Numerical proper reparametrization of space curves and surfaces

Simplifying rational parametrizations of surfaces is a basic problem in CAD (computer-aided design). One important way is to reduce their tracing index, called proper reparametrization. Most existing proper reparametrization work is symbolic, yet in practical environments the surfaces are usually gi...

Descripción completa

Detalles Bibliográficos
Autores: Pérez Díaz, Sonia|||0000-0002-0174-5325, Shen, Li-Yong, Yang, Zhengfeng
Tipo de recurso: artículo
Fecha de publicación:2019
País:España
Institución:Universidad de Alcalá (UAH)
Repositorio:e_Buah Biblioteca Digital Universidad de Alcalá
Idioma:inglés
OAI Identifier:oai:ebuah.uah.es:10017/41549
Acceso en línea:http://hdl.handle.net/10017/41549
https://dx.doi.org/10.1016/j.cad.2019.07.001
Access Level:acceso abierto
Palabra clave:Numerical/symbolic reparametrization
Space curve
Rational surface
Approximately improper/proper
Matemáticas
Mathematics
id ES_4bd7a787deecd36d5fa22f63f7af0734
oai_identifier_str oai:ebuah.uah.es:10017/41549
network_acronym_str ES
network_name_str España
repository_id_str
spelling Numerical proper reparametrization of space curves and surfacesPérez Díaz, Sonia|||0000-0002-0174-5325Shen, Li-YongYang, ZhengfengNumerical/symbolic reparametrizationSpace curveRational surfaceApproximately improper/properMatemáticasMathematicsSimplifying rational parametrizations of surfaces is a basic problem in CAD (computer-aided design). One important way is to reduce their tracing index, called proper reparametrization. Most existing proper reparametrization work is symbolic, yet in practical environments the surfaces are usually given with perturbed coefficients hence need a numerical technique of reparametrization considering the intrinsic properness of the perturbed surfaces. We present algorithms for reparametrizing a numerically rational space curve or surface. First, we provide an efficient way to find a parametric support transformation and compute a reparametrization with proper parametric support. Second, we develop a numerical algorithm to further reduce the tracing index, where numerical techniques such as sparse interpolation and approximated GCD computations are involved. We finally provide the error bound between the given rational curve/surface and our reparametrization result.Agencia Estatal de InvestigaciónElsevier20192019-11-0120192019-11-0120202020-11-01journal articlehttp://purl.org/coar/resource_type/c_6501NAhttp://purl.org/coar/version/c_be7fb7dd8ff6fe43info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10017/41549https://dx.doi.org/10.1016/j.cad.2019.07.001reponame:e_Buah Biblioteca Digital Universidad de Alcaláinstname:Universidad de Alcalá (UAH)InglésengAgencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 MTM2017-88796-P COMPUTACION SIMBOLICA: NUEVOS RETOS EN ALGEBRA Y GEOMETRIA Y SUS APLICACIONESopen accesshttp://purl.org/coar/access_right/c_abf2Attribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/info:eu-repo/semantics/openAccessoai:ebuah.uah.es:10017/415492026-06-18T11:13:07Z
dc.title.none.fl_str_mv Numerical proper reparametrization of space curves and surfaces
title Numerical proper reparametrization of space curves and surfaces
spellingShingle Numerical proper reparametrization of space curves and surfaces
Pérez Díaz, Sonia|||0000-0002-0174-5325
Numerical/symbolic reparametrization
Space curve
Rational surface
Approximately improper/proper
Matemáticas
Mathematics
title_short Numerical proper reparametrization of space curves and surfaces
title_full Numerical proper reparametrization of space curves and surfaces
title_fullStr Numerical proper reparametrization of space curves and surfaces
title_full_unstemmed Numerical proper reparametrization of space curves and surfaces
title_sort Numerical proper reparametrization of space curves and surfaces
dc.creator.none.fl_str_mv Pérez Díaz, Sonia|||0000-0002-0174-5325
Shen, Li-Yong
Yang, Zhengfeng
author Pérez Díaz, Sonia|||0000-0002-0174-5325
author_facet Pérez Díaz, Sonia|||0000-0002-0174-5325
Shen, Li-Yong
Yang, Zhengfeng
author_role author
author2 Shen, Li-Yong
Yang, Zhengfeng
author2_role author
author
dc.subject.none.fl_str_mv Numerical/symbolic reparametrization
Space curve
Rational surface
Approximately improper/proper
Matemáticas
Mathematics
topic Numerical/symbolic reparametrization
Space curve
Rational surface
Approximately improper/proper
Matemáticas
Mathematics
description Simplifying rational parametrizations of surfaces is a basic problem in CAD (computer-aided design). One important way is to reduce their tracing index, called proper reparametrization. Most existing proper reparametrization work is symbolic, yet in practical environments the surfaces are usually given with perturbed coefficients hence need a numerical technique of reparametrization considering the intrinsic properness of the perturbed surfaces. We present algorithms for reparametrizing a numerically rational space curve or surface. First, we provide an efficient way to find a parametric support transformation and compute a reparametrization with proper parametric support. Second, we develop a numerical algorithm to further reduce the tracing index, where numerical techniques such as sparse interpolation and approximated GCD computations are involved. We finally provide the error bound between the given rational curve/surface and our reparametrization result.
publishDate 2019
dc.date.none.fl_str_mv 2019
2019-11-01
2019
2019-11-01
2020
2020-11-01
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
NA
http://purl.org/coar/version/c_be7fb7dd8ff6fe43
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv http://hdl.handle.net/10017/41549
https://dx.doi.org/10.1016/j.cad.2019.07.001
url http://hdl.handle.net/10017/41549
https://dx.doi.org/10.1016/j.cad.2019.07.001
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv Agencia Estatal de Investigación http://dx.doi.org/10.13039/501100011033 Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016 MTM2017-88796-P COMPUTACION SIMBOLICA: NUEVOS RETOS EN ALGEBRA Y GEOMETRIA Y SUS APLICACIONES
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
Attribution-NonCommercial-NoDerivatives 4.0 International
http://creativecommons.org/licenses/by-nc-nd/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:e_Buah Biblioteca Digital Universidad de Alcalá
instname:Universidad de Alcalá (UAH)
instname_str Universidad de Alcalá (UAH)
reponame_str e_Buah Biblioteca Digital Universidad de Alcalá
collection e_Buah Biblioteca Digital Universidad de Alcalá
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869407588699865088
score 15,300719

Similares en LA Referencia