Journal ArticleDOI
Smooth interpolation of large sets of scattered data
Richard Franke,Greg Nielson +1 more
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Methods for solving the following data fitting problems are discussed: Given the data (xi,yi,fi), i = 1,...,N construct a smooth bivariate function S with the property that S(xi, Yi) = fi, i = 2, N.Abstract:
: Methods for solving the following data fitting problems are discussed: Given the data (xi,yi,fi), i = 1,...,N construct a smooth bivariate function S with the property that S(xi,yi) = fi, i = 1,...,N. Because the desire to fit this type of data is encountered frequently in many areas of scientific applications, an investigation of the available methods for solving this problem was undertaken. Several aspects, such as computational efficiency, fitting characteristics and ease of implementation, were analyzed and compared. Within the context of a general purpose method for large sets of data, two of these methods emerged as being generally superior to the others. It is the purpose of this paper to describe these two methods and present examples illustrating their use and application. FORTRAN programs which implement these methods are available upon request. (Author)read more
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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.
Journal ArticleDOI
Scattered data interpolation: tests of some methods
TL;DR: 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.
Journal ArticleDOI
Locally Weighted Learning
TL;DR: The survey discusses distance functions, smoothing parameters, weighting functions, local model structures, regularization of the estimates and bias, assessing predictions, handling noisy data and outliers, improving the quality of predictions by tuning fit parameters, and applications of locally weighted learning.
Journal ArticleDOI
Scattered data interpolation with multilevel B-splines
TL;DR: The paper describes a fast algorithm for scattered data interpolation and approximation that makes use of a coarse to fine hierarchy of control lattices to generate a sequence of bicubic B-spline functions whose sum approaches the desired interpolation function.
Proceedings ArticleDOI
Multi-level partition of unity implicits
TL;DR: A new shape representation is presented, the multi-level partition of unity implicit surface, that allows us to construct surface models from very large sets of points, and can accurately represent sharp features such as edges and corners by selecting appropriate shape functions.
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
Algorithm 526: Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points [E1]
TL;DR: A method of blvariate interpolation and smooth surface fitting is developed for z values given at points irregularly distributed in the x-y plane for Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points.
Book ChapterDOI
Software for C1 Surface Interpolation
TL;DR: This chapter discusses algorithm and underlying theory of software for C1 surface interpolation, an interpolation algorithm that is interfaced with algorithms for contour plotting or surface perspective plotting for data given on a rectangular grid.
Journal ArticleDOI
Drawing Contours from Arbitrary Data Points
TL;DR: This paper describes a computer method for drawing, on an incremental plotter, a set of contours when the height is available only for some arbitrary collection of points, based on a distance-weighted, least-squares approximation technique, suitable not only for mathematically derived data, but also for data of geographical and other non-mathematical origins.
ReportDOI
Fitting surfaces to scattered data
TL;DR: A variety of numerical methods for fitting a function to data given at a set of points scattered throughout a domain in the plane are surveyed in this article, including polynomials, spline functions, and rational functions.