Drawing Planar Graphs with Circular Arcs

Cheng, C. C. and Duncan, Christian A. and Goodrich, Michael T. and Kobourov, Stephen G. (1999) Drawing Planar Graphs with Circular Arcs. In: Graph Drawing 7th International Symposium, GD’99, September 15-19, 1999 , pp. 117-126(Official URL: http://dx.doi.org/10.1007/3-540-46648-7_12).

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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) \times O(n) grid, while maintaining \Theta(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.

Item Type: Conference Paper
Additional Information: 10.1007/3-540-46648-7_12
Classifications: G Algorithms and Complexity > G.070 Area / Edge Length
M Methods > M.600 Planar
G Algorithms and Complexity > G.210 Bends
P Styles > P.120 Circular
URI: http://gdea.informatik.uni-koeln.de/id/eprint/278

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