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Application Of Spline Interpolation Methods To Engineering Problems
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Book Synopsis Application of Spline Interpolation Methods to Engineering Problems by : James B. Cheek
Download or read book Application of Spline Interpolation Methods to Engineering Problems written by James B. Cheek and published by . This book was released on 1971 with total page 62 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper was prepared to familiarize practicing scientists and engineers with the cubic spline interpolation technique as a possible tool in curve fitting for computer programs for which more commonly used techniques may be unsuitable or of limited value. The spline technique is compared with more common methods, specifically piecewise linear and polynomial, and examples of applications of the technique to engineering problems are presented.
Book Synopsis Topics in Splines and Applications by : Young Kinh-Nhue Truong
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.
Book Synopsis Splines and Variational Methods by : P. M. Prenter
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.
Book Synopsis Cardinal Spline Interpolation by : I. J. Schoenberg
Download or read book Cardinal Spline Interpolation written by I. J. Schoenberg and published by SIAM. This book was released on 1973-01-01 with total page 131 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Spline-Interpolation Solution of One Elasticity Theory Problem by : Elena A. Shirokova
Download or read book Spline-Interpolation Solution of One Elasticity Theory Problem written by Elena A. Shirokova and published by Bentham Science Publishers. This book was released on 2011 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The book presents methods of approximate solution of the basic problem of elasticity for special types of solids. Engineers can apply the approximate methods (Finite Element Method, Boundary Element Method) to solve the problems but the application of the"
Book Synopsis Mathematical Methods and Algorithms for Real-Time Applications by : Charles K. Chui
Download or read book Mathematical Methods and Algorithms for Real-Time Applications written by Charles K. Chui and published by . This book was released on 1990 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt: The notion of super splines and vertex splines is introduced and studied. Quasi-interpolation formulas for real-time applications are constructed. The method of noncommutative blending of quasi-interpolation and vertex spline interpolation is introduced to yield interpolation schemes which are local, flexible, and of optimal approximation orders. These formulas can be applied to real-time interpolation by means of table-look-up or FIR implementation. Applications to engineering problems such as parallel implementation of the extended Kalman filter and Hankel-norm frequency domain methods are studied. Wavelets are constructed by applying cardinal splines, and hence, they are readily available for real-time interpolation and orthogonal wavelet decompositions and reconstructions. (KR).
Book Synopsis Methods of Shape-preserving Spline Approximation by : Boris I. Kvasov
Download or read book Methods of Shape-preserving Spline Approximation written by Boris I. Kvasov and published by World Scientific. This book was released on 2000 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Handbook of Splines by : Gheorghe Micula
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.
Book Synopsis Application of spline functions to engineering problems by : Homer Bruce Sallee
Download or read book Application of spline functions to engineering problems written by Homer Bruce Sallee and published by . This book was released on 1972 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Theory and Applications of Spline Functions by : Thomas Nall Eden Greville
Download or read book Theory and Applications of Spline Functions written by Thomas Nall Eden Greville and published by . This book was released on 1969 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Spline Functions by : Larry L. Schumaker
Download or read book Spline Functions written by Larry L. Schumaker and published by SIAM. This book was released on 2015-01-01 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes in detail the key algorithms needed for computing with spline functions and illustrates their use in solving several basic problems in numerical analysis, including function approximation, numerical quadrature, data fitting, and the numerical solution of PDE's. The focus is on computational methods for bivariate splines on triangulations in the plane and on the sphere, although both univariate and tensor-product splines are also discussed. The book contains numerous examples and figures to illustrate the methods and their performance. All of the algorithms in the book have been coded in a separate MATLAB package available for license. The package can be used to run all of the examples in the book and also provides readers with the essential tools needed to create software for their own applications. In addition to the included bibliography, a list of over 100 pages of additional references can be found on the book's website.
Book Synopsis Smoothed Point Interpolation Methods: G Space Theory And Weakened Weak Forms by : Gui-rong Liu
Download or read book Smoothed Point Interpolation Methods: G Space Theory And Weakened Weak Forms written by Gui-rong Liu and published by World Scientific. This book was released on 2013-08-16 with total page 697 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on the widely used finite element method (FEM) and the latest Meshfree methods, a next generation of numerical method called Smoothed Point Interpolation Method (S-PIM) has been recently developed. The S-PIM is an innovative and effective combination of the FEM and the meshfree methods, and enables automation in computation, modeling and simulations — one of the most important features of the next generation methods. This important book describes the various S-PIM models in a systematic, concise and easy-to-understand manner. The underlying principles for the next generation of computational methods, G space theory, novel weakened weak (W2) formulations, techniques for shape functions, formulation procedures, and implementation strategies are presented in detail. Numerous examples are provided to demonstrate the efficiency and accuracy of the S-PIM solutions in comparison with the FEM and other existing methods. Effective techniques to compute solution bounds employing both S-PIM and FEM are highlighted to obtain certified solutions with both upper and lower bounds.The book also presents a systematically way to conduct adaptive analysis for solutions of desired accuracy using these bound properties, which is another key feature of the next generation of computational methods. This will benefit researchers, engineers and students who are venturing into new areas of research and computer code development.
Book Synopsis Interpolating Cubic Splines by : Gary D. Knott
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.
Book Synopsis Curve and Surface Fitting with Splines by : Paul Dierckx
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.
Book Synopsis The Theory of Splines and Their Applications by : J. H. Ahlberg
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.
Book Synopsis Computer Methods for Engineering with MATLAB® Applications, Second Edition by : Yogesh Jaluria
Download or read book Computer Methods for Engineering with MATLAB® Applications, Second Edition written by Yogesh Jaluria and published by CRC Press. This book was released on 2011-09-08 with total page 635 pages. Available in PDF, EPUB and Kindle. Book excerpt: Substantially revised and updated, Computer Methods for Engineering with MATLAB® Applications, Second Edition presents equations to describe engineering processes and systems. It includes computer methods for solving these equations and discusses the nature and validity of the numerical results for a variety of engineering problems. This edition now uses MATLAB in its discussions of computer solution. New to the Second Edition Recent advances in computational software and hardware A large number of MATLAB commands and programs for solving exercises and to encourage students to develop their own computer programs for specific problems Additional exercises and examples in all chapters New and updated references The text follows a systematic approach for obtaining physically realistic, valid, and accurate results through numerical modeling. It employs examples from many engineering areas to explain the elements involved in the numerical solution and make the presentation relevant and interesting. It also incorporates a wealth of solved exercises to supplement the discussion and illustrate the ideas and methods presented. The book shows how a computational approach can provide physical insight and obtain inputs for the analysis and design of practical engineering systems.
Book Synopsis Curves and Surfaces for Computer Graphics by : David Salomon
Download or read book Curves and Surfaces for Computer Graphics written by David Salomon and published by Springer Science & Business Media. This book was released on 2007-03-20 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Requires only a basic knowledge of mathematics and is geared toward the general educated specialists. Includes a gallery of color images and Mathematica code listings.
