### Abstract

A space-filling curve 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 D-dimensional space so that every cell is visited exactly once. There are numerous kinds of space-filling curves. The difference between such curves is in their way of mapping to the one-dimensional space. Selecting the appropriate curve for any application requires knowledge of the mapping scheme provided by each space-filling curve. A space-filling curve consists of a set of segments. Each segment connects two consecutive multi-dimensional points. Five different types of segments are distinguished, namely, Jump, Contiguity, Reverse, Forward, and Still. A description vector V = (J,C,R,F,S), where J,C,R,F, and S, are the percentages of Jump, Contiguity, Reverse, Forward, and Still segments in the space-filling curve, encapsulates all the properties of a space-filling curve. The knowledge of V facilitates the process of selecting the appropriate space-filling curve for different applications. Closed formulas are developed to compute the description vector V for any D-dimensional space and grid size N for different space-filling curves. A comparative study of different space-filling curves with respect to the description vector is conducted and results are presented and discussed.

Original language | English |
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Pages | 149-154 |

Number of pages | 6 |

Publication status | Published - 1 Dec 2002 |

Event | Tenth ACM International Symposium on Advances in Geographic Information Systems - McLean, VA, United States Duration: 8 Nov 2002 → 9 Nov 2002 |

### Other

Other | Tenth ACM International Symposium on Advances in Geographic Information Systems |
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Country | United States |

City | McLean, VA |

Period | 8/11/02 → 9/11/02 |

### ASJC Scopus subject areas

- Computer Science(all)

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## Cite this

*Performance of multi-dimensional space-filling curves*. 149-154. Paper presented at Tenth ACM International Symposium on Advances in Geographic Information Systems, McLean, VA, United States.