Drawing planar graphs with circular arcs

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 usin g exactly one circular are. We also give an algorithm for drawing n-vertex planar graphs such that the edges are sequences of two continuous circular area. The algorithm runs in O(n) time and embeds the graph on the O(n) x O( n) grid, while maintaining Theta (1/d(upsilon)) angular resolution, where d (upsilon) is the degree of vertex upsilon. Since in this case we use circul ar arcs of infinite radius, this is also the first algorithm that simultane ously achieves good angular resolution, small area, and at most one bend pe r edge using straight-line segments. Finally, we show how to create drawing s in which edges are smooth C-1-continuous curves, represented by a sequenc e of at most three circular arcs.