Smooth orthogonal layouts

M. A. Bekos, Michael Kaufmann, Stephen G Kobourov, A. Symvonis

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

We study the problem of creating smooth orthogonal layouts for planar graphs. While in traditional orthogonal layouts every edge is made of a sequence of axis-aligned line segments, in smooth orthogonal layouts every edge is made of axis-aligned segments and circular arcs with common tangents. Our goal is to create such layouts with low edge complexity, measured by the number of line and circular arc segments. We show that every 4-planar graph has a smooth orthogonal layout with edge complexity 3. If the input graph has a complexity-2 traditional orthogonal layout, we can transform it into a smooth complexity-2 layout. Using the Kandinsky model for removing the degree restriction, we show that any planar graph has a smooth complexity-2 layout.

Original languageEnglish (US)
Pages (from-to)575-595
Number of pages21
JournalJournal of Graph Algorithms and Applications
Volume17
Issue number5
DOIs
StatePublished - 2013

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Layout
Planar graph
Arc of a curve
Line segment
Tangent line
Transform
Restriction
Line
Graph in graph theory

ASJC Scopus subject areas

  • Geometry and Topology
  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Computer Science(all)
  • Computer Science Applications

Cite this

Smooth orthogonal layouts. / Bekos, M. A.; Kaufmann, Michael; Kobourov, Stephen G; Symvonis, A.

In: Journal of Graph Algorithms and Applications, Vol. 17, No. 5, 2013, p. 575-595.

Research output: Contribution to journalArticle

Bekos, MA, Kaufmann, M, Kobourov, SG & Symvonis, A 2013, 'Smooth orthogonal layouts', Journal of Graph Algorithms and Applications, vol. 17, no. 5, pp. 575-595. https://doi.org/10.7155/jgaa.00305
Bekos, M. A. ; Kaufmann, Michael ; Kobourov, Stephen G ; Symvonis, A. / Smooth orthogonal layouts. In: Journal of Graph Algorithms and Applications. 2013 ; Vol. 17, No. 5. pp. 575-595.
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