On Multi-dimensional Hilbert Indexings
Indexing schemes for grids based on space-filling curves (e.g., Hilbert indexings) find applications in numerous fields. Hilbert curves yield the most simple and popular scheme. We extend the concept of curves with Hilbert property to arbitrary dimensions and present first results concerning their structural analysis that also simplify their applicability. As we show, Hilbert indexings can be completely described and analyzed by “generating elements of order 1”, thus, in comparison with previous work, reducing their structural complexity decisively.
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