Download presentation

Presentation is loading. Please wait.

Published byColton Boyson Modified over 2 years ago

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

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

3
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
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
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
6 Related Work u H3 has its roots in graph-drawing and focus+context work

7
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
8 2D Tree Drawing (cont’d) MosiacG System Zyers and Stasko Image from: http://www.w3j.com/1/ayers.270/pap er/270.html

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

10
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
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
12 Hyperbolic Focus+Context Hyperbolic Tree Browser, Lamping, Rao Image from: http://www.acm.org/sigchi/chi9 5/Electronic/documnts/papers/jl _figs/strip1.htm

13
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
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

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

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

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

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

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

20
20 Demo

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

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

23
23 Questions?

Similar presentations

OK

GRAPHICS. PURPOSE OF GRAPHICS IN WEB DESIGN Graphics add visual/aesthetic appeal to the information on the web page, helping to maintain viewer interest.

GRAPHICS. PURPOSE OF GRAPHICS IN WEB DESIGN Graphics add visual/aesthetic appeal to the information on the web page, helping to maintain viewer interest.

© 2018 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on technical topics related to electrical engineering Ppt on seasons of the year Ppt on different mode of transport Ppt on positive thinking Ppt on human nutrition and digestion quiz Ppt on carbon cycle in nature Ppt on pin diode spice Ppt online downloader for games Ppt on sports day ideas Ppt on earth movements and major landforms in texas