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3D modelling with C2 continuous PDE surface patches

dc.contributor.authorFu, Haibin
dc.contributor.authorBian, Shaojun
dc.contributor.authorLi, Ouwen
dc.contributor.authorMacey, Jon
dc.contributor.authorIglesias Prieto, Andrés 
dc.contributor.authorChaudhry, Ehtzaz
dc.contributor.authorYou, Lihua
dc.contributor.authorZhang, Jian Jun
dc.contributor.otherUniversidad de Cantabriaes_ES
dc.date.accessioned2022-03-21T19:06:37Z
dc.date.available2022-03-21T19:06:37Z
dc.date.issued2022
dc.identifier.issn2227-7390
dc.identifier.otherTIN2017-89275-Res_ES
dc.identifier.urihttp://hdl.handle.net/10902/24267
dc.description.abstractIn this paper, we present a new modelling method to create 3D models. First, characteristic cross section curves are generated and approximated by generalized elliptic curves. Then, a vector-valued sixth-order partial differential equation is proposed, and its closed form solution is derived to create PDE surface patches from cross section curves where two adjacent PDE-surface patches are automatically stitched together. With the approach presented in this paper, C2 continuity between adjacent surface patches is well-maintained. Since surface creation of the model is transformed into the generation of cross sectional curves and few undetermined constants are required to describe cross sectional curves accurately, the proposed approach can save manual operations, reduce information storage, and generate 3D models quickly.es_ES
dc.description.sponsorshipThis research is supported by the PDE-GIR project, which has received funding from the European Union Horizon 2020 Research and Innovation Programme under the Marie SkodowskaCurie grant agreement No 778035. Andres Iglesias also thanks the project TIN2017-89275-R funded by MCIN/AEI/10.13039/501100011033/FEDER “Una manera de hacer Europa”.es_ES
dc.format.extent20 p.es_ES
dc.language.isoenges_ES
dc.publisherMDPIes_ES
dc.rightsAttribution 4.0 International. © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.es_ES
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/*
dc.sourceMathematics 2022, 10(3), 319es_ES
dc.subject.other3D modellinges_ES
dc.subject.otherGeneralized elliptic curveses_ES
dc.subject.otherC2 continuityes_ES
dc.subject.otherPDE-based surface generationes_ES
dc.subject.otherSixth-order PDEes_ES
dc.subject.otherAnalytical mathematical expressionses_ES
dc.title3D modelling with C2 continuous PDE surface patcheses_ES
dc.typeinfo:eu-repo/semantics/articlees_ES
dc.relation.publisherVersionhttps://doi.org/10.3390/math10030319es_ES
dc.rights.accessRightsopenAccesses_ES
dc.relation.projectIDinfo:eu-repo/grantAgreement/EC/H2020/778035/EU/PDE-based geometric modelling, image processing, and shape reconstruction/PDE-GIR/es_ES
dc.relation.projectIDinfo:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/TIN2017-89275-R/ES/SWARM INTELLIGENCE PARA MODELADO Y RECONSTRUCCION DE FORMAS EN GRAFICOS POR COMPUTADOR, IMAGENES MEDICAS Y ROBOTICA/
dc.identifier.DOI10.3390/math10030319
dc.type.versionpublishedVersiones_ES


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Attribution 4.0 International. © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.Excepto si se señala otra cosa, la licencia del ítem se describe como Attribution 4.0 International. © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.