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Data-Driven Space-Filling Curves.

Liang Zhou, Chris R Johnson, Daniel Weiskopf

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    Summary
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    We introduce a novel data-driven space-filling curve for enhanced 2D and 3D data visualization. This method improves feature preservation by creating a Hamiltonian path that optimizes data and spatial coherency.

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    Area of Science:

    • Computer Science
    • Data Visualization

    Background:

    • Effective visualization of complex datasets is crucial for scientific discovery.
    • Existing space-filling curves can struggle to preserve spatial relationships in data.
    • Multiscale and high-dimensional data present unique visualization challenges.

    Purpose of the Study:

    • To propose a novel data-driven space-filling curve method for 2D and 3D visualization.
    • To enhance data coherency and feature preservation during linearization.
    • To extend the method for multiscale data analysis.

    Main Methods:

    • A data-driven approach using a Hamiltonian path to approximate an objective function.
    • The objective function balances data value similarity and spatial coherency.
    • An extended variant utilizes quadtrees and octrees for multiscale data.

    Main Results:

    • The proposed space-filling curve linearization better preserves spatial features compared to existing methods.
    • The method demonstrates effectiveness in multivariate and ensemble visualizations.
    • Successful application to 2D and 3D data on regular grids and multiscale particle simulations.

    Conclusions:

    • The data-driven space-filling curve offers improved data coherency and feature preservation.
    • The method is versatile, applicable to various visualization tasks including multiscale analysis.
    • Numerical comparisons and examples validate its effectiveness over traditional techniques.