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.2017.14
URN: urn:nbn:de:0030-drops-72234
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2017/7223/
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Barth, Lukas ; Niedermann, Benjamin ; Rutter, Ignaz ; Wolf, Matthias

Towards a Topology-Shape-Metrics Framework for Ortho-Radial Drawings

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LIPIcs-SoCG-2017-14.pdf (2 MB)

Abstract

Ortho-Radial drawings are a generalization of orthogonal drawings to grids that are formed by concentric circles and straight-line spokes emanating from the circles' center. Such drawings have applications in schematic graph layouts, e.g., for metro maps and destination maps.

A plane graph is a planar graph with a fixed planar embedding. We give a combinatorial characterization of the plane graphs that admit a planar ortho-radial drawing without bends. Previously, such a characterization was only known for paths, cycles, and theta graphs, and in the special case of rectangular drawings for cubic graphs, where the contour of each face is required to be a rectangle.

The characterization is expressed in terms of an ortho-radial representation that, similar to Tamassia's orthogonal representations for orthogonal drawings describes such a drawing combinatorially in terms of angles around vertices and bends on the edges. In this sense our characterization can be seen as a first step towards generalizing the Topology-Shape-Metrics framework of Tamassia to ortho-radial drawings.

BibTeX - Entry

@InProceedings{barth_et_al:LIPIcs:2017:7223,
  author =	{Lukas Barth and Benjamin Niedermann and Ignaz Rutter and Matthias Wolf},
  title =	{{Towards a Topology-Shape-Metrics Framework for Ortho-Radial Drawings}},
  booktitle =	{33rd International Symposium on Computational Geometry (SoCG 2017)},
  pages =	{14:1--14:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-038-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{77},
  editor =	{Boris Aronov and Matthew J. Katz},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/7223},
  URN =		{urn:nbn:de:0030-drops-72234},
  doi =		{10.4230/LIPIcs.SoCG.2017.14},
  annote =	{Keywords: Graph Drawing, Ortho-Radial Drawings, Combinatorial Characterization, Bend Minimization, Topology-Shape-Metrics}
}

Keywords: Graph Drawing, Ortho-Radial Drawings, Combinatorial Characterization, Bend Minimization, Topology-Shape-Metrics
Collection: 33rd International Symposium on Computational Geometry (SoCG 2017)
Issue Date: 2017
Date of publication: 20.06.2017

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