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 proceedingChapterAcademic

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 languageEnglish
Title of host publicationGraph Drawing and Network Visualization - 30th International Symposium, GD 2022, Revised Selected Papers
EditorsPatrizio Angelini, Reinhard von Hanxleden
PublisherSpringer, Cham
Pages389-403
Number of pages15
Volume13764
ISBN (Electronic)978-3-031-22203-0
ISBN (Print)978-3-031-22202-3
DOIs
Publication statusPublished - 2023
EventThe 30th International Symposium on Graph Drawing and Network Visualization - Tokyo, Japan
Duration: 13 Sept 202216 Sept 2022
https://graphdrawing.github.io/gd2022/

Publication series

SeriesLecture Notes in Computer Science
Volume13764
ISSN0302-9743

Symposium

SymposiumThe 30th International Symposium on Graph Drawing and Network Visualization
Abbreviated titleGD 2022
Country/TerritoryJapan
CityTokyo
Period13/09/2216/09/22
Internet address

Fingerprint

Dive into the research topics of 'Morphing Rectangular Duals'. Together they form a unique fingerprint.
  • Morphing Rectangular Duals

    Chaplick, S., Kindermann, P., Klawitter, J., Rutter, I. & Wolff, A., 6 Dec 2021.

    Research output: Working paper / PreprintPreprint

Cite this