Smooth Orthogonal Layouts

  • Michael A. Bekos
  • Michael Kaufmann
  • Stephen G. Kobourov
  • Antonios Symvonis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7704)

Abstract

We study the problem of creating smooth orthogonal layouts for planar graphs. While in traditional orthogonal layouts every edge is made of a sequence of axis-aligned line segments, in smooth orthogonal layouts every edge is made of axis-aligned segments and circular arcs with common tangents. Our goal is to create such layouts with low edge complexity, measured by the number of line and circular arc segments. We show that every biconnected 4-planar graph has a smooth orthogonal layout with edge complexity 3. If the input graph has a complexity-2 traditional orthogonal layout, we can transform it into a smooth complexity-2 layout. Using the Kandinsky model for removing the degree restriction, we show that any planar graph has a smooth complexity-2 layout.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Michael A. Bekos
    • 1
  • Michael Kaufmann
    • 1
  • Stephen G. Kobourov
    • 2
  • Antonios Symvonis
    • 3
  1. 1.Institute for InformaticsUniversity of TübingenGermany
  2. 2.Department of Computer ScienceUniversity of ArizonaUSA
  3. 3.School of Applied Mathematics and Physical SciencesNTUAGreece

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