IEICE TRANSACTIONS on Information
A Novel Construction Method for n-Dimensional Hilbert Space-Filling Curves
Summary :
We develop a novel construction method for n-dimensional Hilbert space-filling curves. The construction method includes four steps: block allocation, Gray permutation, coordinate transformation and recursive construction. We use the tensor product theory to formulate the method. An n-dimensional Hilbert space-filling curve of 2r elements on each dimension is specified as a permutation which rearranges 2rn data elements stored in the row major order as in C language or the column major order as in FORTRAN language to the order of traversing an n-dimensional Hilbert space-filling curve. The tensor product formulation of n-dimensional Hilbert space-filling curves uses stride permutation, reverse permutation, and Gray permutation. We present both recursive and iterative tensor product formulas of n-dimensional Hilbert space-filling curves. The tensor product formulas are directly translated into computer programs which can be used in various applications. The process of program generation is explained in the paper.
- Publication
- IEICE TRANSACTIONS on Information Vol.E93-D No.7 pp.1807-1815
- Publication Date
- 2010/07/01
- Publicized
- Online ISSN
- 1745-1361
- DOI
- 10.1587/transinf.E93.D.1807
- Type of Manuscript
- PAPER
- Category
- Fundamentals of Information Systems
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Chih-Sheng CHEN, Shen-Yi LIN, Min-Hsuan FAN, Chua-Huang HUANG, "A Novel Construction Method for n-Dimensional Hilbert Space-Filling Curves" in IEICE TRANSACTIONS on Information,
vol. E93-D, no. 7, pp. 1807-1815, July 2010, doi: 10.1587/transinf.E93.D.1807.
Abstract: We develop a novel construction method for n-dimensional Hilbert space-filling curves. The construction method includes four steps: block allocation, Gray permutation, coordinate transformation and recursive construction. We use the tensor product theory to formulate the method. An n-dimensional Hilbert space-filling curve of 2r elements on each dimension is specified as a permutation which rearranges 2rn data elements stored in the row major order as in C language or the column major order as in FORTRAN language to the order of traversing an n-dimensional Hilbert space-filling curve. The tensor product formulation of n-dimensional Hilbert space-filling curves uses stride permutation, reverse permutation, and Gray permutation. We present both recursive and iterative tensor product formulas of n-dimensional Hilbert space-filling curves. The tensor product formulas are directly translated into computer programs which can be used in various applications. The process of program generation is explained in the paper.
URL: https://global.ieice.org/en_transactions/information/10.1587/transinf.E93.D.1807/_p
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@ARTICLE{e93-d_7_1807,
author={Chih-Sheng CHEN, Shen-Yi LIN, Min-Hsuan FAN, Chua-Huang HUANG, },
journal={IEICE TRANSACTIONS on Information},
title={A Novel Construction Method for n-Dimensional Hilbert Space-Filling Curves},
year={2010},
volume={E93-D},
number={7},
pages={1807-1815},
abstract={We develop a novel construction method for n-dimensional Hilbert space-filling curves. The construction method includes four steps: block allocation, Gray permutation, coordinate transformation and recursive construction. We use the tensor product theory to formulate the method. An n-dimensional Hilbert space-filling curve of 2r elements on each dimension is specified as a permutation which rearranges 2rn data elements stored in the row major order as in C language or the column major order as in FORTRAN language to the order of traversing an n-dimensional Hilbert space-filling curve. The tensor product formulation of n-dimensional Hilbert space-filling curves uses stride permutation, reverse permutation, and Gray permutation. We present both recursive and iterative tensor product formulas of n-dimensional Hilbert space-filling curves. The tensor product formulas are directly translated into computer programs which can be used in various applications. The process of program generation is explained in the paper.},
keywords={},
doi={10.1587/transinf.E93.D.1807},
ISSN={1745-1361},
month={July},}
Copy
TY - JOUR
TI - A Novel Construction Method for n-Dimensional Hilbert Space-Filling Curves
T2 - IEICE TRANSACTIONS on Information
SP - 1807
EP - 1815
AU - Chih-Sheng CHEN
AU - Shen-Yi LIN
AU - Min-Hsuan FAN
AU - Chua-Huang HUANG
PY - 2010
DO - 10.1587/transinf.E93.D.1807
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E93-D
IS - 7
JA - IEICE TRANSACTIONS on Information
Y1 - July 2010
AB - We develop a novel construction method for n-dimensional Hilbert space-filling curves. The construction method includes four steps: block allocation, Gray permutation, coordinate transformation and recursive construction. We use the tensor product theory to formulate the method. An n-dimensional Hilbert space-filling curve of 2r elements on each dimension is specified as a permutation which rearranges 2rn data elements stored in the row major order as in C language or the column major order as in FORTRAN language to the order of traversing an n-dimensional Hilbert space-filling curve. The tensor product formulation of n-dimensional Hilbert space-filling curves uses stride permutation, reverse permutation, and Gray permutation. We present both recursive and iterative tensor product formulas of n-dimensional Hilbert space-filling curves. The tensor product formulas are directly translated into computer programs which can be used in various applications. The process of program generation is explained in the paper.
ER -
English
