License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.SoCG.2018.42
URN: urn:nbn:de:0030-drops-87550
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/8755/
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van Goethem, Arthur ; Verbeek, Kevin

Optimal Morphs of Planar Orthogonal Drawings

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LIPIcs-SoCG-2018-42.pdf (0.8 MB)

Abstract

We describe an algorithm that morphs between two planar orthogonal drawings Gamma_I and Gamma_O of a connected graph G, while preserving planarity and orthogonality. Necessarily Gamma_I and Gamma_O share the same combinatorial embedding. Our morph uses a linear number of linear morphs (linear interpolations between two drawings) and preserves linear complexity throughout the process, thereby answering an open question from Biedl et al. [Biedl et al., 2013].
Our algorithm first unifies the two drawings to ensure an equal number of (virtual) bends on each edge. We then interpret bends as vertices which form obstacles for so-called wires: horizontal and vertical lines separating the vertices of Gamma_O. We can find corresponding wires in Gamma_I that share topological properties with the wires in Gamma_O. The structural difference between the two drawings can be captured by the spirality of the wires in Gamma_I, which guides our morph from Gamma_I to Gamma_O.

BibTeX - Entry

@InProceedings{vangoethem_et_al:LIPIcs:2018:8755,
  author =	{Arthur van Goethem and Kevin Verbeek},
  title =	{{Optimal Morphs of Planar Orthogonal Drawings}},
  booktitle =	{34th International Symposium on Computational Geometry (SoCG 2018)},
  pages =	{42:1--42:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-066-8},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{99},
  editor =	{Bettina Speckmann and Csaba D. T{\'o}th},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/8755},
  URN =		{urn:nbn:de:0030-drops-87550},
  doi =		{10.4230/LIPIcs.SoCG.2018.42},
  annote =	{Keywords: Homotopy, Morphing, Orthogonal drawing, Spirality}
}

Keywords: Homotopy, Morphing, Orthogonal drawing, Spirality
Collection: 34th International Symposium on Computational Geometry (SoCG 2018)
Issue Date: 2018
Date of publication: 08.06.2018

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