共查询到10条相似文献,搜索用时 140 毫秒
1.
Günther Nürnberger Vera Rayevskaya Larry L. Schumaker Frank Zeilfelder 《Constructive Approximation》2005,23(1):33-59
We describe a method which can be used to interpolate
function values at a set of scattered points
in a planar domain using bivariate polynomial splines
of any prescribed smoothness.
The method starts with an arbitrary given triangulation
of the data points, and involves refining some of the
triangles with Clough-Tocher splits.
The construction of the interpolating splines requires
some additional function values at selected points in
the domain, but no derivatives are needed at any point.
Given n data points and a corresponding
initial triangulation, the interpolating spline can be
computed in just O(n) operations.
The interpolation method is local
and stable, and provides optimal order approximation of smooth
functions. 相似文献
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加密网格点二元局部基插值样条函数 总被引:1,自引:0,他引:1
1.简介 由于在理论以及应用两方面的重要性,多元样条引起了许多人的注意([6],[7]),紧支撑光滑分片多项式函数对于曲面的逼近是一个十分有效的工具。由于它们的局部支撑性,它们很容易求值;由于它们的光滑性,它们能被应用到要满足一定光滑条件的情况下;由于它们是紧支撑的,它们的线性包有很大的逼近灵活性,而且用它们构造逼近方法来解决的系统是 相似文献
4.
Hendrik Speleers 《Constructive Approximation》2013,37(1):41-72
We construct a suitable B-spline representation for a family of bivariate spline functions with smoothness r≥1 and polynomial degree 3r?1. They are defined on a triangulation with Powell–Sabin refinement. The basis functions have a local support, they are nonnegative, and they form a partition of unity. The construction involves the determination of triangles that must contain a specific set of points. We further consider a number of CAGD applications. We show how to define control points and control polynomials (of degree 2r?1), and we provide an efficient and stable computation of the Bernstein–Bézier form of such splines. 相似文献
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Algorithms are presented for fitting a Powell-Sabin spline toa set of scattered data. Both the detemination of least-squaresand smoothing splines are considered. For the latter we adoptthe philosophy of an existing tensor product spline algorithm.The triangulation is determined in an automatic and adaptiveway. The algorithm employs a single parameter to control thetradeoff between closeness of fit and smoothness of fit. The Powell-Sabin splines are represented in terms of locallysupported basis functions. The use of the Bernstein-Bzier ordinatesof these B-splines results in efficient calculations. Numericalexamples illustrate the usefulness of the given algorithms. 相似文献
6.
This article presents and compares two approaches of principal component (PC) analysis for two-dimensional functional data on a possibly irregular domain. The first approach applies the singular value decomposition of the data matrix obtained from a fine discretization of the two-dimensional functions. When the functions are only observed at discrete points that are possibly sparse and may differ from function to function, this approach incorporates an initial smoothing step prior to the singular value decomposition. The second approach employs a mixed effects model that specifies the PC functions as bivariate splines on triangulations and the PC scores as random effects. We apply the thin-plate penalty for regularizing the function estimation and develop an effective expectation–maximization algorithm for calculating the penalized likelihood estimates of the parameters. The mixed effects model-based approach integrates scatterplot smoothing and functional PC analysis in a unified framework and is shown in a simulation study to be more efficient than the two-step approach that separately performs smoothing and PC analysis. The proposed methods are applied to analyze the temperature variation in Texas using 100 years of temperature data recorded by Texas weather stations. Supplementary materials for this article are available online. 相似文献
7.
It is shown that bivariate interpolatory splines defined on a rectangleR can be characterized as being unique solutions to certain variational problems. This variational property is used to prove the uniform convergence of bivariate polynomial splines interpolating moderately smooth functions at data which includes interpolation to values on a rectangular grid. These results are then extended to bivariate splines defined on anL-shaped region.This research was supported by a University of Kansas General Research Grant. 相似文献
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Bivariate Polynomial Natural Spline Interpolation Algorithms with Local Basis for Scattered Data 总被引:3,自引:0,他引:3
Lutai Guan 《Journal of Computational Analysis and Applications》2003,5(1):77-101
Because of its importance in both theory and applications, multivariate splines have attracted special attention in many fields. Based on the theory of spline functions in Hilbert spaces, bivariate polynomial natural splines for interpolating, smoothing or generalized interpolating of scattered data over an arbitrary domain are constructed with one-sided functions. However, this method is not well suited for large scale numerical applications. In this paper, a new locally supported basis for the bivariate polynomial natural spline space is constructed. Some properties of this basis are also discussed. Methods to order scattered data are shown and algorithms for bivariate polynomial natural spline interpolating are constructed. The interpolating coefficient matrix is sparse, and thus, the algorithms can be easily implemented in a computer. 相似文献
9.
The penalized spline method has been widely used for estimating univariate smooth functions based on noisy data. This paper studies its extension to the two-dimensional case. To accommodate the need of handling data distributed on irregular regions, we consider bivariate splines defined on triangulations. Penalty functions based on the second-order derivatives are employed to regularize the spline fit and generalized cross-validation is used to select the penalty parameters. A simulation study shows that the penalized bivariate spline method is competitive to some well-established two-dimensional smoothers. The method is also illustrated using a real dataset on Texas temperature. 相似文献
10.
The piecewise algebraic curve is a kind generalization of the classical algebraic curve. Nöther-type theorem of piecewise algebraic curves on the cross-cut partition is very important to construct the Lagrange interpolation sets for a bivariate spline space. In this paper, using the properties of bivariate splines, the Nöther-type theorem of piecewise algebraic curves on the arbitrary triangulation is presented. 相似文献