• Corpus ID: 17888931

Harmonious Hilbert curves and other extradimensional space-filling curves

@article{Haverkort2012HarmoniousHC,
  title={Harmonious Hilbert curves and other extradimensional space-filling curves},
  author={Herman J. Haverkort},
  journal={ArXiv},
  year={2012},
  volume={abs/1211.0175}
}
This paper introduces a new way of generalizing Hilbert's two-dimensional space-filling curve to arbitrary dimensions. The new curves, called harmonious Hilbert curves, have the unique property that for any d' < d, the d-dimensional curve is compatible with the d'-dimensional curve with respect to the order in which the curves visit the points of any d'-dimensional axis-parallel space that contains the origin. Similar generalizations to arbitrary dimensions are described for several variants of… 

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