Pointed drawings of planar graphs

Authors:
Oswin Aichholzer;GüNter Rote;André Schulz;Birgit Vogtenhuber
Affiliations:
Institute for Software Technology, Graz University of Technology, Austria;Institut für Informatik, Freie Universität Berlin, Germany;Institut für Mathematsche Logik und Grundlagenforschung, Universität Münster, Germany;Institute for Software Technology, Graz University of Technology, Austria
Venue:
Computational Geometry: Theory and Applications
Year:
2012

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Abstract

We study the problem how to draw a planar graph crossing-free such that every vertex is incident to an angle greater than @p. In general a plane straight-line drawing cannot guarantee this property. We present algorithms which construct such drawings with either tangent-continuous biarcs or quadratic Bezier curves (parabolic arcs), even if the positions of the vertices are predefined by a given plane straight-line drawing of the graph. Moreover, the graph can be drawn with circular arcs if the vertices can be placed arbitrarily. The topic is related to non-crossing drawings of multigraphs and vertex labeling.