Optimal 3D Angular Resolution for Low-Degree Graphs

  • David Eppstein
  • Maarten Löffler
  • Elena Mumford
  • Martin Nöllenburg
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6502)


We show that every graph of maximum degree three can be drawn in three dimensions with at most two bends per edge, and with 120° angles between any two edge segments meeting at a vertex or a bend. We show that every graph of maximum degree four can be drawn in three dimensions with at most three bends per edge, and with 109.5° angles, i.e., the angular resolution of the diamond lattice, between any two edge segments meeting at a vertex or bend.


Maximum Degree Angular Resolution Horizontal Segment Diamond Lattice Edge Segment 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • David Eppstein
    • 1
  • Maarten Löffler
    • 1
  • Elena Mumford
    • 2
  • Martin Nöllenburg
    • 1
  1. 1.Department of Computer ScienceUniversity of CaliforniaIrvineUSA
  2. 2.EindhovenThe Netherlands

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