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...
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsRecommended Reading
Hilbert D. Ueber stetige abbildung einer linie auf ein flashenstuck. Math Ann. 1891;38:459–60.
Mandelbrot BB. Fractal geometry of nature. New York: W. H. Freeman; 1977.
Peano G. Sur une courbe qui remplit toute une air plaine. Math Ann. 1890;36(1):157–60.
Sagan H. Space filling curves. Berlin: Springer; 1994.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2018 Springer Science+Business Media, LLC, part of Springer Nature
About this entry
Cite this entry
Mokbel, M.F., Aref, W.G. (2018). Space-Filling Curves. In: Liu, L., Özsu, M.T. (eds) Encyclopedia of Database Systems. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-8265-9_349
Download citation
DOI: https://doi.org/10.1007/978-1-4614-8265-9_349
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-8266-6
Online ISBN: 978-1-4614-8265-9
eBook Packages: Computer ScienceReference Module Computer Science and Engineering