Scattered data interpolation: tests of some methods
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TLDR
In this paper, the evaluation of methods for scattered data interpolation and some of the results of the tests when applied to a number of methods are presented. But the evaluation process involves evaluation of the methods in terms of timing, storage, accuracy, visual pleasantness of the surface, and ease of implementation.Abstract:
Absract. 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 representative perspective plots of several surfaces.read more
Citations
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References
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Proceedings ArticleDOI
A two-dimensional interpolation function for irregularly-spaced data
TL;DR: In many fields using empirical areal data there arises a need for interpolating from irregularly-spaced data to produce a continuous surface as discussed by the authors, and it is assumed that a unique number (such as rainfall in meteorology, or altitude in geography) is associated with each data point.
Journal ArticleDOI
Multiquadric equations of topography and other irregular surfaces
TL;DR: In this paper, a method of representing irregular surfaces that involves the summation of equations of quadric surfaces having unknown coefficients is described, and procedures are given for solving multiquadric equations of topography that are based on coordinate data.
Journal ArticleDOI
Surfaces generated by moving least squares methods
Peter Lancaster,K. Salkauskas +1 more
TL;DR: In this article, an analysis of moving least squares (m.l.s.) methods for smoothing and interpolating scattered data is presented, in particular theorems concerning the smoothness of interpolants and the description of m. l.s. processes as projection methods.
Book ChapterDOI
Splines minimizing rotation-invariant semi-norms in Sobolev spaces
TL;DR: A family of semi-norms is defined, subject to some interpolating conditions, providing interpolation methods that preserve polynomials of degree≤m−1 and converge in Sobolev spaces Hm+s(Ω).
Journal ArticleDOI
The intrinsic random functions and their applications
TL;DR: The intrinsic random functions (IRF) are a particular case of the Guelfand generalized processes with stationary increments and constitute a much wider class than the stationary RF, and are used in practical applications for representing nonstationary phenomena as discussed by the authors.