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Representation of a Monotone Curve by a Contour with Regular Change in Curvature
The problem of modelling a smooth contour with a regular change in curvature representing a monotone curve with specified accuracy is solved in this article. The contour was formed within the area of the possible location of a convex curve, which can interpolate a point series. The assumption that i...
Autores principales: | , , , , , , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2021
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8305980/ https://www.ncbi.nlm.nih.gov/pubmed/34356464 http://dx.doi.org/10.3390/e23070923 |
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author | Havrylenko, Yevhen Kholodniak, Yuliia Halko, Serhii Vershkov, Oleksandr Miroshnyk, Oleksandr Suprun, Olena Dereza, Olena Shchur, Taras Śrutek, Mścisław |
author_facet | Havrylenko, Yevhen Kholodniak, Yuliia Halko, Serhii Vershkov, Oleksandr Miroshnyk, Oleksandr Suprun, Olena Dereza, Olena Shchur, Taras Śrutek, Mścisław |
author_sort | Havrylenko, Yevhen |
collection | PubMed |
description | The problem of modelling a smooth contour with a regular change in curvature representing a monotone curve with specified accuracy is solved in this article. The contour was formed within the area of the possible location of a convex curve, which can interpolate a point series. The assumption that if a sequence of points can be interpolated by a monotone curve, then the reference curve on which these points have been assigned is monotone, provides the opportunity to implement the proposed approach to estimate the interpolation error of a point series of arbitrary configuration. The proposed methods for forming a convex regular contour by arcs of ellipses and B-spline ensure the interpolation of any point series in parts that can be interpolated by a monotone curve. At the same time, the deflection of the contour from the boundaries of the area of the possible location of the monotone curve can be controlled. The possibilities of the developed methods are tested while solving problems of the interpolation of a point series belonging to monotone curves. The problems are solved in the CAD system of SolidWorks with the use of software application created based on the methods developed in the research work. |
format | Online Article Text |
id | pubmed-8305980 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-83059802021-07-25 Representation of a Monotone Curve by a Contour with Regular Change in Curvature Havrylenko, Yevhen Kholodniak, Yuliia Halko, Serhii Vershkov, Oleksandr Miroshnyk, Oleksandr Suprun, Olena Dereza, Olena Shchur, Taras Śrutek, Mścisław Entropy (Basel) Article The problem of modelling a smooth contour with a regular change in curvature representing a monotone curve with specified accuracy is solved in this article. The contour was formed within the area of the possible location of a convex curve, which can interpolate a point series. The assumption that if a sequence of points can be interpolated by a monotone curve, then the reference curve on which these points have been assigned is monotone, provides the opportunity to implement the proposed approach to estimate the interpolation error of a point series of arbitrary configuration. The proposed methods for forming a convex regular contour by arcs of ellipses and B-spline ensure the interpolation of any point series in parts that can be interpolated by a monotone curve. At the same time, the deflection of the contour from the boundaries of the area of the possible location of the monotone curve can be controlled. The possibilities of the developed methods are tested while solving problems of the interpolation of a point series belonging to monotone curves. The problems are solved in the CAD system of SolidWorks with the use of software application created based on the methods developed in the research work. MDPI 2021-07-20 /pmc/articles/PMC8305980/ /pubmed/34356464 http://dx.doi.org/10.3390/e23070923 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Havrylenko, Yevhen Kholodniak, Yuliia Halko, Serhii Vershkov, Oleksandr Miroshnyk, Oleksandr Suprun, Olena Dereza, Olena Shchur, Taras Śrutek, Mścisław Representation of a Monotone Curve by a Contour with Regular Change in Curvature |
title | Representation of a Monotone Curve by a Contour with Regular Change in Curvature |
title_full | Representation of a Monotone Curve by a Contour with Regular Change in Curvature |
title_fullStr | Representation of a Monotone Curve by a Contour with Regular Change in Curvature |
title_full_unstemmed | Representation of a Monotone Curve by a Contour with Regular Change in Curvature |
title_short | Representation of a Monotone Curve by a Contour with Regular Change in Curvature |
title_sort | representation of a monotone curve by a contour with regular change in curvature |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8305980/ https://www.ncbi.nlm.nih.gov/pubmed/34356464 http://dx.doi.org/10.3390/e23070923 |
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