Journal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
Volume 420, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.cam.2022.114841
Keywords
Radial basis functions; Spline approximation; Hole filling; Smoothing surface; Volume constraints
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This article presents a method for filling and fitting a 3D point dataset with a hole using a surface. The filling patch must meet a prescribed volume condition, and a radial basis function is used to minimize an energy functional, considering the dataset fitting, volume constraint, and fairness of the function.
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.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
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