Piecewise Bivariate Hermite Interpolations for Large Sets of Scattered Data

Piecewise Bivariate Hermite Interpolations for Large Sets of Scattered Data

The requirements for interpolation of scattered data are high accuracy and high efficiency. In this paper, a piecewise bivariate Hermite interpolant satisfying these requirements is proposed. We firstly construct a triangulation mesh using the given scattered point set. Based on this mesh, the computational point (x, y) is divided into two types: interior point and exterior point. The value of ...

Error bounds for bivariate piecewise hermite interpolation

Adaptive Thinning for Bivariate Scattered Data

This paper studies adaptive thinning strategies for approximating a large set of scattered data by piecewise linear functions over triangulated subsets. Our strategies depend on both the locations of the data points in the plane, and the values of the sampled function at these points — adaptive thinning. All our thinning strategies remove data points one by one, so as to minimize an estimate of...

Thinning and Approximation of Large Sets of Scattered Data

Having various concrete industrial applications in mind we focus on surface fitting to large scattered data sets. We describe a general method for modelling data which incorporates both filtering using triangulations, and hierarchical interpolation based on compactly supported radial basis functions. The uniformity of the data points plays a significant role. The utility of the method is confir...

Functional Modelling of Large Scattered Data Sets Using Neural Networks

We propose a self-organising hierarchical Radial Basis Function (RBF) network for functional modelling of large amounts of scattered unstructured point data. The network employs an error-driven active learning algorithm and a multi-layer architecture, allowing progressive bottom-up reinforcement of local features in subdivisions of error clusters. For each RBF subnet, neurons can be inserted, r...