Planar and Poly-Arc Lombardi Drawings
  In Lombardi drawings of graphs, edges are represented as circular arcs, and the edges incident on vertices have perfect angular resolution. However, not every graph has a Lombardi drawing, and not every planar graph has a planar Lombardi drawing. We introduce k-Lombardi drawings, in which each edge may be drawn with k circular arcs, noting that every graph has a smooth 2-Lombardi drawing. We show that every planar graph has a smooth planar 3-Lombardi drawing and further investigate topics connecting planarity and Lombardi drawings. 
Christian A. Duncan and David Eppstein and Michael T. Goodrich and   Stephen G. Kobourov and Maarten L\"offler
cs.CG cs.DM