Smooth orthogonal layouts

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

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 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 biconnected 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)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Pages150-161
Number of pages12
Volume7704 LNCS
DOIs
StatePublished - 2013
Event20th International Symposium on Graph Drawing, GD 2012 - Redmond, WA, United States
Duration: Sep 19 2012Sep 21 2012

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume7704 LNCS
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other20th International Symposium on Graph Drawing, GD 2012
CountryUnited States
CityRedmond, WA
Period9/19/129/21/12

Fingerprint

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

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Bekos, M. A., Kaufmann, M., Kobourov, S. G., & Symvonis, A. (2013). Smooth orthogonal layouts. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7704 LNCS, pp. 150-161). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7704 LNCS). https://doi.org/10.1007/978-3-642-36763-2_14

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

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7704 LNCS 2013. p. 150-161 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 7704 LNCS).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Bekos, MA, Kaufmann, M, Kobourov, SG & Symvonis, A 2013, Smooth orthogonal layouts. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 7704 LNCS, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 7704 LNCS, pp. 150-161, 20th International Symposium on Graph Drawing, GD 2012, Redmond, WA, United States, 9/19/12. https://doi.org/10.1007/978-3-642-36763-2_14
Bekos MA, Kaufmann M, Kobourov SG, Symvonis A. Smooth orthogonal layouts. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7704 LNCS. 2013. p. 150-161. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/978-3-642-36763-2_14
Bekos, Michael A. ; Kaufmann, Michael ; Kobourov, Stephen G ; Symvonis, Antonios. / Smooth orthogonal layouts. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 7704 LNCS 2013. pp. 150-161 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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