Fitting and filling of 3D datasets with volume constraints using radial basis functions under tension

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/).

Automated summary

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.