Curve and Surface Fitting with SplinesThe fitting of a curve or surface through a set of observational data is a recurring problem across numerous disciplines such as applications. This book describes the algorithms and mathematical fundamentals of a widely used software package for data fitting with tensor product splines. It gives a survey of possibilities, benefits, and problems commonly confronted when approximating with this popular type of function. Dierkx demonstrates in detail how the properties of B-splines can be fully exploited for improving the computational efficiency and for incorporating different boundary or shape preserving constraints. Special attention is also paid to strategies for an automatic and adaptive knot selection with intent to obtain serious data reductions. The practical use of the smoothing software is illustrated with many theoretical and practical examples. |
Contents
BIVARIATE SPLINES | 23 |
PowellSabin splines | 33 |
AN INTRODUCTION | 43 |
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algorithm approximation domain B-spline coefficients band matrix Boor boundary knots calculating Ci,j consider contour map corresponding criterion cubic spline CURFIT curve fitting data points data values derivative determine Dierckx divided difference equations evaluation example Figure FITPACK follows FORTRAN given graph grid interior knots interpolation interval IOPT iterations knot insertion knot set least-squares problem least-squares solution least-squares spline linear m₁ Mathematics method minimization non-zero number of knots Numerical Analysis obtained optimal overdetermined system parameter polynomial position properties R₁ rank deficiency routine satisfied scattered data set of data set of knots simply smoothing factor smoothing function smoothing spline smoothing spline sp(x specific spherical harmonic spline curve spline function spline s(x spline surface squared residuals sum of squared surface fitting tensor product spline thin plate spline triangles unit disk univariate variable vector y-direction zero Zq,r ди