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3D modelling with C2 continuous PDE surface patches

Identificadores del recurso

2227-7390

TIN2017-89275-R

http://hdl.handle.net/10902/24267

10.3390/math10030319

Procedencia

(Repositorio Abierto de la Universidad de Cantabria)

Ficha

Título:: 3D modelling with C2 continuous PDE surface patches
Tema:: 3D modelling; Generalized elliptic curves; C2 continuity; PDE-based surface generation; Sixth-order PDE; Analytical mathematical expressions
Descrición:: In 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.; This 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”.
Fonte:: Mathematics 2022, 10(3), 319
Idioma:: English
Relación:: https://doi.org/10.3390/math10030319; info:eu-repo/grantAgreement/EC/H2020/778035/EU/PDE-based geometric modelling, image processing, and shape reconstruction/PDE-GIR/; info: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/
Autor/Productor:: Fu, Haibin; Bian, Shaojun; Li, Ouwen; Macey, Jon; Iglesias Prieto, Andrés; Chaudhry, Ehtzaz; You, Lihua; Zhang, Jian Jun
Editor:: MDPI
Otros colaboradores/productores:: Universidad de Cantabria
Dereitos:: 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.; http://creativecommons.org/licenses/by/4.0/; openAccess
Data:: 2022-03-21T19:06:37Z; 2022
Tipo de recurso:: info:eu-repo/semantics/article; publishedVersion

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14. <dc:subject>PDE-based surface generation</dc:subject>
15. <dc:subject>Sixth-order PDE</dc:subject>
16. <dc:subject>Analytical mathematical expressions</dc:subject>
17. <dc:description>In 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.</dc:description>
18. <dc:description>This 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”.</dc:description>
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