Planar and poly-arc Lombardi drawings

Authors

  • Christian A. Duncan Quinnipiac University, Hamden, CT
  • David Eppstein UC Irvine, CA
  • Michael T. Goodrich UC Irvine, CA
  • Stephen G. Kobourov University of Arizona, Tucson, AZ
  • Maarten Löffler Utrecht University
  • Martin Nöllenburg TU Wien http://orcid.org/0000-0003-0454-3937

DOI:

https://doi.org/10.20382/jocg.v9i1a11

Abstract

In Lombardi drawings of graphs, edges are represented as circular arcs and the edges incident on vertices have perfect angular resolution. It is known that not every planar graph has a planar Lombardi drawing. We give an example of a planar 3-tree that has no planar Lombardi drawing and we show that all outerpaths do have a planar Lombardi drawing. Further, we show that there are graphs that do not even have any Lombardi drawing at all. With this in mind, we generalize the notion of Lombardi drawings to that of (smooth) $k$-Lombardi drawings, in which each edge may be drawn as a (differentiable) sequence of $k$ circular arcs; we show that every graph has a smooth $2$-Lombardi drawing and every planar graph has a smooth planar $3$-Lombardi drawing. We further investigate related topics connecting planarity and Lombardi drawings.

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Published

2018-09-07

Issue

Vol. 9 No. 1 (2018)

Section

Articles

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