Multivariate interpolation of large sets of scattered data
ACM Transactions on Mathematical Software (TOMS)
Algorithm 661: QSHEP3D: quadratic Shepard method for trivariate interpolation of scattered data
ACM Transactions on Mathematical Software (TOMS)
Multistep scattered data interpolation using compactly supported radial basis functions
Journal of Computational and Applied Mathematics - Special issue on scattered data
Error estimates for interpolation by compactly supported radial basis functions of minimal degree
Journal of Approximation Theory
Algorithm 792: accuracy test of ACM algorithms for interpolation of scattered data in the plane
ACM Transactions on Mathematical Software (TOMS)
Algorithm 660: QSHEP2D: Quadratic Shepard Method for Bivariate Interpolation of Scattered Data
ACM Transactions on Mathematical Software (TOMS)
A two-dimensional interpolation function for irregularly-spaced data
ACM '68 Proceedings of the 1968 23rd ACM national conference
Local hybrid approximation for scattered data fitting with bivariate splines
Computer Aided Geometric Design
Computers & Mathematics with Applications
Shape preserving surface reconstruction using locally anisotropic radial basis function interpolants
Computers & Mathematics with Applications
Edge-driven Image Interpolation using Adaptive Anisotropic Radial Basis Functions
Journal of Mathematical Imaging and Vision
Fast and accurate interpolation of large scattered data sets on the sphere
Journal of Computational and Applied Mathematics
Quasi-interpolation for data fitting by the radial basis functions
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
A new approach for shape preserving interpolating curves
Computers & Mathematics with Applications
An efficient implementation of RBF-based progressive point-sampled geometry
GMP'06 Proceedings of the 4th international conference on Geometric Modeling and Processing
Original article: Recovering functions: A method based on domain decomposition
Mathematics and Computers in Simulation
A meshless interpolation algorithm using a cell-based searching procedure
Computers & Mathematics with Applications
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An efficient method for the multivariate interpolation of very large scattered data sets is presented. It is based on the local use of radial basis functions and represents a further improvement of the well known Shepard's method. Although the latter is simple and well suited for multivariate interpolation, it does not share the good reproduction quality of other methods widely used for bivariate interpolation. On the other band, radial basis functions, which have proven to be highly useful for multivariate scattered data interpolation, have a severe drawback. They are unable to interpolate large sets in an efficient and numerically stable way and maintain a good level of reproduction quality at the same time. Both problems have been circumvented using radial basis functions to evaluate the nodal function of the modified Shepard's method. This approach exploits the flexibility of the method and improves its reproduction quality. The proposed algorithm has been implemented and numerical results confirm its efficiency.