Spline Interpolation Algorithms-2 Dimension PDF Download

Author: Spath
Publisher:
ISBN: 9780867203455
Category :
Languages : en
Pages : 300

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Author: Helmuth Späth
Publisher: CRC Press
ISBN: 1439864721
Category : Computers
Languages : en
Pages : 312

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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: Helmuth Späth
Publisher: CRC Press
ISBN: 1439864713
Category : Computers
Languages : en
Pages : 416

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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: James R. Schiess
Publisher:
ISBN:
Category : Calculus of tensors
Languages : en
Pages : 30

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Author: M. J. D. Powell
Publisher:
ISBN:
Category :
Languages : en
Pages : 21

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Book Description

Author: Gary D. Knott
Publisher: Springer Science & Business Media
ISBN: 1461213207
Category : Computers
Languages : en
Pages : 247

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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: Boris I. Kvasov
Publisher: World Scientific
ISBN: 9789810240103
Category : Mathematics
Languages : en
Pages : 360

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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

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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: M. J. D. Powell
Publisher:
ISBN:
Category : Applied mathematics
Languages : en
Pages : 11

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Book Description

Author: Borislav D. Bojanov
Publisher: Springer
ISBN: 9780792322290
Category : Computers
Languages : en
Pages : 292

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Book Description
This volume provides a comprehensive introduction to the theory of spline functions. Emphasis is given to new developments, such as the general Birkhoff-type interpolation, the extremal properties of splines, their prominent role in the optimal recovery of functions, and multivariate interpolation by polynomials and splines. The book has thirteen chapters dealing, respectively, with interpolation by algebraic polynomials, the space of splines, B-splines, interpolation by spline functions, natural spline functions, perfect splines, monosplines, periodic splines, multivariate B-splines and truncated powers, multivariate spline functions and divided differences, box splines, multivariate mean value interpolation, multivariate polynomial interpolations arising by hyperplanes, and multivariate pointwise interpolation. Some of the results described are presented as exercises and hints are given for their solution. For researchers and graduate students whose work involves approximation theory.