Filling holes under non-linear constraints

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URI: https://hdl.handle.net/10481/80058
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Author
Custódio, Ana Luisa; Fortes Escalona, Miguel Ángel; Sajo-Castelli, A. M.
Editorial
Springer Nature
Date
2023
Referencia bibliográfica
Custódio, A.L., Fortes, M.A. & Sajo-Castelli, A.M. Filling holes under non-linear constraints. Comp. Appl. Math. 42, 72 (2023). [https://doi.org/10.1007/s40314-023-02210-3]
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Funding for open access publishing: Universidad de Granada/CBUA; National funds through the FCT - Fundação para a Ciência e a Tecnologia; Projects UIDB/00297/2020 and UIDP/00297/2020 (Center for Mathematics and Applications)
Abstract
In this paper we handle the problem of filling the hole in the graphic of a surface by means of a patch that joins the original surface with C1-smoothness and fulfills an additional non-linear geometrical constraint regarding its area or its mean curvature at some points. Furthermore, we develop a technique to estimate the optimum area that the filling patch is expected to have that will allow us to determine optimum filling patches by means of a system of linear and quadratic equations. We present several numerical and graphical examples showing the effectiveness of the proposed method.
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