Morphing Rectangular Duals

Steven Chaplick; Philipp Kindermann; Jonathan Klawitter; Ignaz Rutter; Alexander Wolff

doi:10.1007/978-3-031-22203-0_28

Morphing Rectangular Duals

Steven Chaplick, Philipp Kindermann, Jonathan Klawitter^*, Ignaz Rutter, Alexander Wolff

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

Abstract

A rectangular dual of a plane graph G is a contact representations of G by interior-disjoint axis-aligned rectangles such that (i) no four rectangles share a point and (ii) the union of all rectangles is a rectangle. A rectangular dual gives rise to a regular edge labeling (REL), which captures the orientations of the rectangle contacts.

We study the problem of morphing between two rectangular duals of the same plane graph. If we require that, at any time throughout the morph, there is a rectangular dual, then a morph exists only if the two rectangular duals realize the same REL. Therefore, we allow intermediate contact representations of non-rectangular polygons of constant complexity. Given an n-vertex plane graph, we show how to compute in O(n(3)) time a piecewise linear morph that consists of O(n(2)) linear morphing steps.

Original language	English
Title of host publication	Graph Drawing and Network Visualization (GD 2022)
Editors	Patrizio Angelini, R. von Hanxleden
Publisher	Springer, Cham
Pages	389-403
Volume	13764
ISBN (Electronic)	978-3-031-22203-0
ISBN (Print)	978-3-031-22202-3
DOIs	https://doi.org/10.1007/978-3-031-22203-0_28
Publication status	Published - 2023
Event	The 30th International Symposium on Graph Drawing and Network Visualization - Tokyo, Japan Duration: 13 Sept 2022 → 16 Sept 2022 https://graphdrawing.github.io/gd2022/

Publication series

Series	Lecture Notes in Computer Science
Volume	13764
ISSN	0302-9743

Symposium

Symposium	The 30th International Symposium on Graph Drawing and Network Visualization
Abbreviated title	GD 2022
Country/Territory	Japan
City	Tokyo
Period	13/09/22 → 16/09/22
Internet address	https://graphdrawing.github.io/gd2022/

Access to Document

10.1007/978-3-031-22203-0_28

1 Preprint

Morphing Rectangular Duals
Chaplick, S., Kindermann, P., Klawitter, J., Rutter, I. & Wolff, A., 6 Dec 2021.
Research output: Working paper / Preprint › Preprint

Cite this

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title = "Morphing Rectangular Duals",

abstract = "A rectangular dual of a plane graph G is a contact representations of G by interior-disjoint axis-aligned rectangles such that (i) no four rectangles share a point and (ii) the union of all rectangles is a rectangle. A rectangular dual gives rise to a regular edge labeling (REL), which captures the orientations of the rectangle contacts.We study the problem of morphing between two rectangular duals of the same plane graph. If we require that, at any time throughout the morph, there is a rectangular dual, then a morph exists only if the two rectangular duals realize the same REL. Therefore, we allow intermediate contact representations of non-rectangular polygons of constant complexity. Given an n-vertex plane graph, we show how to compute in O(n(3)) time a piecewise linear morph that consists of O(n(2)) linear morphing steps.",

author = "Steven Chaplick and Philipp Kindermann and Jonathan Klawitter and Ignaz Rutter and Alexander Wolff",

note = "Publisher Copyright: {\textcopyright} 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.; The 30th International Symposium on Graph Drawing and Network Visualization, GD 2022 ; Conference date: 13-09-2022 Through 16-09-2022",

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doi = "10.1007/978-3-031-22203-0_28",

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editor = "Patrizio Angelini and {von Hanxleden}, R.",

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Chaplick, S, Kindermann, P, Klawitter, J, Rutter, I & Wolff, A 2023, Morphing Rectangular Duals. in P Angelini & R von Hanxleden (eds), Graph Drawing and Network Visualization (GD 2022). vol. 13764, Chapter 28, Springer, Cham, Lecture Notes in Computer Science, vol. 13764, pp. 389-403, The 30th International Symposium on Graph Drawing and Network Visualization, Tokyo, Japan, 13/09/22. https://doi.org/10.1007/978-3-031-22203-0_28

Morphing Rectangular Duals. / Chaplick, Steven; Kindermann, Philipp; Klawitter, Jonathan et al.
Graph Drawing and Network Visualization (GD 2022). ed. / Patrizio Angelini; R. von Hanxleden. Vol. 13764 Springer, Cham, 2023. p. 389-403 Chapter 28 (Lecture Notes in Computer Science, Vol. 13764).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Academic

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