### 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 C^{1}-continuous curves, represented by a sequence of at most three circular arcs.

Original language | English (US) |
---|---|

Pages (from-to) | 405-418 |

Number of pages | 14 |

Journal | Discrete and Computational Geometry |

Volume | 25 |

Issue number | 3 |

State | Published - 2001 |

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### ASJC Scopus subject areas

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

### Cite this

*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.

Research output: Contribution to journal › Article

*Discrete and Computational Geometry*, vol. 25, no. 3, pp. 405-418.

}

TY - JOUR

T1 - Drawing planar graphs with circular arcs

AU - Cheng, C. C.

AU - Duncan, C. A.

AU - Goodrich, M. T.

AU - Kobourov, Stephen G

PY - 2001

Y1 - 2001

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0035590704&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035590704&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0035590704

VL - 25

SP - 405

EP - 418

JO - Discrete and Computational Geometry

JF - Discrete and Computational Geometry

SN - 0179-5376

IS - 3

ER -