Geodesic
Planar Confluent Orthogonal Drawings of 4-Modal Digraphs
Journal of Graph Algorithms and Applications, Tome 27 (2023) no. 7, pp. 523-540.

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In a planar confluent orthogonal drawing (PCOD) of a directed graph (digraph) vertices are drawn as points in the plane and edges as orthogonal polylines starting with a vertical segment and ending with a horizontal segment. Edges may overlap in their first or last segment, but must not intersect otherwise. PCODs can be seen as a directed variant of Kandinsky drawings or as planar L-drawings of subdivisions of digraphs. The maximum number of subdivision vertices in any edge is then the split complexity. A PCOD is upward if each edge is drawn with monotonically increasing y-coordinates and quasi-upward if no edge starts with decreasing y-coordinates. We study the split complexity of PCODs and (quasi-)upward PCODs for various classes of graphs.
DOI : 10.7155/jgaa.00632
Keywords: directed plane graphs, Kandinsky drawings, L-drawings, curve complexity, irreducible triangulations, upward planar, quasi-upward planar 
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Sabine Cornelsen; Gregor Diatzko. Planar Confluent Orthogonal Drawings of 4-Modal Digraphs. Journal of Graph Algorithms and Applications, Tome 27 (2023) no. 7, pp. 523-540. doi : 10.7155/jgaa.00632. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00632/

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