Rational RBF-based partition of unity method for efficiently and accurately approximating 3D objects
This work addresses the problem of accurate and efficient 3D reconstruction from large point clouds, which is important for computer graphics and geometric modeling.
The authors propose a Partition of Unity method using Rational Radial Basis Functions for efficient and accurate 3D object reconstruction from large scattered data sets. Numerical results demonstrate improved performance over standard methods.
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.