3 Ideas behind H3 u Creating an optimal layout for a general graph is tough u Creating an optimal layout for a tree is easier u Often it is possible to use domain- specific knowledge to create a hierarchical structure from a graph
4 Stumbling Blocks u The deeper the tree, the more nodes; exponential growth u You can see an overview, or you can see fine details, but not both
5 Solution u A layout based on hyperbolic space, that allows for a focus + context view u H3 used to lay out hierarchies of over 20 000 nodes
6 Related Work u H3 has its roots in graph-drawing and focus+context work
7 2D Graph and Tree Drawing u Thinking very small-scale u Frick, Ludwig, Mehldau created categories for graphs; # of nodes ranged from 16 in the smallest category, to > 128 in the largest
8 2D Tree Drawing (cont’d) MosiacG System Zyers and Stasko Image from: http://www.w3j.com/1/ayers.270/pap er/270.html
10 3D Graph Drawing (cont’d) u Other work centered around the idea of a mass-spring system – Node repel one another, but links attract – Difficulty in converging when you try to scale the systems u Aside: Eric Brochu is doing similar work in 2D - http://www.cs.ubc.ca/~ebrochu/mmmvis.htm
11 3D Tree Drawing Cone Trees, Robertson, Mackinlay, Card Image from: http://www2.parc.com/istl/projects/uir/pubs/items/UIR-1991- 06-Robertson-CHI91-Cone.pdf
13 Alternate Geometry u Information at: http://cs.unm.edu/~joel/NonEuclid/ u Euclidean geometry – 3 angles of a triangle add up to? – Shortest distance between two points? u Spherical geometry – How we think about the world – Shortest way from Florida to Philippines?
14 Alternate Geometry (cont’d) u Hyperbolic Geometry / Space – Is important to the Theory of Relativity – The “fifth” dimension – Can be projected into 2-D as a pseudosphere – Key: As a point moves away from the center towards the boundary circle, its distance approaches infinity
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