Symmetric derivates, scattered, and semi-scattered sets

Scattered Linear Sets and Pseudoreguli

In this paper, we show that one can associate a pseudoregulus with every scattered linear set of rank 3n in PG(2n − 1, q3). We construct a scattered linear set having a given pseudoregulus as associated pseudoregulus and prove that there are q − 1 different scattered linear sets that have the same associated pseudoregulus. Finally, we give a characterisation of reguli and pseudoreguli in PG(3, ...

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...

Norming Sets and Scattered Data Approximation on Spheres

This short note deals with approximation order of spaces spanned by (x;), x 2 X, with a positive deenite kernel on a sphere and X a given set of nodes. We estimate both the L 2-and the L 1-error, if the function to be approximated is assumed to be rather smooth, thus deviating from the usual assumption that the function stems from thèna-tive space' of the kernel. It is of interest that, based o...

3 D Terrain Reconstruction Using Scattered Data Sets

Graph-Based Surface Reconstruction Using Structures in Scattered Point Sets

We present an algorithm for the reconstruction of a surface from an unorganized set of points in space. The point data may be obtained from a laser range scanner or any other digitizing tool to describe the shape of the object(s). The basic idea of the algorithm is to construct some kind of wire frame for the surface, the so–called surface description graph. This is performed by applying severa...