Geodesic
Orthogonal Drawings of Plane Graphs Without Bends
Journal of Graph Algorithms and Applications, Advances in Graph Drawing. Special Issue on Selected Papers from the Ninth International Symposium on Graph Drawing, GD 2001 , Tome 7 (2003) no. 4, pp. 335-362.

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In an orthogonal drawing of a plane graph each vertex is drawn as a point and each edge is drawn as a sequence of vertical and horizontal line segments. A bend is a point at which the drawing of an edge changes its direction. Every plane graph of the maximum degree at most four has an orthogonal drawing, but may need bends. A simple necessary and sufficient condition has not been known for a plane graph to have an orthogonal drawing without bends. In this paper we obtain a necessary and sufficient condition for a plane graph G of the maximum degree three to have an orthogonal drawing without bends. We also give a linear-time algorithm to find such a drawing of G if it exists. 
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     author = {Md. Saidur Rahman and Takao Nishizeki and Mahmuda Naznin},
     title = {Orthogonal {Drawings} of {Plane} {Graphs} {Without} {Bends}},
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Md. Saidur Rahman; Takao Nishizeki; Mahmuda Naznin. Orthogonal Drawings of Plane Graphs Without Bends. Journal of Graph Algorithms and Applications, 
							Advances in Graph Drawing. Special Issue on Selected Papers from
    the Ninth International Symposium on Graph Drawing, GD 2001
					, Tome 7 (2003) no. 4, pp. 335-362. doi : 10.7155/jgaa.00074. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00074/

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