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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 2^{r} elements on each dimension is specified as a permutation which rearranges 2^{rn} 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

The copyright of the original papers published on this site belongs to IEICE. Unauthorized use of the original or translated papers is prohibited. See IEICE Provisions on Copyright for details.

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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 2^{r} elements on each dimension is specified as a permutation which rearranges 2^{rn} 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 2^{r} elements on each dimension is specified as a permutation which rearranges 2^{rn} 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},}

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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 2^{r} elements on each dimension is specified as a permutation which rearranges 2^{rn} 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 -