Layout with Circular and Other Non-linear Constraints Using Procrustes Projection
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.
- 5.Dwyer, T.: Scalable, versatile and simple constrained graph layout. In: Proc. Eurographics/IEEE-VGTC Symp. on Visualization (Eurovis 2009). IEEE, Los Alamitos (2009) (to appear)Google Scholar
- 13.Everson, R.: Orthogonal, but not orthonormal, procrustes problems. Advances in Computational Mathematics (submitted) (1998), http://secamlocal.ex.ac.uk/people/staff/reverson/uploads/Site/procrustes.pdf
- 15.Hu, Y.: Efficient and high quality force-directed graph drawing. The Mathematica Journal 10(1), 37–71 (2005)Google Scholar
- 16.Jakobsen, T.: Advanced character physics. In: San Jose Games Developers’ Conference (2001), http://www.gamasutra.com/resource_guide/20030121/jacobson_01.shtml
- 18.Müller, M., Heidelberger, B., Hennix, M., Ratcliff, J.: Position based dynamics. In: Proc. of Virtual Reality Interactions and Physical Simulations (VRIPhys), pp. 71–80 (2006)Google Scholar
- 19.Six, J.M., Tollis, I.G.: A framework for user-grouped circular drawings. In: Liotta, G. (ed.) GD 2003. LNCS, vol. 2912, pp. 135–146. Springer, Heidelberg (2004)Google Scholar