Optimal 3D Angular Resolution for Low-Degree Graphs

Details Optimal 3D Angular Resolution for Low-Degree Graphs Optimal 3D Angular Resolution for Low-Degree Graphs

2010-08-31

arxiv.org/abs/1009.0045v1

Computer Science

Computational Geometry

18 pages, 10 figures. Extended version of paper to appear in Proc. 18th Int. Symp. Graph Drawing, Konstanz, Germany, 2010

Scientific paper

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-degree 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-degree angles, i.e., the angular resolution of the diamond lattice, between any two edge segments meeting at a vertex or bend.

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