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

Original language | English (US) |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Publisher | Springer Verlag |

Pages | 117-126 |

Number of pages | 10 |

Volume | 1731 |

ISBN (Print) | 3540669043, 9783540669043 |

DOIs | |

State | Published - 1999 |

Externally published | Yes |

Event | 7th International Symposium on Graph Drawing, GD 1999 - Prague, Czech Republic Duration: Sep 15 1999 → Sep 19 1999 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
---|---|

Volume | 1731 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 7th International Symposium on Graph Drawing, GD 1999 |
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Country | Czech Republic |

City | Prague |

Period | 9/15/99 → 9/19/99 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*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

}

TY - GEN

T1 - Drawing Planar Graphs with Circular Arcs

AU - Cheng, C. C.

AU - Duncan, C. A.

AU - Goodrich, M. T.

AU - Kobourov, Stephen G

PY - 1999

Y1 - 1999

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 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.

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 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.

UR - http://www.scopus.com/inward/record.url?scp=84958980832&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958980832&partnerID=8YFLogxK

U2 - 10.1007/3-540-46648-7_12

DO - 10.1007/3-540-46648-7_12

M3 - Conference contribution

SN - 3540669043

SN - 9783540669043

VL - 1731

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 117

EP - 126

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

PB - Springer Verlag

ER -