Locality and Bounding-Box Quality of Two-Dimensional Space-Filling Curves

  • Herman Haverkort
  • Freek van Walderveen
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5193)


Space-filling curves can be used to organise points in the plane into bounding-box hierarchies (such as R-trees). We develop measures of the bounding-box quality of space-filling curves that express how effective different curves are for this purpose. We give general lower bounds on the bounding-box quality and on locality according to Gotsman and Lindenbaum for a large class of curves. We describe a generic algorithm to approximate these and similar quality measures for any given curve. Using our algorithm we find good approximations of the locality and bounding-box quality of several known and new space-filling curves. Surprisingly, some curves with bad locality by Gotsman and Lindenbaum’s measure, have good bounding-box quality, while the curve with the best-known locality has relatively bad bounding-box quality.


Curve Section Unit Region Query Response Time Outer Corner Perimeter Ratio 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Herman Haverkort
    • 1
  • Freek van Walderveen
    • 1
  1. 1.Dept. of Computer ScienceEindhoven University of Technologythe Netherlands

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