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



We consider the problem of reconstructing 3D objects via meshfree interpolation methods. In this framework, we usually deal with large data sets and thus develop an efficient local scheme via the well-known partition of unity method. The main contribution in this paper consists in constructing the local interpolants for the implicit interpolation by means of rational radial basis functions. Numerical experiments, devoted to test the accuracy of the scheme, confirm that the proposed method is particularly performing when 3D objects, or more in general implicit functions defined by scattered points, need to be approximated.


Meshless approximation Partition of unity method Rational RBF approximation Reconstruction of 3D objects 

Mathematics Subject Classification

65D05 65D17 65D15 



This research has been accomplished within Rete ITaliana di Approssimazione (RITA) and supported by: GNCS-INdAM and the research project Radial basis functions approximations: stability issues and applications, No. BIRD167404.


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© SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2018

Authors and Affiliations

  1. 1.Dipartimento di Matematica “Tullio Levi-Civita”Università di PadovaPadovaItaly

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