Planar and Poly-Arc Lombardi Drawings

Christian Duncan, David Eppstein, Michael T. Goodrich, Stephen Kobourov, Maarten Löffler, Martin Nöllenburg

Research output: Contribution to journalArticleAcademicpeer-review


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.
Original languageEnglish
Pages (from-to)328-355
Number of pages28
JournalJournal of Computational Geometry
Issue number1
Publication statusPublished - 2018




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