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Space-Filling Curves

  • Reference work entry
Encyclopedia of GIS

Synonyms

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

Definition

A space-filling curve (SFC) is a way of mapping a multi‐dimensional space into a 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 N D − 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 to preserve the locality...

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Recommended Reading

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, University of Minnesota, Minneapolis, MN, USA

    Mohamed F. Mokbel

  2. Department of Computer Science, Purdue University, Indianapolis, IN, USA

    Walid G. Aref

Authors
  1. Mohamed F. Mokbel
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  2. Walid G. Aref
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Editor information

Editors and Affiliations

  1. Faculty of Computer Science and Engineering, University of Minnesota, Minneapolis, MN, 55455, USA

    Shashi Shekhar (McKnight Distinguished University Professor) (McKnight Distinguished University Professor)

  2. Management Science and Information Systems Department, Rutgers Business School Newark and New Brunswick Rutgers, the State University of New Jersey, Newark, NJ, 07102, USA

    Hui Xiong (Assistant Professor) (Assistant Professor)

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© 2008 Springer-Verlag

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Mokbel, M., Aref, W. (2008). Space-Filling Curves. In: Shekhar, S., Xiong, H. (eds) Encyclopedia of GIS. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35973-1_1233

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