1 / 21

Space-Filling Curves in Information Visualization

Space-Filling Curves in Information Visualization. Jiwen Huo jhuo@cgl.uwaterloo.ca. Space-filling curves. Definition: A continuous curve which passes through every point of a closed n-cell in Euclidean n-space E n is called a space filling curve (SFC). Application of SFC.

richardoliver
Download Presentation

Space-Filling Curves in Information Visualization

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. Space-Filling Curves in Information Visualization Jiwen Huo jhuo@cgl.uwaterloo.ca

  2. Space-filling curves • Definition: • A continuous curve which passes through every point of a closed n-cell in Euclidean n-space En is called a space filling curve (SFC).

  3. Application of SFC • Mapping multi-dimensional space to one dimensional sequence • Applications in computer science: • Database multi-attribute access • Image compression • Information visualization • ……

  4. Categories of SFC • Non-recursive • Z-Scan Curve • Snake Scan Curve • Recursive • Hilbert Curve • Peano Curve • Gray Code Curve

  5. Non-recursive Space Filling Curves Z-Scan Curve Snake Scan Curve

  6. Recursive Space Filling Curves Hilbert Curve Gray Code Curve Peano Curve

  7. 3D SFC Hilbert Curve Z Curve Peano Curve

  8. Hilbert Curve Z Curve Z Curve Hilbert Curve Good Good Properties of SFCs • Coherent in Continuity • Clustering Property • Direction Preserving

  9. Coherent in Continuity

  10. Clustering property Z H

  11. Direction Preserving P1: (X1, Y1) X1 > X2> X3 P2: (X2, Y2) Y1 > Y2> Y3 P3: (X3, Y3) Z(P1) > Z(P2) > Z(P3) H(P3) < H(P1) < H(P2)

  12. SFC in Information Visualization • Example Data • Color (R, G, B: [0, 255]) • Data with obvious geometric pattern • 4D Hyper Sphere • Data without obvious geometric pattern • Iris flowers (5 attributes, 3 classes) • Example SFC • Z-Curve • Hilbert Curve

  13. (160, 100) (160, 100, 100) ? 100 Visualizing Color (RGB)

  14. Visualizing Color (RGB) Z-Curve Mapping

  15. Visualizing Color (RGB) Hilbert Curve Mapping

  16. Visualizing Color (RGB) Green & Blue Z Red H

  17. Z-Curve Visualizing 4D Hyper-Sphere Surface • Hilbert Curve

  18. Z-Curve Hilbert Curve The Visualization of Iris Flowers

  19. Extension to Hilbert Curve

  20. The Visualization of Iris Flowers • Extended Hilbert Curve

  21. Questions? Suggestions?

More Related