An inventory of three-dimensional Hilbert space-filling curves

Details An inventory of three-dimensional Hilbert space-filling curves An inventory of three-dimensional Hilbert space-filling curves

2011-09-11

arxiv.org/abs/1109.2323v1

Computer Science

Computational Geometry

25 pages, 13 figures

Scientific paper

Hilbert's two-dimensional space-filling curve is appreciated for its good locality properties for many applications. However, it is not clear what is the best way to generalize this curve to filling higher-dimensional spaces. We argue that the properties that make Hilbert's curve unique in two dimensions, are shared by 10694807 structurally different space-filling curves in three dimensions. These include several curves that have, in some sense, better locality properties than any generalized Hilbert curve that has been considered in the literature before.

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