## Invited Talk

Special Topics in Computer Science

Department of Computer Science and Information Engineering

National Chung Cheng University

March 17, 2003

##
Hilbert Space Filling Curves: Theory and Applications

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黃秋煌教授

逢甲大學資訊工程學系

### Abstract

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
$2^n \times 2^n$ 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.