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

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