On Smooth Orthogonal and Octilinear Drawings: Relations, Complexity and Kandinsky Drawings

  • Michael A. Bekos
  • Henry Förster
  • Michael Kaufmann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10692)


We study two variants of the well-known orthogonal drawing model: (i) the smooth orthogonal, and (ii) the octilinear. Both models form an extension of the orthogonal, by supporting one additional type of edge segments (circular arcs and diagonal segments, respectively).

For planar graphs of max-degree 4, we analyze relationships between the graph classes that can be drawn bendless in the two models and we also prove NP-hardness for a restricted version of the bendless drawing problem for both models. For planar graphs of higher degree, we present an algorithm that produces bi-monotone smooth orthogonal drawings with at most two segments per edge, which also guarantees a linear number of edges with exactly one segment.



The authors would like to thank Patrizio Angelini and Martin Gronemann for useful discussions.


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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Michael A. Bekos
    • 1
  • Henry Förster
    • 1
  • Michael Kaufmann
    • 1
  1. 1.Wilhelm-Schickhard-Institut für InformatikUniversität TübingenTübingenGermany

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