Recent work on constrained graph layout has involved projection of simple two-variable linear equality and inequality constraints in the context of majorization or gradient-projection based optimization. While useful classes of containment, alignment and rectangular non-overlap constraints could be built using this framework, a severe limitation was that the layout used an axis-separation approach such that all constraints had to be axis aligned. In this paper we use techniques from Procrustes Analysis to extend the gradient-projection approach to useful types of non-linear constraints. The constraints require subgraphs to be locally fixed into various geometries - such as circular cycles or local layout obtained by a combinatorial algorithm (e.g. orthogonal or layered-directed) - but then allow these sub-graph geometries to be integrated into a larger layout through translation, rotation and scaling. © 2010 Springer-Verlag.
CITATION STYLE
Dwyer, T., & Robertson, G. (2010). Layout with circular and other non-linear constraints using Procrustes projection. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5849 LNCS, pp. 393–404). https://doi.org/10.1007/978-3-642-11805-0_37
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