Geometric Hermite interpolation by rational curves of constant width

A constructive characterization of the support function for a rationally parameterized curve of constant width is given. In addition, a Hermite interpolation problem for such kind of curves is solved, which yields a method to determine a rational curve of constant width that passes through a set of...

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Detalles Bibliográficos
Autores: Arnal, A., Beltran, J. V., Monterde, J., Rochera, D.
Tipo de recurso: artículo
Estado:Versión enviada para evaluación y publicación
Fecha de publicación:2023
País:España
Institución:Basque Center for Applied Mathematics (BCAM)
Repositorio:BIRD. BCAM's Institutional Repository Data
OAI Identifier:oai:bird.bcamath.org:20.500.11824/1639
Acceso en línea:http://hdl.handle.net/20.500.11824/1639
https://doi.org/10.1016/j.cam.2023.115598
Access Level:acceso embargado
Palabra clave:Constant width curve
Projective hedgehog
Geometric Hermite interpolation
Rational parameterization
Support function
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spelling Geometric Hermite interpolation by rational curves of constant widthArnal, A.Beltran, J. V.Monterde, J.Rochera, D.Constant width curveProjective hedgehogGeometric Hermite interpolationRational parameterizationSupport functionA constructive characterization of the support function for a rationally parameterized curve of constant width is given. In addition, a Hermite interpolation problem for such kind of curves is solved, which yields a method to determine a rational curve of constant width that passes through a set of free points with the corresponding tangent directions. Finally, the case of piecewise rational support functions is considered, which increases the design freedom. The procedure is presented in the general case of hedgehogs of constant width taking the advantage of projective hedgehogs, so that some constraints must be taken to ensure convexity of the desired curve.Funding for the other authors not affiliated with BCAM: Grant PID2021-124577NBI00 funded by MCIN/AEI/10.13039/501100011033 and by “ERDF A way of making Europe”. Project PID2019-104927GB-C21 funded by MCIN/AEI/10.13039/501100011033. Project UJI-B2022-19 funded by Universitat Jaume I. Project CIAICO/2021/180 funded by Generalitat Valenciana.info202320232023info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/1639https://doi.org/10.1016/j.cam.2023.115598reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://www.sciencedirect.com/science/article/pii/S0377042723005423info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/CEX2021-001142-Sinfo:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2022-2025Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/embargoedAccessoai:bird.bcamath.org:20.500.11824/16392026-06-19T12:47:47Z
dc.title.none.fl_str_mv Geometric Hermite interpolation by rational curves of constant width
title Geometric Hermite interpolation by rational curves of constant width
spellingShingle Geometric Hermite interpolation by rational curves of constant width
Arnal, A.
Constant width curve
Projective hedgehog
Geometric Hermite interpolation
Rational parameterization
Support function
title_short Geometric Hermite interpolation by rational curves of constant width
title_full Geometric Hermite interpolation by rational curves of constant width
title_fullStr Geometric Hermite interpolation by rational curves of constant width
title_full_unstemmed Geometric Hermite interpolation by rational curves of constant width
title_sort Geometric Hermite interpolation by rational curves of constant width
dc.creator.none.fl_str_mv Arnal, A.
Beltran, J. V.
Monterde, J.
Rochera, D.
author Arnal, A.
author_facet Arnal, A.
Beltran, J. V.
Monterde, J.
Rochera, D.
author_role author
author2 Beltran, J. V.
Monterde, J.
Rochera, D.
author2_role author
author
author
dc.subject.none.fl_str_mv Constant width curve
Projective hedgehog
Geometric Hermite interpolation
Rational parameterization
Support function
topic Constant width curve
Projective hedgehog
Geometric Hermite interpolation
Rational parameterization
Support function
description A constructive characterization of the support function for a rationally parameterized curve of constant width is given. In addition, a Hermite interpolation problem for such kind of curves is solved, which yields a method to determine a rational curve of constant width that passes through a set of free points with the corresponding tangent directions. Finally, the case of piecewise rational support functions is considered, which increases the design freedom. The procedure is presented in the general case of hedgehogs of constant width taking the advantage of projective hedgehogs, so that some constraints must be taken to ensure convexity of the desired curve.
publishDate 2023
dc.date.none.fl_str_mv 2023
2023
2023
info
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/submittedVersion
format article
status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/1639
https://doi.org/10.1016/j.cam.2023.115598
url http://hdl.handle.net/20.500.11824/1639
https://doi.org/10.1016/j.cam.2023.115598
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://www.sciencedirect.com/science/article/pii/S0377042723005423
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/CEX2021-001142-S
info:eu-repo/grantAgreement/Gobierno Vasco/BERC/BERC.2022-2025
dc.rights.none.fl_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
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rights_invalid_str_mv Reconocimiento-NoComercial-CompartirIgual 3.0 España
http://creativecommons.org/licenses/by-nc-sa/3.0/es/
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dc.format.none.fl_str_mv application/pdf
dc.source.none.fl_str_mv reponame:BIRD. BCAM's Institutional Repository Data
instname:Basque Center for Applied Mathematics (BCAM)
instname_str Basque Center for Applied Mathematics (BCAM)
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