Smooth Orthogonal Layouts

Bekos, Michael A. and Kaufmann, Michael and Kobourov, Stephen G. and Symvonis, Antonios (2013) Smooth Orthogonal Layouts. In: 20th International Symposium, GD 2012, September 19-21, 2012 , pp. 150-161(Official URL:

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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.

Item Type: Conference Paper
Additional Information: 10.1007/978-3-642-36763-2_14
Classifications: G Algorithms and Complexity > G.280 Canonical Ordering
P Styles > P.120 Circular
P Styles > P.600 Poly-line > P.600.300 Mainly Orthogonal

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