Methods of Shape-preserving Spline Approximation
Methods of Shape-preserving Spline Approximation

Author: Boris I. Kvasov

Publisher: World Scientific

Published: 2000

Total Pages: 360

ISBN-13: 9789810240103

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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.

Shape-Preserving Approximation by Real and Complex Polynomials
Shape-Preserving Approximation by Real and Complex Polynomials

Author: Sorin G. Gal

Publisher: Springer Science & Business Media

Published: 2010-06-09

Total Pages: 359

ISBN-13: 0817647031

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First comprehensive treatment in book form of shape-preserving approximation by real or complex polynomials in one or several variables Of interest to grad students and researchers in approximation theory, mathematical analysis, numerical analysis, Computer Aided Geometric Design, robotics, data fitting, chemistry, fluid mechanics, and engineering Contains many open problems to spur future research Rich and updated bibliography

Multivariate Splines
Multivariate Splines

Author: Charles K. Chui

Publisher: SIAM

Published: 1988-01-01

Total Pages: 192

ISBN-13: 0898712262

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Subject of multivariate splines presented from an elementary point of view; includes many open problems.

Curve and Surface Fitting with Splines
Curve and Surface Fitting with Splines

Author: Paul Dierckx

Publisher: Oxford University Press

Published: 1995

Total Pages: 308

ISBN-13: 9780198534402

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The fitting of a curve or surface through a set of observational data is a very frequent problem in different disciplines (mathematics, engineering, medicine, ...) with many interesting applications. This book describes the algorithms and mathematical fundamentals of a widely used software package for data fitting with (tensor product) splines. As such it gives a survey of possibilities and benefits but also of the problems to cope with when approximating with this popular type of function. In particular it is demonstrated in detail how the properties of B-splines can be fully exploited for improving the computational efficiency and for incorporating different boundary or shape preserving constraints. Special attention is also paid to strategies for an automatic and adaptive knot selection with intent to obtain serious data reductions. The practical use of the smoothing software is illustrated with many examples, academic as well as taken from real life.

Handbook on Splines for the User
Handbook on Splines for the User

Author: Eugene V. Shikin

Publisher: CRC Press

Published: 1995-07-14

Total Pages: 238

ISBN-13: 9780849394041

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Splines find ever increasing application in the numerical methods, computer-aided design, and computer graphics areas. The Handbook on Splines for the User not only provides an excellent introduction to basic concepts and methods but also includes the SplineGuide-a computer diskette that allows the reader to practice using important programs.These programs help the user to build interpolating and smoothing cubic and bicubic splines of all classes. Programs are described in Fortran for spline functions and C for geometric splines. The Handbook describes spline functions and geometric splines and provides simple, but effective algorithms. It covers virtually all of the important types of cubic and bicubic splines, functions, variables, curves, and surfaces. The book is written in a straightforward manner and requires little mathematical background. When necessary, the authors give theoretical treatments in an easy-to-use form. Through the Handbook on Splines for the User, introduce yourself to the exciting world of splines and learn to use them in practical applications and computer graphics.

The Theory of Splines and Their Applications
The Theory of Splines and Their Applications

Author: J. H. Ahlberg

Publisher: Elsevier

Published: 2016-06-03

Total Pages: 297

ISBN-13: 1483222950

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The Theory of Splines and Their Applications discusses spline theory, the theory of cubic splines, polynomial splines of higher degree, generalized splines, doubly cubic splines, and two-dimensional generalized splines. The book explains the equations of the spline, procedures for applications of the spline, convergence properties, equal-interval splines, and special formulas for numerical differentiation or integration. The text explores the intrinsic properties of cubic splines including the Hilbert space interpretation, transformations defined by a mesh, and some connections with space technology concerning the payload of a rocket. The book also discusses the theory of polynomial splines of odd degree which can be approached through algebraically (which depends primarily on the examination in detail of the linear system of equations defining the spline). The theory can also be approached intrinsically (which exploits the consequences of basic integral relations existing between functions and approximating spline functions). The text also considers the second integral relation, raising the order of convergence, and the limits on the order of convergence. The book will prove useful for mathematicians, physicist, engineers, or academicians in the field of technology and applied mathematics.

Approximation and Modeling with B-Splines
Approximation and Modeling with B-Splines

Author: Klaus Hollig

Publisher: SIAM

Published: 2015-07-01

Total Pages: 228

ISBN-13: 1611972949

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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.

Proceedings of the 6th International Conference on Fundamental and Applied Sciences
Proceedings of the 6th International Conference on Fundamental and Applied Sciences

Author: Samsul Ariffin Abdul Karim

Publisher: Springer Nature

Published: 2022-01-05

Total Pages: 775

ISBN-13: 9811645132

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This book highlights latest advancement in Mathematics, Physics and Chemistry. With the theme of “Innovative Science towards Sustainability and Industrial Revolution 4.0”, ICFAS 2020 brings together leading experts, scientific communities and industrialists working in the field of applied sciences and mathematics from all over the world to share the most recent developments and cutting-edge discoveries addressing sustainability and industrial revolution 4.0 in the field. The conference topics include green materials, molecular modelling, catalysis, nanodevices and nanosystems, smart materials applications, solar cells technology, computational mathematics, data analysis and visualization, and numerical analysis. The contents of this book are useful for researchers, students, and industrial practitioners in the areas of Mathematics, Physics and Chemistry as most of the topics are in line with IR 4.0.

Bézier and B-Spline Techniques
Bézier and B-Spline Techniques

Author: Hartmut Prautzsch

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 299

ISBN-13: 3662049198

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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.

Mathematical Aspects of Computer and Information Sciences
Mathematical Aspects of Computer and Information Sciences

Author: Ilias S. Kotsireas

Publisher: Springer

Published: 2016-04-16

Total Pages: 631

ISBN-13: 331932859X

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This book constitutes the thoroughly refereed post-conference proceedings of the 6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015, held in Berlin, Germany, in November 2015. The 48 revised papers presented together with 7 invited papers were carefully reviewed and selected from numerous submissions. The papers are grouped in topical sections on curves and surfaces, applied algebraic geometry, cryptography, verified numerical computation, polynomial system solving, managing massive data, computational theory of differential and difference equations, data and knowledge exploration, algorithm engineering in geometric computing, real complexity: theory and practice, global optimization, and general session.