Discrete & Computational Geometry

, Volume 25, Issue 3, pp 405–418

# Drawing planar graphs with circular arcs

• C. C. Cheng
• C. A. Duncan
• M. T. Goodrich
• S. G. Kobourov
Article

DOI: 10.1007/s004540010080

Cheng, C.C., Duncan, C.A., Goodrich, M.T. et al. Discrete Comput Geom (2001) 25: 405. doi:10.1007/s004540010080

## 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.

© Springer-Verlag New York Inc. 2001

## Authors and Affiliations

• C. C. Cheng
• 1
• C. A. Duncan
• 2
• M. T. Goodrich
• 3
• S. G. Kobourov
• 4
1. 1.Mathematical Sciences DepartmentJohns Hopkins UniversityBaltimoreUSA
2. 2.Department of Computer ScienceUniversity of MiamiCoral GablesUSA
3. 3.Department of Computer ScienceJohns Hopkins UniversityBaltimoreUSA
4. 4.Department of Computer ScienceUniversity of ArizonaTucsonUSA