Cardinal Spline Interpolation
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Author | : I. J. Schoenberg |
Publisher | : SIAM |
Total Pages | : 131 |
Release | : 1973-01-01 |
Genre | : Mathematics |
ISBN | : 9781611970555 |
As this monograph shows, the purpose of cardinal spline interpolation is to bridge the gap between the linear spline and the cardinal series. The author explains cardinal spline functions, the basic properties of B-splines, including B- splines with equidistant knots and cardinal splines represented in terms of B-splines, and exponential Euler splines, leading to the most important case and central problem of the book-- cardinal spline interpolation, with main results, proofs, and some applications. Other topics discussed include cardinal Hermite interpolation, semi-cardinal interpolation, finite spline interpolation problems, extremum and limit properties, equidistant spline interpolation applied to approximations of Fourier transforms, and the smoothing of histograms.
Author | : Maoli Chang |
Publisher | : |
Total Pages | : 122 |
Release | : 1991 |
Genre | : |
ISBN | : |
Author | : I. J. Schoenberg |
Publisher | : |
Total Pages | : 0 |
Release | : 1973 |
Genre | : Interpolation |
ISBN | : |
Author | : Daniel Tien-You Lee |
Publisher | : |
Total Pages | : 142 |
Release | : 1984 |
Genre | : Interpolation |
ISBN | : |
Author | : Boris I. Kvasov |
Publisher | : World Scientific |
Total Pages | : 360 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 9789810240103 |
This book aims to develop algorithms of shape-preserving spline approximation for curves/surfaces with automatic choice of the tension parameters. The resulting curves/surfaces retain geometric properties of the initial data, such as positivity, monotonicity, convexity, linear and planar sections. The main tools used are generalized tension splines and B-splines. A difference method for constructing tension splines is also developed which permits one to avoid the computation of hyperbolic functions and provides other computational advantages. The algorithms of monotonizing parametrization described improve an adequate representation of the resulting shape-preserving curves/surfaces. Detailed descriptions of algorithms are given, with a strong emphasis on their computer implementation. These algorithms can be applied to solve many problems in computer-aided geometric design.
Author | : Gary D. Knott |
Publisher | : Springer Science & Business Media |
Total Pages | : 247 |
Release | : 2012-12-06 |
Genre | : Computers |
ISBN | : 1461213207 |
A spline is a thin flexible strip composed of a material such as bamboo or steel that can be bent to pass through or near given points in the plane, or in 3-space in a smooth manner. Mechanical engineers and drafting specialists find such (physical) splines useful in designing and in drawing plans for a wide variety of objects, such as for hulls of boats or for the bodies of automobiles where smooth curves need to be specified. These days, physi cal splines are largely replaced by computer software that can compute the desired curves (with appropriate encouragment). The same mathematical ideas used for computing "spline" curves can be extended to allow us to compute "spline" surfaces. The application ofthese mathematical ideas is rather widespread. Spline functions are central to computer graphics disciplines. Spline curves and surfaces are used in computer graphics renderings for both real and imagi nary objects. Computer-aided-design (CAD) systems depend on algorithms for computing spline functions, and splines are used in numerical analysis and statistics. Thus the construction of movies and computer games trav els side-by-side with the art of automobile design, sail construction, and architecture; and statisticians and applied mathematicians use splines as everyday computational tools, often divorced from graphic images.
Author | : I. J. Schoenberg |
Publisher | : |
Total Pages | : 38 |
Release | : 1971 |
Genre | : |
ISBN | : |
The main purpose of the paper is to demonstrate the important role of some results of Euler in the theory and practice of cardinal spline interpolation. (Author).
Author | : Rong-Qing Jia |
Publisher | : |
Total Pages | : 186 |
Release | : 1983 |
Genre | : Spline theory |
ISBN | : |
Author | : Samuel Karlin |
Publisher | : |
Total Pages | : 520 |
Release | : 1976 |
Genre | : Mathematics |
ISBN | : |
This volume reports a series of research investigations concerned with spline functions and approximation theory. The common thread of the studies derives from the facts that (1) the subject matter of the individual articles relate and significantly complement each other; 92) part of the genesis and certainly the main developments of these studies occurred at the Weizmann Institute of Science, Rehovot, Israel, commencing about September 1970 through June 1974. The contributions cover aspects of the theory of best approximation and quadratures, the solution of certain extremal problems embracing generalized Landau and Markov-type inequalities for derivative functionals, and a hierarchy of interpolation and convergence properties of classes of spline functions.
Author | : C. A. Micchelli |
Publisher | : |
Total Pages | : 46 |
Release | : 1975 |
Genre | : |
ISBN | : |