Rational RBF-based partition of unity method for efficiently and accurately approximating 3D objects

TL;DR

This paper introduces a rational RBF-based partition of unity method for efficient and accurate meshfree reconstruction of 3D objects from scattered data, improving approximation performance.

Contribution

It develops a novel local interpolation scheme using Rational Radial Basis Functions within the partition of unity framework for 3D object reconstruction.

Findings

Method performs well on implicit 3D object data

Numerical results confirm high accuracy and efficiency

Suitable for large scattered data sets

Abstract

We consider the problem of reconstructing 3D objects via meshfree interpolation methods. In this framework, we usually deal with large data sets and thus we develop an efficient local scheme via the well-known Partition of Unity (PU) method. The main contribution in this paper consists in constructing the local interpolants for the implicit interpolation by means of Rational Radial Basis Functions (RRBFs). Numerical evidence confirms that the proposed method is particularly performing when 3D objects, or more in general implicit functions defined by scattered data, need to be approximated.