Applications of B-spline Approximation to Geometric PDF Download
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Author: Richard F. Riesenfeld
Publisher:
ISBN:
Category : Grafik (datalogi)
Languages : en
Pages : 168
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Book Description
Author: Richard F. Riesenfeld
Publisher:
ISBN:
Category : Grafik (datalogi)
Languages : en
Pages : 168
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Book Description
Author: Klaus Hollig
Publisher: SIAM
ISBN: 1611972949
Category : Mathematics
Languages : en
Pages : 228
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Book Description
B-splines are fundamental to approximation and data fitting, geometric modeling, automated manufacturing, computer graphics, and numerical simulation. With an emphasis on key results and methods that are most widely used in practice, this textbook provides a unified introduction to the basic components of B-spline theory: approximation methods (mathematics), modeling techniques (engineering), and geometric algorithms (computer science). A supplemental Web site will provide a collection of problems, some with solutions, slides for use in lectures, and programs with demos.
Author: Hartmut Prautzsch
Publisher: Springer Science & Business Media
ISBN: 3662049198
Category : Computers
Languages : en
Pages : 299
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Book Description
This book provides a solid and uniform derivation of the various properties Bezier and B-spline representations have, and shows the beauty of the underlying rich mathematical structure. The book focuses on the core concepts of Computer Aided Geometric Design and provides 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 free form surfaces with arbitrary smoothness. The text is beautifully illustrated with many excellent figures to emphasize the geometric constructive approach of this book.
Author: Elaine Cohen
Publisher: CRC Press
ISBN: 1439864209
Category : Computers
Languages : en
Pages : 639
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Book Description
Written by researchers who have helped found and shape the field, this book is a definitive introduction to geometric modeling. The authors present all of the necessary techniques for curve and surface representations in computer-aided modeling with a focus on how the techniques are used in design.
Author: Klaus Hollig
Publisher: SIAM
ISBN: 9780898717532
Category : Mathematics
Languages : en
Pages : 155
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Book Description
Finite Element Methods with B-Splines describes new weighted approximation techniques, combining the computational advantages of B-splines and standard finite elements. In particular, no grid generation is necessary, which eliminates a difficult and often time-consuming preprocessing step. The meshless methods are very efficient and yield highly accurate solutions with relatively few parameters. This is illustrated for typical boundary value problems in fluid flow, heat conduction, and elasticity. Topics discussed by the author include basic finite element theory, algorithms for B-splines, weighted bases, stability and error estimates, multigrid techniques, applications, and numerical examples.
Author: Richard H. Bartels
Publisher: Morgan Kaufmann
ISBN: 9781558604001
Category : Computers
Languages : en
Pages : 504
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Book Description
As the field of computer graphics develops, techniques for modeling complex curves and surfaces are increasingly important. A major technique is the use of parametric splines in which a curve is defined by piecing together a succession of curve segments, and surfaces are defined by stitching together a mosaic of surface patches. An Introduction to Splines for Use in Computer Graphics and Geometric Modeling discusses the use of splines from the point of view of the computer scientist. Assuming only a background in beginning calculus, the authors present the material using many examples and illustrations with the goal of building the reader's intuition. Based on courses given at the University of California, Berkeley, and the University of Waterloo, as well as numerous ACM Siggraph tutorials, the book includes the most recent advances in computer-aided geometric modeling and design to make spline modeling techniques generally accessible to the computer graphics and geometric modeling communities.
Author: Gerald Farin
Publisher: CRC Press
ISBN: 143986411X
Category : Computers
Languages : en
Pages : 242
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Book Description
Putting the G into CAGD, the authors provide a much-needed practical and basic introduction to computer-aided geometric design. This book will help readers understand and use the elements of computer-aided geometric design, curves and surfaces, without the mathematical baggage that is necessary only for more advanced work. Though only minimal backg
Author: Gernot Beer
Publisher: Springer Nature
ISBN: 3030233391
Category : Science
Languages : en
Pages : 342
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Book Description
This book discusses the introduction of isogeometric technology to the boundary element method (BEM) in order to establish an improved link between simulation and computer aided design (CAD) that does not require mesh generation. In the isogeometric BEM, non-uniform rational B-splines replace the Lagrange polynomials used in conventional BEM. This may seem a trivial exercise, but if implemented rigorously, it has profound implications for the programming, resulting in software that is extremely user friendly and efficient. The BEM is ideally suited for linking with CAD, as both rely on the definition of objects by boundary representation. The book shows how the isogeometric philosophy can be implemented and how its benefits can be maximised with a minimum of user effort. Using several examples, ranging from potential problems to elasticity, it demonstrates that the isogeometric approach results in a drastic reduction in the number of unknowns and an increase in the quality of the results. In some cases even exact solutions without refinement are possible. The book also presents a number of practical applications, demonstrating that the development is not only of academic interest. It then elegantly addresses heterogeneous and non-linear problems using isogeometric concepts, and tests them on several examples, including a severely non-linear problem in viscous flow. The book makes a significant contribution towards a seamless integration of CAD and simulation, which eliminates the need for tedious mesh generation and provides high-quality results with minimum user intervention and computing.
Author: G. Farin
Publisher: Elsevier
ISBN: 008053340X
Category : Mathematics
Languages : en
Pages : 849
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Book Description
This book provides a comprehensive coverage of the fields Geometric Modeling, Computer-Aided Design, and Scientific Visualization, or Computer-Aided Geometric Design. Leading international experts have contributed, thus creating a one-of-a-kind collection of authoritative articles. There are chapters outlining basic theory in tutorial style, as well as application-oriented articles. Aspects which are covered include:Historical outline Curve and surface methods Scientific Visualization Implicit methods Reverse engineering.This book is meant to be a reference text for researchers in the field as well as an introduction to graduate students wishing to get some exposureto this subject.
Author: Les Piegl
Publisher: Springer Science & Business Media
ISBN: 3642592236
Category : Computers
Languages : en
Pages : 650
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Book Description
Until recently B-spline curves and surfaces (NURBS) were principally of interest to the computer aided design community, where they have become the standard for curve and surface description. Today we are seeing expanded use of NURBS in modeling objects for the visual arts, including the film and entertainment industries, art, and sculpture. NURBS are now also being used for modeling scenes for virtual reality applications. These applications are expected to increase. Consequently, it is quite appropriate for The.N'URBS Book to be part of the Monographs in Visual Communication Series. B-spline curves and surfaces have been an enduring element throughout my pro fessional life. The first edition of Mathematical Elements for Computer Graphics, published in 1972, was the first computer aided design/interactive computer graph ics textbook to contain material on B-splines. That material was obtained through the good graces of Bill Gordon and Louie Knapp while they were at Syracuse University. A paper of mine, presented during the Summer of 1977 at a Society of Naval Architects and Marine Engineers meeting on computer aided ship surface design, was arguably the first to examine the use of B-spline curves for ship design. For many, B-splines, rational B-splines, and NURBS have been a bit mysterious.
