Drawing planar graphs with circular arcs

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

Research output: Contribution to journalArticle

25 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 that simultaneously achieves 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)
Pages (from-to)405-418
Number of pages14
JournalDiscrete and Computational Geometry
Volume25
Issue number3
StatePublished - 2001

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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

  • Theoretical Computer Science
  • Computational Theory and Mathematics
  • Discrete Mathematics and Combinatorics
  • Geometry and Topology

Cite this

Cheng, C. C., Duncan, C. A., Goodrich, M. T., & Kobourov, S. G. (2001). Drawing planar graphs with circular arcs. Discrete and Computational Geometry, 25(3), 405-418.

Drawing planar graphs with circular arcs. / Cheng, C. C.; Duncan, C. A.; Goodrich, M. T.; Kobourov, Stephen G.

In: Discrete and Computational Geometry, Vol. 25, No. 3, 2001, p. 405-418.

Research output: Contribution to journalArticle

Cheng, CC, Duncan, CA, Goodrich, MT & Kobourov, SG 2001, 'Drawing planar graphs with circular arcs', Discrete and Computational Geometry, vol. 25, no. 3, pp. 405-418.
Cheng, C. C. ; Duncan, C. A. ; Goodrich, M. T. ; Kobourov, Stephen G. / Drawing planar graphs with circular arcs. In: Discrete and Computational Geometry. 2001 ; Vol. 25, No. 3. pp. 405-418.
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