Abstract
Using a previous technique to rotate two-dimensional images on an square pixellated screen unitarily, we can rotate three-dimensional pixellated cubes of side , and also generally -dimensional Cartesian data arrays, also unitarily. Although the number of operations inevitably grows as (because each rotated pixel depends on all others), and Gibbs-like oscillations are inevitable, the result is a strictly unitary and real transformation (thus orthogonal) that is invertible (thus no loss of information) and could be used as a standard.
© 2014 Optical Society of America
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