On embedding a graph in the grid with the minimum number of bends
SIAM Journal on Computing
A framework for drawing planar graphs with curves and polylines
Journal of Algorithms
Drawing High Degree Graphs with Low Bend Numbers
GD '95 Proceedings of the Symposium on Graph Drawing
A Better Heuristic for Orthogonal Graph Drawings
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
Area-Efficient Static and Incremental Graph Drawings
ESA '97 Proceedings of the 5th Annual European Symposium on Algorithms
On the Compuational Complexity of Upward and Rectilinear Planarity Testing
GD '94 Proceedings of the DIMACS International Workshop on Graph Drawing
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
A graph reading behavior: Geodesic-path tendency
PACIFICVIS '09 Proceedings of the 2009 IEEE Pacific Visualization Symposium
Angle and distance constraints on tree drawings
GD'06 Proceedings of the 14th international conference on Graph drawing
Universality considerations in VLSI circuits
IEEE Transactions on Computers
Curvilinear graph drawing using the force-directed method
GD'04 Proceedings of the 12th international conference on Graph Drawing
Planar and poly-arc lombardi drawings
GD'11 Proceedings of the 19th international conference on Graph Drawing
Force-directed edge bundling for graph visualization
EuroVis'09 Proceedings of the 11th Eurographics / IEEE - VGTC conference on Visualization
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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.