The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. ex. Some numerals are expressed as "XNUMX".
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The original paper is in English. Non-English content has been machine-translated and may contain typographical errors or mistranslations. Copyrights notice
Desenvolvemos um novo método de construção para nCurvas de preenchimento de espaço de Hilbert multidimensionais. O método de construção inclui quatro etapas: alocação de blocos, permutação de Gray, transformação de coordenadas e construção recursiva. Usamos a teoria do produto tensorial para formular o método. Um ncurva de preenchimento de espaço de Hilbert tridimensional de 2r elementos em cada dimensão é especificado como uma permutação que reorganiza 2rn elementos de dados armazenados na ordem principal da linha, como na linguagem C, ou na ordem principal da coluna, como na linguagem FORTRAN, até a ordem de passagem de um ncurva de preenchimento de espaço de Hilbert tridimensional. A formulação do produto tensorial de nAs curvas de preenchimento de espaço Hilbert multidimensionais usam permutação de passada, permutação reversa e permutação de Gray. Apresentamos fórmulas de produto tensorial recursivas e iterativas de nCurvas de preenchimento de espaço de Hilbert multidimensionais. As fórmulas do produto tensorial são traduzidas diretamente em programas de computador que podem ser usados em diversas aplicações. O processo de geração do programa é explicado no artigo.
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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},}
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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 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 -