Right Angle Crossing Drawings of Graphs

Abstract

In a RAC drawing of a graph, every two crossing edges form \(\frac{\pi }{2}\) angles at their crossing point. The theoretical study of this type of drawings started in 2009, motivated by cognitive experiments showing that crossings with large angles do not affect too much the readability of a graph layout. Since then, the RAC drawing convention has been widely studied, both from the combinatorial and from the algorithmic point of view. RAC drawings can be also regarded as a generalization of the well-known orthogonal drawing convention, in which every edge is a polyline composed of horizontal and vertical segments only. In a RAC drawing there is no restriction on the slope of the edge segments, hence a vertex of any degree can be represented as a geometric point (planar orthogonal drawings with vertices drawn as points necessarily require vertices of degree at most four). In this chapter, we survey the rich literature on RAC drawings and we briefly illustrate the ideas behind some of the most interesting results.