Slanted Orthogonal Drawings: Model, Algorithms and Evaluations - Bekos, Michael; Kaufmann, Michael; Krug, Robert; Ludwig, Thorsten; Näher, Stefan; Roselli, Vincenzo (Journal of Graph Algorithms and Applications, 2014)
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.