1. Multi-Dimensional Functions cs5984: Information Visualization Chris North

2. Multi-Dimensional Functions y = f(x 1, x 2, x 3, …, x n ) Continuous: y = x 1 3 + 2x 2 2 - 9x 3 Discrete: x i are sampled in a bounded region X i = [0,1,2,…,100] How is this different from Multi-Dimensional Data? Huge scale: 6D with 10 samples/D = 1,000,000 data points Data values at every point in the space

3. Multi-D Data Visualizations… Don’t work well for multi-D functions Example: 5d func sampled on 1-9 for all inputs Parallel coords

5. 1-D: Easy y = f(x) x y

6. 2-D: Easy y = f(x 1, x 2 ) Height field: x2 x1 y

7. 2-D: Easy Color map:y  color

8. 3-D: Hard y = f(x 1, x 2, x 3 ) Color cube:y  color What’s inside? x1 x2 x3

9.  4D: Really Hard y = f(x 1, x 2, x 3, x 4, …, x n ) What does a 5D space look like?!? Approaches: Hierarchical axes (Mihalisin) Nested coordinate frames (Worlds within Worlds) Slicing (HyperSlice) Our spiffy new approach: Radial Focus+Context (Sanjini)

10. Hierarchical Axes 1D view of 3D function: (Mihalisin et al.) f(x 1, x 2, x 3 ) x3 x2 x1

11. Hierarchical Axes 2D view of 4D function (using color maps) y = f(x 1, x 2, x 3, x 4, …, x n ) Discrete: x i = [0,1,2,3,4] x1 x2 x3 x4 y = f(x 1,x 2,0,0) as color

12. Hierarchical Axes Scale? 6d = 3 levels in the 2d approach 10 samples/d = 1,000,000 data points = 1 screen For more dimensions, zoom in on “blocks” For alternate 2d color maps, reorder dimensions

13. Nested Coordinate Frames Feiner, “Worlds within Worlds” Sandip, Ben

14. Slicing Van Wijk, “HyperSlice” Kumar, Kunal

15. Radial Focus+Context Sanjini infovis.cs.vt.edu

16. Comparison Hierarchical axes (Mihalisin): < 6d by 10 samples, ALL slices, view only 2d at a time Nested coordinate frames (Worlds within Worlds) < 5-8d, continuous, no overview, 3d hardware Slicing (HyperSlice): < 10d by 100 samples, 2d slices *Radial Focus+Context (Sanjini) < 10d by 1000 samples, overview, all d uniform, rays Way to go, sanjini!

17. Next Week Book chapter 7 Tues: 1-D Plaisant, “Lifelines” » mahesh, jon Eick, “SeeSoft” » jeevak, alex Thurs: 1-D Mackinlay, “Perspective Wall” » ahmed, ganesh Hibino, “MMVIS” » atul, dananjan

18. Project Proposal due today Literature review: due Sept 27 Goal: become world’s expert on your topic area A few pages What have other people done on the topic? How will yours be new & different? Will be the “Related Work” section of your final paper Resources: ACM & IEEE DL, follow refs, people