Approximation And Modeling With B Splines
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Approximation And Modeling With B Splines
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Author : Klaus Hollig
language : en
Publisher: SIAM
Release Date : 2015-07-01
Approximation And Modeling With B Splines written by Klaus Hollig and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-07-01 with Mathematics categories.
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.
Modeling With Ambient B Splines
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Author : Nicole Lehmann
language : en
Publisher: Logos Verlag Berlin GmbH
Release Date : 2013
Modeling With Ambient B Splines written by Nicole Lehmann and has been published by Logos Verlag Berlin GmbH this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Computers categories.
The present thesis introduces a new approach for the generation of CK-approximants of functions defined on closed submanifolds for arbitrary k ∈ N. In case a function on a surface resembles the three coordinates of a topologically equivalent surface in R3, we even obtain Ck-approximants of closed surfaces of arbitrary topology. The key idea of our method is a constant extension of the target function into the submanifold's ambient space. In case the reference submanifolds are embedded and Ck, the usage of standard tensor product B-splines for the approximation of the extended function is straightforward. We obtain a Ck-approximation of the target function by restricting the approximant to the reference submanifold. We illustrate our method by an easy example in R2 and verify its practicality by application-oriented examples in R3. The first treats the approximation of the geoid, an important reference magnitude within geodesy and geophysics. The second and third example treat the approximation of geometric models. The usage of B-splines not only guarantees full approximation power but also allows a canonical access to adaptive refinement strategies. We elaborate on two hierarchical techniques and successfully apply them to the introduced examples. Concerning the modeling of surfaces by the new approach, we derive numerically robust formulas for the determination of normal vectors and curvature information of a target surface which only need the spline approximant as well as the normal vectors and curvature information of the reference surface.
Approximation Theory Xvi
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Author : Gregory E. Fasshauer
language : en
Publisher: Springer Nature
Release Date : 2021-01-04
Approximation Theory Xvi written by Gregory E. Fasshauer and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-01-04 with Mathematics categories.
These proceedings are based on the international conference Approximation Theory XVI held on May 19–22, 2019 in Nashville, Tennessee. The conference was the sixteenth in a series of meetings in Approximation Theory held at various locations in the United States. Over 130 mathematicians from 20 countries attended. The book contains two longer survey papers on nonstationary subdivision and Prony’s method, along with 11 research papers on a variety of topics in approximation theory, including Balian-Low theorems, butterfly spline interpolation, cubature rules, Hankel and Toeplitz matrices, phase retrieval, positive definite kernels, quasi-interpolation operators, stochastic collocation, the gradient conjecture, time-variant systems, and trivariate finite elements. The book should be of interest to mathematicians, engineers, and computer scientists working in approximation theory, computer-aided geometric design, numerical analysis, and related approximation areas.
Sparse Grids And Applications Munich 2018
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Author : Hans-Joachim Bungartz
language : en
Publisher: Springer Nature
Release Date : 2022-03-14
Sparse Grids And Applications Munich 2018 written by Hans-Joachim Bungartz and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-14 with Mathematics categories.
Sparse grids are a popular tool for the numerical treatment of high-dimensional problems. Where classical numerical discretization schemes fail in more than three or four dimensions, sparse grids, in their different flavors, are frequently the method of choice. This volume of LNCSE presents selected papers from the proceedings of the fifth workshop on sparse grids and applications, and demonstrates once again the importance of this numerical discretization scheme. The articles present recent advances in the numerical analysis of sparse grids in connection with a range of applications including uncertainty quantification, plasma physics simulations, and computational chemistry, to name but a few.
Neutrosophic Sets And Systems Vol 63 2024
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Author : Florentin Smarandache
language : en
Publisher: Infinite Study
Release Date : 2024-02-01
Neutrosophic Sets And Systems Vol 63 2024 written by Florentin Smarandache and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-01 with Mathematics categories.
“Neutrosophic Sets and Systems” has been created for publications on advanced studies in neutrosophy, neutrosophic set, neutrosophic logic, neutrosophic probability, neutrosophic statistics that started in 1995 and their applications in any field, such as the neutrosophic structures developed in algebra, geometry, topology, etc. Neutrosophy is a new branch of philosophy that studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. This theory considers every notion or idea together with its opposite or negation
Sparse Grids And Applications Stuttgart 2014
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Author : Jochen Garcke
language : en
Publisher: Springer
Release Date : 2016-03-16
Sparse Grids And Applications Stuttgart 2014 written by Jochen Garcke and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-16 with Computers categories.
This volume of LNCSE is a collection of the papers from the proceedings of the third workshop on sparse grids and applications. Sparse grids are a popular approach for the numerical treatment of high-dimensional problems. Where classical numerical discretization schemes fail in more than three or four dimensions, sparse grids, in their different guises, are frequently the method of choice, be it spatially adaptive in the hierarchical basis or via the dimensionally adaptive combination technique. Demonstrating once again the importance of this numerical discretization scheme, the selected articles present recent advances on the numerical analysis of sparse grids as well as efficient data structures. The book also discusses a range of applications, including uncertainty quantification and plasma physics.
Geometric Modeling With Splines
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Author : Elaine Cohen
language : en
Publisher: CRC Press
Release Date : 2001-07-18
Geometric Modeling With Splines written by Elaine Cohen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-07-18 with Computers categories.
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.
Mathematical And Computational Methods For Modelling Approximation And Simulation
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Author : Domingo Barrera
language : en
Publisher: Springer Nature
Release Date : 2022-05-08
Mathematical And Computational Methods For Modelling Approximation And Simulation written by Domingo Barrera and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-05-08 with Mathematics categories.
This book contains plenary lectures given at the International Conference on Mathematical and Computational Modeling, Approximation and Simulation, dealing with three very different problems: reduction of Runge and Gibbs phenomena, difficulties arising when studying models that depend on the highly nonlinear behaviour of a system of PDEs, and data fitting with truncated hierarchical B-splines for the adaptive reconstruction of industrial models. The book includes nine contributions, mostly related to quasi-interpolation. This is a topic that continues to register a high level of interest, both for those working in the field of approximation theory and for those interested in its use in a practical context. Two chapters address the construction of quasi-interpolants, and three others focus on the use of quasi-interpolation in solving integral equations. The remaining four concern a problem related to the heat diffusion equation, new results on the notion of convexity in probabilistic metric spaces (which are applied to the study of the existence and uniqueness of the solution of a Volterra equation), the use of smoothing splines to address an economic problem and, finally, the analysis of poverty measures, which is a topic of increased interest to society. The book is addressed to researchers interested in Applied Mathematics, with particular reference to the aforementioned topics.
Sketch Based Interfaces And Modeling
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Author : Joaquim Jorge
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-12-15
Sketch Based Interfaces And Modeling written by Joaquim Jorge 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 2010-12-15 with Computers categories.
The field of sketch-based interfaces and modeling (SBIM) is concerned with developing methods and techniques to enable users to interact with a computer through sketching - a simple, yet highly expressive medium. SBIM blends concepts from computer graphics, human-computer interaction, artificial intelligence, and machine learning. Recent improvements in hardware, coupled with new machine learning techniques for more accurate recognition, and more robust depth inferencing techniques for sketch-based modeling, have resulted in an explosion of both sketch-based interfaces and pen-based computing devices. Presenting the first coherent, unified overview of SBIM, this unique text/reference bridges the two complementary research areas of user interaction (sketch-based interfaces), and graphical modeling and construction (sketch-based modeling). The book discusses the state of the art of this rapidly evolving field, with contributions from an international selection of experts. Also covered are sketch-based systems that allow the user to manipulate and edit existing data - from text, images, 3D shapes, and video - as opposed to modeling from scratch. Topics and features: reviews pen/stylus interfaces to graphical applications that avoid reliance on user interface modes; describes systems for diagrammatic sketch recognition, mathematical sketching, and sketch-based retrieval of vector drawings; examines pen-based user interfaces for engineering and educational applications; presents a set of techniques for sketch recognition that rely strictly on spatial information; introduces the Teddy system; a pioneering sketching interface for designing free-form 3D models; investigates a range of advanced sketch-based systems for modeling and designing 3D objects, including complex contours, clothing, and hair-styles; explores methods for modeling from just a single sketch or using only a few strokes. This text is an essential resource for researchers, practitioners and graduate students involved in human-factors and user interfaces, interactive computer graphics, and intelligent user interfaces and AI.
Spline Functions
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Author : Larry L. Schumaker
language : en
Publisher: SIAM
Release Date : 2015-01-01
Spline Functions written by Larry L. Schumaker and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-01 with Science categories.
This book describes in detail the key algorithms needed for computing with spline functions and illustrates their use in solving several basic problems in numerical analysis, including function approximation, numerical quadrature, data fitting, and the numerical solution of PDE's. The focus is on computational methods for bivariate splines on triangulations in the plane and on the sphere, although both univariate and tensor-product splines are also discussed. The book contains numerous examples and figures to illustrate the methods and their performance. All of the algorithms in the book have been coded in a separate MATLAB package available for license. The package can be used to run all of the examples in the book and also provides readers with the essential tools needed to create software for their own applications. In addition to the included bibliography, a list of over 100 pages of additional references can be found on the book's website.