TY - JOUR
T1 - Non-Euclidean spring embedders
AU - Kobourov, Stephen G.
AU - Wampler, Kevin
N1 - Funding Information:
The authors would like to thank the anonymous referees of the journal and conference versions of the paper for their comments and suggestions. This work is partially supported by the US National Science Foundation under grant ACR-0222920.
PY - 2005/11
Y1 - 2005/11
N2 - 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.
AB - 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.
KW - Force-directed algorithms
KW - Graph drawing
KW - Hyperbolic space
KW - Information visualization
KW - Non-Euclidean geometry
KW - Spherical space
KW - Spring embedders
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U2 - 10.1109/TVCG.2005.103
DO - 10.1109/TVCG.2005.103
M3 - Article
C2 - 16270867
AN - SCOPUS:27644496169
VL - 11
SP - 757
EP - 767
JO - IEEE Transactions on Visualization and Computer Graphics
JF - IEEE Transactions on Visualization and Computer Graphics
SN - 1077-2626
IS - 6
ER -