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Author: Helmuth Späth Publisher: CRC Press ISBN: 1439864713 Category : Computers Languages : en Pages : 416
Book Description
Together with its compagnion volume this book presents a practical introduction to computing spline functions, the fundamental tools for fitting curves and surfaces in computer-aided design (CAD) and computer graphics.
Author: Helmuth Späth Publisher: CRC Press ISBN: 1439864713 Category : Computers Languages : en Pages : 416
Book Description
Together with its compagnion volume this book presents a practical introduction to computing spline functions, the fundamental tools for fitting curves and surfaces in computer-aided design (CAD) and computer graphics.
Author: Helmuth Späth Publisher: CRC Press ISBN: 1439864721 Category : Computers Languages : en Pages : 312
Book Description
These volumes present a practical introduction to computing spline functions, the fundamental tools for fitting curves and surfaces in computer-aided deisgn (CAD) and computer graphics.
Author: Boris I. Kvasov Publisher: World Scientific ISBN: 9789810240103 Category : Mathematics Languages : en Pages : 360
Book Description
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: Borislav D. Bojanov Publisher: Springer Science & Business Media ISBN: 940158169X Category : Mathematics Languages : en Pages : 287
Book Description
Spline functions entered Approximation Theory as solutions of natural extremal problems. A typical example is the problem of drawing a function curve through given n + k points that has a minimal norm of its k-th derivative. Isolated facts about the functions, now called splines, can be found in the papers of L. Euler, A. Lebesgue, G. Birkhoff, J. Favard, L. Tschakaloff. However, the Theory of Spline Functions has developed in the last 30 years by the effort of dozens of mathematicians. Recent fundamental results on multivariate polynomial interpolation and multivari ate splines have initiated a new wave of theoretical investigations and variety of applications. The purpose of this book is to introduce the reader to the theory of spline functions. The emphasis is given to some new developments, such as the general Birkoff's type interpolation, the extremal properties of the splines and their prominant role in the optimal recovery of functions, multivariate interpolation by polynomials and splines. The material presented is based on the lectures of the authors, given to the students at the University of Sofia and Yerevan University during the last 10 years. Some more elementary results are left as excercises and detailed hints are given.
Author: P. M. Prenter Publisher: Courier Corporation ISBN: 0486783499 Category : Mathematics Languages : en Pages : 338
Book Description
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.
Author: Günther Nürnberger Publisher: Springer ISBN: Category : Mathematics Languages : en Pages : 264
Book Description
Splines play an important role in applied mathematics since they possess high flexibility to approximate efficiently, even nonsmooth functions which are given explicitly or only implicitly, e.g. by differential equations. The aim of this book is to analyse in a unified approach basic theoretical and numerical aspects of interpolation and best approximation by splines in one variable. The first part on spaces of polynomials serves as a basis for investigating the more complex structure of spline spaces. Given in the appendix are brief introductions to the theory of splines with free knots (an algorithm is described in the main part), to splines in two variables and to spline collocation for differential equations.A large number of new results presented here cannot be found in earlier books on splines. Researchers will find several references to recent developments. The book is an indispensable aid for graduate courses on splines or approximation theory. Students with a basic knowledge of analysis and linear algebra will be able to read the text. Engineers will find various pactical interpolation and approximation methods.
Author: Gary D. Knott Publisher: Springer Science & Business Media ISBN: 1461213207 Category : Computers Languages : en Pages : 247
Book Description
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: Helmuth Späth
Author: Helmuth Späth
Author: Helmuth Späth
Author: James R. Schiess
Author: Spath
Author: Boris I. Kvasov
Author: Borislav D. Bojanov
Author: 
Author: P. M. Prenter
Author: Günther Nürnberger
Author: Gary D. Knott