Drawing Planar Graphs with Circular ArcsCheng, 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 1519, 1999 , pp. 117126(Official URL: http://dx.doi.org/10.1007/3540466487_12). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/3540466487_12
AbstractIn 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 nvertex 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 straightline 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.
Actions (login required)
