Layout with circular and other non-linear constraints using procrustes projection

  • Authors:
  • Tim Dwyer;George Robertson

  • Affiliations:
  • Microsoft Research, Redmond;Microsoft Research, Redmond

  • Venue:
  • GD'09 Proceedings of the 17th international conference on Graph Drawing
  • Year:
  • 2009

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Abstract

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.