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- W1566774944 abstract "A discrete space-filling curve provides a linear traversal or indexing of a multi-dimensional grid space. We present an analytical study of the locality properties of the m-dimensional k-order discrete Hilbert and z-order curve families, ${H^m_k | k = 1,2,...}$ and ${Z^m_k | k = 1,2,...}$ , respectively, based on the locality measure L δ that cumulates all index-differences of point-pairs at a common 1-normed distance δ. We derive the exact formulas for L δ (H k m ) and L δ (Z k m ) for m = 2 and arbitrary δ that is an integral power of 2, and m = 3 and δ = 1. The results yield a constant asymptotic ratio lim $_{krightarrowinfty}frac{L_delta(H^m_k)}{L_delta(Z^m_k)} > 1$ , which suggests that the z-order curve family performs better than the Hilbert curve family over the considered parameter ranges." @default.
- W1566774944 created "2016-06-24" @default.
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- W1566774944 date "2003-01-01" @default.
- W1566774944 modified "2023-10-18" @default.
- W1566774944 title "On the Locality Properties of Space-Filling Curves" @default.
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- W1566774944 doi "https://doi.org/10.1007/978-3-540-24587-2_40" @default.
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