Abstract. A Lombardi drawing of a graph is defined as one in which vertices are represented as points, edges are represented as circular arcs between their endpoints, and every vertex has perfect angular resolution (angles between consecutive edges, as measured by the tangents to the circular arcs at the vertex, all have the same degree). We describe two algorithms that create "Lombardi-style" drawings (which we also call near-Lombardi drawings), in which all edges are still circular arcs, but some vertices may not have perfect angular resolution. Both of these algorithms take a force-directed, spring-embedding approach, with one using forces at edge tangents to produce curved edges and the other using dummy vertices on edges for this purpose. As we show, these approaches both produce near-Lombardi drawings, with one being slightly better at achieving near-perfect angular resolution and the other being slightly better at balancing vertex placements.
Most relevantly for our work, Chernobelskiy et al. REF introduce a force-directed approach to produce Lombardi-style graph drawings with perfect or near-perfect angular resolution and circular-arc edges.
Force-directed Lombardi-style graph drawing
IN: PROC. 19TH INT. SYMP. ON GRAPH DRAWING
Computer Science