It is well established that edge crossings inhibit human understanding; thus minimising the number of
crossings became the most important criteria in graph drawing, and there has been a great deal of
mathematical research on minimum crossing numbers by mathematicians. Recently, using human
experiments, we showed that edge crossings do not inhibit human understanding if they cross with
This result spawned a new theory in graph drawing and combinatorial geometry on graph
representations with large crossing angles, called RAC (Right Angle Crossing) and LAC (Large Angle
Crossing) drawings. My initial papers on this have high citations. It is interesting that citations to this
paper are evenly split between theoreticians (graph theorists, geometers) and applied researchers
(information visualisation and in the application domains).
W. Huang, S. Hong and P. Eades, "Effects of Crossing Angles", Proceedings of IEEE Pacific Visualization Symposium (PacificVis 2008), IEEE, pp. 41-46, 2008.
In visualizing graphs as node-link diagrams, it is commonly accepted
and employed as a general rule that the number of link crossings
should be minimized whenever possible. However, little attention
has been paid to how to handle the remaining crossings in the
visualization. The study presented in this paper examines the effects
of crossing angles on performance of path tracing tasks. It
was found that the effect varied with the size of crossing angles.
In particular, task response time decreased as the crossing angle
increased. However, the rate of the decrease tended to level off
when the angle was close to 90 degrees. One of the implications of
this study in graph visualization is that just minimizing the crossing
number is not sufficient to reduce the negative impact to the minimum.
The angles of remaining crossings should be maximized as
Q. Nguyen, P. Eades, S. Hong and W. Huang, "Large Crossing Angles in Circular Layouts", Proceedings of Graph Drawing 2010, LNCS, pp. 397-399, 2011.
Recent empirical research has shown that increasing the angle of crossings reduces
the effect of crossings and improves human readability. In this paper, we
introduce a post-processing algorithm, namely MAXCIR, that aims to increase
crossing angles of circular layouts by using Quadratic Programming. Experimental
results indicate that our method significantly increases crossing angles
compared to the traditional equal-spacing algorithm, and that the running time
is fairly negligible.
Emilio Di Giacomo, Walter Didimo, Peter Eades, Seok-Hee Hong, Giuseppe Liotta: Bounds on the crossing resolution of complete geometric graphs. Discrete Applied Mathematics 160(1-2): 132-139 (2012)
The crossing resolution of a geometric graph is the minimum crossing angle at which any two edges cross each other. In this paper, we present upper and lower bounds to the crossing resolution of the complete geometric graphs.