Approximation And Modeling With B Splines
DOWNLOAD
Download Approximation And Modeling With B Splines PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Approximation And Modeling With B Splines book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Approximation And Modeling With B Splines
DOWNLOAD
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
DOWNLOAD
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.
Finite Element Methods With B Splines
DOWNLOAD
Author : Klaus Höllig
language : en
Publisher: Society for Industrial and Applied Mathematics
Release Date : 1987-01-01
Finite Element Methods With B Splines written by Klaus Höllig and has been published by Society for Industrial and Applied Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987-01-01 with Mathematics categories.
The finite element method (FEM) has become the most widely accepted general-purpose technique for numerical simulations in engineering and applied mathematics. Principal applications arise in continuum mechanics, fluid flow, thermodynamics, and field theory. In these areas, computational methods are essential and benefit strongly from the enormous advances in computer technology. B-splines play an important role in approximation and geometric modeling. They are used in data fitting, computer-aided design (CAD), automated manufacturing (CAM), and computer graphics. 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.
Mathematical And Computational Methods For Modelling Approximation And Simulation
DOWNLOAD
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.
Geometric Modeling With Splines
DOWNLOAD
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. They achieve a balance between mathematical rigor
Geometric Modeling
DOWNLOAD
Author : Hans Hagen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometric Modeling written by Hans Hagen 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 Computers categories.
This book is based on lectures presented at an international workshop on geometric modeling held at Hewlett Packard GmbH in Boblingen, FRG, in June 1990. International experts from academia and industry were selected to speak on the most interesting topics in geometric modeling. The resulting papers, published in this volume, give a state-of-the-art survey of the relevant problems and issues. The following topics are discussed: - Methods for constructing surfaces on surfaces: four different solutions to the multidimen sional problem of constructing an interpolant from surface data are provided. - Surfaces in solid modeling: current results on the implementation of free-fonn solids in three well established solid models are reviewed. - Box splines and applications: an introduction to box spline methods for the representation of surfaces is given. Basic properties of box splines are derived, and refinement and evaluation methods for box splines are presented in detail. Shape preserving properties, the construction of non-rectangular box spline surfaces, applications to surface modeling, and imbedding problems, are discussed. - Advanced computer graphics techniques for volume visualization: the steps to be executed in the visualization process of volume data are described and tools are discussed that assist in handling this data. - Rational B-splines: an introduction to the representation of curves and surfaces using rational B-splines is given, together with a critical evaluation of their potential for industrial application.
The Nurbs Book
DOWNLOAD
Author : Les Piegl
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Nurbs Book written by Les Piegl 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 Computers categories.
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'U'R-BS 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.
Methods Of Shape Preserving Spline Approximation
DOWNLOAD
Author : Boris I. Kvasov
language : en
Publisher: World Scientific
Release Date : 2000
Methods Of Shape Preserving Spline Approximation written by Boris I. Kvasov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
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.
Applications Of B Spline Approximation To Geometric Problems Of Computer Aided Design
DOWNLOAD
Author : University of Utah. Department of Computer Science
language : en
Publisher:
Release Date : 1973
Applications Of B Spline Approximation To Geometric Problems Of Computer Aided Design written by University of Utah. Department of Computer Science and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1973 with Geometry categories.
Spline Functions On Triangulations
DOWNLOAD
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.