space-filling curves in information visualization jiwen huo [email protected]
TRANSCRIPT
Space-Filling Curves Space-Filling Curves in Information Visualizationin Information Visualization
Jiwen [email protected]
Space-filling curvesSpace-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).
Application of SFCApplication of SFC
Mapping multi-dimensional space to one dimensional sequence
Applications in computer science: Database multi-attribute access Image compression Information visualization ……
Categories of SFCCategories of SFC
Non-recursive Z-Scan Curve Snake Scan Curve
Recursive Hilbert Curve Peano Curve Gray Code Curve
Non-recursive Space Filling Non-recursive Space Filling CurvesCurves
Z-Scan Curve Snake Scan Curve
Recursive Space Filling CurvesRecursive Space Filling Curves
Hilbert Curve
Gray Code Curve
Peano Curve
3D SFC3D SFC
Z Curve Peano Curve
Hilbert Curve
Properties of SFCsProperties of SFCs
Coherent in Continuity Clustering Property
Direction Preserving
Good
Hilbert CurveZ Curve
Good
Z CurveHilbert Curve
Coherent in ContinuityCoherent in Continuity
Clustering propertyClustering property
Z
H
Direction PreservingDirection 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)
SFC in Information VisualizationSFC 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
Visualizing Color (RGB)Visualizing Color (RGB)
(160, 100)
(160, 100, 100)
100
?
Visualizing Color (RGB)Visualizing Color (RGB)
Z-Curve Mapping
Visualizing Color (RGB)Visualizing Color (RGB)
Hilbert Curve Mapping
Visualizing Color (RGB)Visualizing Color (RGB)
Green & Blue
Red
Z
H
Visualizing 4D Hyper-Sphere SurfaceVisualizing 4D Hyper-Sphere Surface
Z-Curve Hilbert Curve
The Visualization of Iris FlowersThe Visualization of Iris Flowers
Z-Curve Hilbert Curve
Extension to Hilbert CurveExtension to Hilbert Curve
The Visualization of Iris FlowersThe Visualization of Iris Flowers
Extended Hilbert Curve
Questions? Questions?
Suggestions? Suggestions?