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; we show that every graph has a smooth 2-Lombardi drawing and every planar graph has a smooth planar 3-Lombardi drawing. We also investigate related topics connecting planarity and Lombardi drawings.

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Lombardi drawings are drawings of graphs in the plane so that every edge is represented by a circular arc and every vertex has perfect angular resolution. We study planar Lombardi drawings for outerpaths, i.e., outerplanar graphs whose dual is a path. We show that every outerpath has an outerplanar Lombardi drawing and present a linear-time algorithm to construct it.


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keywords: Computational Geometry, Graph Drawing, Graphs Theory

Journal Article (peer-reviewed)

Christian Duncan, David Eppstein, Maarten Löffler, Martin Nöllenburg, Michael T. Goodrich, Stephen Kobourov
Planar and Poly-Arc Lombardi Drawings
Journal of Computational Geometry
9, 1, 328–355, 2018
http://dx.doi.org/10.20382/jocg.v9i1a11

Conference Proceedings (peer-reviewed)

Christian Duncan, David Eppstein, Maarten Löffler, Michael T. Goodrich, Stephen Kobourov
Planar and Poly-Arc Lombardi Drawings
Proc. 19th Symposium on Graph Drawing
LNCS, 7034, 308–319, 2011
http://dx.doi.org/10.1007/978-3-642-25878-7_30

Workshop or Poster (weakly reviewed)

Maarten Löffler, Martin Nöllenburg
Planar Lombardi Drawings of Outerpaths
Proc. 20th Symposium on Graph Drawing
561–562, 2012

Archived Publication (not reviewed)

Christian Duncan, David Eppstein, Maarten Löffler, Michael T. Goodrich, Stephen Kobourov
Planar and Poly-Arc Lopmbardi Drawings
1109.0345, 2011
http://arXiv.org/abs/1109.0345

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