1 / 23

H3: Laying Out Large Directed Graphs in 3D Hyperbolic Space

H3: Laying Out Large Directed Graphs in 3D Hyperbolic Space. Andrew Chan CPSC 533C March 24, 2003. H3. Image from: http://graphics.stanford.edu/papers/h3/fig/nab0.gif. Ideas behind H3. Creating an optimal layout for a general graph is tough Creating an optimal layout for a tree is easier

nibal
Download Presentation

H3: Laying Out Large Directed Graphs in 3D Hyperbolic Space

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. H3: Laying Out Large Directed Graphs in 3D Hyperbolic Space Andrew Chan CPSC 533C March 24, 2003

  2. H3 Image from: http://graphics.stanford.edu/papers/h3/fig/nab0.gif

  3. Ideas behind H3 • Creating an optimal layout for a general graph is tough • Creating an optimal layout for a tree is easier • Often it is possible to use domain-specific knowledge to create a hierarchical structure from a graph

  4. Stumbling Blocks • The deeper the tree, the more nodes; exponential growth • You can see an overview, or you can see fine details, but not both

  5. Solution • A layout based on hyperbolic space, that allows for a focus + context view • H3 used to lay out hierarchies of over 20 000 nodes

  6. Related Work • H3 has its roots in graph-drawing and focus+context work

  7. 2D Graph and Tree Drawing • Thinking very small-scale • 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/paper/270.html

  9. 3D Graph Drawing SGI fsn file-system viewer Image from: http://www.sgi.com/fun/images/fsn.map2.jpg

  10. 3D Graph Drawing (cont’d) • 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 • 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

  12. Hyperbolic Focus+Context Hyperbolic Tree Browser, Lamping, Rao Image from: http://www.acm.org/sigchi/chi95/Electronic/documnts/papers/jl_figs/strip1.htm

  13. Alternate Geometry • Information at: http://cs.unm.edu/~joel/NonEuclid/ • Euclidean geometry • 3 angles of a triangle add up to? • Shortest distance between two points? • Spherical geometry • How we think about the world • Shortest way from Florida to Philippines?

  14. Alternate Geometry (cont’d) • 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

  15. H3’s Layout Image from: http://graphics.stanford.edu/papers/h3/fig/nab0.gif

  16. Finding a Tree from a Graph • Most effective if you have domain-specific knowledge • Examples: • File system • Web site structure • Function call graphs

  17. Tree Layout Cone tree layout versus H3 Layout Image from: http://graphics.stanford.edu/papers/h3/html/node12.htm#conefig

  18. Sphere Packing • Need an effective way to place information • Cannot place spheres randomly • Want to have a fast algorithm

  19. Sphere Packing (cont’d) Image from: http://graphics.stanford.edu/papers/h3/fig/incrhemi.gif

  20. Demo

  21. Strengths • Can easily see what the important structures are and the relationships between them • Can let you ignore “noise” in data • Animated transitions • Responsive UI

  22. Weaknesses • Starting view only uses part of the sphere • Moving across the tree can disorient you; cost of clicking on the wrong place is high • Labels not present if node too far from center

  23. Questions?

More Related