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Shen-Yi Lin, Chih-Shen Chen, Li Liu+ and Chua-Huang Huang
Department of Information Engineering and Computer Science
Feng Chia University
Taichung, 407 Taiwan
+Graduate Institute of Medical Informatics
Taipei Medical University
Taipei, 110 Taiwan
We present a tensor product formulation for Hilbert space-filling curves. Both recursive
and iterative formulas are expressed in the paper. We view a Hilbert space-filling
curve as a permutation which maps two-dimensional 2n ¡Ñ 2n data elements stored in the
row major or column major order to the order of traversing a Hilbert curve. The tensor
product formula of Hilbert space-filling curves uses several permutation operations:
stride permutation, radix-2 Gray permutation, transposition, and anti-diagonal transposition.
The iterative tensor product formula can be manipulated to obtain the inverse Hilbert
permutation. Also, the formulas are directly translated into computer programs
which can be used in various applications including image processing, VLSI component
layout, and R-tree indexing, etc.
Received October 27, 2005; revised April 25, June 21 & August 28, 2006; accepted September 7, 2006.
Communicated by Chin-Teng Lin.