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arXiv · 1109.0345

Planar and Poly-Arc Lombardi Drawings

Christian A. Duncan·David Eppstein·Michael T. Goodrich·Stephen G. Kobourov·Maarten Löffler
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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.

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Christian A. Duncan, David Eppstein, Michael T. Goodrich, Stephen G. Kobourov, Maarten Löffler. 2011-09-02. Planar and Poly-Arc Lombardi Drawings. https://doi.org/10.20382/jocg.v9i1a11

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