Local numerical methods for scattered data interpolation often require a smart subdivision of the domain in geometrical polyhedral structures. In particular triangulations in the plane (2D) and tetrahedrizations in the space (3D) are widely used to define interpolation models. In this paper we give a short survey on the main methods for the scattered data problem and we recall preliminaries on ...

A set of software tools that use compactly supported radial basis functions (CSRBFs) to process scattered data is proposed in this paper. To solve problems concerning the processing of scattered data in such applications as reconstruction of functionaly defined geometric objects, surface retouching, and shape modifications, we employ a specially designed C++ software library. Thanks to the effi...

This study deals with constructing a convexity-preserving bivariate C interpolants to scattered data whenever the original data are convex. Sufficient conditions on lower bound of Bézier points are derived in order to ensure that surfaces comprising cubic Bézier triangular patches are always convex and satisfy C continuity conditions. Initial gradients at the data sites are estimated and then m...

This paper is concerned with the evaluation of methods for scattered data interpolation and some of the results of the tests when applied to a number of methods. The process involves evaluation of the methods in terms of timing, storage, accuracy, visual pleasantness of the surface, and ease of implementation. To indicate the flavor of the type of results obtained, we give a summary table and r...

A method for multi-resolution triangulation of 3D scan data is presented. Multi-resolution leads to uniform approximation where the closeness to the 3D scan data can be controlled. The presented approach has two main phases: 1. Extraction of a coarse initial mesh as first approximation of the scan data using the Marching cubes algorithm; 2. Subdivision refinement strategy that iteratively leads...

In real world applications many signals contain singularities, like edges in images. Recent wavelet frame based approaches were successfully applied to reconstruct scattered data from such functions while preserving these features. In this paper we present a recent approach which determines the approximant from shift invariant subspaces by minimizing an `1-regularized least squares problem whic...

Rapidly growing data sizes of scientific simulations pose significant challenges for interactive visualization and analysis techniques. In this work, we propose a compact probabilistic representation to interactively visualize large scattered datasets. contrast previous approaches that represent blocks volumetric using probability distributions, model clusters arbitrarily structured multivariat...