Download or read book Interpolating Cubic Splines written by Gary D. Knott and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Spline Regression Models written by Lawrence C. Marsh and published by SAGE. This book was released on 2001-09-14 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spline Regression Models shows how to use dummy variables to formulate and estimate spline regression models both in situations where the number and location of the spline knots are known in advance, and where estimation is required.
Download or read book The Theory of Splines and Their Applications written by J. H. Ahlberg and published by Elsevier. This book was released on 2016-06-03 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Theory of Splines and Their Applications discusses spline theory, the theory of cubic splines, polynomial splines of higher degree, generalized splines, doubly cubic splines, and two-dimensional generalized splines. The book explains the equations of the spline, procedures for applications of the spline, convergence properties, equal-interval splines, and special formulas for numerical differentiation or integration. The text explores the intrinsic properties of cubic splines including the Hilbert space interpretation, transformations defined by a mesh, and some connections with space technology concerning the payload of a rocket. The book also discusses the theory of polynomial splines of odd degree which can be approached through algebraically (which depends primarily on the examination in detail of the linear system of equations defining the spline). The theory can also be approached intrinsically (which exploits the consequences of basic integral relations existing between functions and approximating spline functions). The text also considers the second integral relation, raising the order of convergence, and the limits on the order of convergence. The book will prove useful for mathematicians, physicist, engineers, or academicians in the field of technology and applied mathematics.
Download or read book Spline Functions Basic Theory written by Larry Schumaker and published by Cambridge University Press. This book was released on 2007-08-16 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic work continues to offer a comprehensive treatment of the theory of univariate and tensor-product splines. It will be of interest to researchers and students working in applied analysis, numerical analysis, computer science, and engineering. The material covered provides the reader with the necessary tools for understanding the many applications of splines in such diverse areas as approximation theory, computer-aided geometric design, curve and surface design and fitting, image processing, numerical solution of differential equations, and increasingly in business and the biosciences. This new edition includes a supplement outlining some of the major advances in the theory since 1981, and some 250 new references. It can be used as the main or supplementary text for courses in splines, approximation theory or numerical analysis.
Download or read book Splines and Variational Methods written by P. M. Prenter and published by Courier Corporation. This book was released on 2013-11-26 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the clearest available introductions to variational methods, this text requires only a minimal background in calculus and linear algebra. Its self-contained treatment explains the application of theoretic notions to the kinds of physical problems that engineers regularly encounter. The text’s first half concerns approximation theoretic notions, exploring the theory and computation of one- and two-dimensional polynomial and other spline functions. Later chapters examine variational methods in the solution of operator equations, focusing on boundary value problems in one and two dimensions. Additional topics include least squares and other Galerkin methods. Many helpful definitions, examples, and exercises appear throughout the book. A classic reference in spline theory, this volume will benefit experts as well as students of engineering and mathematics.
Download or read book Studies in Spline Functions and Approximation Theory written by Samuel Karlin and published by . This book was released on 1976 with total page 520 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book A Study of Splines written by Esmaail Mehvari Nikjeh and published by . This book was released on 1992 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation and Modeling with B Splines written by Klaus Hollig and published by SIAM. This book was released on 2015-07-01 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: B-splines are fundamental to approximation and data fitting, geometric modeling, automated manufacturing, computer graphics, and numerical simulation. With an emphasis on key results and methods that are most widely used in practice, this textbook provides a unified introduction to the basic components of B-spline theory: approximation methods (mathematics), modeling techniques (engineering), and geometric algorithms (computer science). A supplemental Web site will provide a collection of problems, some with solutions, slides for use in lectures, and programs with demos.
Download or read book Spline Models for Observational Data written by Grace Wahba and published by SIAM. This book was released on 1990-09-01 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book serves well as an introduction into the more theoretical aspects of the use of spline models. It develops a theory and practice for the estimation of functions from noisy data on functionals. The simplest example is the estimation of a smooth curve, given noisy observations on a finite number of its values. Convergence properties, data based smoothing parameter selection, confidence intervals, and numerical methods are established which are appropriate to a number of problems within this framework. Methods for including side conditions and other prior information in solving ill posed inverse problems are provided. Data which involves samples of random variables with Gaussian, Poisson, binomial, and other distributions are treated in a unified optimization context. Experimental design questions, i.e., which functionals should be observed, are studied in a general context. Extensions to distributed parameter system identification problems are made by considering implicitly defined functionals.
Download or read book A Study of Splines written by Wayne Tsorng and published by . This book was released on 1991 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Handbook of Splines written by Gheorghe Micula and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: The purpose of this book is to give a comprehensive introduction to the theory of spline functions, together with some applications to various fields, emphasizing the significance of the relationship between the general theory and its applications. At the same time, the goal of the book is also to provide new ma terial on spline function theory, as well as a fresh look at old results, being written for people interested in research, as well as for those who are interested in applications. The theory of spline functions and their applications is a relatively recent field of applied mathematics. In the last 50 years, spline function theory has undergone a won derful development with many new directions appearing during this time. This book has its origins in the wish to adequately describe this development from the notion of 'spline' introduced by 1. J. Schoenberg (1901-1990) in 1946, to the newest recent theories of 'spline wavelets' or 'spline fractals'. Isolated facts about the functions now called 'splines' can be found in the papers of L. Euler, A. Lebesgue, G. Birkhoff, J.
Download or read book Curve and Surface Fitting with Splines written by Paul Dierckx and published by Oxford University Press. This book was released on 1995 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fitting of a curve or surface through a set of observational data is a very frequent problem in different disciplines (mathematics, engineering, medicine, ...) with many interesting applications. This book describes the algorithms and mathematical fundamentals of a widely used software package for data fitting with (tensor product) splines. As such it gives a survey of possibilities and benefits but also of the problems to cope with when approximating with this popular type of function. In particular it is demonstrated 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 examples, academic as well as taken from real life.
Download or read book Multivariate Splines written by Charles K. Chui and published by SIAM. This book was released on 1988-01-01 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: Subject of multivariate splines presented from an elementary point of view; includes many open problems.
Download or read book Topics in Splines and Applications written by Young Kinh-Nhue Truong and published by BoD – Books on Demand. This book was released on 2018-06-06 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: Splines provide a significant tool for the design of computationally economical curves and surfaces for the construction of various objects like automobiles, ship hulls, airplane fuselages and wings, propeller blades, shoe insoles, bottles, etc. It also contributes in the description of geological, physical, statistical, and even medical phenomena. Spline methods have proven to be indispensable in a variety of modern industries, including computer vision, robotics, signal and image processing, visualization, textile, graphic designs, and even media. This book aims to provide a valuable source on splines and their applications. It focuses on collecting and disseminating information in various disciplines including computer-aided geometric design, computer graphics, data visualization, data fitting, power systems, clinical and epidemiologic studies, disease detection, regression curves, social media, and biological studies. The book is useful for researchers, scientists, practitioners, and many others who seek state-of-the-art techniques and applications using splines. It is also useful for undergraduate senior students as well as graduate students in the areas of computer science, engineering, health science, statistics, and mathematics. Each chapter also provides useful information on software developments and their extensions.
Download or read book Interpolation and Approximation with Splines and Fractals written by Peter Robert Massopust and published by . This book was released on 2010 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook is intended to supplement the classical theory of uni- and multivariate splines and their approximation and interpolation properties with those of fractals, fractal functions, and fractal surfaces. This synthesis will complement currently required courses dealing with these topics and expose the prospective reader to some new and deep relationships. In addition to providing a classical introduction to the main issues involving approximation and interpolation with uni- and multivariate splines, cardinal and exponential splines, and their connection to wavelets and multiscale analysis, which comprises the first half of the book, the second half will describe fractals, fractal functions and fractal surfaces, and their properties. This also includes the new burgeoning theory of superfractals and superfractal functions. The theory of splines is well-established but the relationship to fractal functions is novel. Throughout the book, connections between these two apparently different areas will be exposed and presented. In this way, more options are given to the prospective reader who will encounter complex approximation and interpolation problems in real-world modeling. Numerous examples, figures, and exercises accompany the material.
Download or read book A Study of Spline written by Yue-Hsin Chen and published by . This book was released on 1992 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book A Blossoming Development of Splines written by Stephen Mann and published by Morgan & Claypool Publishers. This book was released on 2006-12-01 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this lecture, we study Bézier and B-spline curves and surfaces, mathematical representations for free-form curves and surfaces that are common in CAD systems and are used to design aircraft and automobiles, as well as in modeling packages used by the computer animation industry. Bézier/B-splines represent polynomials and piecewise polynomials in a geometric manner using sets of control points that define the shape of the surface. The primary analysis tool used in this lecture is blossoming, which gives an elegant labeling of the control points that allows us to analyze their properties geometrically. Blossoming is used to explore both Bézier and B-spline curves, and in particular to investigate continuity properties, change of basis algorithms, forward differencing, B-spline knot multiplicity, and knot insertion algorithms. We also look at triangle diagrams (which are closely related to blossoming), direct manipulation of B-spline curves, NURBS curves, and triangular and tensor product surfaces.
