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Drawing Planar Graphs and 1-Planar Graphs Using Cubic Bézier Curves with Bounded Curvature

Authors David Eppstein, Michael T. Goodrich , Abraham M. Illickan

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Author Details

David Eppstein
  • University of California, Irvine, CA, USA
Michael T. Goodrich
  • University of California, Irvine, CA, USA
Abraham M. Illickan
  • University of California, Irvine, CA, USA

Funding

This work was supported in part by NSF Grant 2212129.

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David Eppstein, Michael T. Goodrich, and Abraham M. Illickan. Drawing Planar Graphs and 1-Planar Graphs Using Cubic Bézier Curves with Bounded Curvature. In 32nd International Symposium on Graph Drawing and Network Visualization (GD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 320, pp. 39:1-39:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)
https://doi.org/10.4230/LIPIcs.GD.2024.39

Abstract

We study algorithms for drawing planar graphs and 1-planar graphs using cubic Bézier curves with bounded curvature. We show that any n-vertex 1-planar graph has a 1-planar RAC drawing using a single cubic Bézier curve per edge, and this drawing can be computed in O(n) time given a combinatorial 1-planar drawing. We also show that any n-vertex planar graph G can be drawn in O(n) time with a single cubic Bézier curve per edge, in an O(n)× O(n) bounding box, such that the edges have Θ(1/degree(v)) angular resolution, for each v ∈ G, and O(√n) curvature.

Subject Classification

ACM Subject Classification
  • Theory of computation
Keywords
  • graph drawing
  • planar graphs
  • Bézier curves
  • and RAC drawings

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