Box Splines
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Box Splines
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Author : Carl de Boor
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Box Splines written by Carl de Boor and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Compactly supported smooth piecewise polynomial functions provide an efficient tool for the approximation of curves and surfaces and other smooth functions of one and several arguments. Since they are locally polynomial, they are easy to evaluate. Since they are smooth, they can be used when smoothness is required, as in the numerical solution of partial differential equations (in the Finite Element method) or the modeling of smooth sur faces (in Computer Aided Geometric Design). Since they are compactly supported, their linear span has the needed flexibility to approximate at all, and the systems to be solved in the construction of approximations are 'banded'. The construction of compactly supported smooth piecewise polynomials becomes ever more difficult as the dimension, s, of their domain G ~ IRs, i. e. , the number of arguments, increases. In the univariate case, there is only one kind of cell in any useful partition, namely, an interval, and its boundary consists of two separated points, across which polynomial pieces would have to be matched as one constructs a smooth piecewise polynomial function. This can be done easily, with the only limitation that the num ber of smoothness conditions across such a breakpoint should not exceed the polynomial degree (since that would force the two joining polynomial pieces to coincide). In particular, on any partition, there are (nontrivial) compactly supported piecewise polynomials of degree ~ k and in C(k-l), of which the univariate B-spline is the most useful example.
Box Splines
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Author : Carl De Boor
language : en
Publisher: Springer
Release Date : 1993
Box Splines written by Carl De Boor and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
Combining information previously only available in papers, the authors present basic box spline theory. Chapters discuss box splines defined, the linear algebra of box spline spaces, quasi- interpolants and approximate power, cardinal interpolation and difference equations, approximation by cardinal splines and wavelets, discrete box splines and linear diophantine equations, and subdivision algorithms. Annotation copyright by Book News, Inc., Portland, OR
Handbook Of Splines
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Author : Gheorghe Micula
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Handbook Of Splines written by Gheorghe Micula and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Spline Functions And The Theory Of Wavelets
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Author : Serge Dubuc
language : en
Publisher: American Mathematical Soc.
Release Date : 1999-01-01
Spline Functions And The Theory Of Wavelets written by Serge Dubuc and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-01 with Mathematics categories.
This work is based on a series of thematic workshops on the theory of wavelets and the theory of splines. Important applications are included. The volume is divided into four parts: Spline Functions, Theory of Wavelets, Wavelets in Physics, and Splines and Wavelets in Statistics. Part one presents the broad spectrum of current research in the theory and applications of spline functions. Theory ranges from classical univariate spline approximation to an abstract framework for multivariate spline interpolation. Applications include scattered-data interpolation, differential equations and various techniques in CAGD. Part two considers two developments in subdivision schemes; one for uniform regularity and the other for irregular situations. The latter includes construction of multidimensional wavelet bases and determination of bases with a given time frequency localization. In part three, the multifractal formalism is extended to fractal functions involving oscillating singularites. There is a review of a method of quantization of classical systems based on the theory of coherent states. Wavelets are applied in the domains of atomic, molecular and condensed-matter physics. In part four, ways in which wavelets can be used to solve important function estimation problems in statistics are shown. Different wavelet estimators are proposed in the following distinct cases: functions with discontinuities, errors that are no longer Gaussian, wavelet estimation with robustness, and error distribution that is no longer stationary. Some of the contributions in this volume are current research results not previously available in monograph form. The volume features many applications and interesting new theoretical developments. Readers will find powerful methods for studying irregularities in mathematics, physics, and statistics.
Spline Functions On Triangulations
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Author : Ming-Jun Lai
language : en
Publisher: Cambridge University Press
Release Date : 2007-04-19
Spline Functions On Triangulations written by Ming-Jun Lai and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-19 with Mathematics categories.
Comprehensive graduate text offering a detailed mathematical treatment of polynomial splines on triangulations.
Multivariate Splines
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Author : Charles K. Chui
language : en
Publisher: SIAM
Release Date : 1988-01-01
Multivariate Splines written by Charles K. Chui and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-01 with Mathematics categories.
Subject of multivariate splines presented from an elementary point of view; includes many open problems.
B Zier And B Spline Techniques
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Author : Hartmut Prautzsch
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
B Zier And B Spline Techniques written by Hartmut Prautzsch and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Computers categories.
Computer-aided modeling techniques have been developed since the advent of NC milling machines in the late 40's. Since the early 60's Bezier and B spline representations evolved as the major tool to handle curves and surfaces. These representations are geometrically intuitive and meaningful and they lead to constructive numerically robust algorithms. It is the purpose of this book to provide a solid and unified derivation of the various properties of Bezier and B-spline representations and to show the beauty of the underlying rich mathematical structure. The book focuses on the core concepts of Computer-aided Geometric Design (CAGD) with the intent to provide a clear and illustrative presentation of the basic principles as well as a treatment of advanced material, including multivariate splines, some subdivision techniques and constructions of arbitrarily smooth free-form surfaces. In order to keep the book focused, many further CAGD methods are ex cluded. In particular, rational Bezier and B-spline techniques are not ad dressed since a rigorous treatment within the appropriate context of projec tive geometry would have been beyond the scope of this book.
Subdivision Methods For Geometric Design
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Author : Joe Warren
language : en
Publisher: Morgan Kaufmann
Release Date : 2002
Subdivision Methods For Geometric Design written by Joe Warren and has been published by Morgan Kaufmann this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Art categories.
Subdivision Methods for Geometric Design provides computer graphics students and designers with a comprehensive guide to subdivision methods, including the background information required to grasp underlying concepts, techniques for manipulating subdivision algorithms to achieve specific effects, and a wide array of digital resources on a dynamic companion Web site. Subdivision Methods promises to be a groundbreaking book, important for both advanced students and working professionals in the field of computer graphics.
Curve And Surface Design
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Author : Hans Hagen
language : en
Publisher: SIAM
Release Date : 1992-01-01
Curve And Surface Design written by Hans Hagen and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-01-01 with Mathematics categories.
This collection of ideas and results on topics of curve and surface design is intended for research in the academic environment as well as for practical use in industrial applications. Main emphasis is on minimal energy splines and geometric spline curves, and on techniques beyond tensor product surfaces.
Tutorials On Multiresolution In Geometric Modelling
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Author : Armin Iske
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Tutorials On Multiresolution In Geometric Modelling written by Armin Iske and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
Multiresolution methods in geometric modelling are concerned with the generation, representation, and manipulation of geometric objects at several levels of detail. Applications include fast visualization and rendering as well as coding, compression and digital transmission of 3D geometric objects. This book is based on thirteen tutorials presented during the European Summer School "Principles of Multiresolution in Geometric Modelling", held at the Munich University of Technology, Germany, during August 22-30, 2001. The book covers: subdivision; wavelets; scattered data modelling; and coding and data structures. The tutorials are designed to be introductory in character, and include supporting exercises. Other supplementary material and software can be downloaded from the Web Site www.ma.tum.de/primus 2001/.