Fitting and filling of 3D datasets with volume constraints using radial basis functions under tension González Rodelas, Pedro Fortes Escalona, Miguel Ángel Pasadas Fernández, Miguel Palomares Bautista, Antonio Francisco Radial basis functions Spline approximation Hole filling Smoothing surface Volume constraints Acknowledgments This work was supported by FEDER/Junta de Andalucía-Consejería de Transformación Económica, Industria, Conocimiento y Universidades (Research Project A-FQM-76-UGR20, University of Granada) and by the Junta de Andalucía (Research Groups FQM-191 and TEP-190). Funding for open access charge: Universidad de Granada / CBUA. Given a dataset of 3D points in which there is a hole, i.e., a region with a lack of information, we develop a method providing a surface that fits the dataset and fills the hole. The filling patch is required to fulfill a prescribed volume condition. The fitting–filling function consists of a radial basis functions that minimizes an energy functional involving both, the fitting of the dataset and the volume constraint of the filling patch, as well as the fairness of the function. We give a convergence result and we present some graphical and numerical examples. 2022-10-14T07:28:51Z 2022-10-14T07:28:51Z 2023-03 info:eu-repo/semantics/article M.A. Fortes, P. González, A. Palomares et al. Fitting and filling of 3D datasets with volume constraints using radial basis functions under tension. Journal of Computational and Applied Mathematics 420 (2023) 114841 [https://doi.org/10.1016/j.cam.2022.114841] https://hdl.handle.net/10481/77312 https://doi.org/10.1016/j.cam.2022.114841 eng info:eu-repo/semantics/openAccess Elsevier