title: Non-Euclidean spring embedders.
abstract: We present a conceptually simple approach to generalizing force-directed methods for graph layout from Euclidean geometry to Riemannian geometries. Unlike previous work on non-Euclidean force-directed methods, ours is not limited to special classes of graphs, but can be applied to arbitrary graphs. The method relies on extending the Euclidean notions of distance, angle, and force-interactions to smooth non-Euclidean geometries via projections to and from appropriately chosen tangent spaces. In particular, we formally describe the calculations needed to extend such algorithms to hyperbolic and spherical geometries. We also study the theoretical and practical considerations that arise when working with non-Euclidean geometries.
authors.affiliation: Department of Computer Science, University of Arizona, Tucson, AZ 85721, USA. kobourov@cs.arizona.edu
authors.forename: Stephen G
authors.initials: SG
authors.lastname: Kobourov
authors.forename: Kevin
authors.initials: K
authors.lastname: Wampler
mesh_terms: D000465:Algorithms; D003196:Computer Graphics; D003198:Computer Simulation; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D021621:Imaging, Three-Dimensional / Q000379:methods*; D008962:Models, Theoretical; D012815:Signal Processing, Computer-Assisted