Drawing Planar Graphs with Circular Arcs

C. C. Cheng, C. A. Duncan, M. T. Goodrich, Stephen G Kobourov

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

12 Citations (Scopus)

Abstract

In this paper we address the problem of drawing planar graphs with circular arcs while maintaining good angular resolution and small drawing area. We present a lower bound on the area of drawings in which edges are drawn using exactly one circular arc. We also give an algorithm for drawing n-vertex planar graphs such that the edges are sequences of two continuous circular arcs. The algorithm runs in O(n) time and embeds the graph on the O(n) × O(n) grid, while maintaining Θ(1=d(v)) angular resolution, where d(v) is the degree of vertex v. Since in this case we use circular arcs of infinite radius, this is also the first algorithm to simultaneously achieve good angular resolution, small area and at most one bend per edge using straight-line segments. Finally, we show how to create drawings in which edges are smooth C1-continuous curves, represented by a sequence of at most three circular arcs.

Original languageEnglish (US)
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages117-126
Number of pages10
Volume1731
ISBN (Print)3540669043, 9783540669043
DOIs
StatePublished - 1999
Externally publishedYes
Event7th International Symposium on Graph Drawing, GD 1999 - Prague, Czech Republic
Duration: Sep 15 1999Sep 19 1999

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1731
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other7th International Symposium on Graph Drawing, GD 1999
CountryCzech Republic
CityPrague
Period9/15/999/19/99

Fingerprint

Planar graph
Arc of a curve
Vertex of a graph
Line segment
Use Case
Straight Line
Radius
Drawing
Lower bound
Grid
Curve
Graph in graph theory

ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Cheng, C. C., Duncan, C. A., Goodrich, M. T., & Kobourov, S. G. (1999). Drawing Planar Graphs with Circular Arcs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1731, pp. 117-126). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1731). Springer Verlag. https://doi.org/10.1007/3-540-46648-7_12

Drawing Planar Graphs with Circular Arcs. / Cheng, C. C.; Duncan, C. A.; Goodrich, M. T.; Kobourov, Stephen G.

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1731 Springer Verlag, 1999. p. 117-126 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1731).

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

Cheng, CC, Duncan, CA, Goodrich, MT & Kobourov, SG 1999, Drawing Planar Graphs with Circular Arcs. in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). vol. 1731, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 1731, Springer Verlag, pp. 117-126, 7th International Symposium on Graph Drawing, GD 1999, Prague, Czech Republic, 9/15/99. https://doi.org/10.1007/3-540-46648-7_12
Cheng CC, Duncan CA, Goodrich MT, Kobourov SG. Drawing Planar Graphs with Circular Arcs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1731. Springer Verlag. 1999. p. 117-126. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). https://doi.org/10.1007/3-540-46648-7_12
Cheng, C. C. ; Duncan, C. A. ; Goodrich, M. T. ; Kobourov, Stephen G. / Drawing Planar Graphs with Circular Arcs. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol. 1731 Springer Verlag, 1999. pp. 117-126 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).
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