The aim of this paper is to develop a local positivity preserving scheme when the data amassed from different sources is positioned at sparse points. The proposed algorithm first triangulates the irregular data using Delauny triangulation method, therewith interpolates each boundary and radial curve of the triangle by C¹ rational trigonometric cubic function. Half of the parameters in the descr...

Spaces of polynomial splines deened on planar triangulations are very useful tools for tting scattered data in the plane. Recently, 4, 5], using homogeneous polynomials, we have developed analogous spline spaces deened on triangulations on the sphere and on sphere-like surfaces. Using these spaces, it is possible to construct analogs of many of the classical interpolation and tting methods. Her...

This is a survey of techniques for the interpolation of scattered data in three or more independent variables. It covers schemes that can be used for any number of variables as well as schemes speci cally designed for three variables. Emphasis is on breadth rather than depth, but there are explicit illustrations of di erent techniques used in the solution of multivariate interpolation problems.

In this report we introduce and motivate the problem of reconstructing shapes from partial information. An appropriate mathematical abstraction capturing the notion of a shape in three-dimensional space is a two-dimensional manifold. The concept of the topological type of a manifold plays an important role in reconstruction, and we present a synopsis of the pertinent definitions and results. We...

We present C methods for either interpolating data or for fitting scattered data associated with a smooth function on a two-dimensional smooth manifold Ω embedded into R. The methods are based on a local bivariate Powell-Sabin interpolation scheme, and make use of local projections on the tangent planes. The data fitting method is a two-stage method. We illustrate the performance of the algorit...

We suggest a local hybrid approximation scheme based on polynomials and radial basis functions, and use it to improve the scattered data fitting algorithm of [7]. Similar to that algorithm, the new method has linear computational complexity and is therefore suitable for large real world data. Numerical examples suggest that it can produce high quality artifact–free approximations that are more ...

We present an efficient and uniform approach for the automatic reconstruction of surfaces of CAD (computer aided design) models and scalar fields defined on them, from an unorganized collection of scanned point data. Example applications in the manufacturing domain are the rapid computer model reconstruction of any existing physical part from some three dimensional (3D) points scan of the part’...

A class of multiscale decompositions for scattered discrete data is introduced, motivated by sensor network applications. A specific feature of these decompositions is that they do not rely on any type of mesh or connectivity between the data points. The decomposition is based on a thinning procedure that organizes the points in a multiscale hierarchy and on a local prediction operator based on...