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

doi:https://doi.org/10.1016/j.cam.2022.114841

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Identificadores

URI: https://hdl.handle.net/10481/77312

DOI: https://doi.org/10.1016/j.cam.2022.114841

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Editorial

Elsevier

Materia

Radial basis functions

Spline approximation

Hole filling

Smoothing surface

Volume constraints

Date

2023-03

Referencia bibliográfica

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]

Sponsorship

FEDER/Junta de Andalucía-Consejería de Transformación Económica, Industria, Conocimiento y Universidades (Research Project A-FQM-76-UGR20, University of Granada); Junta de Andalucía (Research Groups FQM-191 and TEP-190); Funding for open access charge: Universidad de Granada / CBUA

Abstract

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.

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