Drawing planar graphs with circular arcs
- 69 Downloads
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.
Unable to display preview. Download preview PDF.
- 6.A. Garg and R. Tamassia. Planar drawings and angular resolution: algorithms and bounds. In Proceedings of the 2nd Annual European Symposium on Algorithms, pages 12–23, 1994.Google Scholar
- 7.M. T. Goodrich and C. G. Wagner. A framework for drawing planar graphs with curves and polylines. In Proceedings of the 6th Annual Symposium on Graph Drawing, pages 153–166, 1998.Google Scholar
- 8.C. Gutwenger and P. Mutzel. Planar polyline drawings with good angular resolution. In Proceedings of the 6th Annual Symposium on Graph Drawing, pages 167–182, 1998.Google Scholar
- 9.G. Kant. Drawing planar graphs using the lmc-ordering. In Proceedings of the 33rd Annual IEEE Symposium on Foundations of Computer Science, pages 101–110, 1992.Google Scholar
- 10.G. Kant. Algorithms for Drawing Planar Graphs. Ph.D. thesis, Department of Computer Science, University of Utrecht, Utrecht, 1993.Google Scholar
- 13.W. Schnyder. Embedding planar graphs on the grid. In Proceedings of the 1st ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 138–148, 1990.Google Scholar
- 15.K. Wagner. Bemerkungen zum vierfarbenproblem. Jahresbericht der Deutschen Mathematiker-Vereinigung, 46:26–32, 1936.Google Scholar