Smooth Orthogonal Layouts

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 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. Submitted: November 2012 Reviewed: May 2013 Revised: October 2013 Accepted: October 2013 Final: October 2013 Published: October 2013 Article type: Regular paper Communicated by: G. Di Battista This article is based on the preliminary version [M. A. Bekos, M. Kaufmann, S. G. Kobourov, A. Symvonis, Smooth Orthogonal Layouts, in: Proc. 20th Int. Symposium on Graph Drawing (GD2012), in: Lecture Notes in Computer Science, Volume 7704, p.p. 150-161, 2013]. The work of M.A. Bekos is implemented within the framework of the Action Supporting Postdoctoral Researchers of the Operational Program Education and Lifelong Learning (Action's Bene ciary: General Secretariat for Research and Technology), and is conanced by the European Social Fund (ESF) and the Greek State. Michael Kaufmann has been supported by Deutsche Forschungsgemeinschaft SPP 1335 'Scalable Visual Analytics'. The work of S. G. Kobourov is supported in part by NSF grant CCF-1115971 and a grant from the Humboldt Foundation. E-mail addresses: [email protected] (M. A. Bekos) [email protected] (M. Kaufmann) [email protected] (S. G. Kobourov) [email protected]