@MISC{Kobourov04non-euclideanspring, author = {Stephen G. Kobourov and et al.}, title = {Non-Euclidean Spring Embedders}, year = {2004} }

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Abstract

We present a method by which force-directed algorithms for graph layouts can be generalized to calculate the layout of a graph in an arbitrary Riemannian geometry. 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.