Evaluation of pairwise distances among points forming a regular orthogonal grid in a hypercube
Cartesian grid is a basic arrangement of points that form a regular orthogonal grid (ROG). In some applications, it is needed to evaluate all pairwise distances among ROG points. This paper focuses on ROG discretization of a unit hypercube of arbitrary dimension. A method for the fast enumeration o...
Main Authors: | , |
---|---|
Format: | Article |
Language: | English |
Published: |
Vilnius Gediminas Technical University
2018-09-01
|
Series: | Journal of Civil Engineering and Management |
Subjects: | |
Online Access: | https://www.tede.vgtu.lt/index.php/JCEM/article/view/5189 |
id |
doaj-125fbae7d69346c2b15b29d41c641f00 |
---|---|
record_format |
Article |
spelling |
doaj-125fbae7d69346c2b15b29d41c641f002021-07-02T12:33:19ZengVilnius Gediminas Technical UniversityJournal of Civil Engineering and Management1392-37301822-36052018-09-0124510.3846/jcem.2018.5189Evaluation of pairwise distances among points forming a regular orthogonal grid in a hypercubeVáclav Sadílek0Miroslav Vořechovský1Institute of Structural Mechanics, Faculty of Civil Engineering, Brno University of TechnologyInstitute of Structural Mechanics, Faculty of Civil Engineering, Brno University of Technology, Czech Republic Cartesian grid is a basic arrangement of points that form a regular orthogonal grid (ROG). In some applications, it is needed to evaluate all pairwise distances among ROG points. This paper focuses on ROG discretization of a unit hypercube of arbitrary dimension. A method for the fast enumeration of all pairwise distances and their counts for a high number of points arranged into high-dimensional ROG is presented. The proposed method exploits the regular and collapsible pattern of ROG to reduce the number of evaluated distances. The number of unique distances is identified and frequencies are determined using combinatorial rules. The measured computational speed-up compared to a naïve approach corresponds to the presented theoretical analysis. The proposed method and algorithm may find applications in various fields. The paper shows application focused on the behaviour of various distance measures with the motivation to find the lower bounds on the criteria of point distribution uniformity in Monte Carlo integration. https://www.tede.vgtu.lt/index.php/JCEM/article/view/5189full factorial designdesign of experimentspairwise distancesAudze-Eglãjs criterionoptimizationperiodic space |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Václav Sadílek Miroslav Vořechovský |
spellingShingle |
Václav Sadílek Miroslav Vořechovský Evaluation of pairwise distances among points forming a regular orthogonal grid in a hypercube Journal of Civil Engineering and Management full factorial design design of experiments pairwise distances Audze-Eglãjs criterion optimization periodic space |
author_facet |
Václav Sadílek Miroslav Vořechovský |
author_sort |
Václav Sadílek |
title |
Evaluation of pairwise distances among points forming a regular orthogonal grid in a hypercube |
title_short |
Evaluation of pairwise distances among points forming a regular orthogonal grid in a hypercube |
title_full |
Evaluation of pairwise distances among points forming a regular orthogonal grid in a hypercube |
title_fullStr |
Evaluation of pairwise distances among points forming a regular orthogonal grid in a hypercube |
title_full_unstemmed |
Evaluation of pairwise distances among points forming a regular orthogonal grid in a hypercube |
title_sort |
evaluation of pairwise distances among points forming a regular orthogonal grid in a hypercube |
publisher |
Vilnius Gediminas Technical University |
series |
Journal of Civil Engineering and Management |
issn |
1392-3730 1822-3605 |
publishDate |
2018-09-01 |
description |
Cartesian grid is a basic arrangement of points that form a regular orthogonal grid (ROG). In some applications, it is needed to evaluate all pairwise distances among ROG points. This paper focuses on ROG discretization of a unit hypercube of arbitrary dimension. A method for the fast enumeration of all pairwise distances and their counts for a high number of points arranged into high-dimensional ROG is presented. The proposed method exploits the regular and collapsible pattern of ROG to reduce the number of evaluated distances. The number of unique distances is identified and frequencies are determined using combinatorial rules. The measured computational speed-up compared to a naïve approach corresponds to the presented theoretical analysis. The proposed method and algorithm may find applications in various fields. The paper shows application focused on the behaviour of various distance measures with the motivation to find the lower bounds on the criteria of point distribution uniformity in Monte Carlo integration.
|
topic |
full factorial design design of experiments pairwise distances Audze-Eglãjs criterion optimization periodic space |
url |
https://www.tede.vgtu.lt/index.php/JCEM/article/view/5189 |
work_keys_str_mv |
AT vaclavsadilek evaluationofpairwisedistancesamongpointsformingaregularorthogonalgridinahypercube AT miroslavvorechovsky evaluationofpairwisedistancesamongpointsformingaregularorthogonalgridinahypercube |
_version_ |
1721329992393031680 |