Generalized plane offsets and rational parameterizations

In the first part of the paper a planar generalization of offset curves is introduced and some properties are derived. In particular, it is seen that these curves exhibit good regularity properties and a study on self-intersection avoidance is performed. The representation of a rational curve as the...

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Detalles Bibliográficos
Autor: 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:20.500.11824/1588
Acceso en línea:http://hdl.handle.net/20.500.11824/1588
https://doi.org/10.1016/j.cagd.2023.102196
Access Level:acceso embargado
Palabra clave:Offset curve
Pythagorean-hodograph curve
Rational parameterization
Support function
Constant width curve
Zindler curve
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spelling Generalized plane offsets and rational parameterizationsRochera, D.Offset curvePythagorean-hodograph curveRational parameterizationSupport functionConstant width curveZindler curveIn the first part of the paper a planar generalization of offset curves is introduced and some properties are derived. In particular, it is seen that these curves exhibit good regularity properties and a study on self-intersection avoidance is performed. The representation of a rational curve as the envelope of its tangent lines, following the approach of Pottmann, is revisited to give the explicit expression of all rational generalized offsets. Other famous shapes, such as constant width curves, bicycle tire-tracks curves and Zindler curves are related to these generalized offsets. This gives rise to the second part of the paper, where the particular case of rational parameterizations by a support function is considered and explicit families of rational constant width curves, rational bicycle tire-track curves and rational Zindler curves are generated and some examples are shown.info202320232023info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/1588https://doi.org/10.1016/j.cagd.2023.102196reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://www.sciencedirect.com/science/article/abs/pii/S0167839623000286info: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:20.500.11824/15882026-06-19T12:47:47Z
dc.title.none.fl_str_mv Generalized plane offsets and rational parameterizations
title Generalized plane offsets and rational parameterizations
spellingShingle Generalized plane offsets and rational parameterizations
Rochera, D.
Offset curve
Pythagorean-hodograph curve
Rational parameterization
Support function
Constant width curve
Zindler curve
title_short Generalized plane offsets and rational parameterizations
title_full Generalized plane offsets and rational parameterizations
title_fullStr Generalized plane offsets and rational parameterizations
title_full_unstemmed Generalized plane offsets and rational parameterizations
title_sort Generalized plane offsets and rational parameterizations
dc.creator.none.fl_str_mv Rochera, D.
author Rochera, D.
author_facet Rochera, D.
author_role author
dc.subject.none.fl_str_mv Offset curve
Pythagorean-hodograph curve
Rational parameterization
Support function
Constant width curve
Zindler curve
topic Offset curve
Pythagorean-hodograph curve
Rational parameterization
Support function
Constant width curve
Zindler curve
description In the first part of the paper a planar generalization of offset curves is introduced and some properties are derived. In particular, it is seen that these curves exhibit good regularity properties and a study on self-intersection avoidance is performed. The representation of a rational curve as the envelope of its tangent lines, following the approach of Pottmann, is revisited to give the explicit expression of all rational generalized offsets. Other famous shapes, such as constant width curves, bicycle tire-tracks curves and Zindler curves are related to these generalized offsets. This gives rise to the second part of the paper, where the particular case of rational parameterizations by a support function is considered and explicit families of rational constant width curves, rational bicycle tire-track curves and rational Zindler curves are generated and some examples are shown.
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
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status_str submittedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/20.500.11824/1588
https://doi.org/10.1016/j.cagd.2023.102196
url http://hdl.handle.net/20.500.11824/1588
https://doi.org/10.1016/j.cagd.2023.102196
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv https://www.sciencedirect.com/science/article/abs/pii/S0167839623000286
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/
info:eu-repo/semantics/embargoedAccess
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)
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