Shape factors and shoulder points for shape control of rational Bézier curves

The weights of rational Bézier curves cannot be regarded as true independent shape factors since they do not enjoy invariance with respect to Moebius (i.e., rational linear) reparametrizations, which do not change the curve shape. However, the existence of such shape factors, also called shape invar...

Descripción completa

Detalles Bibliográficos
Autor: Sánchez-Reyes Fernández, Francisco Javier
Tipo de recurso: artículo
Fecha de publicación:2023
País:España
Institución:Universidad de Castilla-La Mancha
Repositorio:RUIdeRA. Repositorio Institucional de la UCLM
OAI Identifier:oai:ruidera.uclm.es:10578/36381
Acceso en línea:https://hdl.handle.net/10578/36381
Access Level:acceso abierto
Palabra clave:Moebius reparameterization
Rational Bézier curve
Shape factor
Shape invariant
Shoulder point
Weight
id ES_e88ef837250bc422d64e9ca1846fbe84
oai_identifier_str oai:ruidera.uclm.es:10578/36381
network_acronym_str ES
network_name_str España
repository_id_str
spelling Shape factors and shoulder points for shape control of rational Bézier curvesSánchez-Reyes Fernández, Francisco JavierMoebius reparameterizationRational Bézier curveShape factorShape invariantShoulder pointWeightThe weights of rational Bézier curves cannot be regarded as true independent shape factors since they do not enjoy invariance with respect to Moebius (i.e., rational linear) reparametrizations, which do not change the curve shape. However, the existence of such shape factors, also called shape invariants, is well-known. They are associated with each inner control point and are computed as the ratio of weight ratios for three consecutive control points. We show that these shape factors, in addition to their invariance to Moebius reparameterization, provide a more convenient shape control than the customary weights since they exert a more localized push/pull. Each shape factor amounts to that of the conic defined by a triplet of consecutive control points and weights. Thus, shape factors can be controlled in a geometric way using existing techniques for conics by setting the conic rho-factor via moving the associated shoulder point. Each shoulder point moves along a radial direction through its corresponding control point, furnishing a more practical shape handle than sliding the traditional weight points (aka Farin points) on the polygon legs.Elsevier202420242023info:eu-repo/semantics/articlehttps://hdl.handle.net/10578/36381reponame:RUIdeRA. Repositorio Institucional de la UCLMinstname:Universidad de Castilla-La ManchaInglésPID2019-104586RB-I00MCIN/AEI/10.13039/501100011033SBPLY/19/180501/000247info:eu-repo/semantics/openAccessAttribution-NonCommercial-NoDerivs 3.0 Spainhttp://creativecommons.org/licenses/by-nc-nd/3.0/es/oai:ruidera.uclm.es:10578/363812026-05-27T07:36:41Z
dc.title.none.fl_str_mv Shape factors and shoulder points for shape control of rational Bézier curves
title Shape factors and shoulder points for shape control of rational Bézier curves
spellingShingle Shape factors and shoulder points for shape control of rational Bézier curves
Sánchez-Reyes Fernández, Francisco Javier
Moebius reparameterization
Rational Bézier curve
Shape factor
Shape invariant
Shoulder point
Weight
title_short Shape factors and shoulder points for shape control of rational Bézier curves
title_full Shape factors and shoulder points for shape control of rational Bézier curves
title_fullStr Shape factors and shoulder points for shape control of rational Bézier curves
title_full_unstemmed Shape factors and shoulder points for shape control of rational Bézier curves
title_sort Shape factors and shoulder points for shape control of rational Bézier curves
dc.creator.none.fl_str_mv Sánchez-Reyes Fernández, Francisco Javier
author Sánchez-Reyes Fernández, Francisco Javier
author_facet Sánchez-Reyes Fernández, Francisco Javier
author_role author
dc.subject.none.fl_str_mv Moebius reparameterization
Rational Bézier curve
Shape factor
Shape invariant
Shoulder point
Weight
topic Moebius reparameterization
Rational Bézier curve
Shape factor
Shape invariant
Shoulder point
Weight
description The weights of rational Bézier curves cannot be regarded as true independent shape factors since they do not enjoy invariance with respect to Moebius (i.e., rational linear) reparametrizations, which do not change the curve shape. However, the existence of such shape factors, also called shape invariants, is well-known. They are associated with each inner control point and are computed as the ratio of weight ratios for three consecutive control points. We show that these shape factors, in addition to their invariance to Moebius reparameterization, provide a more convenient shape control than the customary weights since they exert a more localized push/pull. Each shape factor amounts to that of the conic defined by a triplet of consecutive control points and weights. Thus, shape factors can be controlled in a geometric way using existing techniques for conics by setting the conic rho-factor via moving the associated shoulder point. Each shoulder point moves along a radial direction through its corresponding control point, furnishing a more practical shape handle than sliding the traditional weight points (aka Farin points) on the polygon legs.
publishDate 2023
dc.date.none.fl_str_mv 2023
2024
2024
dc.type.none.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/10578/36381
url https://hdl.handle.net/10578/36381
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv PID2019-104586RB-I00
MCIN/AEI/10.13039/501100011033
SBPLY/19/180501/000247
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
eu_rights_str_mv openAccess
rights_invalid_str_mv Attribution-NonCommercial-NoDerivs 3.0 Spain
http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:RUIdeRA. Repositorio Institucional de la UCLM
instname:Universidad de Castilla-La Mancha
instname_str Universidad de Castilla-La Mancha
reponame_str RUIdeRA. Repositorio Institucional de la UCLM
collection RUIdeRA. Repositorio Institucional de la UCLM
repository.name.fl_str_mv
repository.mail.fl_str_mv
_version_ 1869422952708046848
score 15,301603

Similares en LA Referencia