Encyclopedia of Database Systems

2018 Edition
| Editors: Ling Liu, M. Tamer Özsu

Space-Filling Curves

  • Mohamed F. Mokbel
  • Walid G. Aref
Reference work entry
DOI: https://doi.org/10.1007/978-1-4614-8265-9_349

Synonyms

Distance-preserving mapping; Linearization; Locality-preserving mapping; Multi-dimensional mapping

Definition

A space-filling curve (SFC) is a way of mapping the multi-dimensional space into the one-dimensional space. It acts like a thread that passes through every cell element (or pixel) in the multi-dimensional space so that every cell is visited exactly once. Thus, a space-filling curve imposes a linear order of points in the multi-dimensional space. A D-dimensional space-filling curve in a space of N cells (pixels) of each dimension consists of ND − 1 segments where each segment connects two consecutive D-dimensional points. There are numerous kinds of space-filling curves (e.g., Hilbert, Peano, and Gray). The difference between such curves is in their way of mapping to the one-dimensional space, i.e., the order that a certain space-filling curve traverses the multi-dimensional space. The quality of a space-filling curve is measured by its ability in preserving the...

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Recommended Reading

  1. 1.
    Hilbert D. Ueber stetige abbildung einer linie auf ein flashenstuck. Math Ann. 1891;38:459–60.MathSciNetzbMATHCrossRefGoogle Scholar
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    Mandelbrot BB. Fractal geometry of nature. New York: W. H. Freeman; 1977.Google Scholar
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    Peano G. Sur une courbe qui remplit toute une air plaine. Math Ann. 1890;36(1):157–60.MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Sagan H. Space filling curves. Berlin: Springer; 1994.zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringUniversity of Minnesota-Twin CitiesMinneapolisUSA
  2. 2.Purdue UniversityWest LafayetteUSA

Section editors and affiliations

  • Dimitris Papadias
    • 1
  1. 1.Department of Computer Science and EngineeringHong Kong University of Science and TechnologyKowloonChina