Planar and Poly-arc Lombardi Drawings

  • Christian A. Duncan
  • David Eppstein
  • Michael T. Goodrich
  • Stephen G. Kobourov
  • Maarten Löffler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7034)


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.


Planar Graph Angular Resolution Equilateral Triangle Correct Angle White Vertex 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Christian A. Duncan
    • 1
  • David Eppstein
    • 2
  • Michael T. Goodrich
    • 2
  • Stephen G. Kobourov
    • 3
  • Maarten Löffler
    • 2
  1. 1.Department of Computer ScienceLouisiana Tech Univ.RustonUSA
  2. 2.Department of Computer ScienceUniversity of CaliforniaIrvineUSA
  3. 3.Department of Computer ScienceUniversity of ArizonaTucsonUSA

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