Planar and poly-arc lombardi drawings

Authors:
Christian A. Duncan;David Eppstein;Michael T. Goodrich;Stephen G. Kobourov;Maarten Löffler
Affiliations:
Department of Computer Science, Louisiana Tech Univ., Ruston, Louisiana;Department of Computer Science, University of California, Irvine, California;Department of Computer Science, University of California, Irvine, California;Department of Computer Science, University of Arizona, Tucson, Arizona;Department of Computer Science, University of California, Irvine, California
Venue:
GD'11 Proceedings of the 19th international conference on Graph Drawing
Year:
2011

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Abstract

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.