Publication History

Abstract

We give an algorithm to morph between two planar orthogonal drawings of a graph, preserving planarity and orthogonality. The morph uses a quadratic number of steps, where each step is a linear morph (a linear interpolation between two drawings). This is the first algorithm to provide planarity-preserving morphs with well-behaved complexity for a significant class of graph drawings. Our method is to morph until each edge is represented by a sequence of segments, with corresponding segments parallel in the two drawings. Then, in a result of independent interest, we morph such parallel planar orthogonal drawings, preserving edge directions and planarity.

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Cited By

Angelini PChaplick SCornelsen SDa Lozzo GRoselli V(2023)Morphing Triangle Contact Representations of TriangulationsDiscrete & Computational Geometry10.1007/s00454-022-00475-9Online publication date: 15-Mar-2023
https://doi.org/10.1007/s00454-022-00475-9
Barrera-Cruz FBorrazzo MDa Lozzo GDi Battista GFrati FPatrignani MRoselli V(2022)How to Morph a Tree on a Small GridDiscrete & Computational Geometry10.1007/s00454-021-00363-867:3(743-786)Online publication date: 2-Feb-2022
https://doi.org/10.1007/s00454-021-00363-8
Chaplick SKindermann PKlawitter JRutter IWolff A(2022)Morphing Rectangular DualsGraph Drawing and Network Visualization10.1007/978-3-031-22203-0_28(389-403)Online publication date: 13-Sep-2022
https://dl.acm.org/doi/10.1007/978-3-031-22203-0_28
Show More Cited By

Index Terms

Morphing orthogonal planar graph drawings
1. Mathematics of computing
  1. Discrete mathematics
    1. Graph theory
      1. Graph algorithms
2. Theory of computation
  1. Randomness, geometry and discrete structures
    1. Computational geometry

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Published In

cover image ACM Transactions on Algorithms

ACM Transactions on Algorithms Volume 9, Issue 4

September 2013

131 pages

ISSN:1549-6325

EISSN:1549-6333

DOI:10.1145/2533288

Issue’s Table of Contents

Copyright © 2013 ACM.

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Association for Computing Machinery

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Publication History

Published: 03 October 2013

Accepted: 01 December 2012

Revised: 01 June 2012

Received: 01 July 2010

Published in TALG Volume 9, Issue 4

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Cited By

Angelini PChaplick SCornelsen SDa Lozzo GRoselli V(2023)Morphing Triangle Contact Representations of TriangulationsDiscrete & Computational Geometry10.1007/s00454-022-00475-9Online publication date: 15-Mar-2023
https://doi.org/10.1007/s00454-022-00475-9
Barrera-Cruz FBorrazzo MDa Lozzo GDi Battista GFrati FPatrignani MRoselli V(2022)How to Morph a Tree on a Small GridDiscrete & Computational Geometry10.1007/s00454-021-00363-867:3(743-786)Online publication date: 2-Feb-2022
https://doi.org/10.1007/s00454-021-00363-8
Chaplick SKindermann PKlawitter JRutter IWolff A(2022)Morphing Rectangular DualsGraph Drawing and Network Visualization10.1007/978-3-031-22203-0_28(389-403)Online publication date: 13-Sep-2022
https://dl.acm.org/doi/10.1007/978-3-031-22203-0_28
Chambers EErickson JLin PParsa SMarx D(2021)How to morph graphs on the torusProceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms10.5555/3458064.3458228(2759-2778)Online publication date: 10-Jan-2021
https://dl.acm.org/doi/10.5555/3458064.3458228
Liotta GMontecchiani FTappini A(2021)Ortho-polygon visibility representations of 3-connected 1-plane graphsTheoretical Computer Science10.1016/j.tcs.2021.02.018863(40-52)Online publication date: Apr-2021
https://doi.org/10.1016/j.tcs.2021.02.018
Di Giacomo ELiotta GMontecchiani F(2021)Orthogonal Planarity Testing of Bounded Treewidth GraphsJournal of Computer and System Sciences10.1016/j.jcss.2021.11.004Online publication date: Dec-2021
https://doi.org/10.1016/j.jcss.2021.11.004
Angelini PBekos MMontecchiani FPfister M(2021)On Morphing 1-Planar DrawingsGraph-Theoretic Concepts in Computer Science10.1007/978-3-030-86838-3_21(270-282)Online publication date: 20-Sep-2021
https://doi.org/10.1007/978-3-030-86838-3_21
van Goethem ASpeckmann BVerbeek K(2019)Optimal Morphs of Planar Orthogonal Drawings IIGraph Drawing and Network Visualization10.1007/978-3-030-35802-0_3(33-45)Online publication date: 28-Nov-2019
https://doi.org/10.1007/978-3-030-35802-0_3
Di Giacomo ELiotta GMontecchiani F(2019)Sketched Representations and Orthogonal Planarity of Bounded Treewidth GraphsGraph Drawing and Network Visualization10.1007/978-3-030-35802-0_29(379-392)Online publication date: 17-Sep-2019
https://dl.acm.org/doi/10.1007/978-3-030-35802-0_29
Barrera-Cruz FBorrazzo MDa Lozzo GDi Battista GFrati FPatrignani MRoselli V(2019)How to Morph a Tree on a Small GridAlgorithms and Data Structures10.1007/978-3-030-24766-9_5(57-70)Online publication date: 5-Aug-2019
https://dl.acm.org/doi/10.1007/978-3-030-24766-9_5
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