An explicit characterization of isochordal-viewed multihedgehogs with circular isoptics

A curve α is called (ϕ, ℓ)-isochordal viewed if a straight segment of constant length ℓ can slide with its endpoints on α and such that their tangents to α at these endpoints make a constant angle ϕ. These tangents determine the so-called ϕ-isoptic curve of α. In this paper, an explicit characteriza...

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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:20.500.11824/1577
Acceso en línea:http://hdl.handle.net/20.500.11824/1577
https://doi.org/10.1016/j.jmaa.2023.127107
Access Level:acceso embargado
Palabra clave:Isoptic curves
Isochordal-viewed curves
Curves of constant Φ-width
Support function
Hedgehogs
Regular polygons
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spelling An explicit characterization of isochordal-viewed multihedgehogs with circular isopticsRochera, D.Isoptic curvesIsochordal-viewed curvesCurves of constant Φ-widthSupport functionHedgehogsRegular polygonsA curve α is called (ϕ, ℓ)-isochordal viewed if a straight segment of constant length ℓ can slide with its endpoints on α and such that their tangents to α at these endpoints make a constant angle ϕ. These tangents determine the so-called ϕ-isoptic curve of α. In this paper, an explicit characterization of all (ϕ, ℓ)-isochordal-viewed multihedgehogs with circular ϕ-isoptics is provided by their support functions, which are obtained as the solutions of a differential equation. This allows to construct any example of these curves in a very simple way from some free parameters. In addition, it is shown that a regular polygon of side length ℓ can slide smoothly along these multihedgehogs.BERC 2022-2025 Severo Ochoa CEX2021-001142-S / MCIN / AEI / 10.13039/501100011033info202320232023info:eu-repo/semantics/articleinfo:eu-repo/semantics/submittedVersionapplication/pdfhttp://hdl.handle.net/20.500.11824/1577https://doi.org/10.1016/j.jmaa.2023.127107reponame:BIRD. BCAM's Institutional Repository Datainstname:Basque Center for Applied Mathematics (BCAM)Ingléshttps://www.sciencedirect.com/science/article/abs/pii/S0022247X23001105Reconocimiento-NoComercial-CompartirIgual 3.0 Españahttp://creativecommons.org/licenses/by-nc-sa/3.0/es/info:eu-repo/semantics/embargoedAccessoai:bird.bcamath.org:20.500.11824/15772026-06-19T12:47:47Z
dc.title.none.fl_str_mv An explicit characterization of isochordal-viewed multihedgehogs with circular isoptics
title An explicit characterization of isochordal-viewed multihedgehogs with circular isoptics
spellingShingle An explicit characterization of isochordal-viewed multihedgehogs with circular isoptics
Rochera, D.
Isoptic curves
Isochordal-viewed curves
Curves of constant Φ-width
Support function
Hedgehogs
Regular polygons
title_short An explicit characterization of isochordal-viewed multihedgehogs with circular isoptics
title_full An explicit characterization of isochordal-viewed multihedgehogs with circular isoptics
title_fullStr An explicit characterization of isochordal-viewed multihedgehogs with circular isoptics
title_full_unstemmed An explicit characterization of isochordal-viewed multihedgehogs with circular isoptics
title_sort An explicit characterization of isochordal-viewed multihedgehogs with circular isoptics
dc.creator.none.fl_str_mv Rochera, D.
author Rochera, D.
author_facet Rochera, D.
author_role author
dc.subject.none.fl_str_mv Isoptic curves
Isochordal-viewed curves
Curves of constant Φ-width
Support function
Hedgehogs
Regular polygons
topic Isoptic curves
Isochordal-viewed curves
Curves of constant Φ-width
Support function
Hedgehogs
Regular polygons
description A curve α is called (ϕ, ℓ)-isochordal viewed if a straight segment of constant length ℓ can slide with its endpoints on α and such that their tangents to α at these endpoints make a constant angle ϕ. These tangents determine the so-called ϕ-isoptic curve of α. In this paper, an explicit characterization of all (ϕ, ℓ)-isochordal-viewed multihedgehogs with circular ϕ-isoptics is provided by their support functions, which are obtained as the solutions of a differential equation. This allows to construct any example of these curves in a very simple way from some free parameters. In addition, it is shown that a regular polygon of side length ℓ can slide smoothly along these multihedgehogs.
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/20.500.11824/1577
https://doi.org/10.1016/j.jmaa.2023.127107
url http://hdl.handle.net/20.500.11824/1577
https://doi.org/10.1016/j.jmaa.2023.127107
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/S0022247X23001105
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)
instname_str Basque Center for Applied Mathematics (BCAM)
reponame_str BIRD. BCAM's Institutional Repository Data
collection BIRD. BCAM's Institutional Repository Data
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