Geodesic
Slanted Orthogonal Drawings: Model, Algorithms and Evaluations
Journal of Graph Algorithms and Applications, Tome 18 (2014) no. 3, pp. 459-489.

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We introduce a new model in the context of non-planar orthogonal graph drawing that we call slanted orthogonal graph drawing. While in traditional orthogonal drawings each edge is made of alternating axis-aligned line segments, in slanted orthogonal drawings intermediate diagonal segments on the edges are permitted, which allows for: (a) smoothening the bends of the produced drawing (as they are replaced by pairs of "half-bends"), and, (b) emphasizing the crossings of the drawing (as they always appear at the intersection of two diagonal segments). We present an approach to compute bend-optimal slanted orthogonal representations, an efficient heuristic to compute close-to-optimal slanted orthogonal drawings with respect to the total number of bends in quadratic area, and a corresponding LP formulation, when insisting on bend-optimality. On the negative side, we show that bend-optimal slanted orthogonal drawings may require exponential area. 
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     author = {Michael Bekos and Michael Kaufmann and Robert Krug and Thorsten Ludwig and Stefan N\"aher and Vincenzo Roselli},
     title = {Slanted {Orthogonal} {Drawings:} {Model,} {Algorithms} and {Evaluations}},
     journal = {Journal of Graph Algorithms and Applications},
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Michael Bekos; Michael Kaufmann; Robert Krug; Thorsten Ludwig; Stefan Näher; Vincenzo Roselli. Slanted Orthogonal Drawings: Model, Algorithms and Evaluations. Journal of Graph Algorithms and Applications, Tome 18 (2014) no. 3, pp. 459-489. doi : 10.7155/jgaa.00332. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00332/

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