Geodesic
Smooth Orthogonal Layouts
Journal of Graph Algorithms and Applications, Tome 17 (2013) no. 5, pp. 575-595.

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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 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.
DOI : 10.7155/jgaa.00305
Keywords: Graph drawing, Orthogonal Graph Drawing, Smooth Orthogonal Layouts, Edge Complexity 
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Michael Bekos; Michael Kaufmann; Stephen Kobourov; Antonios Symvonis. Smooth Orthogonal Layouts. Journal of Graph Algorithms and Applications, Tome 17 (2013) no. 5, pp. 575-595. doi : 10.7155/jgaa.00305. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00305/

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