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    Area of Science:

    • Data processing
    • Computational geometry
    • Digital signal processing

    Background:

    • Previous techniques enabled unitary rotation of 2D pixellated images.
    • Extending these methods to higher dimensions presents computational challenges.

    Purpose of the Study:

    • To develop a unitary rotation method for 3D pixellated cubes and D-dimensional Cartesian data arrays.
    • To ensure the transformation is invertible and preserves information.

    Main Methods:

    • Adaptation of a 2D unitary image rotation technique.
    • Application to N×N×N pixellated cubes and D-dimensional data arrays.
    • Analysis of computational complexity and potential artifacts.

    Main Results:

    • Successful unitary and real (orthogonal) transformation for D-dimensional data.
    • Invertibility confirmed, indicating no information loss.
    • Computational cost scales with N(2D), and Gibbs-like oscillations are inherent.

    Conclusions:

    • The developed method provides a standard for unitary rotation of D-dimensional data.
    • The transformation's invertibility makes it suitable for lossless data manipulation.
    • Potential applications in fields requiring high-dimensional data processing and transformation.