Mathematical Theory Of Subdivision
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Mathematical Theory Of Subdivision
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Author : Sandeep Kumar
language : en
Publisher: CRC Press
Release Date : 2019-07-09
Mathematical Theory Of Subdivision written by Sandeep Kumar and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-09 with Mathematics categories.
This book provides good coverage of the powerful numerical techniques namely, finite element and wavelets, for the solution of partial differential equation to the scientists and engineers with a modest mathematical background. The objective of the book is to provide the necessary mathematical foundation for the advanced level applications of these numerical techniques. The book begins with the description of the steps involved in finite element and wavelets-Galerkin methods. The knowledge of Hilbert and Sobolev spaces is needed to understand the theory of finite element and wavelet-based methods. Therefore, an overview of essential content such as vector spaces, norm, inner product, linear operators, spectral theory, dual space, and distribution theory, etc. with relevant theorems are presented in a coherent and accessible manner. For the graduate students and researchers with diverse educational background, the authors have focused on the applications of numerical techniques which are developed in the last few decades. This includes the wavelet-Galerkin method, lifting scheme, and error estimation technique, etc. Features: • Computer programs in Mathematica/Matlab are incorporated for easy understanding of wavelets. • Presents a range of workout examples for better comprehension of spaces and operators. • Algorithms are presented to facilitate computer programming. • Contains the error estimation techniques necessary for adaptive finite element method. This book is structured to transform in step by step manner the students without any knowledge of finite element, wavelet and functional analysis to the students of strong theoretical understanding who will be ready to take many challenging research problems in this area.
Introduction To The Mathematics Of Subdivision Surfaces
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Author : Lars-Erik Andersson
language : en
Publisher: SIAM
Release Date : 2010-01-01
Introduction To The Mathematics Of Subdivision Surfaces written by Lars-Erik Andersson and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-01 with Mathematics categories.
This is an introduction to the mathematical theory which underlies subdivision surfaces, as it is used in computer graphics and animation. Subdivision surfaces enable a designer to specify the approximate form of a surface that defines an object and then to refine it to get a more useful or attractive version. A considerable amount of mathematical theory is needed to understand the characteristics of the resulting surfaces, and this book explains the material carefully and rigorously. The text is highly accessible, organising subdivision methods in a unique and unambiguous hierarchy which builds insight and understanding. The material is not restricted to questions related to regularity of subdivision surfaces at so-called extraordinary points, but gives a broad discussion of the various methods. It is therefore an excellent preparation for more advanced texts that delve more deeply into special questions of regularity.
Subdivision Surfaces
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Author : Jörg Peters
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-08-24
Subdivision Surfaces written by Jörg Peters 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 2008-08-24 with Mathematics categories.
Since their first appearance in 1974, subdivision algorithms for generating surfaces of arbitrary topology have gained widespread popularity in computer graphics and are being evaluated in engineering applications. This development was complemented by ongoing efforts to develop appropriate mathematical tools for a thorough analysis, and today, many of the fascinating properties of subdivision are well understood. This book summarizes the current knowledge on the subject. It contains both meanwhile classical results as well as brand-new, unpublished material, such as a new framework for constructing C^2-algorithms. The focus of the book is on the development of a comprehensive mathematical theory, and less on algorithmic aspects. It is intended to serve researchers and engineers - both new to the beauty of the subject - as well as experts, academic teachers and graduate students or, in short, anybody who is interested in the foundations of this flourishing branch of applied geometry.
Mathematical Aspects Of Geometric Modeling
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Author : Charles A. Micchelli
language : en
Publisher: SIAM
Release Date : 1995-01-01
Mathematical Aspects Of Geometric Modeling written by Charles A. Micchelli and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-01-01 with Mathematics categories.
This monograph examines in detail certain concepts that are useful for the modeling of curves and surfaces and emphasizes the mathematical theory that underlies these ideas. The two principal themes of the text are the use of piecewise polynomial representation (this theme appears in one form or another in every chapter), and iterative refinement, also called subdivision. Here, simple iterative geometric algorithms produce, in the limit, curves with complex analytic structure. In the first three chapters, the de Casteljau subdivision for Bernstein-Bezier curves is used to introduce matrix subdivision, and the Lane-Riesenfield algorithm for computing cardinal splines is tied into stationary subdivision. This ultimately leads to the construction of prewavelets of compact support. The remainder of the book deals with concepts of "visual smoothness" of curves, along with the intriguing idea of generating smooth multivariate piecewise polynomials as volumes of "slices" of polyhedra. The final chapter contains an evaluation of polynomials by finite recursive algorithms. Each chapter contains introductory material as well as more advanced results.
Wavelet Subdivision Methods
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Author : Charles Chui
language : en
Publisher: CRC Press
Release Date : 2010-08-23
Wavelet Subdivision Methods written by Charles Chui and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-23 with Computers categories.
Prevalent in animation movies and interactive games, subdivision methods allow users to design and implement simple but efficient schemes for rendering curves and surfaces. Adding to the current subdivision toolbox, Wavelet Subdivision Methods: GEMS for Rendering Curves and Surfaces introduces geometry editing and manipulation schemes (GEMS) and covers both subdivision and wavelet analysis for generating and editing parametric curves and surfaces of desirable geometric shapes. The authors develop a complete constructive theory and effective algorithms to derive synthesis wavelets with minimum support and any desirable order of vanishing moments, along with decomposition filters. Through numerous examples, the book shows how to represent curves and construct convergent subdivision schemes. It comprehensively details subdivision schemes for parametric curve rendering, offering complete algorithms for implementation and theoretical development as well as detailed examples of the most commonly used schemes for rendering both open and closed curves. It also develops an existence and regularity theory for the interpolatory scaling function and extends cardinal B-splines to box splines for surface subdivision. Keeping mathematical derivations at an elementary level without sacrificing mathematical rigor, this book shows how to apply bottom-up wavelet algorithms to curve and surface editing. It offers an accessible approach to subdivision methods that integrates the techniques and algorithms of bottom-up wavelets.
Analysis And Design Of Univariate Subdivision Schemes
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Author : Malcolm Sabin
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-08-16
Analysis And Design Of Univariate Subdivision Schemes written by Malcolm Sabin 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 2010-08-16 with Mathematics categories.
‘Subdivision’ is a way of representing smooth shapes in a computer. A curve or surface (both of which contain an in?nite number of points) is described in terms of two objects. One object is a sequence of vertices, which we visualise as a polygon, for curves, or a network of vertices, which we visualise by drawing the edges or faces of the network, for surfaces. The other object is a set of rules for making denser sequences or networks. When applied repeatedly, the denser and denser sequences are claimed to converge to a limit, which is the curve or surface that we want to represent. This book focusses on curves, because the theory for that is complete enough that a book claiming that our understanding is complete is exactly what is needed to stimulate research proving that claim wrong. Also because there are already a number of good books on subdivision surfaces. The way in which the limit curve relates to the polygon, and a lot of interesting properties of the limit curve, depend on the set of rules, and this book is about how one can deduce those properties from the set of rules, and how one can then use that understanding to construct rules which give the properties that one wants.
Stationary Subdivision
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Author : Alfred S. Cavaretta
language : en
Publisher: American Mathematical Soc.
Release Date : 1991
Stationary Subdivision written by Alfred S. Cavaretta 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 1991 with Algorithms categories.
This monograph presents a systematic development of the basic mathematical principles and concepts associated with stationary subdivision algorithms which are used for generating curves and surfaces in computer graphics. Special attention is given to the structure of such algorithms in a multidimensional settings, and the convergence issue is analyzed using appropriate tools from Fourier analysis and functional analysis.
Mathematics And Computation In Imaging Science And Information Processing
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Author :
language : en
Publisher:
Release Date :
Mathematics And Computation In Imaging Science And Information Processing written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Water Waves The Mathematical Theory With Applications
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Author : James Johnston Stoker
language : en
Publisher: Courier Dover Publications
Release Date : 2019-04-17
Water Waves The Mathematical Theory With Applications written by James Johnston Stoker and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-17 with Science categories.
First published in 1957, this is a classic monograph in the area of applied mathematics. It offers a connected account of the mathematical theory of wave motion in a liquid with a free surface and subjected to gravitational and other forces, together with applications to a wide variety of concrete physical problems. A never-surpassed text, it remains of permanent value to a wide range of scientists and engineers concerned with problems in fluid mechanics. The four-part treatment begins with a presentation of the derivation of the basic hydrodynamic theory for non-viscous incompressible fluids and a description of the two principal approximate theories that form the basis for the rest of the book. The second section centers on the approximate theory that results from small-amplitude wave motions. A consideration of problems involving waves in shallow water follows, and the text concludes with a selection of problems solved in terms of the exact theory. Despite the diversity of its topics, this text offers a unified, readable, and largely self-contained treatment.
Wavelet Subdivision Methods
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Author : Charles Chui
language : en
Publisher: CRC Press
Release Date : 2010-08-23
Wavelet Subdivision Methods written by Charles Chui and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-08-23 with Computers categories.
Prevalent in animation movies and interactive games, subdivision methods allow users to design and implement simple but efficient schemes for rendering curves and surfaces. Adding to the current subdivision toolbox, Wavelet Subdivision Methods: GEMS for Rendering Curves and Surfaces introduces geometry editing and manipulation schemes (GEMS) and co