Drawing planar graphs with circular arcs

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

Research output: Contribution to journalArticle

26 Scopus citations

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
DOIs
StatePublished - Apr 2001

ASJC Scopus subject areas

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

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