Creating Surfaces from Scattered Data Using Radial Basis Functions (1995)
| Venue: | in Mathematical Methods for Curves and Surfaces |
| Citations: | 51 - 11 self |
BibTeX
@INPROCEEDINGS{Schaback95creatingsurfaces,
author = {R. Schaback},
title = {Creating Surfaces from Scattered Data Using Radial Basis Functions},
booktitle = {in Mathematical Methods for Curves and Surfaces},
year = {1995},
pages = {477--496},
publisher = {University Press}
}
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Abstract
. This paper gives an introduction to certain techniques for the construction of geometric objects from scattered data. Special emphasis is put on interpolation methods using compactly supported radial basis functions. x1. Introduction We assume a sample of multivariate scattered data to be given as a set X = fx 1 ; : : : ; xN g of N pairwise distinct points x 1 ; : : : ; xN in IR d , called centers, together with N points y 1 ; : : : ; yN in IR D . An interpolating curve, surface, or solid to these data will be the range of a smooth function s : IR d oe\Omega ! IR D with s(x k ) = y k ; 1 k N: (1) Likewise, an approximating curve, surface, or solid will make the differences s(x j ) \Gamma y j small, for instance in the discrete L 2 sense, i.e. N X k=1 ks(x k ) \Gamma y k k 2 2 should be small. Curves, surfaces, and solids will only differ by their appropriate value of d = 1; 2, or 3. We use the term (geometric) objects to stand for curves, surfaces, or solids. Not...
